Process Equipment and
Plant Design
Principles and Practices
Subhabrata Ray
Department of Chemical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal, India
Gargi Das
Department of Chemical Engineering,
Indian Institute of Technology Kharagpur,
Kharagpur, West Bengal, India
Elsevier
Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands
The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom
50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States
Copyright © 2020 Elsevier Inc. All rights reserved.
No part of this publication may be reproduced or transmitted in any form or by any means, electronic or
mechanical, including photocopying, recording, or any information storage and retrieval system, without
permission in writing from the publisher. Details on how to seek permission, further information about the
Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance
Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions.
This book and the individual contributions contained in it are protected under copyright by the Publisher
(other than as may be noted herein).
Notices
Knowledge and best practice in this field are constantly changing. As new research and experience broaden our
understanding, changes in research methods, professional practices, or medical treatment may become
necessary.
Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using
any information, methods, compounds, or experiments described herein. In using such information or
methods they should be mindful of their own safety and the safety of others, including parties for whom they
have a professional responsibility.
To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any
liability for any injury and/or damage to persons or property as a matter of products liability, negligence or
otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the
material herein.
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the Library of Congress
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library
ISBN: 978-0-12-814885-3
For information on all Elsevier publications visit our website at
https://www.elsevier.com/books-and-journals
Publisher: Joe Hayton
Acquisitions Editor: Anita Koch
Editorial Project Manager: Lindsay Lawrence
Production Project Manager: Paul Prasad Chandramohan
Cover Designer: Matthew Limbert
Typeset by TNQ Technologies
Dedicated
to
Our Students
with Whom we have been enjoying a Rich Learning Experience over the years
About the Authors
Subhabrata Ray
Subhabrata did his graduation and post graduation from the Department of Chemical Engineering,
Indian Institute of Technology Kharagpur, and has teaching in his Alma Mater since 1988. Prior to
that, he worked with M/s Indian Oil Corporation Ltd. and M/s TECHNIP-ESIA in various capacities.
Dr. Gargi Das
Gargi had topped the undergraduate and postgraduate courses in chemical engineering from Jadavpur
University and the Indian Institute of Technology Kharagpur, respectively. She is also the recipient of
various awards for her research activities. She has been in teaching in the Department of Chemical
Engineering, Indian Institute of Technology Kharagpur, since 2001.
xvii
Preface
A course on plant and equipment design would be incomplete without a perspective of the relevant
process system. Thus, the design of a distillation column must include at least the broad details of
the associated heat exchangers, piping, safety arrangements and instrumentation. The book is based
on this approach e to include the auxiliaries of a system, be it any specific equipment or a process.
Another specific feature of the book is a separate section on process utilities, instrumentation and
controls and engineered safety of plants. Ideas about these systems, although essential, have traditionally received less prominence.
The last section of the book discusses design of the complete plant e the process packages with
design examples. It summarises the concepts and practices discussed in previous sections and demonstrates their applications in practice. This section is meant specifically to provide an idea of the
capstone projects that the undergraduates may take up as part of their course curriculum.
To expose the learner to the industrial standards and practices, the importance of relevant industrial
codes and practices has been emphasised and referred to wherever necessary, albeit in a limited way.
It is felt that the rookie engineers in industry may find this useful as a resource that covers the basic
concepts along with industrial practices in processes and equipment designs.
The way the book is structured, the user may start with Section I and cover Sections II, III and IV in
any order. One may go through Section V as per one’s interest or as a part of a formal design course.
Subhabrata Ray and Gargi Das
Department of Chemical Engineering
Indian Institute of Technology Kharagpur
xix
Acknowledgement
This book bears the contributions from a number of individuals and institutions. These are everywhere
even though only the names of the authors appear on the cover.
Writing this volume was a pleasure but there were moments of uncertainties too that could be overcome only by the constant support and encouragement of our friends and colleagues. Though the
names are numerous, we must mention Mr. Ashis Nag, Mr. Matilal Bhattacharya and Dr. Susmi
Banerjea. They not only supported us but also contributed actively with technical information on current industrial practices. Their constructive criticisms time and again were invaluable.
The constant encouragement received from our colleagues Prof. Sunando Dasgupta, Prof.
Somenath Ganguly and several others kept us going. Throughout the period, Prof. B. C. Meikap
and Prof. Sudipto Chakraborty supported us with their constant cooperation and pertinent suggestions.
Many of our personal friends including Prof. Anand Patwardhan, Dr. Mohit Ray, Prof. Bitasta Chanda
and Prof. G. Harikrishnan did not let us lose our focus in difficult times.
Over the years of teaching, our students have expressed the need for a comprehensive reference text
addressing different aspects of a process being designed. Their numerous feedback has resulted in this
book. We proudly acknowledge their inquisitive expressions and are grateful for the same. Several of
our students, now working in industry, guided us to shape the content with their ideas on the requirement from industry perspective. The names of Dr. Balaram Suman, Dr. Sahil Malhotra, Mr. Harshit
Madan and Mr Abhishek P. are only a few in the endless list.
The authors acknowledge Mr. Lawrence Lindsay, Ms. Anita Koch, Ms. Sheela Bernardine Josy,
Mr. Chandramohan Paul Prasad and the team from M/s Elsevier who bore with us over the long years
and acceded to our demanding requests. Without their support, publication of this book would never
have been possible.
The authors appreciate the support of Indian Institute of Technology for this wonderful experience.
Subhabrata acknowledges his earlier employers M/s Indian Oil Corporation and M/s TECHNIP-ESIA
for allowing him the opportunity of learning in industrial environment.
Long hours of occupation by the authors working on the book have been borne patiently by our
family members. Their patience and unstinted support is gratefully acknowledged.
Subhabrata Ray and Gargi Das
Department of Chemical Engineering
Indian Institute of Technology Kharagpur
xxi
SECTION
Introduction to
process design
I
Successful design is not the achievement of perfection
but the minimisation and accommodation of imperfection
eHenry Petroski
CHAPTER
General aspects of process design
1
1.1 Process
An industrial process converts feed material to useful product(s) of desired quality in commercial
scale. The steps involved in such a process need to be technically viable, safe, and economical. Such
steps involve heat, mass, momentum transfer, and chemical reaction, independently or in combination.
A process is always designed to perform a specific function. Such a task can be heating of a material
from an initial to a final temperature, mixing of several streams to achieve homogeneity, separation of a
multicomponent material stream or chemical conversion of a reactor feed to products and their subsequent separation.
Simple and complex processes
Simple processes are usually centered around one single or
major equipment. Auxiliary equipment may be required to
complete the functionality. Examples of simple processes can be:
Process
Equipment
Auxiliary equipment
Heating of a stream
Heat
exchanger
Pump, pipe fittings
Sieving for separation of solids
Sieve
Receiving of naphtha from berthed tankers to shore tanks
and its transportation to a petrochemical plant a few
kilometers away
Pump and
pipeline
Storage tanks at berth, if required
Capture of hydrocarbon solvent vapor from a process by
adsorption in an activated carbon bed
Packed bed
Blowers, piping, and pipe fittings
Separation of a mixture of benzene and toluene by
distillation
Distillation
column
Heat exchangers (reboiler,
condenser), pump, and pipe fittings
Drying of compressed air for supply to instruments
Drier
Compressor, filter, pump, and pipe
fittings, compressed air storage
Complex processes constitute of several simpler processes. The process plant converting raw
material to product streams may involve reaction, separation by distillation, extraction, absorption,
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00001-4
Copyright © 2020 Elsevier Inc. All rights reserved.
3
4
Chapter 1 General aspects of process design
drying, filtration, or for that matter any number of “unit operations” and/or “unit processes.” Such
examples can be:
•
•
•
•
•
•
Production of common salt involving crystallization, evaporation, filtration, etc.
Effluent treatment in plants employing several processes required for removal of specific
pollutants present
Coke oven plant that produces coke of different grades and by-products, starting from coal
Catalytic hydro-desulfurization of naphtha that involves reactors and separation systems
Air separation plant to produce oxygen and nitrogen involving compression, Joule-Thomson
cooling, liquefaction and distillation
Distillery consisting of several processes like fermentation, distillation, etc. to produce the
saleable product “spirit.”
Large chemical complexes contain several interlinked plants/processes. Each plant produces
stream(s) that is either a marketable product or is feed stream to another plant within the complex.
There are multiple streams of raw materials, products and by-products within the complex. The
“chemical complex” as a whole produces “products” that are marketable. As examples of large process
complexes, one often talks about the Steel Plant, Fertilizer Plant, Petroleum Refinery, etc. For example,
in a petroleum refinery, crude oil is fractionated to several component streams in its Crude Distillation
Unit (CDU). Although the main operation, in this case, is “distillation,” the facility contains process
steps, such as preheating of crude oil in a heat exchanger network with various hot streams, heating of
crude oil in a furnace before it enters the distillation column, washing of some of the streams with
caustic solution and subsequently with water to remove sulfurous impurities and so on. Several process
plants like cracking units, hydrotreating unit, etc., in a refinery complex, further process the streams
from the CDU.
A process can be designed to operate in “batch mode” or in “continuous mode.” Batch processes for
the same annual capacity will require bigger equipment but offer greater control on the process. Batch
operations are preferred when the processing capacity is low, but the
required control over process parameters is stricter. Also, when the
product value is high compared to the investment in the plant
Batch vs Continuous
equipment, the economical option is often a batch process. These
processes also offer greater variation and flexibility in the use of the
equipment and its operation. As an example, a batch dryer for drying
a specific product can be utilized for drying other products whenever
it is free. Widespread applications of batch processes in the pharmaceutical industry dealing with
relatively lower processing capacity and requiring stringent quality control, clearly illustrate these
facts. In contrast, a continuous plant will require smaller equipment for the same annual capacity. This
allows attainment of higher processing capacity for the same investment. Most large scale/high capacity industries like fertilizer, steel, petroleum refining, petrochemicals are continuous process plants
as it turns out to be the more economic option.
Some plants with low to moderate capacity use combinations of the batch, as well as continuous
processes. In these plants, the output streams from the batch process are stored and processed later in
the continuous processes. In some plants, the order of processing may be reversed. Use of continuous
process avoids interruptions in processing that entail spending energy to start and shut down the
process. Processing steps that take longer time or are difficult to control or require closer checks and
controls operate in “batch mode.”
1.1 Process
5
Engineering design is not just a scientific solution. Merely achieving the functional goal is not
sufficient. The solution must achieve its functional goal economically.
Improved technical performance with the implementation of a “better” or
more efficient design is always associated with the cost to be incurred.
Design
Therefore, the industrial process design has to be an optimum design,
balancing the improved performance and increased cost.
An example can be designing a heat exchanger to cool a stream of 70 m3/hr
of kerosene in a refinery from 90 to 40 C. This is the design objective for the
process and may be achieved by several options:
•
•
•
•
•
use of a water-cooled shell and tube heat exchanger
use of a water-cooled double pipe heat exchanger
use of an air-cooled heat exchanger (fin fan cooler)
direct contact with an immiscible cold fluid (water) followed by gravity separation in a settler.
utilizing some specific cold process stream that needs to be heated; this can be an attractive design
option as it would save energy
There may be many more exotic options for achieving the same design objective. The acceptable
design alternative has to meet the design objective and strive to be economically optimum.
In addition, the following are also considered:
•
Practical deviations in design input parameters
It needs to be appreciated that the design inputs are associated
with a certain level of uncertainty and the design solutions are
worked out based on the best estimates of these inputs. Inputs may
Design Considerations
also change over time due to change in operating conditions of other
sections in the plant, variation in market demand or product specifications and raw material quality. There can be other reasons too. For example, the kerosene stream
known to be available at 90 C in the design stage of the heat exchanger may be available at a slightly
higher temperature (say 94 C) after the equipment has been installed. A “robust design” needs to
accommodate, up to a limit, such uncertainties particularly in quality (temperature, pressure,
composition, etc.) and quantity (flow rates) of the input streams for the process. Safety factors or
design margins take care of this during design calculations but leads to “overdesign.” This is illustrated
in the design problems discussed later in the book. Nevertheless, the extent of overdesign needs to be
optimal as costs increase with a margin of overdesign. Such limits in specific cases are decided based
on industry practice, designers’ experience, and the criticality of the function of the designed process/
equipment. Typically heat exchangers are overdesigned to the extent of 10%e20% of their rated heat
load.
•
Compatibility with rest of the plant or the process complex
Compatibility is enforced by clearly defining the specifications, specifying the design codes and
material standards. Such compatibility is warranted in terms of mechanical features, reliability and
process considerations. Mechanical compatibility is essential for connectivity of different equipment.
This is enforced by using the same standards for the flanges and fixtures for “hooking up” the designed
equipment to existing or other equipment that may have been delivered from a different design group.
6
Chapter 1 General aspects of process design
•
Reliability of the process and mechanical design of equipment
This is ensured by following the relevant standards and codes
•
•
•
•
Available space for the equipment or process being designed
Scope of interchangeability with other equipment or common spare
Ease of operation and maintenance
Safety during erection, commissioning, operation and maintenance.
The process designer needs to be absolutely clear about the functional requirements to be met by
his design output and looks for the following minimal information at the outset:
•
•
•
•
Input and output stream detailsdrange of flow rate, temperature, pressure, composition or any
other available information
Required capacity of the processddefined in terms of maximum, normal and minimum flow rate
(input and/or output) of streams. In some cases, this may even be stated in terms of energy to be
supplied or removed from the system
Spatial location and its limitations, the plot plan, and the preferred orientation of equipment. The
information of the surrounding area, its geographical details, presence of any existing habitation
around the proposed process plant, topology of the plot, details on wind direction (Wind rose),
location of effluent discharge points, preferred dimension of standard equipment or its
components like heat exchanger tube length, etc., are all to be considered in the design phase to
deliver an optimum option.
Specific standards to be followed for designing, e.g., IS 2825/ASME Sec VIII Div.1 for unfired
pressure vessels or TEMAeR for heat exchangers. This is essential for generating a design that is
compatible with the rest of the facility, use of standard material of construction and ensuring the
reliability of the equipment. Standards greatly reduce the time to deliver a reliable design and get
it fabricated. The role of design codes and standards during the design activity, therefore, need no
further emphasis.
Based on the available information, the designer fixes the conditions at the boundary of the process.
In industry parlance, this boundary is the “battery limit.” Battery area refers to the physical area within
which the process resides. Input and output stream details are to be known at the “battery limit” before
proceeding further.
1.2 Design problem and its documentation
Design requirements emerge out of an expression of a functional need. Such a need can be expressed
for a new plant or processing facility. The need for a plant to process naphtha available from a local
refinery and convert it to some useful petrochemical product can be the example of such a functional
need for the design of a petrochemical complex. It is also possible to have the “need” for some
expansion/modification of existing processes/plants. The plant design gets completed by designing the
various equipment of the plant and its piping and utilities in an integrated fashion. The earlier
mentioned example of an arrangement to cool a continuous (70 m3/hr) stream of hot kerosene oil (from
90 to 40 C) before the same is sent to storage is a simple statement expressing the need for an
additional process facility to offer the required functionality, i.e., cooling. It is needless to say that even
1.3 The design process
7
such a process system would include one or more equipment; possibly, a heat exchanger with allied
auxiliary facilities like pumps, piping and pipe fittings that would serve the purpose.
The “expression of functional interest” is followed by documenting the “preliminary design
specifications” (PDS document). This goes beyond just the functional aspects of the proposed design
and attempts to identify and quantify the design deliverables like capacity, material and process fluid
properties, process stream conditions at inlet and outlet of the process, etc. In spite of containing
additional information, the formulation of the design problem at this stage will hardly be complete in
all aspects to embark on the design process.
Generating the complete definition of the design problem is the next step and the outcome of this
step is documented as “detailed design requirements” (DDR document). This document is prepared at
the designer’s initiative with the aim of defining all aspects of the design problem before embarking on
the design procedure. This is based on the response to a questionnaire set framed by the designer
specific to his design assignment. This questionnaire set is usually called “Basic Engineering Design
Questionnaire (BEDQ)” and requests information under various subheadings. Preparation of the
BEDQ document is the joint responsibility of the client and the designer. This serves as the designers’
starting basis and is consulted by the designer as a reference in almost every step of his activity. BEDQ
documents important issues, such as the brief background of the design case, design capacity, size/
dimensional limitations and applicable standards/codes for designs, drawings and materials. This
document even specifies the format of the design deliverables and their documentation standards.
Freezing the mutually agreed version of the “detailed requirements design document” (DRD document) marks the start of the design activity.
Complete design of a process plant consists of the Basic Engineering, followed by Detail Engineering. Basic Engineering includes process selection, equipment selection, PFD/P&ID, functional
description of the system and overall Plot Plan. The process design falls under Basic Engineering.
Equipment mechanical design; piping drawing with support structures, etc., are covered under detail
engineering. Basic Engineering for the process is usually supplied by the technology vendor in the
form of a “Basic engineering package,” and the detailed engineering is carried out by a Detailed
Engineering contractor.
1.3 The design process
Designing always starts in a concept design phase, where the designer considers potential alternatives
and compares those heuristically. Based on heuristics and experience, a finite number of alternatives
are selected. For example, in the kerosene cooling problem, the evaluation of the options considered by
heuristics will probably lead to employing a shell and tube exchanger over the other alternatives.
Selection of design solution is usually based on qualitative considerations followed by quantitative
considerations.
Qualitative considerations can be
•
•
•
•
Soundness of the scientific concept
Fire and Safety risk of plant equipment, manpower involved and surrounding area
Feasibility of practical implementationdthis includes compatibility with existing components of
a plant, in case of retrofit or plant expansion, related designs as well as spatial limitations
Economic attractiveness or advantage of one option over other(s)
8
•
•
•
•
•
•
•
Chapter 1 General aspects of process design
Requirement of auxiliary facilities like utilities and their levels
Waste disposal/environmental considerations
Ease of operation, maintenance, erection, commissioning
Availability of resources for technology, materials, manpower and skill for erection,
commissioning, operation, and maintenance
Project completion time
Designs with proven implementation and performance are preferred
Financing of the project: Capital availabilitydamount and its layout in a time scale
In practice, the first step of the designer is the collection of information and previous documents on
similar design projects. Implementation success, performance and limitations of these are scrutinized.
The design alternatives emerging from this step are often the improved versions of the previous designs and the experience of the designer is an important factor.
Quantitative considerations
Quantitative selection of the best alternative is arrived at through a process of optimization. The
objective function to be optimized can be an economic parameter like payout period, internal rate of
return, the total annualized cost for the plant, etc. Such economic parameters are usually used in case
of large equipment, process systems/plants or projects.
This requires a mathematical model describing the process in terms of the process design variables
namely (1) operating conditions (temperature, pressure, flow, etc.) and (2) equipment specification
parameters (capacity, number of separation stages, etc.). The mathematical model describing the
design will be relationships among the design variables expressed as equations and inequations (“>” or
“<” expressions). Such expressions can be linear as well as nonlinear. The objective function is
expressed in terms of these variables. Set of numerical values of the variables define the process design
output completely.
A multivariable constrained optimization needs to be solved mathematically for optimizing the
objective function without violating the constraints of the model (these expressions are in the form of
“equalities” and “in-equalities”). Design software commonly uses various linear and nonlinear programming solvers for optimization. Some of the algorithms used for nonlinear optimization are Nelder
& Mead, MarquardteLevenberg, Sequential Quadratic Programming. These methods may be used
independently or with other convergence techniques like Wegstein method, NewtoneRaphson, etc.,
which are common for flowsheet simulation convergence.
In the case of large plants/complexes, there can be cases of multiple solutions for the optimization
problem, out of which only one can be implemented. The alternative solutions have the same objective
function value, but the combination of the value of the process parameters (variables) differ. Selection
of the final choice requires the introduction of new criteria that is often qualitative like the ease of
maintenance/operation/etc.
Optimum design
Generation of optimum design of specific equipment requires fixing up a suitable technical criterion
like efficiency (of a furnace, etc.) or specific energy consumption rate that may be optimized where
these technical parameters used as objective function are directly linked to the economics. This leads
1.3 The design process
9
to the technically optimized design coinciding with the optimum economic design. An example of this
is a furnace design that has maximum efficiency within the available funding limitation/constraint(s).
Maximizing furnace efficiency by design reduces fuel cost, which is the dominant component of
operating expense.
Another example of optimized design can be the selection of pipeline size and pump. The smaller
size of pipe requires lower capital investment but increases the line pressure drop. This would require
the pump to develop a high head. A pump with a higher delivery head would, not only cost more but
would also increase the power consumption. This calls for optimizing the pipeline size and the pump
together as a system.
In case of arriving at optimum design of equipment, the overall economic parameter, for example,
annualized total cost comprising of its component contributions from capital investment and operating
cost, is the objective function to be minimized. This is illustrated later in the book while dealing with
optimum design of distillation column.
One may note that multiple optima are also possible in the case of large design problems, for
example, the configuration of large process plants like refinery or fertilizers. This means there can be
more than one combination of capacities of plants in a refinery complex being optimally designed for
maximizing profit.
Design steps
Equipment design is usually a two-stage process. In the first step, the optimum design is arrived at
through an optimization procedure either by solving a rigorous mathematical problem or by using a
graphical procedure. This design is detailed in the next step. An example of this is illustrated in
Chapter 11.
Detailed design of the equipment is carried out by referring to the appropriate “Design Codes and
Standards” for design, materials, and inspection. Relevant codes for the design of specific equipment
are discussed in the corresponding chapters and a list of some relevant codes used in the design of
process equipment is presented in the Appendix section.
1.3.1 Deliverables
Process plants: Plants would consist of several equipment and processes. The simplest representation
of the plant is in terms of Block Flow Diagrams (BFDs) that show the
subprocesses as individual blocks. Block flow diagrams are particularly helpful in getting an overall idea of large and complex plants
consisting of several processes. The purpose is to provide an overview
Block Flow Diagram
and therefore, only the important features are shown in a BFD. The
processing sequence and the interrelation of the processes involved
appear from the connecting lines with an arrowhead at the end connecting the blocks. These lines represent the flow of material and/or energy. The material flows are
called “streams.” The raw material processing capacity, rated production of different products and the
processing capacity of individual units may be labeled in the diagram. A description often accompanies the BFD that briefly explains the plant in terms of the processes involved.
An example of the BFD for a petroleum refinery is shown in Fig. 1.1. The names noted on the
blocks represent the respective process plantsdAtmospheric Distillation, Vacuum Distillation,
Chapter 1 General aspects of process design
Refinery Fuel
Amine Treating
H2 S
Gas
Gas Processing
Light
Naphtha
Merox Treaters
Gas
H2
Gas
Gas
Atmospheric Distillation
Heavy
Crude
Oil
Isomerate
H2
Catalytic
Reformer
Merox Treater
Gas
Diesel Oil
Kerosene
H2
Hydrotreater
Diesel Oil
Hydrocracker Gasoline
Diesel Oil
Gas
i-Butane
Gas Oil
Heavy Vacuum
Gas
Gas
Bottoms
Gas Oil
Evacuated
non-condensibles
FCC Feed
Hydrotreater
Gas Oil
H2
Butenes
Pentenes
Naphtha
Fluid Catalytic
Cracker (FCC)
Light
Vacuum
Vacuum
Distillation
Reformate
Gas H2
Kerosene
Atmospheric
Atmospheric
H2S from
Sour Water Stripper
Gas
H2
Hydrotreater
Naphtha
Sulfur
H2
Isomerization
Plant
Hydrotreater
Claus Sulfur
Plant
LPG
Alkylation
Gas
H2
Hydrotreater
FCC Gas oil
Alkylate
Gasoline Blending Pool
Fuel Gas
Other Gases
Hydrocracker
10
FCC Gasoline
Fuel oil
Heavy
Vacuum
Gas Oil
Air
Asphalt
Blowing
Asphalt
FIGURE 1.1
Block flow diagram of a Refinery.
MEROX treater, Asphalt Blowing, etc. There are 18 process plant blocks in the diagram. The lines
with an arrowhead at one end, connecting the blocks represent the material flow (process stream) from
one process unit to another. External streams entering and leaving the refinery do not have any block
attached to its origin and destination, respectively. The diagram shows Crude oil, the raw material for
the refinery entering the first processdthe Atmospheric Distillation Plant. A stream of sulfur leaves
the refinery from the Claus Sulfur Plant. The Atmospheric Bottoms stream produced in the
Atmospheric Distillation unit is the feed to the Vacuum Distillation unit. One also finds that the
Alkylation Plant of the refinery receives Butenes and Pentenes from the Fluid Catalytic Cracker Unit
as feed.
Process Flow Diagram (PFD) is the starting basis for generating the detailed design of a plant.
They detail the individual processes present as a block in a BFD.
PFD of a plant shows in detail the relationship between the major
components of the system and may also tabulate process design
Process Flow Diagram
values for the components in different operating modes, typically
1.3 The design process
11
minimum, normal, and maximum throughput. Each stream is uniquely numbered, usually within a
circle or a rotated square. Equipment symbols are more or less industry standard, with minor variation
from one engineering company to another.
It normally includes:
•
•
•
•
•
•
•
Process scheme with streamsdconventionally the flow is from left to right
Major equipment symbols, names and identification numbers
Control valves and valves that affect the operation of the system; this is not mandatory
Interconnection with other systems
Major bypass and recirculation lines
System ratings and operational values as minimum, normal and maximum flow, temperature, and
pressure
Composition of streams
The stream details are provided on the PFD sheets as a stream table. The information provided by
stream tables includes
(i) stream flow rate
(ii) flow rates and composition of the stream components
(iii) temperature and pressure
(iv) phases flowing (liquid, solid, vapor or combinations of these)
(v) enthalpy
Tail gas
To
sheet no 3
Water
10
11
2
Air
CW
Filter
8
Compressor
1A
Ammonia
From
sheet no 3
2A
Steam
5
3
1
6
4
Vaporiser
Absorbor
Cooler
Reactor
(Oxidiser)
Filter
W.H.B.
Condenser
CW
7
9
12
Mixer
13
Product
FIGURE 1.2
An example PFD showing part of an ammonia plant.
12
Chapter 1 General aspects of process design
All details/features of a plant need not be present in a PFD. Specific facilities and streams for startup, shut down or emergency may not be shown. A PFD does not include the minor components, piping
systems, piping ratings and other details. These are found in the P&ID. An example PFD is shown in
Fig. 1.2.
A Piping and Instrumentation Diagram (P&ID) is a schematic illustration of the functional
relationship of piping, instrumentation, and system equipment components. This shows all of the piping, including the physical sequence
of branches, reducers, valves, and the equipment. This also shows the
P&ID
instrumentation and control, as well as the control interlocks. P&IDs are
usually drawn using ISO standard symbols. However, slight variations
can be found in P&IDs from some established engineering companies.
A typical P&ID should include:
•
•
•
•
•
•
•
•
•
•
•
•
•
Instrumentation and designations
Process equipment with names and numbers
All valves and their identifications
Process piping, sizes and identification
Miscellaneousdvents, drains, special fittings, sampling lines, etc.
Permanent start-up and flushing lines
Flow directions
Interconnections’ references
Control inputs and outputs, interlocks
Interfaces for class changes
Annunciation inputs
Vendor and contractor interfaces
Intended physical sequence of the equipment
P&IDs use a numbering/coding system to uniquely identify the equipment, piping and instruments.
Such codes may vary from plant to plant as this is usually decided by the technology vendor and the
detailed engineering contractor. As an example, the equipment code in a plant can have a format
xx-EQ-NNN. A specific code of 13-P-011 shall be denoting a pump numbered 11 in a processing unit
having code 13 and a control valve in the same process unit can be uniquely identified as 13-CV-006.
The line numbering normally contains the following information: service fluid code, line size, pipe
material of construction (MOC), line pressure and temperature rating and unique line identification.
Thus a line in the same process unit with identification 13-CA-100-CS-PN16-013 would be interpreted
as CAecompressed air service, 100eDN100 (nominal pipe size), CSecarbon steel, PN-16 line
pressure and temperature rating and 013eLine no.
Two simple P&IDs are shown in Fig. 1.3.
The plant (and/or equipment) layout in the Plot Plan is decided by referring to the PFD. The designer
knows the equipment required from the PFD and decides the plant layout, usually placing the equipment
in a natural sequence of flow of material. However, there are other
considerations like terrain elevations, wind direction, ease of movement
for operation/maintenance and emergency actions and evacuation plans,
Plot plan
the proximity of another existing plant/equipment/locality, location of
facilities like drainage, access for maintenance, transport and fire safety,
1.3 The design process
(A)
13
IAS
(Instrument Air Supply)
FV-3-3040
11FT
10
Mixer
11 M-08
From Transfer Pump
11 P-201
IAS
(Instrument Air Supply)
To Reactor
11 R-102
S
Sample Point
11FT
11
FV-3-3041
From Transfer Pump
11 P-204
SM
(B)
11 L 11
N4
N1
SOLVENT
FROM UNIT 1
11-100-PE-N
N5
N2
11 T 01
PA: 6 basg
M1
11 L 12
11 P1 13
N6
AL
M
N3
100/50
50/100
11 P 01
11-100-PE-N
SOLVENT
TO UNIT 3
FIGURE 1.3
P&ID examples: (A) Reactor feed mixing system, (B) Solvent supply system.
etc. The designer may prefer to locate similar equipment in groups. Piping is routed on elevated “pipe
racks.” This is done so that clear access and passage is available for the movement of personnel and
equipment for operation and maintenance. For the same reason, the electrical and instrumentation cables
are also placed on the elevated “cable racks.” Water piping is usually underground. Plot Plan of the plant
gives the relative location of the equipment and facility in the scaled plan, a vital input for civil design
and construction. It specifies the position of all equipment and structures to scale. This diagram, having
been drawn to scale, is also used to estimate distances. Preliminary estimation of cable length, piping
length, verification of access to equipment for operation/maintenance, etc. are made on the basis of the
information provided in this diagram. In case of large process complexes, small scale 3-d models are
built to visualize the actual location of the equipment and other facilities at the plant site. Established
detailed engineering contractors have their own modeling unit.
Isometric drawings are required to know the exact spatial location and routing details of every
physical item in the plant. Piping and equipment erection is carried out according to these isometric drawings. In any project for even the simplest
equipment, several isometric drawings are required. These are required for
Isometric
every section of the plant. Isometric drawings are a must for getting approval
as per Indian Boiler Regulations (IBR) for facilities handling steam under the
purview of IBR.
Chapter 1 General aspects of process design
Ø2
98
14
202
34
3
Ø
345
Ø6mmX185 nos
25
DEAIL-C
15.4
3
43
36
DETAIL-D
15
M24X3
73.2
DETAIL-A
134.5
N32
28.3
28.3
3
3
8
DETAIL-C
DETAIL-D
DETAIL-B
158.5
45.6
134.5
75
3
15
N31
122
DETAIL-B
DETAIL-A
M24X3
NOTE :
1. N31 & N32-- 1/2**NB, SCH40 NOZZLE with 1/2*NB Flange as per*ASA Class 150/B16.5/BS 1560
2. All bolts are M24X3, 50 mm Lg. as per ANSI B18.2.3.5M-1979
3. All Nuts are M24X3 as per ANSI B18.2.4.1M & M24 regular washer asper ANSIB 18.22M-1981
4. M.O.C. of all equipments, Vessles, Flanges, Pipes, Nozzles, Nut & Bolts IsSS304
DRAIN POT
FIGURE 1.4
Fabrication drawing for a drain port.
Drawings to be supplied to the equipment fabricators must contain all details of the equipment
along with notes required for fabrication. Fabrication drawings,
therefore, contain complete details of the mechanical fabrication,
support and fixing of the equipment and also the fixing/foundation
details, if applicable/relevant. Most large engineering design comFabrication Drawings
panies have their own draughting sections. Projects normally specify
the drawing standards and conventions to be followed. Such standards
fix the drawing sizes (A0, A1, A2, A3, and A4), nameplate details
with the revision number and history and the convention for the views and projections. Fabrication
drawings shall always include a Bill of Materials (BOM). An example of a typical fabrication drawing
is presented in Fig. 1.4 for a Drain Port. This drawing, however, does not show the BOM, nameplate,
and the associated details.
Usually, several sheets are required for fabrication drawing of most equipment, the first being the
General Arrangement Drawing (GAD), followed by the plan, elevations, and sections at appropriate
positions to express all the intricacies of the conceived design to the fabricator. Information contained
in the complete set of drawings must be sufficient to fabricate the equipment, as it contains notes on the
material of construction and the inspection procedures.
Further reading
15
1.4 Organisation of the Book
The book introduces Process Design to the uninitiated. It shall deal with the design of processes and
individual equipment comprising each process. The activity of process design is multifaceted and
requires participation from various subjects that get integrated into the final design. Accordingly,
preliminary knowledge of chemical engineering subjects, particularly exposure to Heat, Mass, and
Momentum transfer theories along with reaction kinetics and thermodynamics are expected from the
reader. The list of prerequisite also includes fundamentals of “Engineering Mechanics” and “Strength
of Materials” along with a preliminary course on the mechanical design of equipment/machine design.
Following a general introduction to the Process Design in Section I, design of specific processes/
equipment for Heat transfer, Mass transfer, and Reaction systems are
covered in Sections II, III and IV respectively. Fluid flow, an essential
component in all process plants, is covered in Section V. A plant in
order to function requires facilities and supplies for Power, Steam, Air,
Topic Layout
Water and Fuel. These are covered in Section VI as “Utilities.” In
addition, this section with heading “Plant Auxiliaries” includes
Instrumentation, Process Control, and Engineered Safety.
Process Packages covering the complete design of plant along with brief examples are discussed in
Section VII.
Further reading
1. Rudd, D. F., & Watson, C. C. (1968). Strategy of process engineering. J.Wiley & Sons.
2. Peters, M. S., Timmerhaus, K. D., & West, R. E. (2006). Plant design and economics for chemical engineers.
Boston: McGraw-Hill.
3. Smith, R. (2016). Chemical process design and integration. Chichester: Wiley.
SECTION
Heat transfer
processes
II
Art without engineering is dreaming.
Engineering without art is calculating.
eSteven Roberts
CHAPTER
Heat transfer processes in
industrial scale
2
2.1 Introduction
Process heat transfer deals with rates of heat exchange in a heat transfer equipment commonly
employed in different engineering processes. The equipment is usually defined by the function it
performs in a process. Exchanger normally transfers heat between fluid streams. The transfer may also
be between a solid surface and a fluid or between solid particulates and a fluid. Exchangers are termed
‘heaters’ when the primary purpose is to heat a process fluid, while ‘coolers’ are employed for cooling.
Steam is the usual heating medium in heaters; circulating hot oil may also serve the same purpose in
several chemical industries. Use of synthetic fluids like ‘Dowtherm’, which is a eutectic mixture of
diphenyl and diphenyl oxide, is also common. Water is usually the cooling medium in coolers and the
water, thus heated, is in turn cooled by evaporative cooling in cooling towers. Due to the current dearth
of water, air is used as a cooling medium particularly in arid areas making fin fan coolers an attractive
option. Condensers are coolers which remove latent instead of sensible heat. Reboilers cater to the heat
requirement of a distillation process and evaporators are employed for concentration of a solution by
evaporation of water. When any fluid beside water is vaporised, the unit is a vaporiser. Heat exchangers
are common in chemical processing, power generation, metallurgical processes, air-conditioning,
refrigeration, automotive applications, etc., where the main purpose is either to cool or heat a stream,
evaporate or condense single or multicomponent fluid streams or to recover or reject heat from a
process.
The difference between furnace and heat exchanger lies in the fact that the heat energy is produced
inside the furnace at the expense of some other form of energy, usually combustion of a fuel or
electrical energy.
In most heat exchangers, heat transfer between fluids takes place through a separating solid wall
and the heat transfer is by indirect contact. In recuperators, the fluids are
separated by a surface across which heat is transferred and the fluids ideally do
not mix or leak into each other. In regenerative heat exchangers, the heat
Exchanger
transfer is intermittent. Thermal energy from the hot fluid is stored in one half
of the cycle and the stored energy is transferred to the cold fluid in the other
half of the cycle. In cases where the fluids exchanging heat are in direct
contact, the exchanger is a ‘direct contact’ type of heat exchanger. A typical example is ‘barometric
condenser’. In general, a heat exchanger consists of (i) heat transfer elements which is the core and
contains the heat transfer surface (in recuperators) or matrix (in regenerators) and (ii) fluid distribution
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00002-6
Copyright © 2020 Elsevier Inc. All rights reserved.
19
20
Chapter 2 Heat transfer processes in industrial scale
elements such as headers, manifolds, tanks, inlet and outlet nozzles, pipes and seals. Primary surface is
the part of the heat transfer surface in direct contact with both hot and cold fluids. Transfer of heat
across the primary surface is by conduction. Fin appendages are added to the primary surface in finned
tube exchangers to increase the rate of heat transfer. Heat conducted through the fin is transferred to
surrounding fluid by convection and also by radiation. Fins are not primary heat transfer surface as they
do not separate the two fluids of the exchanger. In a heat pipe heat exchanger, heat is transported by
condensation and evaporation of the working fluid inside it. In cooling towers, cooling of process water
is predominantly by latent heat transfer due to evaporation of a small amount of water into the air in
contact with it. Except rotary regenerative exchanger (in which the matrix is mechanically driven to
rotate at some design speed) or a scraped surface heat exchanger, other exchangers do not have any
moving part.
2.2 Exchanger types
Due to the large number of heat exchanger configurations, several classification systems are devised
based on the basic operation, construction, heat transfer mechanism and flow arrangements.
•
Mode of heat transfer e direct contact (between immiscible fluids, gaseliquid or vapoureliquid)
and indirect contact type. Indirect contact type may further be classified as direct transfer type,
storage type and fluidised bed exchangers.
Direct transfer exchangers are recuperators. Depending on the geometry, these may be
tubular, plate type and extended surface. Tubular exchangers are classified as double pipe, shell
and tube, spiral flow and pipe coils. Extended surface can be plate fin or tube fin which can be
fitted on either ordinary separating wall or pipe wall. Storage-type exchangers are regenerators. Process industry exchangers are mostly recuperators. Regenerators are less common
but are used in some specific cases, particularly when heat transfer involves a dust laden gas like
the blast furnace gas in steel plants.
•
Flow arrangement e single pass or multipass.
In single pass, the flow of the two fluids can be co-current, countercurrent, cross-flow, split flow or
divided flow. In multipass, the flow can be (a) parallel and counterflow (‘m’ shell passes and ‘n’
tube passes), split flow and divided flow in shell and tube exchangers, (b) cross-counterflow, crossparallel flow and compound flow in extended surface and (c) fluid 1em passes and fluid 2en passes
in plate-type exchangers.
•
Heat transfer mechanism e (a) single-phase convection on both sides, (b) single-phase
convection on one side and two-phase convection on the other side, (c) two-phase convection on
both sides and (d) combined convection and radiation heat transfer.
2.2.1 Recuperator
In direct transfer heat exchangers/recuperators, heat transfer occurs continuously from the hot to
the cold fluid through a dividing wall. The fluids flow simultaneously in separate fluid passages
2.2 Exchanger types
21
and there is no mixing of fluids. Tubular, plate-type and extended surface exchangers are
recuperators.
Tubular heat exchangers are usually the shell and tube, double pipe or spiral tube type. These
have considerable flexibility in design by changing the tube diameter, length and arrangement. They
can be designed for high pressure relative to the environment and high pressure difference between the
fluids. They are the most common type of heat exchanger both for systems without and with phase
change. These are not efficient for gasegas heat exchange but can be used when the pressure is very
high or fouling is a severe problem for at least one of the fluids and no other exchanger will work.
The simplest type of heat exchanger called the double-pipe heat exchanger consists of two
concentric pipes of different diameters, as shown in Fig. 2.1. One fluid flows through the inner pipe,
while the other fluid flows through the annular space between the two pipes. In some cases, there may
be multiple inner pipes housed within an outer pipe. It is primarily used in cooling/heating process
fluids where small heat transfer areas (50 m2) are required. It may be designed in a number of
Th,in
mh
FIGURE 2.1
Tc,out A double-pipe heat exchanger with two hair pins.
mc
Tc,in
mc
Th,out m
h
arrangements such as counterflow, co-current flow and their combinations. Design of double-pipe heat
exchangers is elaborated in Chapter 3.
Shell and tube exchanger is the most common type of heat exchanger in process industries. These
contain a large number of tubes (often a few hundred) enclosed in a shell with their axes parallel to the
shell (Fig. 2.2). Heat transfer takes place as one fluid flows inside the tubes, while the other flows
outside the tubes through the shell. The ends of the tubes are fitted into tubesheet(s). The tubes open to
some large flow areas called headers at both ends of the shell, where the tube-side fluid accumulates
before entering the tubes and after leaving them. In order to increase the heat transfer coefficient and
tube
outlet
shell
inlet
FIGURE 2.2
A shell and tube heat exchanger.
baffles
shell
outlet
tube
inlet
22
Chapter 2 Heat transfer processes in industrial scale
obtain a more compact exchanger for the same heat duty, the shell- and the tube-side fluids are often
made to undergo several changes in flow direction (passes). Multipassing on the tube side is achieved
by dividing the headers with partition plates (pass partition plates). Baffles are generally fitted over
the tube bundle to force the shell-side fluid to flow across the shell to enhance heat transfer, support the
tubes and maintain uniform spacing between them. The assembly of baffles and tubes are held together
by tie rods and spacers. Many variations of this basic type are available e the differences being
mainly in the detailed features of construction and provisions for differential thermal expansion
between the tubes and the shell. These are elaborated in Chapter 4. Typical S&T exchangers
accommodate 50e100 m2 heat transfer area per m3 of equipment volume. Use of extended heat
transfer surfaces (fins/studs) is also possible in these exchangers.
Spiral-type exchangers consist of one or more spirally wound tubular coils fitted in a shell. The
heat transfer rate is higher as compared to a straight tube and for a given duty, the pressure drop is
usually lower than for an equivalent shell and tube exchanger. Spiralling provides high amount of heat
transfer surface in a given volume of the shell. Thermal expansion is not a problem with these
exchangers but mechanical cleaning is almost impossible. In another variation, the construction is
similar to the wound membrane modules used for separation.
Plate heat exchangers (PHEs) are highly compact and have recently gained high popularity. The
hot and cold fluids flow through alternate passages separated by thin plates assembled together. They
can pack about three times heat transfer area per unit equipment volume as compared to S&T
exchangers. Plate-type exchangers are rectangular metal plates held together in a frame, sealed around
the edges by gaskets. The frame usually has a fixed end cover fitted with connecting ports and a
movable end cover. An upper and a lower carrying bar guide the plates and ensure proper alignment.
These plates may be made either by stamping or embossing sheet metal to provide narrow, tortuous
flow passages. This generates severe turbulence, provides high heat transfer coefficient and decreases
fouling tendency. The corrugations also add to plate rigidity and strength. Either plate has four corner
ports which in pairs provide access to flow passages on either side of the plate. The flow arrangement in
the assembly can be seen in Fig. 2.3.
The advantages of PHEs over shell and tube exchangers include (a) very high heat transfer
coefficient, (b) low fouling tendency (10%e25% of shell and tube exchanger), (c) flexibility of
operation e heat transfer surface area can be increased by adding plates, (d) more compact and less
SINGLE-PASS ARRANGEMENT
Fixed End
MULTI-PASS ARRANGEMENT
Movable End
Fixed End
Movable End
Hot In
Cold Out
Cold In
Cold Out
Hot Out
Cold In
Hot In
1 2 3 4 5 6 7 8
Hot Out
1 2 3 4 5 6 7 8
FIGURE 2.3
Flow arrangement in a plate-type exchanger.
2.2 Exchanger types
23
weight per unit volume, (e) low volume of fluid hold up that is important for expensive fluids, (f) faster
transient response and (g) efficient process control. A smaller temperature difference between the
fluids allows good temperature control. In addition, the ease of cleaning makes the PHE useful for
sterilisation/pasteurisation in food and beverage processing and pharmaceutical industries. They are
also used in synthetic rubber industry, paper mills, process heaters/coolers and closed circuit cooling
system of large petrochemical and power plants. The material of gasket and use of plates often limits
the maximum pressure, maximum temperature and maximum pressure and temperature difference
between the fluids. They are usually operated below 1.0 MPa(g) and 150 C to avoid use of expensive
gasket material. Welded PHEs ensure almost leak proof operation but these cannot be dismantled for
cleaning and therefore can be used only with clean fluids. The overall pressure drop is comparable to
shell and tube exchanger. Some of the recent designs of plate-type exchangers include double wall
PHE, spiral PHE, lamella heat exchangers, printed circuit heat exchangers, etc.
Compared to shell and tube exchanger, compact heat exchangers are characterised by a large heat
transfer surface area per unit volume, resulting in lighter devices
with lower footprint and fluid inventory. A gas to fluid exchanger
is classified as ‘compact’ if it has a surface area density (b ¼ ratio
Compact Heat Exchanger
of heat transfer surface area to volume) > 700 m2/m3 or a hydraulic diameter (Dh) 6 mm for operating in a gas stream and b
> 400 m2/m3 for operating in a liquid/phase change stream. A
laminar flow exchanger (mesoscale heat exchanger) has a surface area density greater than about
3000 m2/m3 (100 mm Dh 1 mm) and micro (scale) heat exchanger has b greater than about
15,000 m2/m3 (1 mm Dh 100 mm). Examples of compact heat exchangers are plate fin, tube fin
and rotary regenerators for gas flow on one or both the fluid sides and gasketed, welded or brazed heat
exchangers and printed circuit exchangers for liquid flow. The basic flow arrangement in compact heat
exchangers are single-pass cross-flow, counterflow and multipass cross-counterflow.
The tubular and plate-type exchangers with b less than 700 m2/m3 give a heat exchanger effectiveness around 60% or less. Effectiveness (ε) of a heat exchanger is defined as the ratio of the actual
heat transfer rate to the maximum possible heat transfer rate thermodynamically permitted. This is
discussed in greater detail later in this chapter. For a much higher effectiveness (around 98%), a more
compact surface is required. Fins are usually added to increase surface area and exchanger
compactness for the same temperature difference. Depending on the design, they can increase the
surface area by 5e12 times the primary surface area and the resulting exchanger is referred to as an
extended surface exchanger.
Fins while increasing the heat transfer area may or may not increase the heat transfer coefficient.
Interrupted fins (strips, louvers, etc.) increase area as well as heat transfer coefficient. The increase can
be two- to four-fold. Usually an increase in fin density reduces the heat transfer coefficient associated
with fins. Plate fin and tube fin geometries are the two most common types of extended surface exchangers. Internal fins in tube are less common.
Mostly low finned tubes are used in shell and tube exchangers to increase the surface area on the
shell side when the shell-side heat transfer coefficient is low. Highly viscous liquids, gases or film-wise
condensing vapours on the shell side cause low heat transfer coefficient. Fins add to structural strength.
Fins/studs may also be used to aid thorough mixing of a highly viscous liquid. The low finned tubes
usually have helical or annular fins. Double-pipe exchangers usually employ longitudinal fins. Fins on
the inside of the tube are either integral fins or attached fins. The fin efficiency increases with
24
Chapter 2 Heat transfer processes in industrial scale
channel
heat pipe
fin
Hot fluid channel
Separator
plate
Cold fluid
channel
FIGURE 2.4
Heat pipe heat exchanger.
(i) decreasing annular heat transfer coefficient, (ii) increasing fin thermal conductivity and
(iii) decreasing fin size. Finned tubes are usually unsuitable for fouling and corrosive shelleside fluid.
An air-cooled exchanger is a finned tube exchanger in which the hot process fluid (liquid or
condensing vapour) flows inside the tubes and atmospheric air is circulated by forced or induced draft
over the outside extended surface. The airflow path is kept short through a layer of tubes and the face
area is kept large to keep the fan power low.
A heat pipe is a closed tube or vessel with the inner surface usually lined with a capillary wick
(porous lining, screen or internally grooved wall). A heat pipe
heat exchanger (Fig. 2.4) comprises of a bundle of heat pipes
which are evacuated and partially filled with a heat transfer fluid
Heat Pipe Heat Exchanger
(working fluid sufficient to wet the entire wick). Hot and cold
fluids, usually gases, flow continuously across separate parts of
the exchanger. It is also possible to transfer heat from a hot to a
cold solid by embedding the two ends of the heat pipe exchanger in the two solids.
Heat transferred to the hot end of the heat pipe vaporises the heat transfer fluid inside the pipe. The
vapour travels to the condensing end where it condenses by transferring heat. The condensed liquid
returns to the evaporator section by the capillary action of the wick and/or gravity. A well-designed
heat pipe will operate (transfer heat) as long as there is temperature difference between the hot and
cold sections. Usually the temperature difference between the evaporating and condensing section is
small (w5 C), thus reducing the overall thermal resistance. In gasegas heat exchangers the heat pipes
are usually finned.
2.2.2 Regenerator
Regenerative exchangers are exclusively used for gas to gas sensible heat transfer, e.g., in waste heat
recovery, dry and moist air heat exchange in air driers, etc. In regenerators, both fluids flow alternately
through the same passage. The heat transfer surface is a cellular structure, referred to as matrix or a
porous solid bed. The matrix picks up the heat from the hot fluid and later transfers the same to the cold
2.2 Exchanger types
25
fluid when it flows through the matrix. Hence, the heat transfer is not unidirectional as in recuperators.
To operate with continuous flow of streams and limit the periodic temperature variation of the fluids,
either the matrix is physically moved periodically into and out of the fixed stream of gases (rotary
regenerator) or the gas flow is diverted using valves to and from the fixed matrices (fixed matrix
regenerator). A small amount of fluid is always trapped in the matrix that gets mixed with the other
fluid stream on switching of the fluids. Also a small leakage of the higher pressure fluid to the lower
pressure fluid is expected in real systems. Therefore, it cannot be used for systems where contamination of one fluid by the other is unacceptable. In air heating applications, humid air may transfer
moisture up to about 5% to dry air. The advantages of regenerators over recuperators are
(a) compactness e smaller exchanger for given exchanger effectiveness and pressure drop, (b) cheaper
option, (c) simpler inlet and outlet header design for distribution of gases in the matrix and (d) can
work even with particulate laden gases that cause fouling in recuperators.
2.2.3 Fluidised bed exchanger
In a fluidised bed exchanger, usually the shell side of a two fluid exchanger contains the (fluidised) bed
of fine particulates, e.g., a tube bundle immersed in a fluidised bed of sand or coal particles as
schematically shown in Fig. 2.5. When the bed gets fluidised, there is a thorough mixing of the particles and a nearly uniform temperature in the bed. Much higher heat transfer coefficient is achieved on
Hot flue gases to
particle removal and
heat exchanger
Heat
transfer tubes
Steam
Solid fuels feed
Limestone
Water
Fluidizing air
Ash
FIGURE 2.5
Schematic representation of a fluidized bed boiler.
26
Chapter 2 Heat transfer processes in industrial scale
the fluidised side compared to particle free or dilute phase (particle laden) gas flow. In coal-fired
fluidised bed combustors, the fluid bed exchanger is an efficient way of heat extraction from the
bed. Typical applications of fluidised bed heat exchanger are drying, mixing, adsorption, reaction, coal
combustion and waste heat recovery.
2.2.4 Direct contact heat exchanger
In a direct contact heat exchanger, the hot and the cold fluids come in direct contact and exchange heat.
Most direct contact heat exchangers involve mass transfer in addition to heat transfer as in evaporative
cooling (cooling tower), cooling of hot gases with water spray, barometric condenser, etc. The
enthalpy of phase change is usually predominant in such an exchange. Direct contact exchangers are
advantageous due to (A) very high volumetric heat transfer rates, (B) inexpensive construction due to
minimal hardware requirement, (C) absence of heat transfer surface between the fluids and (D) no
fouling. However, these can be used only for services where direct contact between the streams is
allowable. Cooling tower discussed in Chapter 7 involves such direct contact heat transfer.
2.3 Flow arrangement
Each fluid in the exchanger may flow in single or multiple pass. A fluid makes one pass if it flows once
through the full length of a section of the heat exchanger. If the fluid subsequently reverses its flow
direction after full length flow and flows again through the same section, it makes a second pass.
Multipass arrangements in shell and tube exchangers are elaborated in Chapter 4.
2.3.1 Countercurrent flow exchanger
For single-pass exchangers, the flow of the fluids is usually co-current (parallel to each other in the
same direction) or countercurrent (parallel to each other but in the opposite direction). A higher
effective temperature difference results in case of countercurrent flow for the same inlet temperature of
the fluids and heat duty of the exchanger. This leads to lower heat transfer area and a smaller exchanger
as long as the overall heat transfer coefficient is nearly the same. In addition, the maximum temperature difference across the exchanger tube wall either at the hot or the cold fluid end (for an
equivalent performance) is the lowest and that produces lower thermal stress in countercurrent flow as
compared to the other flow arrangements. There are manufacturing difficulties associated with true
counterflow arrangement in plate fin exchangers.
2.3.2 Co-current flow/parallel flow exchanger
Co-current flow has the lowest exchanger effectiveness among single-pass exchangers for a given
overall thermal conductance (U A e explained later), fluid flow rates and temperatures. These are
preferred when the cold fluid has high viscosity. The entering cold fluid at lower temperature exchanges heat with the entering hot stream at high temperature and gets heated quickly. This reduces its
viscosity and improves the cold fluideside heat transfer coefficient. This also reduces the pressure
drop for the cold fluid. However, the thermal stress in the exchanger at the inlet is higher due to the
higher temperature difference between the fluids.
2.3 Flow arrangement
1
1
27
1
2
2
(A)
(B)
2
(C)
FIGURE 2.6
Cross-flow arrangements: (A) 1 and 2 both unmixed (B) 1 unmixed, 2 mixed (C) 1 and 2 both mixed.
2.3.3 Cross-flow exchanger
Compact exchangers usually employ cross-flow arrangement (two fluids flowing normal to each other).
Cross-flow is further classified as unmixed and mixed flow. In Fig. 2.6, (a) the cross-flow is ‘unmixed’
as the fins force the fluid to flow through a set of interfin spacing and prevent it from moving in the
transverse direction parallel to the tubes. The cross-flow in (b) is ‘mixed’ as the fluid is free to move in
the transverse direction as well. Both fluids are mixed in the arrangement (c). Unmixed flow occurs in a
car radiator. Mixing in the fluid significantly affects the heat transfer characteristics of a heat exchanger.
The thermal effectiveness for cross-flow exchangers lies between co-current and countercurrent
flow arrangements. However, if the desired exchanger effectiveness (this is elaborated later in this
chapter) is above 80%, the cross-flow exchangers may become uneconomic due to its large size. In
such cases, the counterflow arrangement is preferred. Cross-flow pressure drop is lower due to shorter
hydraulic path of the cross-flow fluid. Extended surface exchangers use cross-flow as it ensures simple
header design. Plate-type exchangers and trombone coolers employ cross-flow arrangement. Crossflow exchangers are not very common in process industry.
2.3.4 Split flow exchanger
This is observed in TEMA G shell of a shell and tube exchanger (Fig. 4.5) where the shell-side fluid
enters at the centre of the exchanger and divides into two streams. Each stream flows along the
exchanger length over a longitudinal baffle, makes 180 degrees turn at the end and then flows back
longitudinally to the centre. The streams unite at the centre and leave through the central nozzle. The
tube-side fluid flows straight through the tubes.
2.3.5 Divided flow exchanger
In this exchanger (TEMA J shell, Fig. 4.5), the shell-side stream divides into two after entering at the
centre of the shell. Each stream flows longitudinally along the exchanger length and exits from nozzles
provided at each end of the exchanger. The tube-side fluid flows straight through the tubes.
2.3.6 Multipass exchanger
When the heat exchanger design results in very long lengths or very low velocities or a low effectiveness, a multipass exchanger is the option. Single-pass exchangers can be arranged to form such
28
Chapter 2 Heat transfer processes in industrial scale
Shell fluid
Th,in
CONDENSING
Tube
fluid
Th,in
Th,out
COOLING
Th,out
Tc,out
Tc,in
EVAPORATING
a) BOTH FLUIDS CHANGING
PHASE
Th,in
CONDENSING
HEATING
Tc,out
Th,out
DE-SUPERHEATING
SUBCOOLING
CONDENSING
Tc,out
HEATING
Tt
(B)
Tc,out
Tc,in
Shell fluid
HEATING
b) ONE FLUID CHANGING
PHASE
Tc,in
f) ONE FLUID CHANGING
PHASE
Tube
fluid
Th,in
Th,in
COOLING
COOLING
Tc,out
Th,out
Th,out
EVAPORATING
HEATING
SUPERHEATING
T
EVAPORATING c,out
c) ONE FLUID CHANGING
PHASE
Th,in
Tt
e) COUNTERFLOW , NO PHASE
CHANGE
Th,in
Tc,in
Ts
Tc,in
ONE FLUID CHANGING
PHASE
COOLING
Th,in
Th,out
Ts
PARTIAL
CONDENSATION
Tc,out
Th,out
Tc,out
Tc,in
HEATING
d) PARALLEL FLOW , NO
PHASE CHANGE
HEATING
Tc,in
Tt
CONDENSABLE AND
NON-CONDENSABLE
COMPONENTS
(A)
(C)
FIGURE 2.7
Temperature profile of fluids in different cases.
multipass arrangement. There are also multipass flow arrangements which have no counterpart in
single-pass flow. Multipass shell and tube exchangers may exhibit parallel flow, counterflow, split flow
or divided flow. Temperature profile of fluids for different configuration of exchangers with and
without phase change is shown in Fig. 2.7. Multiple passes increase exchanger effectiveness at the
cost of increased pressure drop.
2.4 Exchanger selection
The aforementioned discussion highlights the variety of available heat exchangers and the large
number of dimensional variables associated with different components of a shell and tube exchanger or
surface geometries for plate-type, extended surface or regenerative exchangers. Regarding selection of
the most suitable exchanger option, one must remember that there is rarely a single option that is best
2.5 Heat exchanger design methodology
29
(optimum) for a given application. Near-optimum heat exchanger designs involve several trade-offs.
For example, a cheaper exchanger can be used at the cost of reduced performance and durability or a
higher performance can be obtained for a heavier or more expensive exchanger. Similarly, a smaller
heat exchanger can be opted at the cost of lower performance or higher pumping power for higher fluid
velocities, etc. The designer needs to arrive at the optimum exchanger for a given application to meet
the design requirements and constraints. Prior experience is the best guide for selection and design of
an exchanger if one or more exchangers are in service for similar applications. Table 2.1 suggests some
selection criteria. It needs to be understood that the values quoted are based on general industrial
practices and information from different sources. These can be altered judiciously for specific design
cases.
To summarise, the most versatile exchanger for a broad range of operating pressure and temperatures are shell and tube exchangers for medium to high heat duties and double-pipe exchangers for
lower heat duties (<500 kW). The shell and tube exchanger is most widely used in chemical industries.
Plate-type exchangers are more economical regardless of the heat transfer performance. For high heat
duties, the least desirable solution is the double-pipe exchanger.
2.5 Heat exchanger design methodology
Heat exchanger design involves (1) Firming up the process and design specifications, (2) Thermal and
hydraulic design, (3) Mechanical Design, fabrication detailing and cost estimation. The final design is
a trade-off between several factors and a system-based optimisation.
Process and design specifications
This covers all necessary information to design and optimise an exchanger for a specific application.
The problem specification for operating conditions, exchanger type, flow arrangement, material and
design/manufacturing/operating considerations is included. The design basis requires input on fluid
mass flow rates and their physical properties, inlet temperature and pressure of both fluids, required
heat duty and maximum allowable pressure drop on both fluid sides, fluctuations in inlet temperature
and pressure, corrosiveness and fouling characteristics of the fluids and operating environment.
The exchanger design needs to meet the functional requirement of (i) transferring the specified heat
duty using the available temperature difference and (ii) ensuring that the
pressure drop remains within the maximum permissible limit for both
fluids. The design should also be evaluated from the viewpoints of erection,
Deliverables
commissioning, operation, cleaning, maintenance and alteration/extension
in future. Design problems discussed in Chapters 3 and 4 illustrate the
design procedure.
Optimum design: Arriving at an optimum exchanger design based on an economic parameter is
difficult and complex. In reality, a balance between the heat transfer coefficient and pressure drop of
each fluid is struck while designing the heat exchanger. Usually the cheapest exchanger of a particular
type that satisfies the duty and pressure drop constraints with the smallest area is the chosen optimum.
Higher heat transfer coefficient in case of shell and tube exchanger (tube/shell side) is achieved by
increasing the number of passes that invariably increase the pressure drop. A higher efficiency is
Table 2.1 Principal features of common heat exchanger types.
Exchanger type
Operating
temperature
Shell and tube
Double pipe
temperatures
· High
limited only by the
temperature
· High
limited only by
material of
construction
Inlet DT typically
limited to 80 C
by differential
thermal expansion
for fixed tube
sheet exchangers
the material of
construction
Inlet DT limited
to 50 C by
differential
thermal
expansion
·
·
Spiral heat
exchanger
Plate type
500 C
Extended surface
Regenerator
Plate fin <650 C
Usually below 150 C
Tube fin e cryogenic
tempearture to 870 C
870 e 2000 C
Operating pressure
High vacuum to
30 MPa on the shell
side and 140 MPa on
the tube side
High vacuum to
30 MPa on the
annulus and
140 MPa on the tube
side
2 MPa
Gasketed
<2.5 e 3 MPa
Welded <4 MPa
Low pressure
(<1000 kPa e 2.5 MPa)
Cryogenic application e
9000 kPa (g)
Welded e 4 MPa
Near
atmospheric
Compactness
(1emost compact)
4
5
3
2
1
1
Cost/unit surface area
For low heat load
(1ehighest cost)
3
4
5
Welded plate 1
(Highest)
Plate and frame e 5
2 or 3
Plate fin less expensive
than tube fin
6
Cost/unit surface area
For high heat load
(1ehighest cost)
2
1
5
Plate and frame e 4
Welded plate 3
1
6
Simplicity in design
and operation
(1esimplest)
3
1
2
4
5
1
Fouling and ease of
cleaning
Moderate to severe
fouling
(More fouling liquid
on tube side)
Moderate to severe
fouling
(More fouling liquid
on tube side)
Only
chemical
cleaning
Possible
Moderate to severe
fouling for one or
both sides in
cryogenic
applications
(<300 C)
Application in
corrosive service
Y
Y
Chance of fluid
leakage and
contamination
N
N
Y
N
(Leakages through
joints between
corrugated fin passage
and header/tube to
header joint)
Fluid and material
compatibility
Versatile
Versatile
Stainless steel
Titaniumenickel
alloy
Metal or ceramic
Usually aluminium
Gas to gas service
Y (with fins)
Y (with fins)
N
Y
Liquideliquid
service
Y
Y
Liquid to gas service
Y, low finned tube
Y, finned tube
N
Phase change
applications
Y
Y
Y,
For P < 2.5 MPa
and T < 200 C
Specific applications
Common in process
and petrochemical
industry
Highly corrosive
heating or cooling
application
Simplest type of
heat exchanger
suitable for low heat
duties
(<500 kW)
-
Not employed even in
moderate fouling
application unless they
can be cleaned
chemically
Moderate
fouling in
gasegas
applications
NA
Y
Y
Y
-
-
Y (High)
(Carryover and
bypass leakage)
N
Y
Second to S&T
exchangers
Cryogenic
applications
with severe
fouling on one
or both sides
Used
extensively in
food and
beverage
industries
N
N
-
-
Common in
cryogenic
applications
Tube fin if only one
fluid at high pressure
(Contains high
pressure fluid on
tube side)
-
Gas to gas
exchanger
Suitable for
particulate
laden gases
which cause
fouling in
recuperators
32
Chapter 2 Heat transfer processes in industrial scale
obtained when the shell-side and tube-side heat transfer coefficients are of the same order of
magnitude. This can be achieved by addition of fins on the fluid side with lower heat transfer coefficient but at the expense of increased capital cost. Such considerations may also influence the selection of the shell-side and tube-side fluid as well as the number of passes. In case the pressure drop
gets limiting, parallel sets of exchangers or parallel heat exchanger trains are considered for large flow
rates. Optimisation of such exchanger trains are carried out in practice using Pinch Technology discussed in Chapter 5.
Heat exchanger design is thus essentially an iterative procedure as the physical layout of the
exchanger can only be decided after the heat transfer area to be provided is known. On the other hand,
the physical/mechanical arrangement of the heat exchanger affects the overall heat transfer coefficient
and consequently the required heat transfer area for delivering the design heat duty.
Based on the problem specification and the design engineer’s experience, an appropriate exchanger
type and flow arrangement is first selected followed by its sizing that complies with the design
specification. This calls for thorough knowledge
of the exchanger types and their construction
Selecting Exchanger Type and configuration
features along with their suitability for different
applications. Table 2.1 may be referred for this
purpose. Some of the related information is
available in the different codes for Shell and Tube Heat Exchanger design (e.g., IS4503 e 1967
(reaffirmed 2003), BS EN ISO 16,812:2007 and TEMA-R/C/B). As discussed in Chapter 1, it is
desirable that the design develops into a standard configuration and size to the extent possible. This
would not only allow use of established thermohydraulic design equations but also minimise the
delivery time, a major consideration in any project. Use of standard dimensions (e.g., size, rating and
number of tubes, shell id, type and % cut of baffles, etc., for a shell and tube exchanger) also goes a
long way to make the fabrication of equipment easy and enables interchangeability of equipment parts,
which reduces inventory of common spare parts (say spare tube bundle). This is particularly important
in large projects.
Next the exchanger geometry and material are selected. The core geometry is selected for tubular
exchangers (shell type, number of passes, baffle geometry, tube layout, etc., for shell and tube
exchanger) and surface geometry for a plate (plate type and size, number of plates, pass arrangements,
gasket type, etc.), extended surface or regenerative exchanger. Some of the criteria for selecting core
geometry are the desired heat transfer performance meeting the maximum limit of pressure drop,
operating pressure and temperature, thermal/pressure stresses, fluid characteristics and total installed
cost. For compact heat exchangers, one needs to select fin type and geometry.
2.6 Design overview for recuperators
Exchanger design consists of thermal and hydraulic aspects as well as arriving at the complete
mechanical details. The thermal and the hydraulic design of the exchanger are interrelated. Mechanical
design aims at realisation of the thermal design in practice, i.e., the detailed equipment specifications
necessary for fabrication/manufacturing and also considerations like stress and vibration analysis.
Appropriate considerations and analysis during the mechanical design is essential to ensure equipment
integrity under steady state, transient, start-up, shutdown, upset, part load operation as well as maintenance.
2.6 Design overview for recuperators
33
2.6.1 Thermal design
The thermal design is based on the heat balance and the heat transfer rate equation conceptualised
below:
(1) Heat balance equation, one for each of the two fluids, considering negligible heat loss from the
exchanger
For only sensible heat transfer with constant specific heat under isobaric conditions, the heat duty
(Q) can be defined as the heat gained by cold fluid which is equal to the heat lost of the hot fluid
Q ¼ ðmc ÞCpc Tc;out Tc;in ¼ ðmh ÞCph Th;in Th;out
(2.1)
In Eqn. 2.1, m is the mass flow rate of streams and Cp is the specific heat capacity. Subscripts c and
h indicate the parameters related to cold and hot fluid and subscripts ‘in’ and ‘out’ refer to the inlet and
outlet condition of each fluid. The heat capacities are measured at average temperature (Tav ) for any
fluid where
Tav ¼ ð Tin þ Tout Þ=2
(2.2)
In case of phase change, the heat load calculation should be based on enthalpy change/latent heat.
Also the exchanger may be considered as consisting of length sections where phase change and no
phase change occur.
(2) Rate equation which reflects a convectioneconduction heat transfer phenomenon in a two-fluid
heat exchanger and shows that the heat transfer rate across a surface is proportional to the heat
transfer area ðAÞ and mean temperature difference ðDTM Þ between the fluids.
Q ¼ UADTM
(2.3)
The overall heat transfer coefficient (U) is the coefficient of proportionality in Eqn. 2.3.
In a design problem, the prime objective is to estimate A (or UA) of an exchanger to satisfy the terminal
values of temperature (sizing problem). In sizing problem, in addition to (UA), one of the four terminal
temperatures or one of the two flow rates may also be unknown (details discussed in Chapters 3 and 4).
In the rating calculation, the inlet temperature, the exchanger geometry and size (A) are known and
the outputs are Q, U and the outlet temperatures.
It is clear from Fig. 2.7 that the temperature difference between the hot and cold fluid driving the
heat transfer is not constant and its value is different for
different flow arrangements for the same inlet and outlet
temperatures.
Log mean temperature difference
For true co-current and countercurrent flow and linear
temperatureeenthalpy curves (U constant along the
exchanger) when DT1 and DT2 are the temperature difference
at the two ends of the exchanger, the log mean temperature
difference ðDTLMTD Þ is given by
DTLMTD ¼
ð DT2
DT1 Þ
DT2
ln
DT1
(2.4)
34
Chapter 2 Heat transfer processes in industrial scale
For a counterflow exchanger,
DT1 ¼ Th;in Tc;out ;
DT2 ¼ Th;out Tc;in
(2.5a)
DT2 ¼ Th;out Tc;out
(2.5b)
and for a parallel flow exchanger,
DT1 ¼ Th;in Tc;in ;
Eqn. 2.4 is applicable for sensible heat transfer when the heat capacities of both streams are
substantially independent of temperature over the range of the process and there is no phase change. It
is also applicable in case of phase chnage at constant pressure for either or both streams containing a
single component.
A few important points:
(i) When both fluids change phase and are pure components (not mixture),
DT1 ¼ DT2 ; and DTLMTD ¼ DT1 ¼ DT2
(ii) For 1 DTAMTD
DT1
DT2
2, DTLMTD can be substituted by arithmetic mean temperature difference
!
DT1 þ DT2
¼
with less than 4% error.
2
DTLMTD is lower than the arithmetic mean DTAMTD and both have the same value in the limiting
case of (i).
(iii) DTLMTD ¼ 0 for DT1 ¼ 0 or DT2 ¼ 0.
(iv) A quick
check of
the thermodynamic feasibility of the process
by ensuring 2Th;out
can be made
Tc;in þTc;out for hot fluid on the shell side and 2Tc;out Th;in þTh;out for cold fluid on the
shell side. This eliminates the possibility of a temperature cross, i.e., the cold fluid outlet
temperature being higher than the hot stream outlet. If these limits are approached, it is
necessary to use multiple 1e2n shells in series.
(iv) If physical properties and overall heat transfer coefficient (U) vary and/or fluid temperature
profile is not smooth along the tube length, a simple and conservative practice is to evaluate the
heat transfer coefficients at the stream inlet and outlet temperatures and use the lower of the two
values. Alternatively, Eqns. (2.1) and (2.3) can be combined to give
Q¼
A½U2 DT2 U1 DT1 U2 DT2
ln
U1 DT1
(2.6a)
If the variation in physical property over the temperature range is too large, the entire heat exchange length is divided into a number of small lengths ðDzÞ and the basic heat transfer equation(s) are
applied to each length element. The results are then summed up, viz.
X
X
Uj Aj DTLMTD;j
(2.6b)
Q¼
Qj ¼
where j refers to the jth element and DTLMTD;j is the log mean temperature difference in the jth
element.
2.6 Design overview for recuperators
35
For all flow arrangements other than true co-current and countercurrent flow, integration of
differential energy and rate equations
yields a complicated implicit or explicit
expression for DTM. For these flow arLog mean temperature difference correction factor e FT
rangements, it is customary to consider
the heat exchanger as a hypothetical
counterflow unit operating at the same
heat capacity ratio and the same terminal temperatures and then incorporate a correction factor FT in
Eqn. 2.3, where FT is defined as the ratio of the true mean temperature difference for countercurrent
flow to the log mean temperature difference or ratio of the actual heat transfer rate in a given
exchanger to that in a counterflow exchanger having the same UA and fluid terminal temperatures.
This gives
Q ¼ FT UADTLMTD;counterflow
(2.7)
where
FT ¼
DTM
q
¼
DTLMTD;counterflow UADTLMTD;counterflow
(2.8)
and DTLMTD;counterflow is calculated using Eqn. 2.5a for all exchangers except parallel flow exchangers
where the same is calculated using Eqn. 2.5b. FT is dimensionless and, in general, a function of the
thermal effectiveness (S), heat capacity ratio (R) and flow arrangement. The thermal effectiveness S is
defined as the ratio of the temperature range (rise or drop) of one fluid (irrespective of whether it is a
cold fluid or a hot fluid) and inlet temperature difference of the two fluids. It is thus different for each
fluid of a two-fluid exchanger.
For fluid 1
S1 ¼
T1;out T1;in
DT1
¼
T2;in T1;in
DTmax
(2.9a)
S2 ¼
T2;in T2;out
DT2
¼
T2;in T1;in
DTmax
(2.9b)
and for fluid 2
The heat capacity ratio (R) for each fluid is
R1 ¼
m1 Cp1 T2;in T2;out
¼
m2 Cp2 T1;out T1;in
R2 ¼
m2 Cp2 T1;out T1;in
¼
m1 Cp1 T2;in T2;out
Explicit expressions for FT in terms of R and S for 1e2 (TEMA E shell) exchanger (see Chapter 4
for TEMA classification) and cross-flow exchanger with one mixed and one unmixed flow are given in
Table 2.2. Further discussions on calculation of FT from terminal temperatures in case of shell and tube
exchanger are provided in Chapter 4.
36
Chapter 2 Heat transfer processes in industrial scale
Table 2.2 FT expressions for specific heat exchanger flow arrangements.
Flow arrangement
Formula
Counterflow
FT ¼ 1
Parallel flow
FT ¼ 1a
a
Cross-flow (single pass)
Fluid 1 unmixed, fluid 2 mixed
Fluid 1 mixed, fluid 2 unmixed
FT ¼
ln½ð1 R1 S1 Þ=ð1 S1 Þ
ðR1 1Þ ln½1 þ ð1=R1 Þ lnð1 R1 S1 Þ
¼
ln½ð1 R2 S2 Þ=ð1 S2 Þ
ð1 1=R2 Þ ln½1 þ R2 lnð1 S2 Þ
FT ¼
ln½ð1 R1 S1 Þ=ð1 S1 Þ
ð1 1=R1 Þ ln½1 þ R1 lnð1 S1 Þ
ln½ð1 R2 S2 Þ=ð1 S2 Þ
ðR2 1Þ ln½1 þ ð1=R2 Þ lnð1 R2 S2 Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ R21 ln½ð1 R1 S1 Þ=ð1 S1 Þ
FT ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
3
2 S1 1 þ R1 1 þ R21
6
7
ð1 R1 Þ ln4
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
5
2
2 S1 1 R1 þ
1 þ R1
¼
1-2 TEMA E-shell fluid mixed
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ R22 ln½ð1 R2 S2 Þ=ð1 S2 Þ
¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
3
2 S2 1 þ R2 1 þ R22
6
7
ð1 R2 Þ ln4
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
5
2
2 S2 1 R2 þ
1 þ R2
Plate heat exchanger
FT ¼ 0:95
Air-cooled exchanger
FT ¼ 0:9
All exchangers with R1 ¼ 0 or N
FT ¼ 1
a
FT is unity for true counterflow and parallel flow exchangers and is less than 1 for all other flow arrangements. A value of FT
close to unity does not mean a highly efficient heat exchanger. It simply means a closer approach to counterflow behaviour for
comparable operating conditions of flow rates and inlet fluid temperatures.
The effectiveness-NTU method
The LMTD correction can be directly applied when all the terminal temperatures are known for a
particular flow condition. A solution by trial is needed when one of the terminal temperatures is unknown.
In such cases, if the overall coefficient is known or can be estimated a priori, the iterative procedure can
be avoided by resorting to the effectiveness-NTU method. The effectiveness (ε) of a heat exchanger is the
ratio of the actual heat transfer rate to the maximum possible heat transfer rate if there was infinite surface
area. One should carefully distinguish between ε and thermal effectiveness (S) introduced earlier.
ε¼
Actual Rate of Heat Transfer in the exchanger ðQÞ
Maximum thermodynamically possible rate of heat transfer ðQ maxÞ
2.6 Design overview for recuperators
37
Considering C to be the product of flow rate and specific heat capacity of either of the fluids, the
effectiveness is defined as follows:
ε¼
Cmax ð Th;in Th;out Þ
Cmin ð Th;in Tc;in Þ
(2.10a)
for the cold fluid as the fluid with minimum C. If the hot fluid is the minimum C fluid, the effectiveness
is defined as follows:
ε¼
Cmax ð Tc;out Tc;in Þ
Cmin ð Th;in Tc;in Þ
(2.10b)
This defines the heat transfer rate as
Q ¼ εCmin Th;in Tc;in
(2.11)
Thus, the heat exchanger effectiveness term depends upon whether the hot fluid or cold fluid
has the lower capacity coefficient Cð ¼ mCp Þ. It is related to the number of transfer units (NTU) or,
ε ¼ f ðNTU; Cr Þ where Cr ¼ Cmin/Cmax and the value of NTUis defined as follows:
NTU ¼ UA=Cmin
(2.12)
Expressions relating ε, NTU and Cr for different configuration of exchangers are available and the
same for the common configurations are provided in Table 2.3.
With sufficient other data known about a heat exchange process, an unknown outlet temperature
can be found by this method directly without any trial calculation as required in the FT method.
The ε-NTU method is used for design of compact heat exchangers, while the LMTD method
is more established and is commonly used for tubular (double-pipe, shell and tube) exchangers.
However, both methods yield identical results within the specified convergence tolerances. It may be
noted that the ε-NTU approach is not valid if the overall heat transfer coefficient varies over the
exchanger length.
The overall heat transfer coefficient U is calculated from the individual thermal resistances per unit
area of either the hot ðAh Þ or the cold fluid ðAc Þ side using
the following expressions.
Overall Heat Transfer Coefficient
1
Uh A h
¼
1
1
þ Rw Ah þ
hh A h
hc Ac
(2.13a)
1
U h Ac
¼
1
1
þ Rw Ac þ
h h Ah
hc Ac
(2.13b)
or
where U1h and U1c are the overall thermal resistances based on the hot surface and cold surface. hh and hc
are the heat transfer coefficients for the hot and cold fluid, respectively, and Rw is the wall thermal
resistance. Areas Ac and Ah are defined in Chapter 3 for double-pipe exchanger.
For (external) finned tube exchangers, the heat transfer area should be based on total outside tube
and fin surface and the heat transfer coefficient h needs to take into account the effective tube wall and
38
Chapter 2 Heat transfer processes in industrial scale
Table 2.3 εLNTU relationships for a few simple cases
Heat
Exchanger
Type
Effectiveness Relation
Parallel Flow
Double pipe
Counter Flow
ε¼
1 exp ½ NTUð1 þ Cr Þ
for Cr s1
1 þ Cr
ε¼
NTU
1 þ NTU
ε¼
1 exp ½ NTUð1 Cr Þ
for Cr < 1
1 Cr exp ½ NTUð1 Cr Þ
ε¼
NTU
1 þ NTU
2
for Cr ¼ 1
qffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ exp NTU 1 þ C 2r
q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
6
2
ε ¼ 26
qffiffiffiffiffiffiffiffiffiffiffiffiffiffi
41 þ C r þ 1 þ C r
1 exp NTU 1 þ C 2r
One shell pass,
2,4,..tube
passes
Standard Shell
and Tube
for Cr ¼ 1
31
7
7
5
N
1 ε Cr
1
1ε
N
for Cr < 1
ε¼
1 ε Cr
Cr
1 ε
N-2N
exchangers
N¼2,.. etc.
Nε
for Cr ¼ 1
1 þ ðN 1Þε
ε ¼ Effectiveness for 1-2 exchanger with same Cr and (1/N) times the
NTU value
ε¼
Cross Flow
Cr NTU 0:78 1
Both fluids
unmixed
ε ¼ 1 exp
Cmax mixed
Cmin unmixed
ε ¼ C1r ½1 expf1 Cr ð1 expð NTUÞÞg
Cmin mixed
Cmax unmixed
ε ¼ 1 exp½ ð1 =Cr Þf1 expð Cr NTUÞg
All heat exchangers with
Cr ¼ 0
NTU 0:22 exp
Cr
ε ¼ 1 expð NTUÞ
fin metal resistance. Since heat is conducted along the fin surface, the fin surface area is less effective
than the bare tube surface. This is accounted for in design by considering a fin effectiveness factor Ef .
1
Uh Ah
¼
1
U c Ac
¼
1
hh Efh
Ah
þ
Rw Ah
þ
1
hc Efc Ac
þ
Rw Ac
þ
1
(2.14a)
or
1
hh Efh
Ah
hc Efc
Ac
(2.14b)
2.6 Design overview for recuperators
39
where Ef is a function of fin dimensions e tf ; Wf ; hf denoting the thickness, width and height of fin
and kf is the thermal conductivity of the fin material.
tan h mLf ;eq
Ef ¼
(2.15)
mLf ;eq
where
m2 ¼
2h
for tf << Wf
kf tf
(2.16)
Fins are usually made of metals with high thermal conductivity. For copper and aluminium fins, Ef
is typically 0.9e0.95. Lf ;eq , the characteristic/equivalent fin height can be expressed as
Lf ;eq ¼ hf þ
for longitudinal fin and
tf
2
(2.17)
Rfc
Lf ;eq ¼ ðRfc Ro Þ 1 þ 0:35 ln
Ro
for radial fin of outer radius Rf , attached to a tube exterior where the corrected radius is
tf
(2.18)
2
Depending upon the nature of the fluids, one or more resistances may dominate the RHS of
Eqn. 2.14. In case of gaseliquid exchanger, the controlling resistance will be
that of the gas, if the heat transfer surface areas are nearly equal for both sides.
Lowest overall thermal resistance in a heat exchanger is obtained when the hotFouling
and cold-side thermal resistances are nearly same. Therefore, fins (extended
surfaces) are used on the gas side to achieve this.
Eqn. 2.13 is valid for a heat exchanger with clean heat transfer surfaces. A film of dirt or scale
eventually builds up on the heat transfer surface with time. This process, called fouling, adds to the
resistance to heat transfer and results in lowering the performance of the exchanger. Fouling in heat
exchangers is traditionally taken care of in the design by considering fouling resistance (RDi and RDo )
that represents the thermal resistances of the dirty films on the inside and outside of the inner pipe. This
resistance is added in series to obtain the overall heat transfer coefficient
Rfc ¼ Rf þ
1
1
¼
UD
U
þ Rdi
þ
Rdo
(2.19)
where U (as Uh or Uc ) is estimated from Eqn. 2.14 and UD is the overall design heat transfer coefficient
considering fouling. Designing an exchange with UD leads to higher heat transfer area than is actually
required for a clean exchanger. The thermal load of new (clean) exchanger will therefore be higher
than its design value. Compared to the design conditions, the new exchanger may therefore show lower
and higher outlet temperatures for the hot and the cold fluid, respectively.
Fouling is a gradual process that not only decreases thermal efficiency but can also perceptibly increase pressure drop due to scale or other deposit. The effect of increasing pressure drop may be more
40
Chapter 2 Heat transfer processes in industrial scale
Table 2.4 Design fouling resistances RD for industrial fluids
(TEMA).
Fluid
R00 d [ RdA (m2K/kW)
Fuel oil No. 2
0.352
Fuel oil No. 6
0.881
Quench oil
0.705
Refrigerants
0.176
Hydraulic fluids
0.176
Ammonia liquids
0.176
Ethylene glycol
solutions
0.352
Exhaust gases
1.761
Natural gas flue gases
0.881
Coal flue gases
1.761
significant than the effect of lower heat addition/removal from the process. Fouled heat exchangers
require cleaning with a chemical solvent and/or mechanical cleaning. Requirement for cleaning is
assessed by comparing the cost of cleaning and equipment downtime vis-a-vis the economic gain from
higher heat transfer and lower pressure drop achievable in the exchanger after cleaning. Higher fluid
velocities and lower temperatures usually result in lower fouling tendency. Fouling also depends strongly
on the specific processes and presence of impurities. A naphtha stream from crude distillation column
with negligible olefins will have very low fouling tendency as compared to a naphtha stream produced
from a cracking unit that will contain olefins. These may polymerise and pose serious fouling problem.
Typical fouling resistance values used in design for various fluids are given in Table 2.4. Further
details are available in Appendix. These should be used with discretion since the fouling factors vary
widely with time and exact circumstances. Selection of design fouling factor is often based on economic considerations. The optimum design results from balancing the additional capital cost of a
larger exchanger (higher area) against the benefit from longer operating time between cleaning that the
larger area will give.
A
The percentage over surface is defined as %OS ¼
1 100, where A is the actual heat
Acalc
transfer surface area in the exchanger and Acalc is the calculated heat transfer surface area based on U.
Oversurface depends on the relative magnitudes of the total fouling allowance and the film and wall
resistances. This is often done for heat exchangers that cannot be easily cleaned. Often in such cases,
25% oversurface is prescribed for shell and tube heat exchangers.
2.7 Estimation of overall design heat transfer coefficient
Overall heat transfer coefficient for different services in industry has typical ranges. This happens
because the technical and economic considerations often fix the type of heat exchanger. Table 2.5 may
be used for obtaining an educated guess of overall design heat transfer coefficient UD based on values
Table 2.5 Typical overall heat transfer coefficient in industrial tubular heat exchangers
(Includes fouling factor).
Fouling
Application
Heat
exchangers
Coolers
Inside fluid
Outside fluid
Typical overall heat transfer
coefficient (W/m2 K)
Hot fluid
Cold fluid
Minimum
Maximum
Water
Water
802
1501
Aqueous solutions
Aqueous solutions
1422
2844
Organic solvents
Organic solvents
102
301
Light oils
Light oils
102
398
Medium organics
Medium organics
114
341
Heavy organics
Light organics
171
341
Heavy organics
Heavy organics
57
227
Light organics
Heavy organics
57
227
Gases
Gases
11
51
Water
Water
1422
2844
Methanol
Water
1422
2844
Organic solvents
Water
250
751
Aqueous solvents
Water
1422
2844
Light oils
Water
353
899
Medium organics
Water
284
711
Heavy oils
Water
63
301
Gases
Water
23
301
Organic solvents
Brine
148
500
Water
Brine
603
1200
Gases
Brine
17
250
Steam
Water
1501
4004
Steam
Aqueous solutions (<2 cP)
1137
3981
Steam
Aqueous solutions (>2 cP)
569
2844
Steam
Organic solvents
500
1001
Steam
Light organics/oils
301
899
Steam
Medium organics
284
569
Steam
Heavy organics/oils
63
449
Steam
Gases
28
301
Dowtherm
Heavy oils
51
301
Dowtherm
Gases
23
199
Flue gases
Steam
28
102
Flue gases
Hydrocarbon vapours
28
102
Heaters
Continued
42
Chapter 2 Heat transfer processes in industrial scale
Table 2.5 Typical overall heat transfer coefficient in industrial tubular heat exchangers (Includes
fouling factor).dcont’d
Fouling
Condensers
Vaporisers
Inside fluid
Typical overall heat transfer
coefficient (W/m2 K)
Outside fluid
Aqueous vapours
Water
1001
1501
Organic vapours
Water
700
1001
Organics with
noncondensable
Water
500
700
Vacuum condenser
Water
199
500
Steam
Aqueous solutions
1001
1501
Steam
Light organics
899
1200
Steam
Heavy organics
603
899
for a similar system. The tabulated values can be used for the preliminary sizing of equipment for
process evaluation and also as initial guesses for a detailed thermal design. The guess value needs to be
checked with the overall design coefficient, UD obtained from Eqns. (2.13a,b and 2.14a,b) once the
values of individual heat transfer coefficients are known.
The magnitude of the individual coefficients depends on (a) the heat transfer process (conduction,
convection, boiling, condensation, radiation), (b) physical properties and flow rate of the fluid and
(c) geometrical configuration of heat transfer surface. Some of the commonly used correlations
available for estimation of the individual heat transfer coefficients (h) under different input conditions
are presented in Table 2.6. The correlation usually express h as Nusselt number ðNu ¼ hDe =kÞ
or Stanton number ðSt ¼ Nu =RePr ¼ h =ðrUCp ÞÞ where k; r; U; Cp refer to the thermal conductivity
(W/mK), density (kg/m3), velocity (m/s) and specificheat capacity (J/kgK)
of the fluid, all properties
evaluated at the average bulk fluid temperature
T þT
Tf ;avg ¼ fi 2 fo
or at the respective caloric
temperature (discussed at the end of this chapter) and De is the equivalent diameter (m). Table 2.7
presents the correlations commonly used for boiling and condensation under different flow conditions.
In Table 2.6,
Re ¼
rUDe GDe
¼
m
m
(2.20)
Cp m
k
(2.21)
Pr ¼
m is fluid viscosity evaluated at Tf ;avg . Refer to the following section for the concept of caloric
temperature for evaluating m.
De ¼ tube inside diameter for flow inside tube, hydraulic diameter for flow in annuli or shell and
twice the gap between the plates in plate-type exchangers. Tw1 þ Tw2
mw ¼ fluid viscosity evaluated at average wall temperature Tw;avg ¼
.
2
Table 2.6 Correlations to estimate heat transfer coefficients.
Flow geometry
Circular and noncircular pipes
of uniform cross section
Flow condition
Turbulent
flow
Re 104
Corresponding equation
(I)
Nu ¼ C
ðPrÞ
Re0:8
0:33
m
mw
Range of applicability/Remarks
ð0:5 < Pr < 17; 000Þ
ðL=D > 10Þ
0:14
C ¼ 0.021 (gases)
¼ 0.023 (nonviscous liquids)
¼ 0.027(viscous liquids)
(II)
St ¼ E
Re0:205
St ¼ Nu=ðRe PrÞ
ðPrÞ0:505
where E ¼ 0:0225 exp 0:0225ðln PrÞ2
(III) "
2 #
De 3
Nu ¼ 1 þ
L
C Re0:8 ðPrÞ0:33
Circular pipes
Laminar flow
(Re < 2100)
ð10 < L=D < 60Þ
ð0:5 < Pr < 100Þ
m
mw
0:14 (IV)
1 0:14
3
m
Nu ¼ 1:86 RePr DL
mw
Annulus
(For double-pipe exchanger)
Laminar flow in
Forced convection
D2 0:8
Nu ¼ 3:66 þ 1:2
D1
"
0:5 #
D2
De 0:8
0:19 1 þ 0:14
RePr
D1
L
þ
De
1 þ 0:117 RePr
L
D1 ¼ outside diameter of inner pipe
D2 ¼ inside diameter of outer pipe
De ¼ equivalent diameter ¼ ðD2 D1 Þ
In circular and noncircular
pipes of uniform cross section
Transition region
(2100 < Re < 104)
(VII)
Lower of the h value from eqns (I) and (IV)
(VIII)
ðRePrD=LÞ1=3 ðm=mw Þ0:14 > 2
ðRePrD=LÞ1=3 ðm=mw Þ0:14 < 2
(V)
Nu ¼ 3:66
(VI)
ð0:5 < Pr < 17; 000Þ
0:14
De 2=3
m
Nu ¼ 0:116 Re2=3 125 Pr 1=3 1 þ
mw
L
Nu based on equivalent diameter (De)
Nu based on equivalent diameter (De)
Continued
Table 2.6 Correlations to estimate heat transfer coefficients.dcont’d
Flow geometry
Forced convection in external
flow over flat plate
Flow condition
Re < 5 105
Re > 5 105
Corresponding equation
(IX)
Nu ¼ 0:664 Re1=2
Plate heat exchanger
Turbulent flow
0:037
Outside bank of tubes with
plain transverse fins
Re0:65
ðPrÞ0:4
m
mw
0:14
(XII)
1þB jH ¼ 0:5
0:08Re0:6821 þ 0:7Re0:1772
Dshell
B ¼ baffle spacing
Cross-flow
(XIII)
p f tf
pf
hf
tf
where pf , tf and hf are the pitch, thickness and height of
the fin
Re evaluated for bare tube (no fins)
Nu ¼ 0:134 Re0:681 Pr 0:33
Air-side coefficient in air
coolers for
pf ¼ 2:3mm
tf ¼ 0:48mm
hf ¼ 15:9mm
Inside tube
Þ ðPrÞ1=3
Re0:8 870
(XI)
Nu ¼ 0:26
Shell-side heat transfer
coefficient
For square pitch and segmental
bafflesa
ðPrÞ1=3
(X)
Nu ¼
(XIV)
Nu ¼ 0:104 Re0:681 Pr 0:33
Water flow
(XV)
4200ð1:35 þ 0:02tÞV 0:8
D0:2
i
Di ¼ inside diameter of tube ðmÞ
V ¼ Velocity in tube (m/s)
T ¼ temperature C
hi ¼ inside heat transfer coefficient (W/m2 C)
hi ¼
a
Refer to Chapter 4 for segmental baffle.
Compiled from various resources.
Range of applicability/Remarks
ðPr > 0:6Þ
All fluid properties evaluated at film
temperature (Tf)
ð0:6 < Pr > 60Þ
Re upto 108
All fluid properties evaluated at film
temperature (Tf)
Table 2.7 Heat transfer coefficient under boiling and condensation.
Flow geometry
Flow condition
Generalised correlation
rcon ðrcon rv Þg 1=3
mcon G
Condensation outside horizontal tubes
Low vapour and liquid flow rates
Flowing condensate film undisturbed
ðhcon Þ1 ¼ 0:95 kcon
Condensation outside tube bundle with
ðNr Þ tubes in a vertical row
Laminar flow
Smooth condensate flow from tube to tube
ðhcon ÞNr ¼ ðhcon Þ1ðNr Þ1=4
Flow not smooth from tube to tube
Condensation on horizontal tube
Single tube or a single row of tubes
Condensation inside vertical tube
Inlet stream saturated vapour
Vapour totally condenses to give single-phase
condensate flow inside tubes
(Boyko, L. D., and G. N. Kruzhilin. “Heat
transfer and hydraulic resistance during
condensation of steam in a horizontal tube and
in a bundle of tubes’.” International Journal of
Heat and Mass Transfer 10.3 (1967): 361e373)
"
#1=4
3 r ðr r Þgl
kcon
l l
v
ðhc Þ ¼ 0:728
ml ðTv Tw ÞD0
Condensation outside tube bundle
Air-free saturated steam
Subcooled condensate flow
Pool boiling
(Forster, H. K., and Novak Zuber. “Dynamics
of vapor bubbles and boiling heat transfer’.”
AIChE Journal 1.4 (1955): 531e535)
Subscript 1 refers to top tube
r ðr rv Þg 1=3 1=6
Nr
ðhcon ÞNr ¼ 0:95 kcon con con
mcon Gh
Wcon
Gh ¼
; Wcon ¼ total condensate flow
LNt
k 3 rl ðrl rv Þgl 1=4
ðhc Þ ¼ 0:728 con
ml ðTv Tw ÞD0
2
rffiffiffiffiffiffiffiffi 3
rcon
1
þ
rv 7
kcon 0:8 0:43 6
7
6
Re Pr 6
ðhcon Þv;BK ¼ 0:021
7
5
4
2
Di
8000 ðW=m2 C
200 ðW=m2 C
"
ðhnb Þ ¼ 0:00122
s0:5 m0:29
l0:24 r0:24
v
l
"
Mostinski correlation
(Eqn. 9.2b, 9.4, Serth, Robert W. Process
heat transfer. Academic press, 2010)
ðhnb Þ ¼ 0:00417ðPc Þ
Film boiling heat transfer coefficient
(Bromley, L.A., heat transfer in stable film
boiling, CEP 46, 5, 221e227, 1950)
kv ðrl rv Þrv gl 1=4
ðhfb Þ ¼ 0:62
mv Do ðTw Tsat Þ
Do in m
Compiled from various resources.
#
0:45 r0:49
kl0:79 Cpl
l
0:69
0:7
ðQÞ
ðTw Tsat Þ0:24 ðPw Psat Þ0:75
P
1:8
Pc
Pc in bar
0:17
P
þ4
Pc
1:2
10 #
P
þ10
Pc
46
Chapter 2 Heat transfer processes in industrial scale
It is often convenient to correlate heat transfer data in terms of heat transfer factor jh defined as
0:14
m
0:67
jh ¼ StðPrÞ
(2.22)
mw
The jh factor correlates with Reynolds number in both laminar and turbulent flow regime, similar to
the correlation of friction factor with Reynolds number for pressure drop. The correlation can be used
for circular and noncircular pipes of uniform cross section by using hydraulic diameter instead of tube
diameter for noncircular cases. Since pipes are rougher than heat exchanger tubes, a more accurate
result can be obtained for heat transfer coefficient in exchanger tubes by rearranging Eqn. (I) in
Table 2.6 as
0:14
1
hi D i
m
Nu ¼
¼ jh ½RePr 3
(2.23)
mw
kf
=
Kern (see Further Reads) defines heat transfer factor as
0:14
m
1=3
jH ¼ NuðPrÞ
mw
(2.24)
where jH ¼ jh Re
In Table 2.7,
ðhcon Þ1 ¼ mean condensation film coefficient for a single tube (W/m2 C)
kcon ¼ condensate thermal conductivity (W/m C)
rcon ¼ condensate density (kg/m3)
rv ¼ vapour density (kg/m3)
mcon ¼ condensate viscosity (Pa.s)
All condensate properties are evaluated at average temperature of condensing and tube wall
temperature
g ¼ acceleration due to gravity (m/s2)
L ¼ tube length (m)
NT ¼ total number of tubes in tube bundle
Nr ¼ average number of tubes in vertical tube row
(¼two-thirds of the number of tubes in the central row)
G ¼ condensate loading per unit tube length (kg/m s)
G ¼ W2=3 ¼ modified condenser loading
LNT
W ¼ condensate rate (kg/s)
L ¼ tube length (m)
nT ¼ number of tubes
ðhnb Þ and ðhfb Þ ¼ nucleate pool boiling and film boiling coefficient (W/m2 C)
kl ; Cpl ; rl ml ¼ thermal conductivity (W/m2 C), specific heat, density of liquid (kg/m3),
viscosity of liquid (Pa.s)
l ¼ latent heat of condensation/vaporisation (J/kg)
rv ¼ density of vapour (kg/m3)
2.7 Estimation of overall design heat transfer coefficient
47
Tw ¼ wall temperature ( C)
Tsat ¼ saturation temperature ( C) of boiling liquid
Pw ; Psat ¼ saturation pressure corresponding to Tw and Tsat
P ¼ operating pressure (bar)
Pc ¼ critical pressure of the liquid (bar)
Q ¼ heat flux (W/m2)
The estimation of individual heat transfer coefficients using
equations provided in Table 2.6 requires fluid physical properties
namely density, viscosity and thermal conductivity. These properties vary with temperature and since the formulae involve a
Caloric Temperature
single value of property, either an averaging or a correction to the
average property value is necessary. Whenever the range of
temperature change of a fluid is small, arithmetic averaging of the
property at the outlet and inlet temperatures for the fluid suffices as a good approximation. For
some fluids like heavy petroleum hydrocarbon fractions, the thermophysical properties are a
strong function of temperature. Particularly the kinematic viscosity for high viscous liquids (e.g.,
heavy petroleum cuts, reduced crude oil, short residue, lubricating oil distillates, etc.) varies
significantly with temperature. When these fluids flow through exchangers and the temperature
change is large, there is substantial variation of heat transfer coefficient along the exchanger. In
such exchanger calculations, evaluating the heat transfer coefficients at the arithmetic average
temperature generates unsatisfactory results. This is avoided by introducing the concept of caloric
temperature, a hypothetical temperature between the inlet and outlet at which the fluid thermophysical properties are used to calculate the heat transfer coefficient. One may note that the caloric
temperature values are different for the shell and the tube fluids such that evaluation and use of the
individual heat transfer coefficients at respective caloric temperatures satisfy the basic equation.
Q ¼ Ucaloric AðDTÞ
(2.25)
The caloric temperature concept is based on an assumption that the overall heat transfer coefficient
varies linearly with temperature between the terminal points. The procedure therefore should include a
characteristic nature of variation of the thermophysical properties (primarily viscosity) with temperature for the fluids involved. The procedure for estimating the caloric temperature is detailed in
Chapter 5 of ‘Process Heat Transfer’ by D. Q. Kern for petroleum fluids.
Based on the discussions presented in this chapter, the
design of double-pipe and shell and tube heat exchangers is
discussed in Chapters 3 and 4. Chapter 5 deals with heat
Organisation of Section II
exchanger network analysis and Chapters 6 and 7 deal with the
design of two typical heat exchange equipment involving phase
change namely design of an evaporator and cooling tower. One
may refer to the book (see Further Reads) by Shah and Sekulic
and Towler and Sinnott for design of other types of exchanger.
48
Chapter 2 Heat transfer processes in industrial scale
Further reading
1. Shah, R. K., & Sekuliâc, D. P. (2012). Fundamentals of heat exchanger design. John Wiley & Sons.
2. Towler, G. P., & Sinnott, R. K. (2008). Chemical engineering design: Principles, practice and economics
of plant and process design. Amsterdam: Elsevier/Butterworth-Heinemann.
3. Kern, D. Q. (1990). Process heat transfer. New York: McGraw-Hill.
4. Serth, R. W. (2007). Process heat transfer principles and applications. Amsterdam: Elsevier.
CHAPTER
Double pipe heat exchanger
3
3.1 Introduction
The double-pipe heat exchanger is probably the simplest to construct and is used for low heat load
applications. As shown in Fig. 3.1, these may comprise of a single tube or multiple tubes inside a shell.
Commercially available single tube double-pipe sections range from 50 mm through 100 mm
(200 through 400 ) pipe size shells with inner tubes varying
from 19 mm to 65 mm (3/400 to 2 1/200 ) pipe size.
The exchanger with a bundle of U tubes inside a pipe of
Multi-tube double-pipe exchanger
150 mm diameter and above uses segmental baffles (discussed
in Chapter 4) and is referred to as hairpin or jacketed U tube
exchanger. Multi tubular double-pipe sections may contain 7 to
64 tubes within the outer tube. Nevertheless, sections containing more than seven tubes per section are
rarely used since they have limited economic advantage for most services. If the particular service
requires fractional portions or short tube lengths of a multi-tube section, single tube sections are more
economical. One end of the tube element is free-floating for thermal expansion. The two fluids usually
flow in countercurrent mode for the highest thermal performance for a given surface area. However, for
an almost constant wall temperature, the flow can be co-current. Double-pipe
sections have been designed for pressure up to 165 bar (g) (2400 psig) on the
shell side and up to 1033 bar (g) (15,000 psig) on the tube side. Metal-to metal
ground joints, ring joints or confined ‘O’-rings are used in the front end cloFinned tube
sures at lower pressures.
In general, the tubes used are plain, but some applications use low-fin
tubes for the inner pipes that provide about 2.5 times the external surface
area. Finned tubes in double-pipe exchangers are economical if the heat transfer coefficient for the
fluid flowing in the annular area is less than 75% of the tube side coefficient. The fins are
longitudinally attached to the inner tube either by welding, brazing, or mechanical bonding.
Usually, single tubes have longitudinal fins while multi-tubes have radial fins. The fins 16 to 48 per
tube are 12.5e25 mm (1/2 to 1 inch) high and 0.9e1.3 mm (35e50 miles) thick and the fin height
is dictated by the clearance between the inner and the outer pipe. Shorter fins have higher fin
efficiency. The minimum thickness is rarely below 0.8 mm. Fin efficiency increases with
decreasing annular coefficient and increasing fin thermal conductivity. Low-fin tubes are costlier
by 50%e70% compared to plain tubes.
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00003-8
Copyright © 2020 Elsevier Inc. All rights reserved.
49
50
Chapter 3 Double pipe heat exchanger
FIGURE 3.1
A: Double-pipe heat exchanger. B: Double-pipe heat exchanger stack. C: Multi-tubular double-pipe heat
exchanger.
Multi-tube exchangers with fins, typically use 12 to 20 fins per tube that are nominally 6 mm (1/400 )
high and 0.9 mm thick. Normally, only bare tubes are used in sections containing more than 19 tubes.
In a double-pipe exchanger sealing between the outer and the inner tube is by a gland seal. Gland
packings are common wherever there is a
shaft protruding through a body and the
leakage of fluid from the body through the
Sealing arrangement between the outer and inner tube
junction of the shaft is to be prevented. Such
examples are common; every valve has its
stem passing through such a gland seal. The
seal is provided by a packing between the inner pipe/shaft and the outer pipe. The packing, uniformly
compressed against a restrictor by a ring, provides a leak-proof seal. The pressure on the ring is varied
by tightening a gland, which may either be threaded or flanged (in case of high-pressure application).
The gland not only prevents any leakage of fluid from the annular space but also ensures the concentric
configuration of the inner and the outer pipe.
The detail of the gland sealing arrangement can be seen in Fig. 3.1A.
Double-pipe sections can be combined in a variety of series/parallel arrangements to provide the
required surface area while maintaining pressure drop limitations.
Sections installed in series are normally mounted one on top of the
other (Fig. 3.1B), and the sections in parallel are placed side by
Series/Parallel arrangement
side. A combination of series-parallel arrangement elaborated in
para 3.3 can be achieved by a combination of side-by-side and oneover-the other modules.
Advantages and disadvantages
3.2 Design
•
•
•
•
•
•
•
•
•
51
Double-pipe exchangers are perhaps the simplest heat exchanger.
Flow distribution is not a problem, and dismantling and cleaning are easy.
As the dimensions are small, these exchangers are suitable when either or both the fluids are at
very high pressure.
Since double-pipe sections permit true countercurrent or true co-current flow, they may be of
particular advantage when very close temperature approaches are required. Countercurrent flow
results in lower surface area requirements, usually below 28 m2 (300 sq. ft) for services having a
temperature cross.
In some cases where the thermal resistances of the two fluid films are essentially the same, it is
found that for small heat loads, the installation of double-pipe units is more economical than shell
and tube units, which are economical, mostly in larger sizes.
Hairpin exchangers are cheaper than shell and tube exchangers at very small sizes and can be
specified for areas from 7 to 150 m2
They are easier to fabricate using standard bought out pipes and pipe fittings. Shortened delivery
time results from the use of stock components that can be assembled into standard sections.
Potential need for expansion joint is eliminated in U-tube construction.
Double-pipe exchangers are modular and are used in applications requiring adding and dismantling
the modules or the rearrangement of sections for new services, thus ensuring flexibility.
Nevertheless, multiple hairpin sections are not always economically competitive with a single shell
and tube heat exchanger. They are more expensive on a cost per unit area basis and are generally used for
small capacity applications where the total heat transfer surface area is less than 50 m2. Compared to
shell and tube exchangers or other more compact heat exchanger types, these require more floor space
and also entail a large number of points at which leakage may occur. In addition, proprietary closure
design requires special gaskets, and a longer length is required to bring about the required heat transfer.
3.2 Design
Double-pipe heat exchanger design involves the estimation of heat transfer area and pressure drop at
the tube and the shell side. After determining the required heat exchanger surface area for counterflow
or parallel flow, the pipe sizes and the number of bends are finalised.
3.2.1 Input data
The input data is the same as that in the case of any other type of exchanger. Table 3.1 contains the
items of input data pertaining to the inner and outer fluids. In addition, information on the nature of the
fluids, e.g., flammability, corrosive nature, fouling tendency, solid concentration, etc., as applicable,
are also considered.
3.2.2 Deliverables
Design output is the details to be filled in the heat exchanger datasheet. A typical datasheet is shown in
Table 3.1.
In addition, the design references: Process calculation references (Methods: Kern, HTRI, etc.);
Mechanical standard class (TEMA, BIS, etc.) are also to be furnished as part of design documentation.
Complete fabrication drawing consisting of the following are required to be included: General
arrangement drawings including stacking plan, if required; shell, nozzles and support details, other
connections (vent, drain, instruments, etc.); tube bundle and its component details, if provided; details
of the head.
52
Chapter 3 Double pipe heat exchanger
Table 3.1 Double-pipe exchanger data sheet.
DOUBLE PIPE HEAT EXCHANGER DATA SHEET
UNITS OF MEASUREMENT : (SI)
1
Service Of Unit:
2
Site:
Arrangement Shell
3
Size
Type
2
4
Surface/Unit (Eff.)
m
5
PERFORMANCE OF ONE UNIT
6
Fluid Allocation
7
Fluid Name
8
Fluid Quantity, Total
kg/hr
9
Vapor (In/Out)
kg/hr
10
Liquid
kg/hr
11
Steam
kg/hr
12
Water
kg/hr
13
Non-Condensate (Mw)
kg/hr
14
°C
Temperature
No Of Units:
Manufacturer
Parallel
Series: Tube
Section/Unit
Density (Vapor/Liquid)
Viscosity (Vapor/Liquid)
Molecular Weight
Specific Heat (Vapor/Liquid)
Thermal Coductivity (Vapor/Liquid)
Surface Tension
Boiling Point
Latent Heat
Inlet Pressure
Velocity
Pressure Drop. Allowable/Calculated
kg/m3
cP
kg/kmol
kJ/kg°C
W/m°C
Dyn/cm
°C
kJ/kg
barg
m/s
bar
26
27
Fouling Resistance (Min.)
Heat Exchanged
m2 °C/W
MW
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
Transfer Rate
CONSTRUCTION OF ONE SHELL
W/m2 °C
Date
Description
Series
m
TUBE SIDE
Thk.
mm (Ave/Min)
Thk.
Thk.
mm
mm
%Cut
mm:
Thk.
2
TUBE SIDE
MTD (Corrected) (Weighted)
SHELL SIDE
Rev.
Parallel:
Surface/Section (Eff.)
SHELL SIDE
15
16
17
18
19
20
21
22
23
24
25
Design Pressure
barg
°C
Design Temperature Max/Min
Corrosion Allowance
mm
mm
Insulation THK. In/Out
Connections
In
Size &
Out
Rating
Tube No.
O.D.
(mm):
Tube Type
Fins:
No.
Height
mm:
Shell
O.D.
mm:
Tube Sheet - Stationary
Baffles-Cross
Type
Shell Return Bend - Housing Material
Tube Side Closure - Type
External Return Bend: OD
Gasket - Shell Side
Code Requirements
Double Pipe Type?
Remarks:
Item No:
°C
Sketch
Length mm:
Pitch
Material
Type
Material
Impingement Protection
Spacing:c/c
Cover Material
mm:
Deg
Material
mm:
Inlet
mm
Material
Material
mm:
Tube Side
No
Stamp
Multi Tube Type?
App.1
Flow Angle
App.2
App.3
3.2 Design
53
3.2.3 Codes and standards
Common standards for double-pipe heat exchangers are TEMA and API 660. There is no Indian (BIS)
code. Hairpin sections are specially designed units, which are normally not built to any industry
standard other than ASME Code. However, TEMA tolerances are normally incorporated wherever
applicable.
3.2.4 Guidelines to select inner and outer fluid
The guideline for selecting the inner and outer fluid is the same for a shell and tube exchanger and a
double-pipe exchanger. The general guidelines for preliminary selection are presented in Table 3.2.
They are general in nature and not rigid rules. Optimal fluid placement depends on several servicespecific factors, as well.
Table 3.2 General guidelines for selecting the shell and tube side fluids.
Tube side fluid
Shell side fluid
fluid
viscous fluid
· High-temperature
· More
At higher temperature the allowable stress is lower.
The critical Reynolds number for turbulent flow is
Since tubes have a much lower diameter as compared
to a shell, they can withstand higher pressure at the
same temperature. This makes the design safer.
Further, this ensures lower heat losses from the
exchanger to the surroundings and lower cost of
exchanger insulation.
200 on the shell side. Thus for the same Re, when the
flow is laminar in tubes, the shell flow may be turbulent. However, if the flow is still laminar in the
shell, it is directed through the tubes, as this ensures a
more accurate prediction of both heat transfer and
flow distribution.
· Dirty and fouling fluids
· Liquid with a lower flow rate
hazardous or expensive fluid
· More
The chance of leaking out is less.
undergoing a phase change, e.g., condensing
· Fluid
steam/vapour
Tubes are easier to clean. Fouling tendency is lower
due to fewer stagnation points. Usually cooling water
is used in tubes for this reason.
Also, the tube fluid, mostly flowing at a higher velocity, would have lower fouling (less deposit). Mechanical cleaning is easier for tubes. Slurry is
preferred in the tube side for this reason.
at a higher pressure
· Fluid
The lower diameter of tubes calls for a lower wall
thickness compared to the shell.
fluid
· Corrosive
Only the tubes and not the shell is exposed to the
corrosive environment. A corrosive fluid in the shell
would affect both the shell and the tubes. In addition,
it is cheaper to fabricate tubes from expensive
corrosion-resistant materials.
· Streams with low flow rates
These are placed in tubes to obtain increased velocity
and turbulence.
To avoid multi-pass construction that will have
LMTD correction factor below unity. Turbulent flow
may also result due to lower critical Reynolds number
for the shell side.
Shell side offers a lower pressure drop. Vapour-liquid
mixtures resulting from vapour condensation is
allowable in vertical condensers.
for which pressure drop limit is lower, or there is
· Fluid
a chance of exceeding the same, e.g., fluid of high
viscosity.
that has poorer heat transfer characteristics:
· Fluid
As the critical Reynolds number for turbulent flow is
200 on the shell side.
· Fluid with large DT (>40 C)
54
Chapter 3 Double pipe heat exchanger
3.2.5 Design considerations
Heat exchangers shall be designed to conform to specified shell side and tube side design pressure with
respect to ambient. Designs based on differential pressure of the shell and tube side is not permitted.
Minimum design pressure shall be 10% above the maximum operating pressure or maximum operating pressure plus 2 bar (200 kPa), whichever is greater. Double-pipe sections have been designed for
up to 165 bar (g) (2400 psig) pressure on the shell side and up to 1033 bar (g) (15,000 psig) pressure on
the tube side.
Minimum design temperature shall be 10% above maximum operating temperature or maximum
operating temperature plus 28 C, whichever is greater.
Tube elements shall be removable without cutting the shell or connecting piping and without
disconnecting the shell piping. One end of the tube element shall be free-floating for thermal
expansion. No internal screwed connections shall be allowed. Over-all length shall be approximately
10 m. The minimum outside tube diameter of the tube element shall be 25.4 mm (100 ) and minimum
thickness shall be equivalent to 12 BWG tubing or Schedule 40 pipe. All pipes and tubings used in
construction of exchangers shall be seamless.
Minimum corrosion allowance on pressurised steel pressure parts shall be 3 mm for hydrocarbon
services, except for tubes.
The heat transfer area and heat transfer coefficients shall be based on the total effective outside tube
and fin surface. The effective tube wall and fin metal resistance shall be considered in calculating the
heat transfer coefficient. Finned tubes should not be used where fouling is expected on the shell side, or
the fins are likely to be exposed to a corrosive medium. A hairpin exchanger is not permitted if fouling
is expected in the tube side.
Cooling water is normally passed through the tube side. The minimum allowed water velocity is 1 m/s.
Fouling factors for circulating cooling water may be taken 0.35 m2. C/kW or 0.00,035 m2. C/W
(0.002 ft2.h. F/Btu).
The suitability of using a hairpin exchanger in a given application may be evaluated by
computing the product of heat transfer coefficient and area (UA). For preliminary evaluation, (UA)
of 80 kW/K may be considered to be the upper economic limit for hairpin type units. Above this
value, the unit may be uneconomical for a hairpin type design. If a hairpin is applied, it may require
multiple ND 400 (1600 ) multi-tube sections. In the range of 53e80 kW/K one or more ND 300 (1200 )
to ND 400 (1600 ) multi-tube sections will normally be required. In the range of 26e53 kW/K one or
more ND 100 (400 ) to ND 300 (1200 ) multi-tube sections will normally be required. Below 26 kW/K,
both double-pipe and multi-tube sections should be compared based on economics. Table 3.3 lists
typical sizes for hairpin type exchangers.
Table 3.3 Typical hairpin type exchanger sizes.
Double-pipe
Multi-tube
Shell dia., ND mm (inch)
50e150 (2e600 )
80e4300 (300 e1600 )
Tube dia., ND mm (inch)
20e100 (3=400 e400 )
20e25 (3=400 e100 )
No. of longitudinal fins, Nf, when used
20 to 48
0 or 16 or 20
Fin height, hf mm (inch), when provided
10e25 (0.375e100 )
0e12.7 (0e1=200 )
Surface m2/6 m (ft2/20 ft)
3e12.2 (10e40)
23e60 (75e1500)
Fin thickness, tf, mm (inch)
0.889 (0.03500 ) for weldable metals, 0.5 (0.19700 ) for soldered fins below
12.5 mm height and 0.8 (0.031500 ) for fins above 12.5 mm height
3.2 Design
55
3.2.6 Thermal design
The following outlines the steps of calculation for a tube-in-tube double-pipe exchanger utilising the
applicable equations outlined in Chapter 2.
For a double-pipe exchanger, the heat transfer area A in Eq. 2.3 is the outer surface area of the inner
conduit. The size designation for heat exchanger tubes is different from
pipes. The nominal outside diameter of a heat exchanger tube is its actual
(outside) diameter and the wall thickness is specified by Birmingham Wire
Heat transfer area
Gage (BWG) instead of Schedule number.
Thus Eq. 2.3 reduces to
A ¼ Ao ¼ pDo L ¼
Q
Uo DTLMTD
(3.1)
U in Eq. 3.1 is obtained from Eq. 2.13 based on the outer diameter of the inner pipe, viz.
1
1 Do lnðDo =Di Þ
Do
¼ þ
þ
Uo ho
2kw
hi D i
(3.2)
Overall Heat Transfer Coefficient
Subscripts o and i denote conditions at the tube outside and
inside, respectively. Thus, (1/Uo) is the overall thermal resistance based on the tube outside area, hi and ho are the heat transfer coefficient for the inner and annular
fluids and Di, Do are the inner and outer diameter of the tube. Incorporating the dirt factors RDi and RDo
for the inner and outer wall of the tube respectively, the design overall heat transfer coefficient for a
finned multi-tube double-pipe exchanger can be expressed as
1
1
Atotal lnðDo =Di Þ Atotal
RDo
RDi Atotal
þ
¼
þ
þ
þ
UD ho Ef ;effective
2pkw L
hi Ai Ef ;effective
Ai
(3.3)
One may note that UD is defined with respect to the total area Atotal. Although fins can be attached
to both internal and external pipe surface, external fins are most frequently used. Accordingly,
Ef,effective the weighted fin efficiency for the entire finned surface, is associated with the pipe outer wall
only in Eq. 3.3 where Ef,effective is given as
Ef ;effective ¼
Aprime þ Ef Af
Atotal
(3.4)
The area of the prime surface (Aprime), longitudinal fin surface (Af) and total cross-sectional area
(Atotal) is e
Aprime ¼ ðpDo Nf tf ÞnL
tf
Af ¼ 2nNf hf þ
L
2
Atotal ¼ Aprime þ Af
(3.5a)
(3.5b)
(3.5c)
56
Chapter 3 Double pipe heat exchanger
Nf is the number of longitudinal fins having height hf and thickness tf on each tube and n is the number
of finned tubes, each of length L.
The typical dimensional configuration of finned tubes used in industry is shown in Table 3.4. The
exact values can also be obtained from finned tube manufacturers.
Table 3.4 Typical double-pipe exchanger configurations (A) single inner pipe, (B) multiple
pipes.
(A) 40 Schedule single inner pipe
Outer pipe
Nominal
diameter, inch
Wall
thickness, mm
2
Inner pipe
OD, mm
Wall
thickness,
mm
Fin height
hf, mm
20
25.4
2.77
11.1
20
25.4
2.77
23.8
48.3
3.68
12.7
60.3
3.91
12.7
48.3
3.68
25.4
40
60.3
3.91
19.05
48
73.0
5.16
12.7
OD, mm
Max. no of fins/
tube Nf
3.91
60.3
3
5.49
88.9
3.5
5.49
88.9
36
3.5
5.74
101.6
40
4
6.02
114.3
36
4
6.02
114.3
4
6.02
114.3
(B) 40 Schedule multiple inner pipes
Outer pipe
Inner pipe
Max. no
of fins
per tube,
Nf
7
7
168.3
7.11
6
OD, mm
Wall
thickness,
mm
Fin
height
hf,
mm
16
19.02
2.11
5.33
20
22.2
2.11
5.33
19
16
19.02
2.11
5.33
168.3
14
16
19.02
2.11
5.33
7.11
168.3
7
20
20.04
2.77
12.7
8
8.18
219.1
19
16
19.02
2.11
8.64
8
8.18
219.1
19
20
22.2
2.11
7.11
8
8.18
219.1
19
20
25.4
2.77
5.33
8
8.18
219.1
19
16
19.02
2.11
7.11
8
8.18
219.1
19
20
22.2
2.11
5.33
Wall
thickness,
mm
OD,
mm
4
6.02
114.3
4
6.02
114.3
6
7.11
6
Nominal
diameter, inch
Number of
tubes, n
3.2 Design
57
Since double-pipe exchangers employ longitudinal fins, Ef in Eq. 3.4 is given by Eq. 2.18 reproduced below
Lf ;eq ¼ hf þ tf =2
(2.18)
If both fluids are in turbulent flow, the heat transfer coefficients (hi) and (ho) for plain tubes may be
computed from the same correlation using a suitably defined
equivalent diameter (De); otherwise, special attention must
be given to the annular region. Referring to Table 2.6 and
Individual Heat Transfer Coefficients
using the nomenclatures defined therein, for turbulent flow,
Re > 10,000.
hDe =k ¼ 0:027
ðDe G=mÞ0:8
ðCp m=kÞ0:33
ðm=mw Þ 0:14
(3.6a)
[Some prefer replacing 0.027 with 0.023 for double pipe]
Intermediate flow range (10,000 > Re > 2100)
i
h
hDe =k ¼ 0:116 ðDe G=mÞ2=3 125 ðCp m=kÞ1=3
ðm=mw Þ0:14
h
i
1 þ ðDi =LÞ2=3
(3.6b)
Laminar flow, Reð ¼ De G=mÞ<2100
hDe =k ¼ 1:86½ðk=De ÞðCp m=kÞDe =L1=3 ðm=mw Þ0:14
(3.6c)
in terms of jH
The heat transfer coefficients (ho) for finned
! tube in the annulus has been expressed
Cp m 1=3 m 0:14
h 0 De
r Vo D e
as a function of Reynolds number Reo ¼ o
factor jH ¼
mw
k
k
m
by Kern and Krauss (1972).
1=3
þ 4:9 107 Re2:618
for Nf ¼ 24
jH ¼ 0:0263Re0:9145
o
o
1=3
þ 4:9 107 Re2:618
for Nf ¼ 36
jH ¼ 0:0116Re1:032
o
o
(3.7a)
(3.7b)
Eq. 3.7a and 3.7b predict nearly the same values of jH for Reo > 1000.
Fluid flow properties usually are functions of the flow temperature and may be evaluated at the
caloric temperature. If the temperature difference of flow is moderate or the fluids have a viscosity less
than 1 cP at cold terminal temperature, Tf,avg (arithmetic average temperature) is used instead of
caloric temperature.
mw in the Sieder-Tate correction factor ðm=mw Þ of Eq. 3.6 is estimated at the average wall temperature of the inner pipe given by
58
Chapter 3 Double pipe heat exchanger
Tw ¼
hi Ti;avg þ ho ðDo =Di ÞTo;avg
hi þ ho ðDo =Di Þ
(3.8)
Wall Temperature
Eq. 3.8 is obtained by assuming that the entire heat transfer occurs between the fluids at their average temperature through the wall of the inner
pipe. For hot fluid flowing through the inner pipe, this gives
hi Ai Ti;avg Tw ¼ ho Ao Tw To;avg
(3.9)
where Ti,avg and To,avg are the average temperature for the inner and outer fluids, respectively.
Use of Eq. 3.8 involves an iterative procedure since Tw is required to calculate (hi) and (ho) and vice
versa. Initially, the values of (hi) and (ho) are calculated by assuming ðm=mw Þ ¼ 1. The calculated
values of (h) are used to calculate Tw and obtain mw. The viscosity correction factor for each fluid is
then multiplied to the preliminary values of (hi) and (ho) to obtain the final value of the film coefficients. A single iteration usually suffices.
For finned tubes, the viscosity correction factor for the fluid in the inner pipe ðm=mw Þi is calculated
at Tprime, the temperature of the prime surface and for the outer fluid ðm=mw Þo is calculated at Twf, the
weighted average temperature of the extended and prime surfaces. The derivation for the two wall
temperatures is based on the assumption that all the heat is transferred between the streams at their
average temperatures, Ti,avg and To,avg or
(3.10)
Q ¼ hi Ai Ti;avg Tprime ¼ ho Ef ATotal Tprime To;avg
Where Twf is defined by
Q ¼ ho Atotal Twf To;avg
(3.11)
This gives the expressions of the wall temperatures as
hi Ti;avg þ ho Ef ;effective ðAtotal =Ai ÞTo;avg
hi þ ho Ef ;effective ðAtotal =Ai Þ
hi Ef ;effective Ti;avg þ hi 1 Ef ;effective þ ho Ef ;effective ðAtotal =Ai Þ To;avg
Twf ¼
hi þ ho Ef ;effective ðAtotal =Ai Þ
Tprime ¼
(3.12a)
(3.12b)
The equivalent diameter (De) is the inside diameter (Di) for the inner pipe.
Equivalent diameter (De) for the annulus is four times the mean hydraulic radius rH that is defined
as the ratio of flow area and wetted perimeter.
De ¼ Dio Do
(3.13a)
Equivalent diameter, De
where Dio is the inner diameter of the outer pipe.
According to Kern (1950) the wetted perimeter for heat transfer
calculations is the outer circumference of the inner tube (pDo).
Therefore, the equivalent diameter (D0e ) for thermal calculations as defined by Kern (1950) is
D0e ¼
D2io D2o
Do
(3.13b)
3.2 Design
59
p 2
Dio D2o . Eq. 3.13b has been used for evaluation of both
4
Nusselt Number as well as Reynolds number.
However, the Reynolds number estimation for calculation of pressure drop is always based on
Eq. 3.13a. In this book, De both for thermal as well as pressure drop calculations have been evaluated
by Eq. 3.13a.
For plain multi-tube hairpin exchangers containing n tubes each of OD (Do) housed within an outer
pipe of diameter (Dio), the expressions for flow area [A ¼ ðp =4Þ D2io nD2o ] and wetted perimeter
½ðpÞðDio þ nDo Þ gives the expression for equivalent diameter as
2
Dio nD2o
(3.13c)
De 0 ¼
ðDio þ nDo Þ
Where the cross-sectional area is
The above expression reduces to Eq. 3.13a for n ¼ 1.
In a finned annulus, with
being Lf, the equivalent diameter Def obtained as four times
the fin length
the flow area A ¼ ðp=4Þ D2io nD2o nNf Lf tf divided by the wetted perimeter for heat transfer
½ðpÞðDio þ nDo Þ þ 2nNf Lf is
p D2io nD2o 4nNf Lf tf
(3.13d)
Def ¼
pðDio þ nDo Þ þ 2nNf Lf
3.2.7 Hydraulic design
The pressure drop for flow through the straight length of annulus is expressed in liquid (fluid) head as.
DHfo ¼
4fo G2o Lo
2gr2o De
(3.14a)
Pressure drop in straight length
and for the inner pipe, it is
DHfi ¼
4fG2i Li
2gr2i Di
(3.14b)
G is the mass velocity of the fluid, g is the acceleration due to gravity, r is fluid density, L is the length
of the corresponding section, and f is the Fanning friction factor. When several double-pipe exchangers
are connected in series, annulus to annulus and pipe to pipe, the length (L) in Eq. (3.14), is the total for
the entire path. The friction factor ( f ) in Eq. 3.14 is expressed as a function of Reynolds number,
defined as
Rei ¼
Gi Di
mi;average
(3.15a)
60
Chapter 3 Double pipe heat exchanger
for the inner fluid
and Reo ¼
Go De
mo;average
(3.15b)
based on De for the annulus
Turbulent flow
Flow in tubes; with 5 % tolerance: fi ¼ 0:0014 þ 0:125=ðReÞ0:32
(3.16a)
Flow in clean; iron and steel pipes; with 10 % tolerance : fi ¼ 0:0035 þ 0:246=ðReÞ0:42 (3.16b)
Laminar flow
Flow in tubes:
fi ¼ 16=Rei
(3.16c)
and for the outer fluid
3
2
1
ðD
Þ
=D
o
io
5
fo ¼ ð16=Reo Þ4
1 þ ðDo =Dio Þ2 þ 1 ðDo =Dio Þ2 =lnðDo =Dio Þ
2
(3.16d)
For longitudinal finned tubes, the friction factor for the annular region is
h
i
fof ¼ exp 0:08172ðlnReof Þ2 1:7434ðlnReof Þ 0:6806 for ðRe > 400Þ
(3.16e)
and
fof ¼ 16=Reof
for ðRe 400Þ
(3.16f)
Since fins tend to destabilise laminar flow, the critical Reynolds number is 400 in the finned
annulus.
A minor modification is often made to Eq. 3.14 by incorporating a viscosity correction
factor (f) to account for the effect of variable fluid property on friction factor in non-isothermal
flow, viz
0:14
m
f¼
for laminar flow
(3.17a)
mw
0:25
m
f¼
for turbulent flow
(3.17b)
mw
This modifies the pressure drop equation (Eq. 3.14a,b) for the outer and inner fluid as
4fo G2o Lo 1
DHf ;o ¼
2gr2o De0 f
(3.18a)
3.2 Design
4fG2i Li 1
DHf ;i ¼
2gr2i Di f
61
(3.18b)
Minor pressure losses due to the entrance and exit effects and return bends of each hairpin are
usually estimated in terms of velocity heads. For inner pipes of double-pipe exchangers connected
in series, the bend pressure loss is usually negligible, but the same may
be significant for the annuli.
In an exchanger with NHP number of hairpins connected in series, the
Bend pressure drop
total pressure drop due to direction change is
DHf ;o;bend ¼
ð2NHP 1ÞVo2
2g
(3.19)
Where Vo is the velocity of the outer fluid.
Inner pipe: With the inlet and exit piping aligned with the inner pipe, the entrance and exit losses
can be neglected. However, in multi-tube exchangers, the losses at the
two tube sheets are taken as one tube velocity head per hairpin for turbulent flow.
Entry and exit losses
Annulus nozzle entry and exit losses are accounted as e
Laminar flow: For Re 100, three velocity heads for head loss in the entry and the exit nozzle
together. For Re < 100, the loss depends on Re.
Turbulent flow: one velocity head for the entry and 0.5 velocity head for the exit nozzle.
For exchangers with internal return bends, nozzle head loss is given by
2ðNHP ÞVn2
; for turbulent flow
2g
(3.20a)
4ðNHP ÞVn2
; for laminar flow and Re > 100
2g
(3.20b)
DHn ¼
DHn ¼
Where Vn is nozzle velocity.
In case the exchanger has external return bends, the pressure drop is double of the value estimated
by Eq. 3.20.
The total pressure drop in the annular section is:
(3.21a)
DPo ¼ DHf ;o þ DHf ;o;bend þ DHn ro g
Total pressure Drop
and in the inner pipe is: DPi ¼ DHf ;i ri g
(3.21b)
62
Chapter 3 Double pipe heat exchanger
Typically, the maximum allowable design pressure drops in a double-pipe heat exchanger in 0.7 kg/cm2
for both inner and outer pipes. If the calculated pressure drop exceeds the allowable limit, the designer
needs to select a larger pipe diameter or decide to connect sections in parallel or a combination of series
and parallel. The flow with a higher volumetric flow rate is usually sent to the side with a higher flow
cross-sectional area.
3.3 Series-parallel configuration of hairpins
Pressure drop constraint in double pipe exchanger can often be met by dividing only the specific stream
exceeding the pressure drop limit in parallel branches. Fig. 3.2 shows such a configuration with the annuli
in series and the inner pipes connected in parallel just for two hairpins. Several such hairpins may be
configured. Each hairpin has counterflow, but the overall flow arrangement is not a true countercurrent. The
departure from true counterflow operation in a serieseparallel arrangement is accounted for by the LMTD
correction factor FT discussed in Chapter 2. For x number of parallel branches
FT ¼
xð1 PÞln
FT ¼
where, P ¼
Rx
xðR 1Þ
Pð1 xÞ
ð1 xÞ
ð1 PÞ1=x
R¼1
(3.22a)
for
(3.22b)
for
þ
x
ln½ð1 PÞ=ð1 PRÞ
ðR xÞ
x
þ
ln
1=x
R
Rð1 PRÞ
Rs1
Tp;out Tp;in
Tp;out Tp;in
and R ¼
Ts;in Ts;out
Ts;in Ts;out
Tp,out, Tp,in, Ts,out and Ts,in are the outlet and the inlet temperatures of the streams ( p and s) that flow
parallel and in series through the set of hairpins.
s
Tp,out
Ts,in
Hairpin 1
Hairpin 2
P
Ts,out
Tp,in
FIGURE 3.2
Two hairpins with annuli in series and inner pipes in parallel.
3.4 Design illustration
63
3.4 Design illustration
3.4.1 Design steps
The design output is the exchanger geometry meeting the heat load target and constraints of pressure
drop. This can be met by several combinations of inner and outer pipe sizes and corresponding series,
or series-parallel configuration of hairpins. Considering the pipe sizes to be the designer’s choice, the
steps to be followed by the designer are the following:
:
:
1. Input data: cp;c ; cp;h; any 5 of {mh ,mc ,Th,in,Th,out,Tc,in,Th,out,}
2. Calculate heat load, Q from enthalpy balance of hot/cold stream.
:
:
Find the unknown variable in the set {mh ,mc ,Th,in,Th,out,Tc,in,Th,out,}.
3. Estimate Tc,avg ¼ (Tc,in þ Tc,out)/2, Th,avg ¼ (Th,in þ Th,out)/2,
4. Note rc,avg, kc,avg, mc,avg at Tc,avg and rc,avg, kc,avg, mc,avg at Th,avg for calculations. Also, note the
variation of viscosity with temperature for both liquids.
5. Decide the maximum limit of DPi,max,DPo,max or the same for the two fluids streams.
6. Select inner and outer tube/pipe specifications (typical starting values can be 1.2500 and 200 ND
40 Schedule pipes of length 6 m or 6.5 m). Note down values of Di, Di,o, tw ¼ (Dio Di)/2,
Do, Lstd. Note kwall value.
7. Note the values of RDo and RDi to be considered. These are often associated with the two fluids.
8. Select the inner and the annulus fluid, and these are, henceforth, designated by the subscripts
i and o, respectively. The new set of variables with these subscripts is derived from those
mentioned in steps 2, 3 and 4. Consider a counterflow configuration.
:
:
:
:
9. Ai ¼ pD2i /4, Ao ¼ p(D2i,o D2o)/4, Gi ¼ mi Ai , Go ¼ mo Ao , De ¼ (Di,o Do), mi and mo are
the mass flow rates of the inner and the outer fluids
10. Rei ¼ DiGi/mi,avg, Reo ¼ DeGo/mo,avg, Pri ¼ cp,imi,avg/ki,avg, Pro ¼ cp,0mo,avg/ko,avg
11. Assume fi ¼ 1, fo ¼ 1 as initial guess.
12. Compute
hi and ho from Eqs. 3.6 and 3.7
ho D e
13. IF
< 0.75, THEN
hi D i
Place fluid with lower h in the annulus and provide fins on the inner pipe. Select Nf, Lf, tf, hf
for the finned tube(s) from Tables 3.3 and 3.4 and decide on number of tubes, n. One may
start with n ¼ 1 and increase later if required.
Calculate Lf,eq(Eq. 2.18), m (Eq. 2.16), Ef (Eq. 2.15), Aprime, A and Atotal (Eq. 3.5), Ef,effective
(Eq. 3.4), Def (Eq. 3.13d).
Calculate ho (Eq. 3.7), assuming fo ¼ 1
Calculate (Atotal/Aprime) and use it in Eq. 3.12 a and b to calculate Tprime and Twf. Refer to fluid
0:14
property data and note mo,w value at Twf. Calculate fo;new ¼ mo;avg mo;w
. Calculate Tw
(Eq. 3.8). Refer to fluid property data and note mi,w value at Twf. Calculate
0:14
fi;new ¼ mi;avg mi;w
.
64
Chapter 3 Double pipe heat exchanger
IF (abs((fo,new e fo)/fo,new) < 0.02) and (abs((fo,new e fo)/fo,new) < 0.02) THEN
GO TO Step 14
ELSE
GO TO Step 12
END
ELSE
Calculate Tw from Eq.3.8 and proceed to calculate hi from Eq. 3.6.
GO TO Step 14
END
14. Calculate UD (Eq. 3.3). Calculate LMTD using FT from Eq. 3.22 if series-parallel configuration
is chosen, else LMTD to be calculated directly from {Th,in,Th,out,Tc,in,Th,out,}.
15. Calculate Ao (Eq. 3.1). Ltotal ¼ Ao/(pDi,o), NHP ¼ Ltotal/(2Lstd); Round off Ltotal to next higher
value of Lstd so that there are integral number of hairpins.
16. Calculate fi corresponding to Rei (Eq. 3.16). Calculate De’(Eq. 3.13c). Calculate Reo
(Eq. 3.15b). Calculate fo corresponding to Reo (Eq. 3.16 def).
17. Calculate DHf,o (Eq. 3.18a), DHf,o,bend (Eq. 3.19) and DHn (Eq. 3.20)
Calculate DPo (Eq. 3.21a).
Calculate DHf,i (Eq. 3.18b). Calculate DPi (Eq. 3.21b).
18. IF DPi > DPi,max THEN
Switch fluids and check for pressure drop.
IF even after switching fluids, the pressure drop limits are exceeded THEN
connect annuli in parallel and tubes in series. Recalculate FT using Eq. 3.22.
Go to step 9.
END
ELSE
Print Design output and fill up the rest of the form shown in Table 3.1.
END
3.4.2 Design example
Problem: Design a double-pipe heat exchanger to cool 2000 kg/hr of 5% w/w caustic solution from 80 C
to 40 using cooling water available at 33 C. The maximum return temperature for the cooling water
stream is 45 C. The dirt factor for caustic and cooling water may be taken as 0.00035 m2K/W and
0.00018 m2K/W. The maximum pressure for the cooling water and the caustic pump header are 5 and
4 kg/cm2(g), respectively, and the maximum allowable pressure drop is 0.7 kg/cm2 for both the fluids.
Viscosity variation of cooling water and 5% w/w caustic lye with temperature
T ( C)
30
40
50
60
70
80
90
100
Water mw(Pa.s)
0.8
103
0.65
103
0.55
103
0.47
103
0.40
103
0.35
103
0.31
103
0.28
103
5% w/w Caustic
mc(Pa.s)
1.03
103
0.83
103
0.69
103
0.58
103
0.50
103
0.43
103
0.38
103
0.33
103
3.4 Design illustration
65
Solution
Caustic inlet, 80 C,
2000 kg/hr (0.5556 kg/s)
Caustic exit, 40 C
/
Tc,avg ¼ 60 C (Following properties are at 60 C)
Cp;c ¼ 3983:2 kJ=kg.K
mc ¼ 5:8 104 Pa.s
rc ¼ 1055 kg=m3
kc ¼ 0:688 W=m.K
Rd;c ¼ 0:00035 m2 .K=W
Prc ¼ Cp;c mc kc ¼ 3:3579
CW exit, 33 C
CW inlet. 33 C
)
Tw,avg ¼ 39 C (Following properties are at 39 C)
Cp;w ¼ 4185 kJ=kg.K
mw ¼ 6:65 104 Pa.s
rw ¼ 1000 kg=m3
kw ¼ 0:6541 W=m.K
Rd;w ¼ 0:00018 m2 :K=W
Prw ¼ Cp;w mw kw ¼ 4:254
DT1 ¼ 80 45 ¼ 35 C
LMTD ¼ 17.3974 C
DT2 ¼ 40 33 ¼ 7 C
Q ¼ mc :Cp;c : Tc;in Tc;out ¼ 8.8515 104 W
mc ¼ 0:5555; mw ¼ Q = ðCp;w ðTw;out Tw;in Þ ¼ 0.5555 kg=s
LMTD ¼ 17.3974 C.
We choose 40 sch., 1.500 x 200 ND double-pipe heat exchanger made from steel pipes. Maximum
pressure in the system being 6 kg/cm2(g) (w75 psig), we choose all fittings with a 150 lbs rating. For
this, size of piping,
Di ¼ 34.98 mm ¼ 0.03498 m; ¼ 52.48 mm ¼ 0.05248 m; ¼ 42.1 mm ¼ 0.0421 m
Ai ¼ pD2i =4 ¼ 9.6101 104 m2 ; ¼ 7.7106 104 m
2
Since Ai > Ao, the higher flow of water is considered for the inner pipe
Vi ¼ mw =ðrw :Ai Þ ¼ 1:8375 m=s; Vo ¼ mc =ðrc :Ao Þ ¼ 0:6829 m=s
Gi ¼ mw =ðAi Þ ¼ 1834:5 kg= m2 :s ; Go ¼ mo =ðAo Þ ¼ 720:5116 kg= m2 :s
Pr;t ¼ Pr;w ¼ 4:254; Pr;o ¼ Pr;c ¼ 3:3579
Ret ¼ Di :Vi :rw =mw ¼ 96497; Reo ¼ Di;o Do :Vo :rc =mc ¼ 12; 895
Assuming ft ¼ 1 and fo ¼ 1, Nut ¼ 0:027:ðRet Þ0:8 :ðPrt Þ0:33 :ft ¼ 423:1341;
66
Chapter 3 Double pipe heat exchanger
Nuo ¼ 0:027:ðReo Þ0:8 :ðPro Þ0:33 :fo ¼ 78:2158
hi ¼ Nut :ðkw=Di Þ ¼ 7911:7 W=ðm2 .K
ho ¼ Nuo :ðkc=ðDo Di ÞÞ ¼ 5184:2 W=ðm2 .K
ho Dio
¼ 0:7886 > 0:75, and hence no need of finned tubes.
hi Do
hi Tw;avg þ ho ðDo =Di ÞTc;avg
¼ 48:2592+ C
Tw ¼
hi þ ho ðDo =Di Þ
Estimating ft and fo e
0:14
0:14 mw @ 39o C
6:65 104
fi;new ¼
¼
¼ 1:0225
mw @ 48:2592o C
5:6741 104
0:14
0:14 mc @ 40o C
5:8 104
fo;new ¼
¼
¼ 0:9712
mw @ 48:2592o C
7:1437 104
ho Dio
¼ 0:75. This is a marginal case when one need not
hi D o
go for finned tubes and the same is opted for ease of fabrication.
Based ft;new and fo;new , hi ¼ 5035:2 and
Tw;new ¼
hi Tw;avg þ ho ðDo =Di ÞTc;avg
¼ 47:9941 C
hi þ ho ðDo =Di Þ
Recalculated ft;new and fo;new does not show significant change and the iteration is stopped.
Uc ¼ 1=ð1 = ho þ Dio = ðhi :Di Þ þ Dio :lnðDio = Di Þ = ð2:kwall ÞÞ ¼ 1700:3
UD ¼ 1=f1 = Uc þ Rc þ Rw :ðDio = Di Þg ¼ 865:98
Total heat transfer area based on outer surface of inner tube, A ¼ Q/(UD.LMTD) ¼ 5.8752 m2.
Minimum length of tube ¼ A/(pDio) ¼ 35.63 m.
We adopt a standard tube length of 6 m and provide three hairpins that make the total tube length to
be 36 m. NHP ¼ 3, Ltotal ¼ 36 m.
Pressure drop.
Pressure drop in straight pipe length.
Ret ¼ 96,497, is turbulent flow and Eq. 3.16b is applicable.
fi ¼ 0:0035 þ 0:246=ðRet Þ0:42 ¼ 0:0055
DHf ;i ¼
4fi G2i Ltotal
¼ 3:8759 m
2gr2i Di
Reo ¼ 12,895, is turbulent flow and Eq. 3.16b is applicable.
fo ¼ 0:0035 þ 0:246=ðReo Þ0:42 ¼ 0:0081
Further reading
DHf ;o ¼
67
4fo G2o Ltotal
¼ 1:59 m
2gr2o ðDo Dio Þ
Pressure drop in bends.
ð2N 1ÞV 2
Annulus: DHf ;o;bend ¼ HP2g o ¼ 0:1189 m
Inner fluid: Neglected.
Pressure drop in nozzles.
The nozzle and the pipe sizes are chosen to be the same, and hence, the flow is turbulent in the
nozzles.
DHi;n ¼
DHo;n ¼
2
2ðNHP ÞVi;n
¼ 1:03 m
2g
2
2ðNHP ÞVo;n
¼ 0:1426 m
2g
Total pressure drop.
Inner fluid (Cooling water) ¼ (1.03 þ 3.8759) 1000 9.81 ¼ 48,126.9 Pa ¼ 0.48 kg/cm2
Annular fluid (Caustic) ¼ (0.1426 þ 0.1189 þ 1.59) 1055 9.81 ¼ 19,162 Pa ¼ 0.20 kg/cm2
Pressure drop for both fluids being well within limit, these are not corrected for the tube wall
temperature using Eq. 3.17.
e
Thus total pressure drop limits are met for both fluids.
The summary sheet in Table 3.1 can be filled with the data arrived at above. The exchanger can be
fabricated from bought out components with 150 lbs pressure rating.
References
Kern, D. Q. (1950). Process heat transfer. Tata McGraw-Hill Education.
Kern, D. Q., & Kraus, A. D. (1972). Extended surface heat transfer.
Further reading
Serth, Robert, W. (2007). Process heat transfer-principles and applications. Elsevier.
CHAPTER
Shell and tube heat exchanger
4
4.1 Introduction
Shell and tube exchangers are the most common equipment in process industries for heat transfer
between flowing fluid streams. These can have heat transfer area ranging from 0.1 to 100,000 m2
and can be used over a wide range of pressure and temperature conditions ranging from vacuum to
1000 kg/cm2 pressure and from cryogenic temperature to 1000 C. In addition, these can be
fabricated using a wide range of materials and are suitable for high pressure operations. Ease of
cleaning enables their usage for dirty fluids and slurries. They also provide a relatively larger heat
transfer surface per unit volume and weight (typically 50e100 m2 heat transfer area per m3 of
equipment volume) and require a minimum number of connections. Well-established design procedure and fabrication techniques make these exchangers versatile for a wide range of applications,
namely (i) steam generators, condensers, boiler feed water heaters and oil coolers in power plants;
(ii) condensers and evaporators in air conditioning and refrigeration applications and (iii) waste
heat recovery and heating and cooling applications involving process liquids and gases/vapours
with and without phase change. They can also be designed for special operating conditions like
vibration, heavy fouling, highly viscous fluids, erosion, corrosion, toxicity, etc. Nevertheless, they
are not normally used in automotive and aircraft applications because of their relatively large size
and weight.
4.1.1 General description
The major components of a shell and tube exchanger are shell, front end head, rear end head, baffles,
tubes and tube sheet. The tube sheet assembly comprising of tube bundle, baffles, tie rods, and spacers
is fitted in the exchanger shell and closed at the ends with heads.
Shell
Shells are available with inside diameters up to 3 m ð12000 Þ. Shells with 610 mm ð2400 Þ or
lower diameters are generally made from steel pipes, while larger sizes are made from rolled steel
plates.
Exchanger Head(s)
Inside the shell, the tubes are arranged in a bundle and held in place by a pair of header plates (tube
sheet). One end has a tube sheet fixed to the shell. This is the stationary tube sheet and the head
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00004-X
Copyright © 2020 Elsevier Inc. All rights reserved.
69
70
Chapter 4 Shell and tube heat exchanger
closure fixed at this end is called the ‘stationary head’ or ‘channel’. Tube sheet at the other end
may or may not be fixed to the shell. Exchangers with stationary tube sheets at both ends are fixed
tube exchangers. These are cheaper and easy to construct but cause large thermal stresses on the
tubes and the shell.
To avoid high stresses, the more expensive and difficult to construct options namely floating head
exchangers or U-tube exchangers are opted for a large difference in temperature between the shell-side
fluid and the tube-side fluid. In floating head exchangers, the differential expansion of the shell and the
tube bundle is accommodated by fixing the tube sheet to the shell cover at one end only. This
arrangement (floating head) allows relative longitudinal movement due to thermal expansion between
the shell and the tubes. The shell at the floating head end is closed by a shell cover. Another way to
accommodate the differential expansion is to use ‘U’ tubes (‘U-tube exchangers’) that allow free
expansion and contraction of the individual tubes within the shell. The U-tube exchangers have only
one (stationary) tube sheet. In some cases, exchanger shell may have an integrated expansion joint.
This is less popular but is found in gas service exchangers in steel plants.
Tube-side fluid enters and exits through nozzles fitted on the heads, while nozzles on the shell allow
for entry and exit of the shell-side fluid.
Tubes
In most applications, plain tubes are used. However, when additional surface area is required to
compensate for low heat transfer coefficient on the shell-side, low finned tubing is used. Low fin
height maintains reasonably high fin efficiency and provides around two to three times the surface
area of plain tubes while decreasing fouling on the fin side. As already mentioned, the tubes are
attached to the header plate (tube sheet). Two methods of attaching tubes to the tube sheet are
shown in Fig. 4.1.
(A)
Tube sheet
Tube wall
(B)
Ferrule
Tube sheet
Tube wall
Turning
slot
Groove
Packing
FIGURE 4.1
Typical arrangements for fixing tubes to the tube sheet: (A) tube rolling and (B) ferrule.
4.1 Introduction
71
Tube size is specified typically in terms of diameter and wall thickness. Smaller diameter tubes
yield higher heat transfer coefficient and result in a more compact exchanger,
while larger diameter tubes are easier to clean and are more rugged. For
mechanical cleaning, the smallest practical size is 19.05 mm, while for
Size and number
chemical cleaning, smaller tubes can be used provided plugging does not
occur. Detailed dimensions of heat exchanger tubes are provided in Sections
4.4 and 4.6.2. One may note that unlike commercial pipes, the nominal
diameter of heat exchanger or condenser tubes is the actual outside diameter (usually specified in
inches) within a very strict tolerance and the tube thickness is expressed as BWG (Birmingham wire
gauge) and not Schedule number used for commercial pipes.
The number of tubes in an exchanger depends on the fluid flow rates and available pressure drop
(Section 4.4). When solids are present, the velocity is kept high enough to prevent settling. If the tubes
are too close to each other, the tube sheet becomes weak. The number of tubes that can be placed
within a shell is function of tube layout, tube outside diameter, pitch, number of passes and shell
diameter. This information for square and triangular layouts is provided in Table 4.8.
Tube layout is characterised by the included angle between tubes. The angle is defined with respect
to flow direction. Two standard layouts are square and equilateral triangle. The
equilateral triangular layout can be oriented at 30 degrees or 60 degrees to the
flow direction and the square layout at 45 degrees and 90 degrees. 30 degrees,
Pitch and layout
45 degrees and 60 degrees are staggered and 90 degrees is in line. Choice
between different tube layouts can be made based on their features listed in
Table 4.1. Under comparable conditions of flow and tube size, the heat transfer
coefficient for triangular arrangement is about 25% higher than that for square arrangement. The
triangular layout also provides a more compact arrangement, usually resulting in smaller shell
diameter and stronger header sheet for a specified shell-side flow area. It is preferred when the
operating pressure difference between the two fluids is large. Square pitch (45 degrees and 90 degrees
layouts) is adopted for ease of jet or mechanical cleaning of tube outer surface and a minimum
cleaning lane of 6 mm (1/400 ) is provided. The 90 degrees layout is preferred for vaporising applications as it provides vapour escape lanes. This also provides the lowest heat transfer coefficient and the
lowest pressure drop among the different arrangements.
If mechanical cleaning is not required, the 30 degrees layout is preferred for single-phase laminar
or turbulent flow and condensing applications involving a high DT range. The 60 degrees layout is
preferred for condensing application involving a low DT range and for boiling applications. Square
layout is generally not used in the fixed header sheet design since mechanical cleaning is anyhow
infeasible under this condition.
The shortest centre to centre distance between successive tubes is tube pitch (PT) and the minimum
distance between adjacent tubes is tube ‘clearance’ (tube pitch minus tube outside diameter ¼ PT Do).
The selection of tube pitch is a compromise between a close pitch (small values of PT/Do) for increased
shell-side heat transfer and surface compactness and an open pitch (large values of PT/Do) for decreased
tendency of shell-side plugging and easy shell-side cleaning. According to IS 4503:1967, tubes are
spaced with a minimum centre to centre distance of 1.25 times the tube outer diameter. The basis of
limiting PT/Do as 1.25 stems from the consideration that header plate (tube sheet) becomes too weak for
proper rolling of the tubes and causes leaky joints when tubes are too close. Though the designer has the
freedom to choose a suitable pitch, usually a standard tube pitch and layout is chosen based on Table 4.8.
72
Chapter 4 Shell and tube heat exchanger
Table 4.1 Commonly used tube layouts and their features.
Triangular
Rotated
triangular
60 degrees
30 degrees
Square
Rotated
square
Pattern
Angle with flow
direction
45 degrees
1.25 to 1.5 times Do (see Table 4.8)
Typical pitch, PT
Considerations
90 degrees
Shell-side
pressurea drop
3
1
4
2
Shell-side heat
transfer
coefficienta
3
1
4
2
Shell-side fluid
fouling
tendency
Difficult to mechanically clean tube
outer surface e preferable option
when shell fluid has low fouling
tendency
Easy to mechanically clean tube
outer surface e no specific
preference for shell fluid based
on fouling tendency
Shell diameter
for the same
number of tubes
of same size
Lower (more compact)
Higher (less compact)
Large operating pressure difference
between the two fluids
Ease of jet or mechanical
cleaning
Not used in fixed header sheet
design
Boiling
applications
Condensing
applications
involving a low
DT range
Vaporising
applications
due to vapour
escape lanes
General
Characteristics
and Specific
applications
Single-phase
laminar or
turbulent flow
Condensing
applications
involving a
high DT range
a
1e4 decreasing.
Tube sheet
The tube sheet isolates the shell-side and tube-side fluid. Reduction in the effective length of the tube
due to tube sheet thickness needs to be accounted for when calculating the available area for heat
transfer. In applications where any intermixing of process fluids cannot be allowed due to safety or
process reasons, double tube sheets are used with the space in between those kept vented.
4.1 Introduction
73
Baffle
Most exchangers use baffles in tube bundle to make the shell-side fluid follow a narrower cross flow
path across the tubes. This increases the velocity and turbulence and results in higher shell-side heat
transfer coefficient. Baffles also ensure structural rigidity by supporting the tubes and prevent tube
vibration and sagging.
The clearance between baffle and shell (baffle clearance) should be low enough to minimise short
circuiting of fluid through such gap. However, if the clearance is too low the pull out of the tube bundle
for repair and maintenance becomes difficult. The centre to centre distance between baffles is called
baffle pitch or baffle spacing. Baffle spacing B, shell inside diameter Ds, tube outside diameter Do and
pitch type and value PT governs the flow passage of the shell-side fluid thus influencing the level of
turbulence and shell-side heat transfer coefficient.
Usually baffles are ‘segmental’ or ‘disc-and-doughnut’ type. These along with orifice type baffles
are shown in Fig. 4.2. Segmental baffles force the shell-side fluid to travel across the tube bundle and
the disc-and-doughnut type forces the fluid to flow across the tubes alternately towards the shell
centre and away. The single and double segmental baffles divert the flow most effectively across the
tubes and are most frequently used. Disc-and-doughnut baffles are usually employed for dirty fluid
in the shell side.
The geometrical parameters defining segmental baffle (Fig. 4.2A and B) are (a) baffle clearance,
(b) baffle cut and (c) baffle pitch. The percent cut in segmental baffle
refers to the % of diameter cut off as unrestricted passage of the fluid.
Lower % cut increases heat transfer coefficient at the cost of pressure
Segmental baffle
drop in the shell side. Typically, baffle cut is about 25%. The designer
also needs to decide baffle spacing or the maximum distance between
successive baffles. It depends on the extent of support required by the
tubes. Practical range of baffle spacing for single segmental baffle is Ds =5 to Ds . Spacing closer than
(A)
(C)
(B)
(D)
Orifice
A
A′
Section A - A′
FIGURE 4.2
Baffle types: (A) single segmented, (B) double segmented, (C) disc-and-doughnut and (D) orifice baffle.
74
Chapter 4 Shell and tube heat exchanger
Ds =5 causes large pressure drop and leakages that nullify the heat transfer advantage of closer
spacing. Baffle spacing and not the baffle cut determines the effective velocity of the shell-side fluid
and hence has the greatest influence on shell-side pressure drop.
Baffle orientation is important for shell-side phase change. In case of vaporisation/boiling on the
shell side, the baffle cut may be either vertical or horizontal depending on the service. For shell-side
condensation, the cut is vertical to allow for condensate flow towards the outlet without significant
liquid holdup due to baffle.
The triple segmental baffles are used for low pressure applications. Sealing strips are used to
minimise channelling of fluid between outer row of tubes and shell. They usually consist of metal
strips attached to baffles and running between shell and outer tubes.
Disc-and-doughnut baffles (Fig. 4.2C) have alternate outer rings and inner discs to direct the flow
radially across the tube bundle. Generally, the disk diameter is more than Ds =2, and the diameter of the
doughnut hole is less than Ds =2. This arrangement eliminates the potential bundle-to-shell gap bypass
stream and provides a lower pressure drop as compared to single segmental baffles for the same unsupported tube span. The disadvantages are (i) the tie rods to hold baffles are within the tube bundle
and (ii) the central tubes are supported by disk baffles which in turn are supported only by tubes in the
overlap of the larger diameter disk over the doughnut hole.
In an orifice baffle, shell-side fluid flows through the clearance between tube outside diameter and
baffle-hole diameter (Fig. 4.2D). Rod baffles are used for services where
pressure drop can become a constraint with other baffle types. In this case,
flow is parallel to the tubes and flow-induced vibrations are practically
Other baffle types
eliminated by baffle support of the tubes.
Tie rods and spacers
The baffles are a part of the tube bundle assembly and are held in position by tie rods and spacer
sleeves on the rods. Tie rods are fixed at one end in the blind tapped holes in the tube sheet. Other end
of the tie rod ends passes through baffles and are fixed with a nut after the last baffle.
Impingement baffle
Some of the tubes in the outer layer of tube bundle face impingement by fluid entering through the inlet
nozzle. These tubes get eroded particularly when kinetic energy of the fluid is high and also when the
entering fluid is a mix of vapour and liquid. Such tubes are protected against erosion by a plate barrier
called ‘impingement plate’ or ‘impingement baffle’. Impingement plates are fitted immediately facing
the shell-side fluid entry nozzle and are fixed to the tie rods. The location of this baffle within the shell
is critical to minimise the associated pressure drop and the high velocity of the shell-side fluid after the
baffle. Accordingly, sufficient area needs to be provided between the nozzle and plate and between
plate and tube bundle. This is often achieved either by omitting some of the tubes from the circular
bundle or by modifying the nozzle to form an expanded section.
Multipass exchanger
Based on the number of shell and tube passes, shell and tube exchangers are designated as nem
exchanger. The first number n refers to the number of shell passes and the second number m refers to
the number of tube passes. The simplest configuration is 1e1, with one shell and one tube pass. Use of
4.1 Introduction
75
odd number of tube passes (3, 5, etc.) though permitted in design code (TEMA), is rarely used due to
their complicated construction and associated mechanical problems in fabrication and operation.
In case of single-tube pass configuration, the tube-side fluid flows through all the tubes in a shell in
the same direction, i.e., all tubes are fed from the front stationary head and
discharge into the rear end head. In multiple tube pass, there are separate
bunches of tubes where the tube-side fluid flows from the front to the rear
Pass partition plate
end and then back to the front head. This is achieved either by U tubes or
by pass partition plates designed integral to the stationary head and the rear
head. They guide the tube-side fluid to enter and exit specific bunch of
tubes thus ensuring long passage lengths within a fixed shell length. Each bunch contains almost the
same number of tubes to achieve same flow area per pass. Increasing the number of passes for the same
total number of tubes thus increases the tube-side velocity, turbulence and heat transfer coefficient.
Higher tube-side velocity also reduces fouling tendency. However, the increased velocity and additional turns (change in direction of fluid flow) significantly increase the tube-side pressure drop.
In case of a 1e2 exchanger, there will be pass partition plate only on the front end. The tube-side
fluid entry and exit nozzles are on opposite sides of the stationary head for even number of passes. The
number of tube passes is often limited by the allowable pressure drop and generally range from 1 to 10.
The standard design has one, two, or four tube passes. If a higher pressure drop is acceptable, it is
desirable to have fewer but longer tubes (reduced flow area and increased flow length). The cross flow
area (perpendicular to the flow direction in tubes) in the channel depends on the channel depth, and its
diameter is fixed by tube sheet diameter.
Shell passes
The path of the shell fluid may also require several reversal of direction to make the exchanger
compact. This is achieved by longitudinal baffles assembled integrated with the tube sheet. A single
longitudinal baffle ensures two passes for the fluid in a shell as can be seen in the ‘F’ type shell in
Fig. 4.5. It is also possible to configure a 2e4 exchanger by appropriately joining the nozzles of two
identical 1e2 exchangers as shown in Fig. 4.3. In a similar fashion, other n-2n exchangers can be
configured by suitably combining 1e2 exchangers.
FIGURE 4.3
A 2e4 exchanger configured by connecting two identical 1e2 exchangers.
76
Chapter 4 Shell and tube heat exchanger
4.1.2 Heat exchanger installations and commissioning
When the exchanger being designed is a part of an existing process system, compatibility is of
utmost importance. If exchangers for similar services already exist in the plant, it is often better to
add one that can provide interchangeability or have common spares like tube bundle, tubes, etc.
Space for erection, operation and maintenance is also a major consideration. The space needs to have
drainage facility for proper and safe disposal of the drained fluids before maintenance. Utility
connections that are required for flushing, pressure testing, cleaning, etc., should be available.
Bypassing the shell side or the tube side of an exchanger is not usually desirable as this lead to low
flow through the equipment resulting in enhanced fouling. However, in large continuous plants, such
bypass and equipment isolation arrangements are provided for flexibility. This allows the heat exchangers to be decommissioned, cleaned and maintained, while the rest of the plant and equipment
remain in operation. Valve and piping schematic for such arrangement is shown in Fig. 4.4. The
exchanger can be isolated by gate valves V1, V2, V3 and V4 and the stream flows bypassing the
exchanger can be regulated by globe valves V5 and V6.
Prior to commissioning, ensure that the equipment is fully filled. The correct procedure of a heat
exchanger is to start the cold fluid flow before or simultaneously with the
hot fluid flow. If the hot stream continues to flow while the isolation valves
V1, V2 on the cold liquid line are shut, the cold fluid trapped in the tube side
Commissioning
of the exchanger would heat up, expand and get pressurised. This overpressure gets relieved through the safety valve SV, commonly called the
thermal safety valve (TSV). Installation of TSV is thus always on the cold
liquid line and is installed whenever there is a chance of trapped cold fluid getting heated and
overpressurised. Absence/malfunction of TSV may lead to gasket rupture or even deformation/
mechanical failure of metal.
V4
SV (TSV)
V1
V2
V6
V3
V5
FIGURE 4.4
Heat exchanger with bypassing arrangement for both shell and tube sides.
4.2 Codes and standards
77
4.2 Codes and standards
A thorough knowledge of the applicable code is essential to arrive at complete specification of the
exchanger and generate the fabrication drawings. The following standard codes are referred for design
of shell and tube exchangers. National standards and codes specified by the client are also to be
applied.
TEMA e Tubular Exchangers Manufacturer’s Association (TEMA) is used almost worldwide.
TEMA standards refer to the ASME boiler code (Section I) or pressure vessel code (Section VIII,
Div. I) according to the services of the heat exchanger and define a three-letter code which represents
the configuration of the exchanger.
•
•
•
Class R: design and fabrication of unfired shell and tube heat exchangers for generally severe
requirements of petroleum and related processing applications
Class C: design and fabrication of unfired shell and tube heat exchangers for generally moderate
requirements of commercial and general process applications
Class B: design and fabrication of unfired shell and tube heat exchangers for chemical process
service
TEMA designations are shown in Fig. 4.5 and the exchanger parts are labelled in Fig. 4.6 for
illustrative purpose. It is worthwhile to mention that the Indian code IS 4503:1967 (reaffirmed
2003) also uses similar nomenclature. The labelling in Fig. 4.6 is detailed in Table 4.2.
API 660: This is the standard of the American Petroleum Institute for heat exchangers to be used in
refineries and petroleum-related applications. Most of the refineries and petrochemicals have their heat
exchangers designed as per API 660 or TEMAeR.
The BIS code covering the shell and tube heat exchangers is IS 4503:1967. Its data sheet is
specified by IS 10123:1982. Air-cooled exchangers are specified in IS 10470:1983 and its data sheet
is IS 10873:1983. There are other codes applicable to heat exchangers for marine, air conditioning,
etc. IS 4503:1967 e Reaffirmed 2003 (Indian Standards e Specification for Shell and Tube Exchangers) broadly classifies shell- and tube-type heat exchangers as (a) fixed tube plate e nonremovable tube bundle, (b) U-tube e removable tube bundle and (c) floating head e removable tube
bundle. These with subdivisions give the following seven designs: (i) fixed tube plate, (ii) U-tube,
(iii) U-tube reboiler or kettle type, (iv) internal floating head (pull through type), (v) internal floating
head (nonpull through type), (vi) internal floating head (reboiler or kettle) and (vii) floating head
external packed. BIS 4503 refers to IS 2825:1969, Indian standard code for unfired pressure vessels
for some of the mechanical details. It also refers to other BIS codes for materials and standard dimensions of fittings, etc.
BS: British Standards Institution standard no BS ISO 16812 is applicable for shell and tube exchangers in petroleum, petrochemicals and natural gas industries.
DIN and GOST are the German and the Russian standards with specific codes for heat
exchangers.
78
Chapter 4 Shell and tube heat exchanger
FRONT END
STATIONARY HEAD TYPES
REAR END
HEAD TYPES
SHELL TYPES
(L)
(E)
(A)
FIXED TUBESHEET
LIKE “A” STATIONARY HEAD
ONE PASS SHELL
CHANNEL
AND REMOVABLE COVER
(M)
(F)
FIXED TUBESHEET
LIKE “B” STATIONARY HEAD
TWO PASS SHELL
WITH LONGITUDINAL BAFFLE
(B)
(N)
(G)
FIXED TUBESHEET
LIKE “N” STATIONARY HEAD
BONNET (INTEGRAL COVER)
SPLIT FLOW
(P)
(H)
OUTSIDE PACKED FLOATING HEAD
(C) REMOVABLE
TUBE
BUNDLE
ONLY
CHANNEL INTEGRAL WITH TUBESHEET AND REMOVABLE COVER
DOUBLE SPLIT FLOW
(S)
(J)
FLOATING HEAD
WITH BACKING DEVICE
DIVIDED FLOW
(T)
(N)
PULL THROUGH FLOATING HEAD
(K)
CHANNEL INTEGRAL WITH TUBESHEET AND REMOVABLE COVER
KETTLE TYPE REBOILER
(U)
U-TUBE BUNDLE
(D)
(X)
SPECIAL HIGH PRESSURE CLOSURE
(W)
CROSS FLOW
EXTERNALLY SEALED
FLOATING TUBESHEET
FIGURE 4.5
TEMA designations for shell and tube exchangers.
From (1988). Standards of Tubular Exchanger Manufacturers Association (7th ed.), Fig. Ne1.2: Tubular Exchanger Manufacturers
Association, Inc.
4.2 Codes and standards
79
FIGURE 4.6
TEMA classification of exchangers and component nomenclature examples: AES: floating head; BEM: fixed
tube sheet; AEP: floating head e outside packed; CFU: removable U-bundle; AKT: kettle reboiler; AJW:
divided flow e packed tube sheet
Reproduced from Figure N-2 page 1e3 to 1e5 © 1988 Tubular Exchanger Manufacturers Association, Inc.
80
Chapter 4 Shell and tube heat exchanger
Table 4.2 Standard TEMA heat exchanger terminology/nomenclature.
Tag in
Fig. 4.6
Terminology/Nomenclature
Tag in
Fig. 4.6
Terminology/Nomenclature
1.
Stationary head e channel
21.
Floating head cover e external
2.
Stationary head e bonnet
22.
Floating tube sheet skirt
3.
Stationary head flange e channel or bonnet
23.
Packing box
4.
Channel cover
24.
Packing
5.
Stationary head nozzle
25.
Packing gland
6.
Stationary tube sheet
26.
Lantern ring
7.
Tubes
27.
Tie rods and spacers
8.
Shell
28.
Transverse baffles or support plates
9.
Shell cover
29.
Impingement plate
10.
Shell flange e stationary head end
30.
Longitudinal baffle
11.
Shell flange e rear head end
31.
Pass partition
12.
Shell nozzle
32.
Vent connection
13.
Shell cover flange
33.
Drain connection
14.
Expansion joint
34.
Instrument connection
15.
Floating tube sheet
35.
Support saddle
16.
Floating head cover
36.
Lifting lug
17.
Floating head cover flange
37.
Support bracket
18.
Floating head backing device
38.
Weir
19.
Split shear ring
39.
Liquid level connection
20.
Slip-on backing flange
From (1988). Standards of Tubular Exchanger Manufacturers Association (7th ed.), Table Ne2, 9: Tubular Exchanger Manufacturers Association, Inc. All rights reserved.
4.3 Design considerations
As with double-pipe exchangers, shell and tube exchangers are also designed with specified pressure
drop constraints on both the streams. However, due to greater variety and complexity of shell and tube
configurations, there are more design variables to be considered. In addition, since the primary flow
pattern in the shell is both transverse and parallel to the tubes, the flow in reality is tortuous and more
complex. This arises because part of the fluid bypasses the main heat transfer surface due to various
leakages namely tube to baffle leakage stream, tube bundle to shell bypass stream and baffle to shell
leakage stream. The amount of these leakage streams can be substantial which may decrease the main
stream flowing across the tube bundle to less than 50% of the total shell-side flow. Presence of these
bypass streams complicates the analysis of shell-side heat transfer and pressure drop. Thus, design of
4.3 Design considerations
81
shell and tube exchanger is more complex as compared to double-pipe exchanger and optimum design
involves the considerations given below.
Process
1. Process fluid assignment to shell and tube side.
2. Specifying stream temperatures.
3. Setting shell-side and tube-side pressure drop design limits.
4. Setting shell-side and tube-side velocity limits.
5. Selection of heat transfer models and fouling coefficients for shell side and tube side fluids.
Mechanical
1. Selection of heat exchanger layout as per the decided code (TEMA/BIS 4503, etc.) and the
number of passes.
2. Specification of tube parameters e size, layout, pitch and material.
3. Setting upper and lower design limits on tube length.
4. Specification of shell-side parameters e material, baffle cut, baffle spacing and clearance.
5. Setting upper and lower design limits on shell diameter, baffle cut and baffle spacing.
4.3.1 Input data for design
a. Input data pertaining to the shell- and tube-side fluids are listed in Table 4.3. In addition to this,
information on the nature of the fluids, e.g., flammability, corrosive nature, fouling tendency, solid
concentration, etc., as applicable are noted. These are used in deciding the type of heat exchanger
suitable for the service.
b. Constructional details like installation (horizontal/vertical/inclined); design pressure and
temperature; preferred options, if any, for the tube geometries (length, OD, thickness), tube pitch
and layout; materials of construction; nozzle size, rating and facing are also noted before
embarking on design.
c. Allowable pressure drop.
4.3.2 Design output
Process design
Output from process design are
- Heat transfer area required to deliver the specified heat duty based on assumptions of exchanger
type and configuration details. This involves detailing of exchanger configuration commonly
summarised by specifying the code classification, e.g., TEMA AES exchanger.
- Overall heat transfer coefficient, film coefficient of both shell and tube side, temperature
difference MTD.
- Pressure drop for shell- and tube-side fluids.
- Design references: process calculation references (procedure for calculation of shell-side and
tube-side heat transfer coefficients; design standard (TEMA, BIS, etc.)).
- Design considerations such as short-term conditions, if required.
82
Chapter 4 Shell and tube heat exchanger
Table 4.3 Input process data for shell/tube-side fluid.
SI
Metric
Requirement
Fluid name
e
e
Yes
Flow rate
kg/s or kg/hr
kg/hr
Yes
kPa(g) or MPa(g)
kg/cm2(g)
Yes
Operating temperature
K
C
Yes
Vapour fraction
w/w
w/w
(Yes)
kW or MW
MM kcal/hr
Yes
m2K/W
m2 hr C/kcal
Yes
W/(m K)
kcal/(m hr C)
Yes
mPa s
cP
Yes
kJ/kg
kcal/kg
Yes
kJ/(kg K)
kcal/(kg C)
Yes
Operating pressure
Heat duty
Fouling factor
Thermal conductivity
Viscosity
Vapour
Enthalpy
Specific heat
Density
Thermal conductivity
Liquid
kg/m
3
2
W/(m K)
3
kg/m
Yes
kcal/(m hr C)
Yes
Viscosity
mPa s
cP
Yes
Enthalpy
kJ/kg
kcal/kg
Yes
kJ/(kg K)
kcal/(kg C)
Yes
Specific heat
Density
Critical pressure
Boiling
2
Range (dewebubble)
kg/m
3
3
kg/m
Yes
2
Notes
For two phase
kPa(abs.)
kg/cm (abs.)
(Yes)
For boiling
C
C
(Yes)
For boiling
Mechanical details
-
-
Shell: material, size and thickness, corrosion allowance, insulation; details of nozzles and flanges.
Tube bundle: tube material, diameter, thickness, length and pitch; baffle geometry (material, type,
cut orientation and %, thickness, spacing and number); tie rods and spacer e number and size;
shell partition dimensions, if applicable.
Stationary and floating head: dimensions of each end, provisions of pass partition plates, if
applicable, details of nozzles and flanges.
Fabrication details
The detailed construction information required to fabricate the exchanger is documented in a set of
complete fabrication drawings. This set consists of
-
General arrangement drawings including stacking plan, if applicable.
Shell, nozzles and support details, other connections (vent, drain, instruments, etc.); stationary
and floating head.
Tube bundle and its component details
4.3 Design considerations
83
Design summary is presented in tabular form as a data sheet. The format suggested in TEMA is
presented in Table 4.4. Formats from other standards differ only marginally.
In large projects, a common table (data sheet) documents the data for several exchangers in the
plant for which design companies like M/s Engineers India Ltd. have their own format.
Table 4.4 Data sheet for shell and tube exchanger (TEMA).
1
Company: XYZ Co.
2
Location: Kharagpur, India
3
Service of unit: Vapour condenser
Our Ref.: J1222E01
4
Item no.: 10E01
Your Ref.: 10E01:
5
Date: Jan 09, 2020
Rev. No.: O
Job No.: J1222
6
Size (mm): 4150
Type: BEM
Connected in: 1 parallel, 1 series
7
Surface/unit (effective) (m2): 269;
8
surface/shell (effective) (m2): 269
shell/unit: 1;
PERFORMANCE OF ONE UNIT
9
Fluid allocation
Shell side
Tube side
10
Fluid name
Inlet vapour
Cold water
11
Fluid quantity, total
kg/s
12.5
105
12
Vapour (In/Out)
kg/s
12.5
0
0
0
13
Liquid
kg/s
0
12.5
105
105
14
Noncondensable
kg/s
0
0
0
0
Temperature (In/Out)
C
46
44
20
30
Dew/bubble point
C
46
44
10.8
564
999
997
0.0085
0.122
1.016
0.804
15
16
17
3
18
Density vapour/liquid
kg/m
19
Viscosity
mPa s
20
Mol. wt. vapour
21
Mol. wt. noncondensable
22
Specific heat
kJ/(kg K)
1.76
2.47
4.19
4.19
23
Thermal conductivity
W/(m K)
0.0174
0.102
0.5937
0.6067
24
Latent heat
kJ/kg
337.4
338.4
25
Pressure (abs.)
Bar
4.9
4.8
5
4.9
26
Velocity
m/s
27
Press. drop, allow./calc.
bar
28
Fouling Resist. (min)
58.6
2
m K/W
9.9
0.2
0.87
0.08
0.00009
0.07
0.08
0.00018; 0.0002
Ao based
Continued
84
Chapter 4 Shell and tube heat exchanger
Table 4.4 Data sheet for shell and tube exchanger (TEMA).dcont’d
29
Heat exchanged 4300 kW; MTD corrected 19.9 C
30
Transfer rate, service
31
W/(m2 K)
Dirty: 930.7 Clean:1274
CONSTRUCTION OF ONE SHELL
32
Sketch
Shell
side
Tube side
33
Design/vac/test pressure.g
bar
6//
6//
34
Design temperature
C
85
85
35
No. of passes per shell
1
2
36
Corrosion allowance
mm
3
3
37
Connections
In
mm
438
305
Out
mm
154
255
Intermediate
mm
/-
/-
38
39
ID
40
Tube nos. 1106; OD 19 mm; Tks-Avg 1.2 mm; Length 4120 mm; Pitch 23.8 mm
41
Tube type
42
Shell
43
Material CS plain tubes
Tube pattern 60
ID 950
OD 974
Shell cover -
Channel or bonnet e CS
Channel cover
e
44
Tube sheet e stationary e CS
Tube sheet
floating
e
45
Floating head cover
Impingement
protection
None
46
Baffle e CS
;
47
Baffle-long
; Seal type
48
Support-tube U-bend; Type
49
Bypass seal
50
Expansion joint; Type;
51
r V 2 @Inlet nozzle 640:
52
Gaskets e Shell side
53
Floating head
54
Code requirement ASME Sec VIII Div 1; TEMA class R e refinery service
55
Weight/Shell 5300
56
Remarks
57
58
mm
Type e Segmental
; Cut(%d) 25
; Spacing 395 (CeC) mm
;
; Tube-tube sheet joint;
@Bundle entrance 1350; @Bundle exit 17 kg/(m s2)
; Tube side
; Filled with water 8720; Bundle 3045 kg
Inlet 570 mm
4.4 Design e FT method
85
4.4 Design e FT method
The steps in a design procedure using FT method are given below. This procedure leads to w10%
overdesign.
1. Compile the required fluid physical properties namely density, viscosity and thermal
conductivity. These properties vary with temperature and since the formulae involve a single
value, either an average property value or a correction to the average is used. Weighted average
values may be taken for fluid mixtures. The concept of average temperature and caloric
temperature in this regard is discussed in Chapter 2.
2. Define duty: heat transfer rate Q, fluid flow rates mc , mh (subscripts c and h refer to the cold and
hot fluid, respectively) and terminal temperatures. The heat transfer between the phases in a
shell and tube exchanger can involve transfer of sensible heat, latent heat or both. For no phase
change in any of the fluids, the heat balance equation is
(2.1)
Q ¼ mc Cpc Tc;out Tc;in ¼ mh Cp;h Th;in Th;out
Subscripts in and out indicate the inlet and outlet condition. In case of phase change, the balance
equation is expressed in terms of enthalpy.
3. Preliminary selection of shell- and tube-side fluid as per the general guidelines provided in
Table 3.2. In horizontal thermosiphon reboiler, the process fluid is in the shell and the heating
stream or steam in the tubes. This is to lower pressure drop in the thermosiphon circuit. Low
flow of cooling water leads to deposits and fouling and it is usually chosen as tube-side fluid. In
most industries using cooling water, nonferrous tubes, commonly brass and copper, are used
because cooling water is corrosive to steel especially for high tube wall temperatures and in
presence of dissolved air. Shells are usually fabricated from steel.
4. Select a value for the design overall heat transfer coefficient, UD. Table 2.5 may be referred to
for providing an educated guess based on values for a similar system.
5. Calculate area required from Eq. (2.7) expressed as
Ao ¼
Q
FT UD DTLMTD;counterflow
(2.7)
where Ao is heat transfer area, i.e., effective tube outside area (m2); Q is total heat duty (W);
DTLMTD;counterflow is the log mean temperature difference ( C) assuming that the heat transferred is a
linear function of temperature difference and FT, the LMTD correction factor can be obtained as
discussed below.
Generalised expressions of FT for n shell passes
As discussed in Chapter 2, FT for multipass exchangers (Fig. 4.7) is expressed as function of
mc Cp;c Th;in Th;out
Tc;out Tc;in
¼
and S ¼
.
R¼
mh Cp;h Tc;out Tc;in
Th;in Tc;in
86
Chapter 4 Shell and tube heat exchanger
For n number of shell passes,
1
1 RS n
1S
When R s 1 Sn ¼
1
1 RS n
R
1S
1
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð1 Sn Þ
R2 þ 1
ln
ðR 1Þ
ð1 RSn Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
and FT ¼
ð2=Sn Þ 1 R þ R2 þ 1
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ln
ð2=Sn Þ 1 R R2 þ 1
When R ¼ 1 Sn ¼
(4.1)
S
1 þ nS S
pffiffiffi
2
Sn
ð1 Sn Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
and FT ¼
ð2=Sn Þ 1 R þ R2 þ 1
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ln
ð2=Sn Þ 1 R R2 þ 1
(4.2)
Subscript n refers to the number of shell passes. The expressions for FT are thus symmetric with
respect to fluid placement.
Tc,out
Tc,in
Th,in
Tc,out
Th,in
Tc,in
Th,out
Th,in
Th,out
Th,in
Tc,out
Tc,out
Tc,in
Tc,in
Flow path
Th,out
Th,out
Flow path
FIGURE 4.7
Temperature profile in a typical 1e2 S&T exchanger.
4.4 Design e FT method
87
While the above expressions are more accurate, it can be shown that FT value for a 1e2 and a 1e8
exchanger for the same service differ by a maximum of 2% and often any exchanger having one
shell pass and two or more even-numbered tube passes can be treated as a 1e2 exchanger with FT
as
FT ¼ ðX=YÞ
where
X¼
and
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðR2 þ 1Þ lnfð1 SÞ=ð1 RSÞg
8
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 9
<2 S R þ 1 ðR2 þ 1Þ =
Y ¼ ðR 1Þ ln
:2 S R þ 1 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðR2 þ 1Þ ;
(4.3)
(4.4)
(4.5)
A low value of FT means higher surface requirement for the exchanger being designed. The
design value of FT is always kept above 0.8. For FT < 0:8, there is a ‘temperature cross’ with heat
transfer from the cold stream back to the hot fluid at some point within the exchanger. In addition,
the slope of FT versus S curve becomes very steep under this condition, making the exchanger
performance sensitive to any changes in design temperatures. However, the value of 0.8 is only
approximate and higher values of FT are required at very large and very small values of R. FT can
be increased by using several shells in series or by increasing the numbers of passes in the same
shell (up to a practical limit of 6). Nevertheless, the curves become steeper with increasing
number of shell passes and require higher FT values. In extreme cases, counterflow exchangers
with FT ¼ 1 may be the only practical configuration. FT is also equal to 1 if either of the fluid is
isothermal as in case of condensation of saturated steam. Usually the single shell arrangement is
more economical, even with more complex internals.
It is important to note that Eqs. (4.3)e(4.5) has been derived from Eqs. (4.1) and (4.2) for n ¼ 1.
In case a single shell pass does not serve the design, this is reflected not only by a value of FT
lower than 0.8 but also an imaginary value of Y from Eq. (4.5). Higher numbers of shell passes
have to be opted in such cases and FT calculated from Eq. (4.1) or (4.2).
6. Based on estimated Ao , decide the exchanger layout and geometry e tube details (pitch,
dimension and passes). Table 4.5 may be referred for this. As a first guess, 19.05 mm or 25.4 mm
may be adopted with PT ¼ 1.25 Do.
Tubes of different material can be chosen from Appendix Table F1.A, which presents the
specifications as per TEMA code. Tube diameters and thickness as per IS 4503:1967 is shown in
Appendix Table F1.B.
7. Decide on exchanger type. This may be based on information summarised in Table 4.6.
8. Estimate the shell inner diameter Ds from the expression
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
CL Ao P2T
(4.6)
Ds ¼ 0:637
CTP Do Le
88
Chapter 4 Shell and tube heat exchanger
Table 4.5 Dimensions of heat exchanger tubes.
OD
in.
5
8
3
4
7
8
1
1 14
1 12
2
Wall thickness
mm
15.88
19.05
22.23
25.40
31.75
38.10
50.80
Inside cross-sectional
area
ID
BWG No.
in.
mm
in.
mm
ft2
m2 3104
12
0.109
2.77
0.407
10.33
0.000903
0.8381
14
0.083
2.11
0.459
11.66
0.00115
1.068
16
0.065
1.65
0.495
12.57
0.00134
1.241
18
0.049
1.25
0.527
13.39
0.00151
1.408
12
0.109
2.77
0.532
13.51
0.00154
1.434
14
0.083
2.11
0.584
14.83
0.00186
1.727
16
0.065
1.65
0.620
15.75
0.00210
1.948
18
0.049
1.25
0.652
16.56
0.00232
2.154
12
0.109
2.77
0.657
16.69
0.00235
2.188
14
0.083
2.11
0.709
18.01
0.00274
2.548
16
0.065
1.65
0.745
18.92
0.00303
2.811
18
0.049
1.25
0.777
19.74
0.00329
3.060
10
0.134
3.40
0.732
18.59
0.00292
2.714
12
0.109
2.77
0.782
19.86
0.00334
3.098
14
0.083
2.11
0.834
21.18
0.00379
3.523
16
0.065
1.65
0.870
22.10
0.00413
3.836
10
0.134
3.40
0.982
24.94
0.00526
4.885
12
0.109
2.77
1.032
26.21
0.00581
5.395
14
0.083
2.11
1.084
27.53
0.00641
5.953
16
0.065
1.65
1.120
28.45
0.00684
6.357
10
0.134
3.40
1.232
31.29
0.00828
7.690
12
0.109
2.77
1.282
32.56
0.00896
8.326
14
0.083
2.11
1.334
33.88
0.00971
9.015
10
0.134
3.40
1.732
43.99
0.0164
15.20
12
0.109
2.77
1.782
45.26
0.0173
16.09
Reproduced from Geankoplis, C. J., (2003). Transport processes and separation process principles (unit operations) (4th ed.).
Reprinted by permission of Pearson Education, Inc., New York, NY.
Eq. (4.7) is obtained by considering that the number of tubes arranged with pitch Pt that can be
fitted inside a cylindrical shell of diameter Ds is
Nt ¼ CTP pD2s
4 CL P2T
(4.7)
4.4 Design e FT method
89
Table 4.6 General guidelines for selection of exchanger type.
Design
requirements
Floating head
split backing ring
Floating head
pull-through
bundle
U-tube
Fixed tube sheet
Provision for
differential
expansion
Individual tubes
free to expand
Expansion joint in
shell
Floating head
Floating head
Removable bundle
Yes
No
Yes
Yes
Replacement of
bundle possible
Yes
Not practical
Yes
Yes
Individual tubes
replaceable
Only those in
outside row
Yes
Yes
Yes
Tube interiors
cleanable
Difficult to do
mechanically, can
be done
chemically
Yes, mechanically
or chemically
Yes, mechanically
or chemically
Yes, mechanically
or chemically
Tube exteriors
with triangular
pitch
Cleanable
Chemically only
Chemically only
Chemically only
Chemically only
Tube exteriors
with square pitch
cleanable
Yes, mechanically
or chemically
Chemically only
Yes, mechanically
or chemically
Yes, mechanically
or chemically
Number of tube
passes
Any practical even
number possible
Normally no
limitations
Normally no
limitations
Normally no
limitations
Internal gaskets
eliminated
Yes
Yes
No
No
Cost comparison
(by TEMA type)
BEU ¼ 1.0
AEU ¼ 1.1
BKU ¼ 1.2
BEM ¼ 1.0
BEN ¼ 1.1
AES ¼ 1.5
AET ¼ 1.5
AKT ¼ 1.8
Reproduced from Removable channel cover makes exchanger cleaning easier compared to an integral head that has nozzles to
which the process piping are attached.
where Nt can be expressed in terms of Ao as
Nt ¼
Ao
pDo Le
(4.8)
In Eq. (4.8), Do is the outer diameter of tube and Le is the net effective tube length available for
contact by the shell-side fluid. This is obtained as total tube length, L minus the thickness of
each tube sheet (and double tube sheets when used). Details of estimating tube sheet thickness
and Le are provided in Sections 4.6.2 and 4.6.3.
90
Chapter 4 Shell and tube heat exchanger
CL in Eq. (4.7) accounts for the area of shell cross section required to accommodate one tube and
depends on the type of pitch chosen: It is 1 for 45 degrees and 90 degrees tube layout and 0.87 for
30 degrees and 60 degrees layout. Constant CTP accounts for the incomplete coverage of shell
cross section due to clearance required between shell and outermost tubes. The value of CTP for
different number of tube passes is presented in Table 4.7.
Table 4.7 Constant to account for incomplete
coverage of shell cross section.
Number of tube passes
1
2
3
CTP
0.93
0.90
0.85
In order to adopt a standard value of Ds , Table 4.8 is referred to select a diameter value just higher
than the Ds value calculated from Eq. (4.6). Table 4.8a and b is adapted from similar tables by
Kern (Appendix Table 9, page 841e842, TMH Edition, 1997; See Further Reading at the end of
this chapter)
9. Note the tube count for the adopted tube layout and number of tube passes from Table 4.8. The
number of tubes thus selected is checked to ensure that the tube-side velocity for water and
similar liquids ranges from 0.9 to 2.4 m/s (3e8 ft/s) and velocity in the shell-side lies within
0.6e1.5 m/s (2e5 ft/s). The lower and upper velocity limits are decided based on fouling and
rate of erosion, respectively. For vapour, the allowable velocity is a function of operating
pressure and fluid density. In general, it varies from 50 to 70 m/s for vacuum, 10e30 m/s for
atmospheric pressure and 5e10 m/s for high pressure services, the lower value in a range being
applicable to high molecular weight fluids.
Additional area to compensate fouling can be provided by increasing the number, diameter or
length of tubes. An increase in tube diameter/number reduces the flow velocity which if
significant, may accelerate fouling. Alternatively, increasing tube length increases area at the
expense of higher pressure drop. Spare exchangers should be considered for continuous
operation using severe fouling systems.
10. Estimate shell-side mass flux (Gs)
The linear velocity and mass flux of the shell-side fluid change continuously across the bundle
since the width of the shell and the number of tubes vary from zero at the top and bottom to
maximum at the shell centre. Therefore, the width of the flow area is taken at the hypothetical
tube row possessing the maximum flow area and corresponding to the centre of the shell. This
gives the shell-side mass velocity as
ms
Gs ¼
(4.9)
Ae
and the linear velocity on the shell side us as
us ¼
Gs
rs
where the bundle cross flow area (Ae) is
Ae ¼
Ds ðPT D0 Þ B
PT
(4.10)
4.4 Design e FT method
Table 4.8a Tube count e square pitch.
19.05 mm
300 4
00 25.4 mm (100 ) OD on 31.75 mm 114 square pitch
OD on 25.4 mm (100 ) square pitch
Shell ID,
mm(in.)
1eP
2eP
4eP
6eP
203 (8)
32
26
20
254(10)
52
52
305(12)
336.5 13 14
387 15 14
438 17 14
489 19 14
540 21 14
590.55 23 14
81
91
8eP
Shell ID,
mm (in.)
1eP
2eP
4eP
20
203 (8)
21
16
14
40
36
254(10)
32
32
26
24
76
68
68
60
48
45
40
38
36
97
90
82
76
70
61
56
52
48
44
137
124
116
108
108
81
76
68
68
64
177
166
158
150
142
112
112
96
90
82
224
220
204
192
188
138
132
128
122
116
277
270
246
240
234
177
166
158
152
148
341
324
308
302
292
305(12)
336.5 13 14
387 15 14
438 17 14
489 19 14
540 21 14
590.55 23 14
213
208
192
184
184
635(25)
413
394
370
356
346
635(25)
260
252
238
226
222
686(27)
481
460
432
420
408
686(27)
300
288
278
268
260
736(29)
553
526
480
468
456
736(29)
341
326
300
294
286
787.4(31)
657
640
600
580
560
787.4(31)
406
398
380
368
358
838(33)
749
718
688
676
648
838(33)
465
460
432
420
414
889(35)
845
824
780
766
748
889(35)
522
518
488
484
472
940(37)
934
914
886
866
838
940(37)
596
574
562
544
532
990.6(39)
1049
1024
982
968
948
9 00 100 31.75 mm 14 OD on 40 mm 116 square pitch
254(10)
16
12
10
305(12)
336.5 13 14
387 15 14
438 17 14
489 19 14
540 21 14
590.55 23 14
30
24
22
16
16
32
30
30
22
22
44
40
37
35
31
56
53
51
48
44
78
73
71
64
56
96
90
86
82
78
127
112
106
102
635(25)
140
135
127
123
6eP
8eP
990.6(39)
665
644
624
612
600
100 700 38.1 mm 12 OD on 47.625 mm 18 square pitch
16
16
12
12
22
22
16
16
29
29
25
24
22
39
39
34
32
29
50
48
45
43
39
62
60
57
54
54
96
305(12)
336.5 13 14
387 15 14
438 17 14
489 19 14
540 21 14
590.55 23 14
78
74
70
66
62
115
635(25)
94
90
86
84
78
Continued
92
Chapter 4 Shell and tube heat exchanger
Table 4.8a Tube count e square pitch.dcont’d
686(27)
166
160
151
146
140
686(27)
112
108
102
98
94
736(29)
193
188
178
174
166
736(29)
131
127
120
116
112
787.4(31)
226
220
209
202
193
787.4(31)
151
146
141
138
131
838(33)
258
252
244
238
226
838(33)
176
170
164
160
151
889(35)
293
287
275
268
258
889(35)
202
196
188
182
176
940(37)
334
322
311
304
293
940(37)
224
220
217
210
202
990.6(39)
370
362
345
342
336
990.6(39)
252
246
237
230
224
Ds is the shell inside diameter, B is the baffle spacing, PT is the tube pitch and ms is the mass flow
rate of the shell-side fluid, all in SI units.
It is interesting to note that if Ds is divided by PT , it gives a fictitious and not necessarily an
integral number of tubes that may be at the centre of the shell. In reality, most layouts do not have
any row of tubes through the centre but two equal rows on either side of it having fewer tubes than
that computed for the centre.
11. Calculate the individual heat transfer coefficients based on fluid properties and chosen geometry
of the heat exchanger.
Heat transfer coefficient hi inside tubes is computed from the appropriate correlation in Table 2.6
of Section 2.7.
The shell-side heat transfer coefficient ho is computed for the tube bundle by considering either
parallel flow (in case of unbaffled bundles) or cross flow across tubes (baffled bundles). Since it is
affected by tube arrangement, tube pitch and number of passes (single/multipass), an appropriate
correlation from Chapter 2 is to be selected for its estimation. Most often, ho is computed
neglecting the leakage due to baffles using the following empirical expression
1
3
6
3
NuDe ¼ 0:36Re0:55
De Prs for 2 10 < ReDe < 1 10
(4.11)
ðNuDe ¼ h De
k Þ the Nusselt number is based on De and shell-side fluid thermal conductivity ks and ðReDe ¼ DeG
m Þ is the Reynolds number for shell-side flow. The shell-side mass
where
o
s
s
s
velocity Gs is estimated from Eq. (4.9) and ms is the dynamic viscosity of the shell-side fluid. De,
the shell-side equivalent diameter can be expressed in case of square pitch as
4 P2T pD2o =4
(4.12a)
De ¼
pDo
and for triangular pitch as
4 P2T sin 60 pD2o =4
De ¼
pDo
(4.12b)
4.4 Design e FT method
Table 4.8b Tube count e triangular pitch.
19.05 mm
300 4
5 00 OD on 33.3 mm 116
triangular pitch
19.05 mm
300 4
93
OD on 25.4 mm (100 ) triangular pitch
Shell
ID, mm(in.)
1eP
2eP
4eP
6eP
8eP
Shell ID,
mm(inch)
1eP
2eP
4eP
6eP
203(8)
36
32
26
24
18
203(8)
37
30
24
24
254(10)
62
56
47
42
36
254(10)
61
52
40
36
305(12)
336.5 13 14
387 15 14
1
438 17 4
489 19 14
540 21 14
590.55 23 14
109
98
86
82
78
127
114
96
90
86
170
160
140
136
128
239
224
194
188
178
301
282
252
244
234
361
342
314
306
290
442
420
386
378
364
305(12)
336:5 13 14
387 15 14
1
438 17 4
489 19 14
540 21 14
590:55 23 14
635(25)
532
506
468
446
434
686(27)
637
602
550
536
524
736(29)
721
692
640
620
787.4(31)
847
822
766
722
838(33)
974
938
878
889(35)
1102
1068
940(37)
1240
990.6(39)
1377
8eP
92
82
76
74
109
106
86
82
74
151
138
122
118
110
203
196
178
172
166
262
250
226
216
210
316
302
278
272
260
384
376
352
342
328
635(25)
470
452
422
394
382
686(27)
559
534
488
474
464
594
736(29)
630
604
556
538
508
720
787.4(31)
745
728
678
666
640
852
826
838(33)
856
830
774
760
732
1004
988
958
889(35)
970
938
882
864
848
1200
1144
1104
1072
940(37)
1074
1044
1012
986
870
1330
1258
1248
1212
100 14 triangular pitch
990.6(39)
25.40 mm (100 ) OD on 31.75 mm
203(8)
21
16
16
14
254(10)
32
32
26
24
305(12)
336.5 13 14
387 15 14
438 17 14
489 19 14
1
540 21 4
590.55 23 14
55
52
48
46
44
68
66
58
54
50
91
86
80
74
72
131
118
106
104
94
163
152
140
136
128
199
188
170
164
160
241
232
212
212
635(25)
294
282
256
686(27)
349
334
302
70
1206
1176
1128
1100
1078
100 9 00 31.75 mm 14 OD on 40 mm 116 triangular pitch
254(10)
20
18
14
32
30
26
22
20
38
36
32
28
26
54
51
45
42
38
69
66
62
58
54
95
91
86
78
69
117
112
105
101
95
202
305(12)
336.5 13 14
387 15 14
438 17 14
489 19 14
1
540 21 4
590.55 23 14
140
136
130
123
117
252
242
635(25)
170
164
155
150
140
296
286
686(27)
202
196
185
179
170
Continued
94
Chapter 4 Shell and tube heat exchanger
Table 4.8b Tube count e triangular pitch.dcont’d
736(29)
397
376
338
334
316
736(29)
235
228
217
212
202
787.4(31)
472
454
430
424
400
787.4(31)
275
270
255
245
235
838(33)
538
522
486
470
454
838(33)
315
305
297
288
275
889(35)
508
592
562
546
532
889(35)
357
348
335
327
315
940(37)
674
664
632
614
598
940(37)
407
390
380
374
357
990.6(39)
766
736
700
688
672
990.6(39)
449
436
425
419
407
00 00 38.10 mm 112 OD on 47.625 mm 178 triangular pitch
305(12)
336.5 13 14
1
387 15 4
438 17 14
489 19 14
540 21 14
590.55 23 14
18
14
14
14
27
22
18
16
14
36
34
32
30
27
48
44
42
38
36
61
58
55
51
48
76
72
70
66
61
95
91
86
80
76
635(25)
115
110
105
98
95
686(27)
136
131
125
118
115
736(29)
160
154
147
141
136
787.4(31)
184
177
172
165
160
838(33)
215
206
200
190
184
889(35)
246
238
230
220
215
940(37)
275
268
260
252
246
990.6(39)
307
299
290
284
275
12
4.4 Design e FT method
95
NuDe calculated from Eq. (4.11) gives ho as
ho ¼
NuDe ks
De
(4.13)
ho does not change much from initial estimate unless the number of tubes changes by a large
amount. ho z5000 W m2 K is often used as an initial guess.
In case of single-phase heat transfer, the following nature of variation with respect to shell-side
and tube-side fluid mass velocities is considered
Turbulent flow:
ho a G0:55
and hi a G0:8
s
t
(4.14a)
ho a G0:85
and hi a G0:33
s
t
(4.14b)
Laminar flow:
Heat transfer coefficients in case of condensation and boiling are only slightly affected by mass
velocity and depend primarily on the physical properties of the fluid. Therefore, these
coefficients are often considered to be almost constant.
12. Calculate the overall heat transfer coefficient U from Eq. (3.3) and compare it with the design
UD value
1
1
1
Rdi Atotal
Atotal
¼ Rdo þ
þ
þ Rw þ
(3.3)
U
ho Ef ;effective
Ai
h i Ai
where Rw , the tube wall resistance, is calculated for bare tubes as
Do
Do
ln
Rw ¼
2kw
Do 2t
and for integral circumferentially finned tube as
Do þ 2Nf hf ðDo þ hf Þ
t
Rw ¼ ln
kw
Do t
(4.15a)
(4.15b)
Do is bare tube outside or root diameter (mm), hf is fin height (mm), t is tube wall thickness (mm),
Nf is the number of fins per mm and kw is the tube material thermal conductivity (W/m2K). The Rd
needs to be in the range suggested for similar service (see Table 2.4).
13. Check if U > UD.
This ensures that the exchanger will have a margin in the heat transfer load Q when design inlet
temperatures, fluid flow rates and properties are set. If the calculated value differs significantly,
return to Step 5 with the calculated U.
If the estimated duty falls below the required duty, then as next trial, the exchanger physical
details are altered e.g. increase in the number of passes, increased tube length, etc. In some cases,
interchanging the shell-side and the tube-side fluids can also be an alternative.
14. Optimise the design: repeat Steps 5 to 10, as necessary, to determine the cheapest exchanger that
will satisfy the duty. Usually that corresponds to the one with the smallest area.
96
Chapter 4 Shell and tube heat exchanger
4.5 Pressure drop estimation
Design problems specify the upper limits of pressure drop for the shell-side and the tube-side fluids.
As a general guide, the allowable pressure drop for liquids is 35 kPa for low viscosity (ml < 1 mPa-s)
and 50e70 kPa for viscosity ranging from 1 to 10 mPa-s. For gases and vapours, the allowable
pressure drop is 0.4e0.8 kPa for high vacuum services, 0:1 absolute pressure for medium vacuum,
0:5 system gauge pressure for 1e2 bar pressure and 0:1 system gauge pressure above 10 bar
pressure. Several valid thermal design alternatives may meet the pressure drop limit(s). It is common to
consider 70 kPa as the pressure drop limit in general chemical processes.
Adopting a design with high pressure drop shall incur higher operating cost as fluid circulation
requires some form of pump or fan that shall consume additional power. Apart from the fluid properties, other factors, namely the nature of flow (laminar or turbulent) and the passage geometry,
strongly affect pressure drop. A fluid also experiences entrance loss as it enters the heat exchanger core
due to a sudden reduction in flow area and a loss due to a sudden expansion as the fluid exits the core.
In addition, if the density changes through the core as a result of heating or cooling, an acceleration or
deceleration in flow is experienced. This also contributes to the overall pressure drop (or gain).
The pressure loss components are therefore
Core loss: Pressure drop for flow with mass velocity G and mean density rm is estimated based on
Fanning’s equation as
Dpc ¼
4fL G2
Dh 2rm
(4.16)
Dh and L are the hydraulic diameter and length of the flow passage, f is the Fanning’s friction factor for
the flow condition.
If the core fluid density varies from rin to rout , the pressure drop due to acceleration (or deceleration) incurred in the core is given by
G2 1
1
Dpa ¼
(4.17)
2 rin rout
Entry and exit loss: Entry loss is estimated based on Bernoulli’s equation, coupled with a loss
coefficient Kc associated with the flow area contraction ratio bin as
G2
Dpin ¼ 1 b2in þ Kc 2rin
(4.18)
bin is defined as the ratio of the minimum area to the frontal area and rin is density at inlet.
Exit loss is also estimated similarly using the following expression
G2
Dpe ¼ 1 b2e þ Ke 2re
Parameters with subscript ‘e’ refer to expansion in passage area at the exit.
(4.19)
4.5 Pressure drop estimation
97
Considering negligible dependence of loss coefficients on Reynolds number, Kc and Ke can be
expressed in terms of area ratio as
Ke z ð1 be Þ2
(4.20a)
Kc z 0:42 ð1 bi Þ2
(4.20b)
and
Total pressure drop: The total pressure drop Dpt and Dps across the tube side and the shell side of
the heat exchanger is obtained by adding the individual contributions explained above.
Dpt ¼ Dpin;t þ Dpc;t þ Dpa;t þ Dpe;t
(4.21a)
Dps ¼ Dpin;s þ Dpc;s þ Dpa;s þ Dpe;s
(4.21b)
and
In all expressions, subscripts t and s signify the tube side and the shell side, respectively.
Fluid pumping power is related to the total pressure drop and flow rate as
! 1
mt
1
ms
Dpt ; and Ws;t ¼
Dps
(4.22)
Wp;t ¼
hp ; t
hs ;t
et
es
where hp is pump efficiency.
Kern (Kern, Donald Quentin. Process heat transfer. Tata McGraw-Hill Education, 1997) suggested
another way to estimate pressure drop
a) For the tube-side fluid, one velocity head loss per return bend is considered and the expression is
4ft Lp Np
1
2
Dpt ¼ rt ut þ 4Np
(4.23)
2
Di
where ut is tube-side velocity, Lp is the tube length per pass, Np is the number of tube passes, Di is tube
inside diameter, rt is the average density of the tube-side fluid, ft is the Fanning’s friction factor for the
flow condition in the tubes decided by the Reynolds’ number for flow through tubes.
b) For the shell-side fluid considering cross flow across the tube banks, the pressure drop expression is
Dps ¼
fs G2s ðNb þ 1ÞDs
2rs De
(4.24)
where Nb is the number of baffles and ðNb þ1Þ is the number of crosses, i.e., the number of times the
shell-side fluid crosses the tube bundle. There is an odd number of crosses when both shell nozzles are
on opposite sides of the shell and an even number if both shell nozzles are on the same side. For close
baffle spacing ð 152.4 mm; i.e. 600 Þ, one baffle may be omitted if the number of crosses is not an
integer.
fs , the Fanning’s friction factor, can be expressed in the range: 400 < Res 106 as
f ¼ expf0:576 0:19 lnðRes Þg
(4.25)
As mentioned earlier, Res ¼ Gs De=ms in the shell considering cross flow across the tube bank
ms Pt
, where ðC ¼ PT do Þ is the gap between the outer
and shell-side mass flux, Gs ¼
Ds C B
98
Chapter 4 Shell and tube heat exchanger
diameter of tubes perpendicular to the flow direction. De, the shell equivalent diameter, is defined
in Eq. (4.12) for triangular and square pitch.
Some useful relationships for quick evaluation of the different design alternatives around a base
design are given below
1. in turbulent flow Dps ðor Dpt Þ a u2
(4.26)
2. in laminar flow Dps ðor Dpt Þ a u
(4.27)
3. Dps ðDBLÞ ¼ Dps ðSEGÞ=8
(4.28)
4. Dps ðJÞ ¼ Dps ðEÞ=8
(4.29)
5. Dpt a ðNp Þ3
(4.30)
where
u: linear velocity
Dps ; Dpt : shell- and tube-side pressure drop excluding nozzle
DBL, SEG: double segmental baffle, segmental baffle
J & E: TEMA shell type
Np : No. of tube passes
4.6 Mechanical detailing
The mechanical details to be passed on to the fabricator are the general arrangement and the fabrication detail drawing(s). This would completely specify the material(s) of construction; dimension of
component parts that make the tube bundle assembly, shell and heads and the nozzles. While such
details are finalised by the mechanical engineering group, the process design team needs to be familiar
with the codes and generate the basic specifications dealt as follows. Intricacies of fabrication steps/
procedure and inspection are intentionally omitted.
4.6.1 Exchanger material
A major consideration for selecting exchanger material is corrosiveness of the working fluids. Carbon
steel is a commonly adopted exchanger material. Mechanical strength becomes important in high
temperature applications. Process industry often uses admiralty brass tubes when the environment is
neither too acidic nor too alkaline, e.g., overhead condenser of crude distillation columns. Stainless
steel is used for food processing or fluids that require corrosion resistant and smooth surface. The best
guidance for selection of material is provided by past experience with similar services and materials.
Table 4.9 shows typical HE material used for different services.
4.6.2 Tube length
Tube bundles are assembled out of tubes, tube sheets, baffles, tie rods and spacers. Standard tube
length according to IS 4503:1967 are 0.5, 1, 2.5, 3, 4, 5 and 6 m. Choosing standard tube length
4.6 Mechanical detailing
99
is preferred from the point of economy and common spares inventory holding. Industrial designs
mostly use tube length of 2.5 m and higher.
Choosing longer tube length (for a given surface area) requires fewer tubes and less complicated
tube sheet with fewer holes drilled. This also decreases the shell diameter resulting in lower cost.
However, mechanical cleaning is limited to 6 m (20 ft) tubes and shorter, although standard exchangers can be built with tubes up to 12 m (40 ft). Maximum tube length limit may also be dictated by
transportation limitation (up to 30 m typically).
Part of the tube length within the tube sheet (TS) and the portion within the dead space in the
floating head are not considered for heat transfer and baffle spacing calculations. However, in case of U-tubes, a credit for the bend portion is
considered. The effective tube length (Le ), i.e., the length used for
Effective tube length
calculating heat transfer area and baffle spacing, is estimated as follows
Table 4.9 Materials for noncorrosive and corrosive service.
Service
Material
Noncorrosive service
Any HE type, T < 100 C
Al and austenitic Cr-Ni steel
Any HE type, 100 <T < 45 C
3 12 Ni steel
Any HE type, 45 <T < 0 C
Carbon steel (impact tested)
Any HE type, 0 <T < 500 C
Carbon steel
Shell and tube T > 500 C
Refractory lined steel
Corrosive service
Mildly corrosive serve; tempered cooling water
Carbon steel
Sulphur bearing oils at T > 300 C; hydrogen at
elevated temperature
Ferritic Co-Mo and Cr-Mo alloys
Tubes for moderately corrosive service; cladding
for shell and channel in contact with corrosive
sulphur bearing oil
Ferritic Cr steel
Corrosion resistance duties
Austenitic Cr-Ni steel
Mildly corrosive fluids
Aluminium
Freshwater cooling in surface condensers;
seawater cooling
Copper allow: admiralty brass, cupronickel
Resistance to mineral acids and chloridecontaining acids
High Ni-Cr-Mo alloys
Seawater cooler and condensers
Titanium
Highly corrosive services
Carbon/graphite
Exposure to sea and brackish water
Coatings: aluminium, epoxy resins
Channels for seawater coolers
Lining: lead, rubber
General corrosion resistance
Lining: austenitic Cr-Ni steel
100
Chapter 4 Shell and tube heat exchanger
Fixed tube sheet:
Le ¼ L 2 TS; ð1Þ
(4.31a)
Le ¼ L 2 TS XLZ; ð2Þ
(4.31b)
Le ¼ L TS XU; ð3; 4Þ ðnozzle at=after U-bendÞ
(4.31c)
Le ¼ L TS 50 mm; ð 5; 6Þ ðnozzle before U-bendÞ
(4.31d)
Floating head:
U-tube
and
(1) Calculation of TS discussed in next section.
(2) XLZ: Floating head dead space (S or T type rear end). This is decided by the floating head flange
bolt size and the difference between the shell and tube thermal expansion. Rough estimates of
XLZ are presented in Table 4.10.
(3) XU: U-bend length (only the curved portion). Calculated as OTL/3, OTL being the outer tube
limit diameter estimated as, OTL ¼ Ds e (bundle-to-shell clearance). The bundle-to-shell
clearance discussed in Section 4.6.6 depends on the type of tube bundle. It should not be less
than the value listed in Table 4.11.
(4) The U-bend is included in the effective length but this should be confirmed with the client’s
criteria.
(5) 50 mm indicates the distance between TL (tangent length marking) and the last baffle.
(6) The smallest diameter of U-bend that can be turned without deforming the outside diameter of
the tube at the bend is 3e4 times the tube outside diameter, Do .
Table 4.10 Estimated floating head dead space (XLZ in mm).
Design pressure pdesign in kg/cm2(g)a
Shell ID
a
10
20
30
40
250 mm
190
200
210
220
500 mm
210
230
240
250
750 mm
230
260
280
300
1000 mm
250
290
320
350
1300 mm
270
320
360
400
1500 mm
290
350
400
450
Of shell or tube, whichever is higher.
4.6 Mechanical detailing
101
Table 4.11 Minimum clearance between bundle and shell ID.
Bundle to shell clearance (Ds eOTL), mm
Ds mm
Fixed tube, U-Tube
w200
10.9
35
w250
10.8
34.9
w300
10.9
Split ring floating head(1)
w350
w400
9.5
35
w450
w500
10
w550
w600
w650
w700
w750
10.5
45
w800
w850
w900
w950
w1000
w1050
12
51
w1100
w1200
15
>1200
30
60
(1)
Add 100 mm for pull through floating head (TEMAeT).
4.6.3 Tube sheet details
In order to allow sufficient thickness to fix the tubes, the thickness of the tube sheet TS should not be
less than the tube outside diameter for tubes up to 25 mm diameter. Table 4.12 lists the minimum TS
required for different tube diameters.
For Ds 500 mm, TS is higher of 50 mm or the value (in mm) calculated from Eq. (4.32)
pffiffiffiffiffiffiffiffiffiffiffiffiffi
(4.32)
TS ¼ Ds pdesign =58:3
where shell inside diameter Ds is in mm and pdesign is design pressure in kg/cm2(g) of shell or tube,
whichever is higher.
102
Chapter 4 Shell and tube heat exchanger
For Ds < 500 mm, TS is higher of Ds =10 or the value calculated from Eq. (4.32).
Typically, for design, the thickness of each tube sheet may be estimated from experience as 38 mm
for low-pressure units and 50e150 mm for high-pressure exchangers (14e27 kg/cm2).
Effective tube sheet thickness for strength calculation is measured from bottom of pass partition
groove minus shell-side corrosion allowance and corrosion allowance on the tube side in excess of the
groove depth. Tube sheet thickness calculation based on strength is not included here and the detailed
calculation may be referred from Appendix 7 of IS 4503 or from the TEMA code.
Tube sheet hole diameter as per TEMA code is decided based on the chosen option of ‘standard fit’
or ‘special close fit’. Table 4.12 includes the tube sheet hole diameter and its tolerance for different
tube diameters. ‘Special close fit’ is provided only when required by client. It is used for austenitic
steel tubes for corrosion resistance.
Blind holes are drilled into the tube sheet and are tapped to create thread to attach tie rods and
spacer supports. Pass partition plates are also grooved into the tube sheet e typically 5 mm deep
groove. Typical depth of groove in tube sheet for rolling of tubes is 3 mm.
Table 4.12 Minimum permissible tube sheet thickness.
Permissible deviation in
hole diameter, mm
Do , mm
Minimum
TS, mm
Standard fit hole
diameter, mm
Special close fit
hole diameter, mm
6
6
Do þ 0:2
10
10
12
12
Standard
fit
Special
close fit
Do þ 0:15
0.1
0.05
Do þ 0:2
Do þ 0:15
0.1
0.05
Do þ 0:2
Do þ 0:15
0.1
0.05
16
13
Do þ 0:2
Do þ 0:15
0.1
0.05
18, 19, 20
15
Do þ 0:2
Do þ 0:15
0.1
0.05
25, 25.4
19
Do þ 0:3
Do þ 0:2
0.1
0.05
31.8, 32
22.4
Do þ 0:4
Do þ 0:3
0.1
0.05
38, 40
25.4
Do þ 0:5
Do þ 0:4
0.2
0.08
4.6.4 Tube pass pattern
Pass patterns in the tube sheet can be Ribbon, H-banded (or mixed) or Quadrant as shown in Fig. 4.8.
During tube sheet layout, it may not be possible to provide exactly same number of tubes per pass. The
choice of pass pattern is based on minimising the deviation in tube counts per pass and pass by-pass
flow in pass-lane. Though the preferable deviation in tube counts per pass is below 5%, up to 10%
deviation may be allowed. H-banded or quadrant pass-lane arrangements have lower bypass flow in the
pass-lane when the baffle orientation is vertical.
In case the tube count per pass varies above 5%, flow velocity in the passes need to be checked for
limitations in velocity. This is particularly important for flow of cooling water and slurry.
4.6 Mechanical detailing
Ribbon
H-banded or Mixed
103
Quadrant
FIGURE 4.8
Typical tube pass patterns in the tube sheet.
4.6.5 Finned tubes
In general, the tubes are plain but some applications use low-fin tubes that provide about 2.5 times the
external surface area. Typically, 250e1200 fins/m of tube length is provided and these fins are 0.3 mm
thick and 1.3 mm high. Fin height of maximum 6.35 mm may be used. Low-fin tubes are costlier by
50%e70% compared to bare tubes and are used when (i) shell-side fouling resistance (Rd) is low,
typically below 0.00053 m2 K/W or (ii) ratio of the total heat transfer resistance (including fouling) in
the shell side is twice or more than that in the tube side.
4.6.6 Segmental baffles (transverse baffles in BIS code)
Baffle spacing is selected within the upper limit of shell ID ðDs Þ and the lower
limit of Ds =5 or 50 mm, whichever is higher. Optimal baffle spacing is around
40%e60% of shell diameter. Spacing in case of inlet and outlet baffles is
Baffle spacing
different from rest of the baffles. As a first trial, these can be assumed as twice
the nozzle ID or 300 mm, whichever is higher. Maximum baffle spacing is
decided from the limit on maximum unsupported length of tube specified in
design codes. Table 4.13a and 4.13b specifies the maximum unsupported length of tubes as per IS
4503:1967 and TEMA code, respectively.
The allowable baffle cut for segmental and double segmental baffles range from 10% to 49% and
10%e30%, respectively. 25% cut is recommended for segmental and singlephase service. The commonly used baffle cut in refineries is also 25%.
In case of a large size exchanger ðDs > 1000 mmÞ, even 10w15% cut
Baffle cut, clearance
is acceptable. 45% cut is recommended for mixed-phase service to avoid
and thickness
vapour accumulation at the top of the shell, except for small size
exchangers ðDs < 500 mmÞ.
The baffle edge should be located on the tube pitch centre or tube centre. The outer tube limit
(OTL) should be away from the baffle edge by a minimum gap ‘x’ to prevent breakage due to tube
vibration. This is shown in Fig. 4.9. The periphery of the baffle needs to be away from the shell inside
diameter by a clearance 2x. Minimum bundle to shell clearance required for easy pull out of bundle is
shown in Table 4.11.
104
Chapter 4 Shell and tube heat exchanger
Table 4.13a Maximum unsupported straight tube length (IS 4503).
Unsupported length upper limit, m
Do , mm
Material of tube e carbon and high
alloy steels up to 400 C/Light alloy
steels up to 450 C/NickeleCopper
up to 315 C/Nickel up to 450 C/
Nickelechromiumeiron up to
540 C
Material of tube e aluminium
and aluminium alloys/Copper
and copper alloys
6
0.6
0.5
10, 10.2
0.8
0.7
12
1.1
0.9
16
1.3
1.1
18, 19, 20
1.5
1.3
25, 25.4
1.8
1.6
31.8, 32
2.2
1.9
38, 40
2.5
2.2
Table 4.13b Maximum unsupported tube span (TEMA).
Tube material and temperature limits ( C)
Do , mm
Carbon steel, other alloys up to
400 C
Low alloy up to 455 C
Copperenickel up to 316 C
Nickel up to 454 C
Ni-Cr-Fe alloy up to 538 C
Aluminium, aluminium alloys
Copper, copper alloys
Titanium, titanium alloys
@ code allowable max.
Temperature
19.0 or 19.05
1525 mm
1320 mm
25.0 or 25.4
1880 mm
1625 mm
Baffles are fabricated from sheets of standard thickness. These are not pressure parts but require
sufficient thickness for mechanical integrity that depends on shell diameter as well as baffle spacing.
Required baffle thickness according to IS 4503 is presented in Table 4.14.
Removable bundles weighing above 5450 kg are provided with bundle skid bars (minimum two
nos.) to facilitate bundle removal. These bars protrude 0.8 mm beyond baffle OD.
4.6.7 Tie rods
Tie rods are made from the same material as the baffles. Actual number of tie rods and its minimum
diameter as per IS:4503 are listed in Table 4.15. Other combinations of number and diameter with
4.6 Mechanical detailing
105
X
Baffle
OTL
FIGURE 4.9
Outer tube limit to baffle edge clearance.
Table 4.14 Baffle thickness as per IS 4503.
Distance between adjacent baffles, mm
Nominal shell
diameter, mm
150
>150 and
£300
>300 and
£450
>450 and
£600
>600 and
£750
>750
> 150 and 400
1.5
3
4
6
10
10
> 400 and 700
3
4
6
10
10
12
> 700 and 1000
4
6
8
10
12
16
> 1000
6
6
10
12
16
16
Table 4.15 Tie rods e dimension and number as per IS 4503.
Nominal Ds , mm
Minimum tie rod
diameter, mm
Minimum no. of tie
rods
> 150 and 400
10
4
> 400 and 700
10
6
> 700 and 900
13
6
> 900 and 1200
13
8
> 1200
13
10
equivalent metal area are permissible but the minimum number of tie rods should be 4 and the
minimum diameter of each should be 10 mm. One end of the tie rod is threaded into holes (8e10 mm
depth) in the tube sheet and the other end is fixed to the last baffle with a nut. Spacer sleeve of
appropriate length on the tie rods placed between two consecutive baffles holds the baffles firmly in
106
Chapter 4 Shell and tube heat exchanger
D nØ
Impingement
Baffle (WIB×LIB)
H
h
tIB
WIB
Inner face
FIGURE 4.10
Impingement plate dimensions.
place. Spacers have inside diameter slightly more than the tie rod diameter. Baffles, tie rods and
spacers are not pressure parts. One may refer to the appropriate code for further mechanical details of
these.
4.6.8 Impingement baffle
Fluid exiting shell inlet nozzle hits the row of tubes facing the nozzle and may erode these tubes if the
kinetic energy of the impinging fluid is high. Kinetic energy per unit volume of fluid is 12 rs;in u2s;in ,
where rs;in and us;in is the density and the velocity of the entering shell-side fluid. Impingement baffles
(Fig. 4.10) are employed to obstruct the entering flow hitting the frontal tubes when the kinetic energy
of the entering fluid (specified in terms of rs;in u2s;in ) exceeds the following limits:
kg
(i) Noncorrosive, nonabrasive, single-phase fluid: 2230 m:s
2
kg
(ii) All other liquids, including a liquid at its bubble point: 740 m:s
2
In case of two-phase fluid, the mean density should be calculated assuming a homogeneous
vapoureliquid mixture. For all gases and vapours, including all nominally saturated vapours and
liquidevapour mixtures, impingement baffles are provided. These are also provided in case of slurries.
Impingement baffles are affixed to the tie rods and their suggested dimensions are listed in
Table 4.16 with the relevant notations marked in Fig. 4.10.
4.6.9 Shell dimensions
Nominal diameter of exchanger shell refers to its OD rounded off to the nearest mm. Small diameter
shells can be fabricated from pipes. The standard pipe shell diameters are 159, 219, 267, 324, 368, 419,
Table 4.16 Dimensions related to impingement baffle (Fig. 4.9) for different nozzle sizes.
Nominal
nozzle
size, mm
50
75
101.6
152.4
203.2
254
305
355.6
406.4
457.2
508
609.6
>609.6
in.
200
300
400
600
800
1000
1200
1400
1600
1800
2000
2400
> 2400
LIB ðmmÞ
110
140
170
220
270
320
370
400
460
510
560
660
Nozzle
OD þ 50
4.6 Mechanical detailing
Dn ¼ nozzle ID; H ðDn =4Þ; WIB ðDn þ 50 mmÞ; h 10 mm; tIB 6 mm.
107
108
Chapter 4 Shell and tube heat exchanger
Table 4.17 Nominal shell diameter as per BIS (IS 2844:1964).
Nominal diameters in mm
100
600
(1500)
2400
(4250)
125
700
1600
2600
4500
150
800
(1700)
2800
(4750)
200
900
1800
3000
5000
250
1000
(1900)
3200
300
1100
2000
(3400)
(350)
1200
(2100)
3600
400
(1300)
2200
(3800)
500
1400
(2300)
4000
Values in bracket are second preference.
457, 508, 558.8, 606.9, 660.11, 711.2, 762, 812.8, 863.6, 914.4 and 1016 mm. For shells fabricated
from sheets, IS 2844:1964 specifies the nominal diameter listed in Table 4.17. The standard wall
thickness for shells with inside diameter ranging from 300 mm ð1200 Þ to 600 mm ð2400 Þ is 13.3 mm (3/8
in.) which is satisfactory for shell side inside pressure up to 20 kg/cm2 (300 psi). Higher wall thickness
is necessary for greater pressures. Shells with diameter above 600 mm ð2400 Þ can be fabricating by
rolling of sheets.
Since the shell has to accommodate the tube bundle, its diameter is decided by the number and size
of tubes, tube pitch and type and the number of shell and tube passes.
Certain points may be noted while selecting the shell dimensions:
-
-
Shells shorter than three times the shell diameter often suffer from poor fluid distribution and
excessive entry and exit losses. So they are likely to be more expensive than a longer, smaller
diameter exchanger of the same area especially if the shell-side fluid is at high pressures.
Shells longer than 15 times the shell diameter are difficult for mechanical handling, require a large
clearway for bundle removal or retubing and show the effects of diminishing return on costs.
Usually shell diameter to tube length ratio is kept between 1/5 to 1/15. BIS suggests 1/10.
Conventional heat exchangers have 6:1 or 8:1 ratio of effective tube length to shell diameter with
a pronounced trend towards the higher value as pressure drop prediction procedures have
improved.
4.6.10 Channel and channel cover
These can be single pieceebonnet type or have a separate flat cover bolted at the end as shown in
Fig. 4.11A and B.
Depth of channel needs to be sufficient to provide sufficient area of crossover for flow to reverse its
direction. This crossover area in the channel cover should be minimum 1.3 times the cross section of
4.6 Mechanical detailing
(A)
(B)
Channel
Tube sheet
Shell
109
Flat cover
Gasket
FIGURE 4.11
Channel cover: (A) single piece, (B) flat cover on channel.
all tubes in a pass. The channel thickness is calculated using the pressure vessel design codes (Chapter
17). The same code is used to find the thickness of the flat channel cover tchannel in mm as
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Ds C pdesign
tchannel ¼
(4.33)
10
fall;stress
where Ds ¼ diameter of the shell/cover in mm; pdesign ¼ design pressure in kgf/cm2;
fall;stress ¼ allowable stress value in kgf/mm2 at design temperature and C ¼ 0:25 when the cover is
bolted with full faced gaskets and C ¼ 0:3 when cover bolted with narrow faced or ring type gaskets.
The thickness is finally arrived at by addition of corrosion allowance margin. Minimum thickness,
including corrosion allowance for the pass partition plates, is 10 mm for alloy channels. It is minimum
10 mm for nominal channel diameter of 600 mm and minimum 13 mm for nominal diameter above
600 mm. Typical depth of pass partition grooves in channel cover is 5 mm as already mentioned and
there should be a minimum remaining thickness of 3 mm of base material. Channel flanges are
designed using pressure vessel code.
4.6.11 Nozzles
Heat exchanger nozzles are sized to match process piping and are based on process considerations
using standard maximum allowable velocity of the fluid. It is economic to make nozzles from standard
pipes of nearest diameter in most cases and the nozzle size is usually same as that of the connecting
pipe. The design practice states that the total nozzle pressure drop for either the shell side or the tube
side should not exceed about 25% of the total, except for low pressure drop services like condensers or
reboilers. In case of one tube pass exchanger, the pressure drop across inlet nozzle of the tube side
should not exceed 25% of the total. This avoids flow maldistribution on the tube side due to high
110
Chapter 4 Shell and tube heat exchanger
velocity head. Too high pressure drop in nozzles lead to a jetting
action
that may cause flow
maldistribution. For axial nozzles to avoid tube end erosion, the r u2 value should be below
8930 kg/m s2. Table 4.18 can be used as a guide for nozzle sizing. Nozzle thickness and all flange
designs are based on pressure vessel design codes e ASME (for TEMA) and IS 2825 (for IS 4503).
Table 4.19 contains guidelines for selecting nozzle thickness. Generally, the hot side fluid should be
introduced from top to bottom and the cold side fluid from bottom to top. Typical nozzle orientation for
the hot and the cold streams is shown in Fig. 4.12.
Table 4.18 Nozzle sizing.
Shell diameter mm(in.)
Nominal nozzle diameter mm (in.)
101.6e254 (4e10)
50.8 (2)
305e438.15 (12e17.25)
76.2 (3)
489e539.75 (19.25e21.25)
101.6 (4)
584.2e736.6 (23e29)
152.4 (6)
787.4e940 (31e37)
203.2 (8)
990.6e1066.8 (39e42)
254 (10)
Multipass
Tc,out
Tc,in
Th,in
Th,in
Th,out
Tc,in
Th,out
Tc,out
Single Pass
Tc,in
Tc,out
Tc,in
Th,out
Counterflow
Tc,out
Th,out
Tc,in
Tc,out
Th,out
Th,in
Th,in
Th,in
Co-current flow
FIGURE 4.12
Heat exchanger nozzle orientations for ‘hot’ and ‘cold’ streams.
4.7 Design illustration
111
Table 4.19 Nozzle thickness.
Nominal nozzle
size, mm (in.)
25:4ð100 Þ
00 38:1 112
50:8 ð200 Þ
76:2 ð300 Þ
101:6 ð400 Þ
152:4 ð600 Þ
203:2 ð800 Þ
254 ð1000 Þ
304:8 ð1200 Þ
355:6 ð1400 Þ
406:4 ð1600 Þ
457:2 ð1800 Þ
508 ð2000 Þ
609:6 ð2400 Þ
Corrosion allowance
w1 mm
w3 mm
w6 mm
Sch. 160
Sch. 160
Sch. 160
Sch. 80
Sch. 80
Sch. 80
Sch. 40
Sch. 40
4.6.12 Exchanger support
Horizontal exchangers require saddle support which is designed as per the appropriate code of design for
unfired pressure vessels, i.e., IS 2825 for India, ASME code for TEMA exchangers or other codes that
may be mutually agreed by the manufacturer and the purchaser. When more than one shell is used, these
are usually stacked to reduce floor space requirement and also to keep the connecting piping short.
4.7 Design illustration
Design a shell and tube heat exchanger to cool 55 m3/hr of light kerosene (55 API) from 130 C to 50 C
using cooling water available at 33 C. Maximum return temperature of cooling water can be 45 C.
Cooling water supply header pressure is 4 kg/cm2(g) and the return header pressure is 2.5 kg/cm2(g).
Supply pressure of kerosene is 6 kg/cm2(g). Maximum allowable total pressure drop for either flow is
0.7 kg/cm2.
Collect rest of the fluid properties from literature. All other data can be taken from TEMA code or
the corresponding IS code. Intermixing of the codes needs to be avoided.
Solution: In this heat exchanger, hot fluid is kerosene and cold fluid is water. The thermal condition
is depicted in Table P4.1. Properties are evaluated at average temperatures as kerosene is a light
hydrocarbon with low viscosity, its viscosity variation with temperature is not drastic and also the
temperature range of water is fairly limited.
Since this is an illustrative example, sticking to a specific design code has not been adhered to. The
reader is advised to refer to the original document of any of the codes, generate the design and compare
the results with those presented.
112
Chapter 4 Shell and tube heat exchanger
Table P4.1 Fluid specifications in design illustration.
/
Th;avg ¼ 90 C
(Following properties are at 90 C)
Cpk ¼ Cph ¼ 2:343 103 J kg K
mk ¼ 0:00027 Pa s
rk ¼ 710 kg m3
kk ¼ 0:148225 W=m K
Prk ¼ Cpk =ðmc kc Þ ¼ 4:2715
Kerosene inlet,
Th;in ¼ 130 C
55 710
¼ 10:8472 kg s
mh ¼
3600
CW exit, Tc;out ¼ 45 C
)
Tc;avg ¼ 39 C
(Following properties are at 39 C)
rw ¼ 992:22 kg m3
mw ¼ 0:000642 Pa s
Cp;w ¼ Cpc ¼ 4:18 103 J kg K
Kerosene exit,
Th;out ¼ 50 C
CW inlet, Tc;in ¼ 33 C
kw ¼ 0:62976 W=m K
Prw ¼ Cp;w mw kw ¼ 4:26
D1 ¼ 130 45 ¼ 85 C
DTLMTD ¼
85 17
¼ 42:25 C
85
ln
17
D2 ¼ 50 33 ¼ 17 C
For the design condition,
R¼
Th;in Th;out 130 50
¼ 6:6667
¼
45 33
Tc;out Tc;in
and
S¼
Tc;out Tc;in
45 33
¼ 0:12371
¼
130 33
Th;in Tc;in
Assuming single shell pass, we calculate FT from Eq. (4.3).
From Eq. (4.4),
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X ¼ R2 þ 1 lnfð1 SÞ=ð1 RSÞg ¼ ð6:6667Þ2 þ 1 ln
and from Eq. (4.5),
1 0:12371
¼ 10:849
1 ð6:6667 0:12371Þ
8
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 9
< 2 S R þ 1 R2 þ 1 =
Y ¼ ðR 1Þ ln
ffi
:2 S R þ 1 þ pffiffiffiffiffiffiffiffiffiffiffiffiffi
R2 þ 1 ;
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 0:12371 6:6667 þ 1 6:66672 þ 1
¼ 5:6667 ln
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 12:236
2 0:12371 6:6667 þ 1 þ 6:66672 þ 1
4.7 Design illustration
113
X
10:849
¼
¼ 0:8866ð> 0:8Þ.
Y
12:236
From heat balance equation (Eq. 2.1)
Q ¼ mh Cp;h Th;in Th;out ¼ 10:8472 2:345 103 ð130 50Þ ¼ 2:0349 106 W
Q
¼ 40:57 kg s.
and mass flow rate of cooling water required mCW ¼ mc ¼
Cp;w Tw;out Tw;in
As mentioned in text, we select cooling water as the tube-side fluid and kerosene is the shell-side
fluid. Henceforth, all properties pertaining to cooling water will be denoted by subscript ‘t’ and those
referring to kerosene will be subscripted by ‘s’.
From Table 2.5, we assume UD ¼ 700 mW2 K (closer to the higher value to arrive at a compact
exchanger with a smaller heat exchange area).
Using Eq. (2.7), we obtain heat transfer area, i.e., effective tube outside area Ao as
This gives FT ¼
Ao ¼
Q
FT UD DTLMTD;counterflow
¼
2:0349 106
¼ 77:31 m2
0:89 700 42:25
From point 6 in Section 4.4, we adopt D0 ¼ 25:4 mm and tube length ¼ 6 m arranged in a
triangular pitch of layout 600 with PT ¼ 1:25D0 ¼ 31:75 mm ¼ 0.03175 m.
From Table 4.5, we select BWG number ¼ 10 which gives wall thickness ¼ 3.4 mm, tube inner
diameter Di ¼ 18:59 mm ¼ 0:01859 m and Ai ¼ 2:714 104 m2 .
Assuming two tube passes with fixed tube sheet (TEMA AJW), we adopt TS ¼ 50 mm as a first
guess and estimate the effective tube length Le from Eq. 4.31(a) as
Le ¼ L 2 TS ¼ 6 ð2 0:05Þ ¼ 5:9 m
This gives shell inner diameter Ds from Eq. (4.6) for CL ¼ 0:87 and CTP ¼ 0:9 (from Table 4.7).
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
CL Ao P2t
0:87 77:31 ð0:03175Þ2
¼ 0:4516 m
Ds ¼ 0:637
¼ 0:637
CTP Do Le
0:9 0:0254 5:9
Referring to Table 4.8b, the next higher shell diameter is Ds ¼ 489 mm ¼ 0.489 m and the corresponding number of tubes Nt ¼ 152.
r Number of tubes per pass ¼ 152/2 ¼ 76, and
Flow area per pass ¼ 2:714 104 76 ¼ 0:0206 m2
This gives cooling water flow velocity (inside tubes)
mCW
40:57
¼ 1:985 m s (lies between 0.9 and 2.4 m/s, so Ok).
¼
ut ¼
rCW Ai;per pass 992:22 0:0206
Considering the operating pressure to be 6 kg/cm2 (higher of the two operating pressures), the
design pressure pdesign ¼ 1:3 6 ¼ 7:8 kg cm2 and from Eq. (4.32),
pffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffiffiffiffiffiffi
489 7:8
TS ¼ Ds pdesign =58:3 ¼
¼ 23:425 mm
58:3
Since Ds < 500 mm, TS is higher of Ds =10 ¼ 49mm or the value calculated from Eq. (4.32).
Accordingly, our initial guess of TS ¼ 50 mm is Ok.
114
Chapter 4 Shell and tube heat exchanger
In order to calculate bundle cross flow area Ae, we adopt B ¼ 0:5Ds ¼ 0:5 0:489 ¼ 0:2445 m,
which is less than the maximum unsupported length as per Table 4.13 and is greater than 50 mm or
Ds =5 (as discussed in Section 4.6.6). and obtain Ae from Eq. (4.10) as
Ae ¼
Ds ðPT D0 Þ B 0:489 ð0.03175 0:0254Þ 0:2445
¼ 0:0239 m2
¼
PT
0.03175
From Eq. (4.9), shell-side mass velocity is
Gs ¼
ms 10:8472
¼ 453:858 kg=m2 s
¼
0:0239
Ae
and the linear velocity on the shell side us is
us ¼
Gs
453:858
¼ 0:6392 m s, which is > 0.6 m/s and <1.5 m/s (Ok as per point 8 in
¼
710
rs
Section 4.4).
In order to estimate ho , shell-side equivalent diameter De is calculated for triangular pitch from
Eq. 4.12(b) as
o
n
4 0:031752 0:866 p ð0:0254Þ2 =4
4 P2T sin 60 pD2o =4
¼ 0:01836 m
¼
De ¼
p 0:0254
pDo
DeGs
0:01836 453:858
¼ 30862:3
¼
0:00027
ms
Since 2 103 < ReDe < 1 106 , we obtain NuDe from Eq. (4.11) as
This gives ReDe ¼
1
0:55
3
NuDe ¼ 0:36Re0:55
ð4:2715Þ0:333 ¼ 172:052
De Prs ¼ 0:36 ð30862:3Þ
And ho from Eq. (4.13) as ho ¼
NuDe ks
172:052 0:148225
W
¼ 1389:02 2 .
¼
0:01836
m K
De
To obtain hi , we use correlation from Table 2.6 i.e., Nu ¼ 0:023 Re0:8 ðPrÞ0:33 where Ret ¼
Di ut rt
0:01859 1:985 992:22
¼ 57031:24.
¼
0:000642
mt
This gives Nut ¼ 0:023 Re0:8
Pr0:333
¼ 0:023 ð57031:24Þ0:8 ð4:26Þ0:33 ¼ 236:768.
t
t
Nui ki
236:768 0:62976
¼ 8020:82 mW2 K.
¼
0:01859
Di
In order to calculate tube wall resistance Rw , we adopt carbon steel (1.5%C) tubes from Table 4.9
and obtain its thermal conductivity kw from literature as 36 W/mK.
and hi ¼ ¼
Considering unfinned tubes, Rw from Eq. (4.15a) is
Do
Do
0:0254
0:0254
m2 K
ln
¼ 1:1 104
Rw ¼
ln
¼
2 36 0:01859
W
2kw
Do 2t
Based on fouling factor Table E1A included in Appendix E, for treated cooling water with inhibitor
for velocity>1 m/s, typical fouling factor is 0.00018 m2K/W and for kerosene it is 0.00018 m2K/W.
4.7 Design illustration
115
Substituting the values in Eq. (3.3), the overall heat transfer coefficient is
1
1
0:00018 0:0254
0:0254
¼ 0:00018 þ
þ 1:1 104 þ
þ
U
1389:0236
0:01859
8020:8236 0:01859
¼ 1:4262 103
m2 K
W
or U ¼ 701:15 mW2 K, which is almost same as the assumed value. So design is Ok (no over design).
Using Kern’s method for pressure drop calculation, Dpt for tube-side fluid can be obtained from
Eq. (4.23) where ft can be obtained from Eq. (3.16a) for turbulent flow in tubes (with 5% tolerance) as
0:125
¼ 5:16 103
ft ¼ 0:0014 þ 0:125=ðReÞ0:32 ¼ 0:0014 þ
ð57031:24Þ0:32
Thus,
4ft Lp Np
1
4 5:16 103 6 2
þ8
þ 4Np ¼ 0:5 992:22 ð1:985Þ2 Dpt ¼ rt u2t 2
0:01859
Di
¼ 302.124 kPa ¼ 0.425 kg=cm2 < 0:7 kg=cm2 limit
For shell-side fluid, Res ¼ 30862:344 and since 400 < Res 106 , f from Eq.(4.25) is
f ¼ exp f0:576 0:19 lnðRes Þg ¼ exp f0:576 0:19 lnð30862:344Þg ¼ 0:2484.
L
6
¼ 24:5z25 and
For baffle spacing B ¼ 0:2445, number of baffles Nb ¼ ¼
B 0:2445
Nb þ 1 ¼ 26.
Since for two tube passes nozzles are on opposite side and ðNb þ1Þ is odd, we consider Nb þ 1 ¼ 27.
This gives pressure drop from Eq. (4.24) as
fs G2s ðNb þ 1ÞDs
0:2484 ð453:858Þ2 27 0:489
¼ 25912:134
¼
2 710 0:01836
2rs De
Pa ¼ 0.26 kg cm2 < 0.7 kg cm2 .
Dps ¼
So the pressure drop for both tube and shell side is within the maximum allowable pressure drop
specified in the problem.
For Ds ¼ 489 mm, the minimum bundle to shell clearance for easy pull out of bundle in case of
fixed tube is 10 mm from Table 4.11 and from Table 4.18, nominal nozzle diameter is 101.6 mm (400 ).
From Table 4.19, the nozzles are fabricated from Schedule 80 pipe with a corrosion allowance of
3 mm.
p
Nozzle cross sectional area Anozzle ¼ ð0:1016Þ2 ¼ 8:107 103 m2
4
And velocity of entering shell-side fluid through nozzle
ms
10:8472
¼
¼ 1:8844 m s.
710 8:107 103
rs Anozzle
This gives rs;in u2s;in ¼ 710 ð1:8844Þ2 ¼ 2521:287 mkgs2 .
This is slightly higher than the limit for noncorrosive, nonabrasive, single-phase fluid, 2230 mkgs2
impingement. However, for this design, impingement baffle is not included as the limit is exceeded
only by a small value.
We adopt single segmental baffle with 25% cut. As per IS 4503, from Table 4.14 for Ds > 400 and
700 and distance between adjacent baffles > 150 and 300, baffle thickness is 4 mm.
us;in ¼
116
Chapter 4 Shell and tube heat exchanger
From Table 4.11, minimum number of six tie rods with minimum diameter of 10 mm is required.
The thickness of the flat channel cover tchannel in mm is obtained from Eq. (4.33) as
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Ds C pdesign
489
0:25 7:8
þ 10 ¼ 17:2
þ Corrosion allowance ¼
tchannel ¼
10
9:5
10
fall;stress
fall;stress ¼ allowable stress value in kgf/mm2 at design temperature (¼ 9.5 kg/mm2, for plate
material as per IS 2002 Gr. I < 250 C), and C ¼ 0:25 as the cover is bolted with full faced gaskets.
Adopted standard plate thickness is 20 mm. Depth of pass partition grooves in channel cover is
5 mm and there should be a minimum thickness of 3 mm of base material.
Further mechanical detailing of the exchanger may be done referring to the code.
Nomenclature
Ae
Ao
B
C
Cp
CL
CTP
De
Dh
Di
Dn
Do
Ds
f
f all;stress
FT
G
hf
hi
ho
Kc
Ke
kw
L
Le
LIB
Lp
m
n
Nb
Nf
Np
Bundle cross flow area (m2)
Heat transfer area, i.e., effective tube outside area (m2)
Baffle spacing (m)
Gap between outer diameter of tubes perpendicular to flow direction (mm)
Specific heat capacity (W/kg C)
Fraction of shell cross-sectional area required to accommodate one tube ()
Factor to account for clearance required between shell and outermost tubes ()
Shell-side equivalent diameter defined in Eq. (4.12) (mm)
Hydraulic diameter (mm)
Inside diameter (mm)
Nozzle inside diameter (mm)
Tube outside diameter for unfinned tubes or root diameter in case of finned tubes (mm)
Shell inside diameter (mm)
Fanning’s friction factor for flow condition as decided by Reynolds’ number ()
Allowable stress value in kgf/mm2 at design temperature
LMTD correction factor ()
Mass flux (kg/s m2)
Fin height (mm)
Heat transfer coefficient inside tubes (W/m2 C)
Shell-side heat transfer coefficient (W/m2 C)
Loss coefficient associated with the flow area contraction ratio at inlet, bin ()
Expansion loss coefficient based on flow area expansion ratio at exit, be ()
Tube material thermal conductivity (W/m2 K)
Total tube length/length of core passage (m)
Net effective tube length available for contact by the shell-side fluid (m)
Length of impingement baffle (mm)
Tube length per pass (m)
Mass flow rate (subscript s for shell-side fluid and t for tube-side fluid, c for cold fluid
and h for hot fluid (kg/s)
Number of shell passes ()
Number of baffles ()
Number of fins per mm ()
Number of tube passes ()
4.7 Design illustration
117
Number of tubes ()
Nusselt number based on De and shell-side fluid thermal conductivity ks ¼ ho De
ks
Design pressure
Prandtl number of shell-side fluid ()
Tube pitch (mm)
Heat transfer rate (W)
Nt
NuDe
pdesign
Pr s
PT
Q
mC
T
T
h;out
R ¼ mhc Cp;c
¼ T h;in
p;h
c;out T c;in
()
Rd
Dirt factor
s
ReDe ¼ DeG
m
s
Reynolds number for shell-side flow based on equivalent shell diameter ()
Tube wall resistance
Rw
T
T c;in
S ¼ Tc;out
()
T
h;in
c;in
t
Tube wall thickness (mm)
tIB
Thickness of impingement baffle (mm)
tchannel
Thickness of the flat channel cover (mm)
T
Temperature ( C)
DT LMTD,counterflow Log mean temperature difference ( C)
TS
Tube sheet thickness (mm)
us
Shell-side flow velocity (m/s)
ut
Tube-side velocity (m/s)
us;in
Velocity of the entering shell-side fluid (m/s)
U
Overall heat transfer coefficient calculated from Eq. (3.3) (W/m2 C)
UD
Design overall heat transfer coefficient (W/m2 C)
W IB
Width of impingement baffle (mm)
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X ¼ ðR2 þ 1Þ ln fð1 SÞ=ð1 RSÞg
pffiffiffiffiffiffiffiffiffiffiffiffiffi
2 S R þ 1 ðR2 þ 1Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffi
Y ¼ ðR 1Þ ln
2
2S Rþ1þ
Dpc
Dpa
Dpe
Dpin
Dps
Dpt
ðR þ 1Þ
Core pressure drop
Pressure drop due to acceleration
Exit pressure loss
Entry pressure loss
Shell-side pressure drop excluding nozzle
Tube-side pressure drop excluding nozzle
Greek symbols
b
rm
rt
rs
rs;in
hp
ms
Flow area ratio with subscript ‘in’ and ‘e’ as contraction ratio at inlet and expansion
ratio at exit
Mean fluid density (kg/m3)
Average density of tube-side fluid (kg/m3)
Average density of shell-side fluid (kg/m3)
Density of the entering shell-side fluid (kg/m3)
Pump efficiency ()
Dynamic viscosity of shell-side fluid
118
Chapter 4 Shell and tube heat exchanger
Subscripts
c
e
h
in
out
s
t
Cold fluid
Expansion in passage area at exit
Hot fluid
Fluid inlet condition
Fluid outlet condition
Shell side
Tube side
Further reading
Kern, D. Q. (1997). Process heat transfer. Tata McGraw-Hill Education.
Ludwig’, E.E. Applied process design for chemical and petrochemical plants; Vol. 3. (3rd ed.). Gulf Professional
Publishing.
Serth, R.,W. (2007). Process heat transfer- principles and applications. Elsevier.
Shah, R. K., & Sekulic, D. P. (2003). Fundamentals of heat exchanger design. John Wiley & Sons.
Towler, G., & Sinnott, R. (2012). Chemical engineering design: Principles, practice and economics of plant and
process design. Elsevier.
CHAPTER
Heat exchanger network analysis
5
5.1 Introduction
In a process, there are streams that are required to be cooled. These are hot streams. Similarly there are
cold streams that are required to be heated. It is technically possible to meet all the heating and cooling
requirements in a plant by employing only hot utilities for the cold and cold utility for the hot streams.
Hot and cold utilities are the external sources of heating and cooling in a process plant and these
constitute a sizeable component of the operating cost. Hot utilities include steam at various pressures,
hot oil, fuel fired or electrical heating furnaces, etc. Common cold utilities are cooling water, ambient
air used in fin fan coolers, refrigerated brine and generation of steam in waste heat boilers, to name a
few. To reduce the utility costs and their requirement, the hot process streams may be used to heat the
cold process streams, wherever possible. One may note that the amount of heat thus exchanged between the hot and the cold streams reduces the requirement of both hot as well as cold utility by the
same amount.
A typical example illustrating the saving in energy by mutual heat exchange between process
streams is shown in Fig. 5.1. It presents a simple continuous distillation process which has hot streams
and cold streams that require cooling and heating, respectively. In Fig. 5.1A, heat is added to the feed
preheat exchanger (E1, 840 kW) and reboiler (E3, 8.7 kW) using steam as hot utility and heat is
removed from overhead condenser (E2, 2 kW), bottom product cooler (E4, 189 kW) and the distillate
cooler (E5, 87 kW) using cooling water as cold utility. Total hot and cold utility loads in this case are
848.7 kW and 278 kW, respectively. Keeping the process same, the heat exchange scheme is slightly
altered and presented in Fig. 5.1B. Here, the available heat from the column bottom hot stream at
105 C is utilised to preheat the cold feed stream from 30 C to 70 C by introducing a feed vs bottom
product exchanger (E6, 189 kW). The interchange of 189 kW heat within the process steams in E6
increases the inlet temperature of E1 from 30 to 70 C and there is a consequential reduction of its heat
load from 840 to 651 kW. Also the exchanger E4 becomes redundant as the heat removed by the same
is now utilised for heating the feed stream. An audit of the hot and cold utility load for this new scheme
shows the figures to be (8.7 þ 651 ¼ ) 659.7 kW and (87 þ 2 ¼ ) 89 kW, respectively. Thus the
requirement of both hot and cold utility in this scheme is lower by 189 kW, the quantity of heat exchange between the hot and cold streams in the process. The new heat exchange scheme is a network of
heat exchangers whose basic types and designs are covered in Chapters 2 to 4. Compared to the
previous scheme (Fig. 5.1A), this new scheme (Fig. 5.1B) has a lower operating cost due to lower
utility consumption but the net effect on capital cost needs to be assessed. It increases due to incorporation of E6, the new heat exchanger and reduces due to lower heat load of E1 and elimination of E4.
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00005-1
Copyright © 2020 Elsevier Inc. All rights reserved.
119
120
Chapter 5 Heat exchanger network analysis
There is a potential economic optimum from the balance of operating cost savings in utility reduction
and the effect of additional capital cost accrued.
(A)
(B)
E2 (2kW)
E2 (2kW)
E5 (87kW)
E5 (87kW)
CW
CW
96% Benzene
96% Benzene
87ºC
87ºC
40ºC
CW
E1 (840kW)
E6 (189kW) E1 (651kW)
Steam
Steam
50% Benzene
30ºC
40ºC
CW
50% Benzene
90ºC
30ºC
70ºC
90ºC
E3 (8.7kW)
E3 (8.7kW)
Steam
Steam
E4 (189kW)
E4 (–)
30% Benzene
105ºC
40ºC
105ºC
30% Benzene
CW
40ºC
FIGURE 5.1
(A) Continuous distillation process with no heat exchange between the hot and the cold process streams.
(B) Continuous distillation process with heat exchange between the hot and the cold process streams to
reduce consumption of utilities.
Several pairing options usually exist for thermal coupling between hot and cold streams, each of
which corresponds to an alternative (thermal) configuration of the process. Thus there are several
feasible solutions that multiply with the number of hot and cold streams involved in the process.
A formal procedure called ‘pinch analysis’ is used to choose the optimum among these alternatives.
The procedure analyses the possible heat exchanges in a system with several hot and cold streams and
brings out the thermal pairing of the process streams that minimises the total annualised cost, i.e. the
total of annual operating cost and the annualised fixed cost. This leads to the configuration of heat
exchanger network which provides the optimum combination between number of heat exchange units
and utility requirement. In the current era of energy crisis, this is an essential tool in arriving at the
design and retrofit configuration of plants that are (thermal) energy intensive like refineries, petrochemicals, steel plants, fertilisers, cement, pulp and paper etc.
Based on the laws of thermodynamics, the two laws of heat integration are
(1) The difference between the heat available in the hot streams and
the heat required for the cold streams is the net amount of heat
that must be removed or supplied.
Laws of Heat Integration
(2) Temperature difference must exist between the hot and the cold
streams for heat transfer to take place. In reality, a minimum
temperature difference (DTmin) between the heat exchanging streams is warranted to ensure a
practical size of the exchanger.
Both the laws are necessary and sufficient conditions for any heat exchanger network design.
5.2 Energy-capital trade-off e two-stream problem
121
5.2 Energy-capital trade-off e two-stream problem
Temperature (°C)
Based on the aforementioned laws, the scope of heat recovery can be determined by plotting the
streams on a temperatureeenthalpy (T H) graph. A two-stream problem or a process with one hot
and one cold stream is the simplest case. The cold stream is heated from a start temperature, TSc ð CÞ to
a target temperature, TTc ð CÞ by the hot stream that in turn cools from TSh ð CÞ to TTh ð CÞ in a
counter-current heat exchanger. Assuming a constant heat capacity flow rate [product of mass flow rate
_ p ] for both the hot (CPh) and the cold stream (CPc), one gets two
and specific heat capacity, CP ¼ Mc
lines1 as shown in Fig. 5.2. The temperature or enthalpy changes for the streams i.e. the slope of the
T H lines cannot be changed for a particular fluid but the relative position of the streams can be
changed by sliding either or both the curves parallel to the enthalpy axis in order to meet the specified
DTmin criteria. This is possible because the reference enthalpy of the two streams is independent of
each other. The region of overlap between the two streams determines the amount of heat recovery
(qrec) possible for the specified DTmin and utilities are necessary for the remaining portions, i.e. in
Fig. 5.2 cold utility is required to recover (q) amount of heat from the hot stream and hot utility is
required to supply (qþ) amount of heat to the cold stream.
TSh
TSc
TTh
qrec
q– Th,rec
TTc
Tc,rec
q+
Hot
stream
Cold
stream
Tc,rec
Th,rec
TSc
TTh
TTc
TSh
ΔTmin
q–
qh
qc
qrec
q+
Enthalpy (kW)
FIGURE 5.2
Heat exchanger example for a two-stream problem.
The amount of energy saving by the heat recovery process can be estimated as follows e The heat
required by the cold stream is
qc ¼ CPc ðTTc TSc Þ
(5.1)
and the heat available in the hot stream is
qh ¼ CPh ðTSh TTh Þ
1
(5.2)
This feature isPjustified for every practical process, with and without phase change. If the heat capacities vary significantly,
the nonlinear CPc line for a stream can be represented by a series of linear segments.
122
Chapter 5 Heat exchanger network analysis
Without any heat exchange between the hot and the cold streams, the annual cost of utility requirement
(Cop,annual) is computed from the unit cost of the hot and cold utility i.e. Ch, and Cc, respectively
multiplied by the hours of operation per annum (tann)
Cop;annual ¼ ðqh Ch þ qc Cc Þ tann
(5.3)
When the hot stream is used to preheat the cold stream, the corresponding energy savings in the
recovery heat exchanger (qrec) is obtained at the expense of an investment (Cex) which is a function of
the heat exchanger area (Aex) computed for a counterflow exchanger as
qrec
Aex ¼
(5.4)
Uex DTLMTDcounterflow
The above expression considers the LMTD correction factor (multiplier to DTLMTDcounterflow ) to be
close to unity. However the same may be incorporated, if multipass exchangers are used.
Following the nomenclature depicted in Fig. 5.2,
TSh Tc;rec Th;rec TSc
TSh Tc;rec
DTLMTDcounterflow ¼
(5.5)
ln Th;rec TSc
where Tc,rec and Th,rec refer to the respective exit temperatures of the cold and the hot streams from the
recovery exchanger.
Overall heat transfer coefficient (Uex) can be obtained from the convective heat transfer coefficient
for the cold (hc) and the hot fluid (hh) as discussed in Chapters 2e4.
The heat recovery (qrec) in Eq. 5.4 is limited by the approach temperature ðDTmin Þ, the temperature
difference between the hot and the cold stream in the exchanger. For constant heat load (qh and qc) of
the hot and cold streams, the energy savings of the hot utility is equal to the energy saving of the cold
utility and the maximum heat recovered is
qrec ¼ CPh ½TSh ðTSc þ DTmin Þ
(5.6)
þ
From Eq (5.6), a higher ðDTmin Þ results in a smaller (qrec) and (Aex) and a higher (q ) and (q ). This
is well evidenced from Fig. 5.2 as lower overlap (qrec) of the curves lead to greater extension of the
curves in the hot and the cold utilities regions.
Mathematically, the optimal ðDTmin Þ is obtained by adding the annual operating cost due to utilities
Cop, annual over a yearly operating time (tann).
Cop;annual ¼ ½Ch ðqh qrec Þ þ Cc ðqc qrec Þ tann
Optimal DTmin
(5.7)
to the annualised investment (Cex) estimate based on annual interest rate fraction
i over the expected lifetime of the plant in years (nex)
ið1 þ iÞnex
(5.8)
Cex ¼
aex ½Aex bex
ð1 þ iÞnex 1
The installed cost of heat exchanger is related to heat transfer area (Aex) by a power law relation
C ¼ aex ðAex Þbex
(5.9)
5.3 Multi-stream problem
and
CPh
CPh
CPh
3
2
ðTSh TSc Þ 1 ðDTmin Þ
þ
CPc
CP
CP
c
c
5
ln4
ðDTmin Þ
CPh Uex
123
1
Aex ¼
(5.10)
The annualised cost curves obtained from Eqs. 5.7 and 5.8 and the sum of both giving the total
annualised cost for heat recovery by a single exchanger is shown in Fig. 5.3. The figure shows that a
smaller ðDTmin Þ results in lower utility cost but the investment required is higher. When the approach
temperature is higher, the investment decreases while the operating costs increase. ðDTmin Þ is thus the
independent variable to determine the optimal size of the heat exchanger.
40
Annual cost
(106 Rs/yr)
30
Total annualised cost
20
Utility (operating) cost
Annualised
investment cost
10
Optimum
ΔTmin
0
0
10
20
30
40
ΔTmin (°C)
FIGURE 5.3
Effect of DTmin on utility and investment cost leading to DTmin;optimum .
5.3 Multi-stream problem
In order to obtain the overview of an actual process, the graphical approach needs to be extended to
several hot and cold streams. The solution begins with the stream specification table which lists the hot and the cold streams identified from the sign
of enthalpy change from an initial state. Format of the same is shown in
Composite Curve
Table 5.1.
124
Chapter 5 Heat exchanger network analysis
Table 5.1 Typical stream specification table.
Stream
No
Stream
type
(Hot/
Cold)
Supply
temperature
TS ð CÞ
Target
temperature
TT ð CÞ
Heat
capacity
flowrate
CPð [ Mcp Þ
DH ½ [ CPðTT LTSÞ Lve
for hot streams Dve for cold
streams
Conventionally, negative DH denotes surplus heat and a deficit is positive i.e. the cold and the hot
streams are associated with þve and eve DH, respectively.
Next, the temperature range is divided into a number of intervals defined by the supply and target
temperatures of the individual streams. Considering that it is feasible to exchange all the heat between
the hot and the cold streams, a composite T H curve is drawn for the hot streams (hot composite
curve) and also a similar curve for the cold streams (cold composite curve). For each curve, we start at
the lowest temperature (specified in the problem) and assign the enthalpy to be zero at that point; the
enthalpy change is calculated as a summation of the contributions from each stream present in
the interval. This is repeated for successive intervals with the start enthalpy of each interval being the
terminal enthalpy of the preceding interval. Likewise, for the hot composite curve, DHh;k in temperature interval of Tk1 to Tk, called the kth interval, is given by
X
(5.11)
DHh;k ¼ ðTk Tk1 Þ CPh;i
i
Subscript h,i denotes the hot stream number i in the kth interval. The same approach is used for
drawing
the cold composite curve whose slope in the kth interval is given by
P
CPc;i
. For constant CP values, the curves are linear in each interval and the
i
cεfcold streams in element kg
slope change occurs only at the start and end temperatures.
The hot composite curve thus represents a single stream equivalent to the individual hot streams in
terms of enthalpy and temperature. Similarly, the cold composite curve represents the individual cold
streams. When plotted on the same axes as shown in Fig. 5.4, it is analogous to plotting the single hot
and cold curve that can exchange heat using counter-current heat exchangers. The hot composite curve
must always lie above the cold composite curve for feasibility of heat transfer and the magnitude of
heat recovery is obtained from the region of overlap between the two composites.
The reference point for enthalpy is arbitrary for each curve and hence the relative position of either
or both the curves can be shifted parallel to the H axis in order to ensure that the minimum vertical
distance between the two curves is the specified ðDTmin Þ. Usually the cold composite is shifted. The
figure has the original cold composite curve in dotted lines and the same after shifting to its final
position is shown as a continuous line. The effect of lowering DTmin due to the shift is also apparent
from the figure and the corresponding magnitude of heat recovery (qrec) and the hot (qþ) and cold (q)
utility requirements are also marked.
5.3 Multi-stream problem
125
Hot composite
curve
Pinch
ΔTmin (original)
ΔTmin
T (°C)
Cold composite
curve (original)
Cold composite
curve (shifted)
q–
qrec
q+
H
FIGURE 5.4
Using the hot and cold composite curves to determine energy targets.
We note that the range of ðDTmin Þ is specified by maximum and minimum (zero) overlap of the two
curves. A reduction of ðDTmin Þ below the closest point of approach (minimum vertical distance between the composites) does not increase the amount of heat recovery. At the other extreme, the point of
zero overlap corresponds to zero heat recovery with all the heating and cooling provided by the
utilities. Within this range, the correct setting of ðDTmin Þ corresponds to an economic minimum
temperature difference. Similar to the two-stream case, this is decided by economic trade-off between
energy and capital cost.
Shifting the composite curves in the T-axis i.e. shifting up or down, is also possible. This would
physically mean that the stream supply and target temperatures are being changed by the same amount
and involves additional heating/cooling for the streams at the ends. Since the savings in utility is
decided by the overlapping region of the curves, these shifts are carried out to increase the heat recovery (qrec) for the network.
5.3.1 Optimal DTmin
Designing the heat exchanger network is targeted at minimising (i) utility requirements (ii) total heat
exchanger area and (iii) the number of heat exchangers to be provided. The first parameter relates to
the operating cost and the rest to the capital cost. Value of
these parameters in a heat exchanger network depends on
the ‘pinch temperature’ as already illustrated and there
Capital-Energy Trade-off in new Design
exists an economic optimum with respect to it. Calculation of these parameters is simple and a fair estimate can
be obtained well ahead of the detailed design. The designer aims at minimising the stated parameters in
order to approach the optimum design.
126
Chapter 5 Heat exchanger network analysis
In large process systems, e.g. in refinery crude preheat trains, there exist several options to match
the heat duties of the hot and the cold streams and the composite curves can be used to set capital cost
targets as well as energy targets to obtain an optimum value of ðDTmin Þ.
The minimum overall surface area (Amin) is computed by considering the area requirement in each
interval.
"
#
Xqi;k X
1
Amin ¼
(5.12a)
DTLMTD;k i hi;k
k
where qi,k and hi.k are the heat duty and heat transfer coefficient for stream i in the kth interval.
Eq. (5.12a) relies on estimates of heat transfer coefficients for individual streams. It is based on the
assumption of (i) heat exchange between the overlapping hot and the cold composite curves across the
entire enthalpy range (ii) negligible wall and fouling resistances in exchanger(s). This arrangement,
equivalent to pure counter-current flow within the overall network, gives the minimum total surface
area. However, employing multi-pass exchangers would result in “non-vertical” heat exchange between the streams. This is handled by incorporating LMTD correction factor (ðFT Þ) resulting in the
following expression
#
"
Xqi;k X
1
Amin ¼
(5.12b)
FT;k DTLMTD;k i hi;k
k
The minimum number of heat exchanger units (Nmin) in a process with total (S) numbers of process
and utility streams involved in heat exchange is given by
Nmin ¼ ðS 1Þ
(5.13)
It is important to note that Eq. (5.13) does not give the minimum number of units for (i) a trivial
case of no heat recovery, i.e. each stream is exchanging heat with a utility (hot/cold) and (ii) exact
matching of duties between hot and cold stream(s). However both these cases hardly occur in practice.
Minimising the network capital cost looks for minimising the total surface area as well as the
number of units in the network.
The capital cost of heat exchangers typically correlates with exchanger area in the power law form
with a bias as shown below
Cex ¼ a þ bðAex Þc
(5.14)
where a, b and c are constants for a given type of heat exchanger and Aex is the heat transfer area of the
exchanger. The minimum capital cost of the network, using average heat transfer area per shell for Ns
shells in Nmin exchangers may be expressed using Eq. (5.14).
The minimum operating cost can be considered to be the minimum annual utility cost that can be
estimated for a minimum utility design. The capital and the operating cost can be combined as
annualised cost by using a capital cost recovery factor. This cost can be minimised with respect to
DTmin to obtain the minimum total cost target and the optimum ðDTmin Þ within the feasible range ahead
of design. This is represented in Fig. 5.5. One may note that this is a generalised representation of the
two-stream case already discussed earlier and depicted in Fig. 5.3.
5.3 Multi-stream problem
127
Fig. 5.5(I) is based on the assumption that the hot and cold streams can match as long as the
temperature driving force is adequate. However, in reality, constraints do exist sometimes from
the considerations of safety, physical location of the two streams within the plant, etc. Therefore the
capital cost minimisation technique and ðDTmin Þ optimisation is particularly applicable for systems
with fewer constraints such as in atmospheric and vacuum distillation preheat trains, FCC unit, etc. in
the petroleum refineries. Some network design software like the KBC-Super Target has capital-energy
optimisation facility.
The influence of pumping cost, a component of the operating cost, on optimum design of network
has not been considered so far. This component of cost depends on the pressure drop in the heat
exchangers as discussed in Chapter 4. The capital cost for pumps and compressors can also be included
in the cost estimate of the network. Fig. 5.5 depicts the effect of neglecting pumping cost on the
optimum value of ðDTmin Þ. Typically the effect is to increase the DTmin;opt value by a small amount as
can be seen in the figure.
T
T
I
qrec
II
qrec
H
H
(A+B+C)
Cost
(A+B)
A
A = HE cost
B = Utility cost
C = Pumping cost
A+B+C = Total cost (with pumping)
B
C
I
ΔTmin, opt
Δ Tmin
III
FIGURE 5.5
Trade-off between utility and exchanger costs leading to minimum cost and the influence of pumping cost on
optimumðDTmin Þ.
5.3.2 Practical values of DTmin
Usually ðDTmin Þ is not less than 10 C in shell and tube exchangers. This requires pure counter-current
flow which is not possible even for single shell and single tube pass due to periodic cross-flow of the
shell side stream. In case of plate type heat exchangers, the value of DTmin can be w5 C and the same
128
Chapter 5 Heat exchanger network analysis
can be 1e2 C for plate fin designs. It is important to note that such constraints apply only to exchangers operating around the pinch point. Additional constraints apply if vaporisation or condensation is occurring at the point of closest approach.
Typical ðDTmin Þ values for various types of processes are presented in Table 5.2. Table 5.3 elaborates on the typical ðDTmin Þ used in retrofit targeting of various refinery processes and Table 5.4
provides ðDTmin Þ values for matching various utility levels and process streams. Utility loads at various
utility levels are introduced while respecting these ðDTmin Þ. The comments provide qualitative
explanation for choice of ðDTmin Þ.
Table 5.2 Typical ðDTmin Þ for various processes.
ðDTmin Þ value
conventionally
adopted ( C)
Sl No
Industrial sector
1
Refining
30e40
2
Petrochemical
10e20
3
Chemical
10e20
4
Cryogenic processes
Comments
heat transfer coefficient
· low
parallel composite curves
· near
· fouling service
heat transfer coefficient due to
· higher
lighter hydrocarbons
· lower fouling
e
heat transfer coefficient due to
· high
low viscosity
· clean fluids allow special exchangers
3e5
with low ðDTmin Þ
Table 5.3 Typical ðDTmin Þ for refinery processes.
ðDTmin Þ( C)
Process
CDU
30e40
VDU
20e30
General remarks
· near parallel composite curves
· wider composite curves compared to CDU but
lower heat transfer coefficients due to heavier
hydrocarbons
Naphtha reformer/
Hydrotreater
30e40
FCC
30e40
Gas oil hydrotreater/
Hydrotreater
30e40
Residue hydrotreater
40
· most of heat transfer in the network is in the feedeffluent exchangers that have parallel composite
curves and limits on DP
· similar to CDU and VDU
of heat exchange is in feed-effluent
· most
exchangers
pressure exchangers require large investment
· high
· separate target for high and low pressure section
e
5.4 Pinch design analysis
129
Table 5.4 Typical ðDTmin Þ for process-utility matches.
Sl No
Match
ðDTmin Þ( C)
1
Steam heating of process
stream
10e20
2
Refrigeration of process
stream
3e5
3
Flue gas heating of process
stream
40
4
Steam generation using flue
gas
25e40
5
Flue gas against air
50
6
Process stream cooling by
CW
15e20
Comments
· high heat transfer coefficient for
steam side
· refrigeration cost is high
· low heat transfer coefficient due to
flue gas
· good heat transfer coefficient for
steam side
· low heat transfer coefficient on
both sides due to air/gas
· depends on whether CW is
competing against refrigeration
Experience-based DTmin can provide practical targets for retrofit modifications since processes that
are similar have similar nature of the composite curves. This enables feasible selection of DTmin based
on experience. For example, in atmospheric distillation column, the composite curves tend to be
parallel to each other due to similarity of mass flow rate of feeds and products of distillation. However,
the selected DTmin based on experience should be backed up by quantitative information as much as
possible. This prevents straying away to non-optimal solutions.
5.4 Pinch design analysis
The minimum temperature difference point(s) between the hot and the cold composite curves on the
TeH graph is the heat recovery pinch point(s) and the corresponding
temperature difference is the pinch temperature DTmin . Normally there is
a single ‘pinch’ location. Exchangers closer to the pinch operate with
Heat Recovery Pinch
lower temperature difference between the hot and the cold stream and are
usually large and expensive. Therefore it is important to locate the pinch
and focus on optimum design of these exchangers.
5.4.1 Locating the pinch using the problem table algorithm
The composite curves can be used to locate the pinch point and set energy targets as already discussed.
Although they are useful in conceptualising the problem, the graphical procedure is often inconvenient
and cumbersome for large and complex networks. The problem table algorithm calculates energy
targets directly without the necessity of graphical construction and is therefore a more convenient
calculation tool.
The temperature interval is divided into sub-intervals for constructing the problem table. Fig. 5.6A
shows a situation when it is not possible to recover the entire heat in each temperature interval. In the
130
Chapter 5 Heat exchanger network analysis
temperature interval T3 to T5, the composite curves do not overlap and hence heat transfer is not feasible
in this temperature range. Relative slopes of the two curves in the specified interval govern the amount of
heat that can be recovered. This is overcome by shifting the hot composite curve lower by ðDTmin = 2Þ
than specified and the cold composite higher by ðDTmin =2Þ. This makes the shifted composite curves
touch at the pinch as shown in Fig. 5.6B. Heat balance between the shifted composite curves within a
shifted temperature interval is now possible since the hot streams are actually hotter than the cold
streams in each shifted temperature interval ðDTmin Þ. The vertical shifting eliminates the problem of
ensuring heat transfer feasibility within the temperature intervals but does not alter the horizontal overlap
between the curves, i.e. the extent of heat recovery and utility requirement remains unaltered.
(A)
Composite
curves
T→
T5
T4
T3
ΔTmin
T2
T1
H→
(B)
T→
Shifted
composite
curves
H→
FIGURE 5.6
(A) Composite curves with infeasible heat transfer in the interval T3 to T5. (B) Shifted composite curves with
feasible heat transfer in the temperature range.
5.4 Pinch design analysis
131
Based on the above discussion, the pinch point is estimated by the following methodology
1) The shifted temperature intervals ðDT Þ are set up from stream supply and target temperatures by
subtracting ðDTmin =2Þ from the hot stream and adding ðDTmin =2Þ to the cold stream
Thus for the hot streams
Th ¼ Th and for the cold streams
Tc ¼ Tc þ
DTmin
2
DTmin
2
(5.15a)
(5.15b)
2) In each shifted temperature interval, the heat deficit/surplus is calculated from energy balance
over the streams present in the interval
P
hX
i
CPc CPh DT (5.16)
DHk ¼
k
i
k
i
Tk is the temperature difference across the shifted interval, k numbered
where DTk ¼ Tðk1Þ
according to decreasing temperature level. As per Eq. (5.16), the intervals with positive DHk signify net heat deficit while a negative value denotes energy surplus.
3) The heat from each interval is then cascaded down the temperature scale such that the output from
each interval serves as the input to the nextlowerinterval. The heat output from any interval is the
input to the interval minus the heat deficit DH
k in that interval. Thus for the first interval,
since
there is no heat input, the output is DH1 and so on. While the deficit heat (positive DHk )
in any interval can be supplied by heat flow from the higher interval, this is infeasible for negative
DHk . Accordingly, negative heat flows need to be eliminated.
4) Provided there is only one hot utility and that is available above the highest temperature of the
streams, this is achieved by addition of the highest negative DHk at the top. It increases all the
heat flows down the temperature intervals without changing the heat balance within them and
results in zero heat flow at one T. This corresponds
point (Tpinch
hot
to thepinch ). Theactual DTmin
DTmin
and cold pinch temperatures are then obtained as Tpinch þ
and Tpinch ,
2
2
respectively.
A typical cascade diagram depicting how heat cascades through the temperature intervals is shown
in the Example problems. While the first cascade with no hot utility is consistent with the first law
requirement, the minimum heating and cooling loads have been fixed to satisfy the second law.
5) The highest negative DHk thus gives the minimum amount of hot utility to be added to the
cascade and the minimum cold utility usage is given by the heat flow out of the lowest (coldest)
shifted temperature interval.
132
Chapter 5 Heat exchanger network analysis
5.4.2 The pinch principle
The pinch design method splits the problem into two independent designs e a hot section design and a
cold section design. Hot section comprises of all streams or parts of
streams hotter than the hot pinch temperature. This involves only
process exchange and utility heating. All streams or parts of streams
Significance of the Pinch
below the cold pinch temperature belong to the cold section where
only process exchange and utility cooling may be involved. Thus no
heat transfer occurs across the network pinch temperature. This is valid provided no heat exchanger
has a temperature difference lower than ðDTmin Þ and ensures minimum achievable requirements of
both utilities.
To summarise, the necessary and sufficient conditions to achieve minimum utility consumption
targets for a process are
•
•
•
No heat transfer across the pinch temperature
No use of cold utility above the pinch
No use of hot utility below the pinch
The logic behind this can be explained as follows
Any heat transferred (say x kW) from above to below the pinch must have been supplied from hot
utility in addition to the minimum requirement. Enthalpy balance below the pinch shows that this heat
transfer also increases the cold utility above the minimum required by the same amount. Any heat
transfer across the pinch therefore doubles the total utility load in the network. This is somewhat
similar to a situation in a distillation column where any additional heat (beyond the minimum boil up
requirement) added to the reboiler will lead to additional condenser cooling load.
In real life complex network designs, exchangers and utility heaters and coolers will almost
inevitably be placed in positions which violate the pinch. This results in using more than the minimum
amount of both hot and cold utility. For retrofit applications, equivalent arguments apply and the design
procedure ‘corrects’ the exchangers which are ‘at fault’, i.e. violate the pinch principle and prevent a
minimum utility design. Often such retrofit in crude preheat exchanger trains in petroleum refineries
lead to increase in crude preheat temperature at the crude heater (furnace) inlet and results in saving in
fuel (hot utility).
5.4.3 Design strategy
Design for the hot and the cold sections start from the pinch around which the restrictions on the stream
matches are maximum. The two problems are then solved independently.
Key to the pinch design method lies in identifying appropriate
stream matches for exchangers operating at the pinch. The three
feasibility criteria for matching the streams are listed in
Feasibility Criteria at the Pinch
Table 5.5. These not only identify appropriate stream matches
but also reveal the need for stream splitting.
5.4 Pinch design analysis
133
Table 5.5 Feasibility criteria for stream matches at the pinch.
Criteria
Reasoning
1) Nout Nin
this implies
Nh Nc ðhot sectionÞ
Nh Nc ðcold sectionÞ
For minimum utility design, since coolers are not allowed above the pinch,
each hot stream in the hot section (above the pinch) must be brought to the
pinch temperature by heat exchange with a cold process stream.
The same logic applies to the cold section (below the pinch) problem.
2) CPout CPin
0CPh CPc ðhot sectionÞ
0CPh CPc ðcold sectionÞa
Since ðDT ¼ DTmin Þ at the pinch, violation results in ðDT < DTmin Þ at the
other end of the exchanger.
3) For any exchanger operating at
the pinch ðDCP DCPov Þ
where
DCP ¼ CPc CPh
X
X
DCPov ¼
CPc CPh
For one exchanger with ðDCP > DCPov Þ, there has to be another
exchanger with negative DCP that violates criteria (2).
The summation is taken over
only those streams that intersect at the pinch
a
It is important to remember that the CP inequality applies only when a match is made between two streams both at the pinch. This
ensures exchangers operating near the pinch have a temperature difference equal to ðDTmin Þ at least on one side. It is not essential
to obey the CP inequality for matches not adjacent to the pinch.
A CP table is used for identifying feasible pinch matches for the hot and the cold section
Pdesign.
This table lists the hot streams followed by the cold streams. The sum ( CP) is
entered below each column. Each table includes only those streams that intersect the
pinch. The feasibility criteria are mentioned on the top as a reminder. Table 5.6
CP table
presents the typical CP table format.
Table 5.6 A typical CP table format for hot/cold section design.
CPh £CPc ðhot sectionÞ Nh £Nc ðhot endÞ
CPh ‡CPc ðcold sectionÞ Nh ‡Nc ðcold endÞ
Stream no.
Hot
Cold
Stream no.
H1
C1
H2
C2
.
.
.
.
.
.
P
CPh ¼
.
P
CPc ¼
.
Total
134
Chapter 5 Heat exchanger network analysis
5.4.4 Grid diagram
A grid representation is used to depict the network, whether new or retrofit. It shows the stream data
and the pinch location. It is used for adjusting the heat transfer
matches between the cold and the hot streams. The hot section
lies to the left and the cold section to the right of the pinch
Grid representation of the Network
temperature as shown in Fig. 5.7. Grid diagrams have hot
streams at the top that run left to right from their supply to
target temperatures. Cold streams are placed below the hot streams and run counter-current. The hot
pinch and the cold pinch temperatures determined from the problem table/composite curves are
marked by vertical dashed lines dividing the diagram into two parts. DTmin is the difference between
the hot and cold pinch temperatures. Process exchangers are represented by circles on the two matched
streams joined by a line. Heater on a cold stream and cooler on a hot stream are shown as single circles
marked with H and C, respectively.
HOT SECTION
Tpinch
COLD SECTION
E3
E1
H1
TS1
TT1
E2
E4
Cooler
H2
TS2
TT2
C
ΔTmin
Heater
TT3
TT4
C1
H
TS3
C2
TS4
FIGURE 5.7
Grid diagram for tick off heuristics.
Tick off heuristic
After identifying the appropriate stream matches, the duty to be assigned to each exchanger is estimated from the “tick off heuristic” which states that the minimum number of units can be obtained if
each exchanger brings one stream from its supply to target temperature or exhausts a utility. The
exhausted stream is ticked off and matches are made for the remaining streams. For process exchangers operating at the pinch, the duty can be taken as the lower of the two-stream duties as the CP
inequality ensures an adequate temperature difference.
Once the matches are made at the pinch, the remaining problem can be solved with greater flexibility since the feasibility criteria need not be satisfied away from the pinch. Other factors like process
constraints, plant layout, controllability and engineering judgement are used to make suitable matches.
Safety is an overriding consideration in all stream matches, including those at the pinch.
5.4 Pinch design analysis
135
The design is completed by satisfying heating and cooling duties by utilising utilities away from
the pinch. A complete network is obtained by joining the hot and cold section configurations at the
pinch as shown in Fig. 5.7 and demonstrated in the design problems. Usually there are more than one
solutions for a real life problem.
While the tick off heuristic ensures minimum number of units, it does not necessarily guarantee
minimum utility requirement. In fact, it can sometimes result in excess utility, leading away from
minimum utility design. Utilisation of excessive temperature difference in pinch exchangers, leaving
too little driving force for exchangers elsewhere in the network may lead to this. If this arises, a
different set of pinch matches can be tried or the duty on the pinch exchanger can be reduced leading to
more than the minimum number of units.
5.4.5 Stream splitting in network design
We are faced with a problem if the number of streams approaching the pinch is more than the number
coming out or (Nin > Nout). This violates feasibility criteria 1 in Table 5.5 for the region around the
pinch and each stream approaching the pinch cannot be matched with an outgoing stream to bring it to
the pinch temperature. Stream splitting is necessary in this situation to equate Nout and Nin. It is
important to remember that during stream splitting, the CP inequality rule cannot be violated.
Stream splitting is also required for matches that do not comply with criteria 2 even if they obey
criteria 1. In this case, we could split an incoming stream to reduce its CP.
The stream splitting procedure during network design is shown in Fig. 5.8.
Start
Consolidate information
on N and CP
Nout ≤ Nin
No
Split incoming stream
No
CPout ≥ CPin
for every match
Yes
Place matches
Stop
FIGURE 5.8
Stream splitting procedure.
Yes
Split outgoing stream
136
Chapter 5 Heat exchanger network analysis
5.4.6 Network simplification: heat load loops and heat load paths
In practice, the resulting network is usually complex and can be further simplified and capital-energy
optimisation can be carried out. Heat load loops and heat load paths leave scope for the designer to
simplify the network or to reduce the overall network cost.
Heat load loops are closed pathways in a system of connections in a HEN and usually arise when
two heat exchangers (one below and one above the pinch) are placed across the same pair of streams.
In this case, one of the exchangers can be eliminated by shifting duties around the loop without
affecting the heat duties on other units that do not belong to the loop. However, such a change will
affect the temperature driving forces in the network. The temperature driving force may become less
than DTmin in some cases, resulting in temperature infeasibility. This implies that some energy flow
across the pinch may be necessary to obtain a practical network design.
A heat load path eliminates DTmin violation that may arise during network simplification by
providing a continuous pathway between a utility heater and a utility cooler. This leads to transfer of
heat loads between heat exchanger units and utilities. Heat loads can be shifted along a path by
alternately adding and subtracting a duty from each successive unit. This procedure does not affect
stream duties but changes intermediate stream temperatures due to change in exchanger duties.
Some commercial software e.g. SuperTarget from M/s KBC can do the optimisation using heat
load loops as well as heat load paths.
5.5 Targeting for multiple utilities
The composite curves in Figs. 5.4 and 5.9A indicate the requirement for the extreme utility levels e
hot utility at temperature higher than the supply temperature of the hot
stream(s) and cold utility cooler than the cold stream(s). However, in
practice the plant utilities are available at several different temperature
Grand Composite Curve
levels e.g. furnace flue gas, steam levels, hot oil circuit, cooling water,
refrigeration levels, etc. The general objective is to maximise the use of
the cheaper utilities and conserve the expensive utility. For example, it
is preferred to use LP steam instead of HP steam and cooling water instead of refrigeration. These can
be incorporated in the composite curve as shown in Fig. 5.9B which shows the construction of the hot
composite curve if we use LP steam to replace part of the HP steam requirement. The maximum LP
consumption that can replace the HP steam consumption is obtained for a temperature difference of
ðDTmin Þ between the composite curves. It can be seen that the shape of the composite curves change
with addition of every new utility level and the overall construction becomes complex for several
utility levels. Such a curve is commonly termed as grand composite curve.
The Grand Composite Curve is also a convenient tool for setting multiple utility targets. It is a plot
of adjusted heat flow ðDH Þ computed from Eq. (5.16) versus shifted temperatures Th and Tc of the
hot and cold streams. The points to be plotted are obtained from the Problem Table. Fig. 5.9C illustrates the construction of the grand composite curve from the enthalpy (horizontal) differences between the shifted composite curves (shown by distance DH in the figure) at different temperature
levels. The two end points of the curve give the minimum hot and cold utility requirement where HP
steam is used for heating and refrigeration is used for cooling the process.
5.6 Design algorithm
137
Fig. 5.9D shows the construction when we introduce intermediate utilities, namely LP steam and
cooling water (CW). A horizontal line at the LP steam temperature level starting from the vertical
(shifted temperature) axis and touching the grand steam composite curve denotes the LP steam
quantity. HP steam satisfies the balance heating duty. This maximises LP steam consumption prior to
use of HP steam and thus minimises the total utilities cost. Similar construction can be performed
below the pinch to maximise the use of cooling water for minimum use of refrigeration.
It is important to note that the horizontal lines indicating different utility levels should be drawn at
the appropriate shifted temperature levels and not at their actual temperatures, i.e. a hot utility is
indicated by a horizontal line at its temperature reduced by ðDTmin =2Þ and a cold utility at its temperature increased by ðDTmin =2Þ.
Thus the construction of the grand composite curve automatically ensures a minimum temperature
difference ðDTmin Þ between the hot and cold process streams (at the process pinch marked in the
figure) as well as between utilities and process streams.
“Utility Pinches” are the points where the LP and CW levels touch the grand composite curve in
Fig. 5.9D. Cross-utility pinch heat flow results in reducing heat load from a
cheaper utility level and adding it to a more expensive utility level. As discussed
earlier, violation of a process pinch also results in heat load penalty for the
Utility Pinch
utilities.
A grid diagram involving multiple utilities should include all utilities so as to
have a network that is balanced with respect to enthalpy.
5.6 Design algorithm
Input data
•
•
•
Process stream heating and cooling information
- Process stream start and target temperature TS ð CÞ & TTð CÞ
- Stream enthalpy change ðDHÞ or product of mass flow rate and heat capacity (CP)
- Stream heat transfer coefficients for heating and cooling streams (hi)
Utility system information
- Available utility (e.g. refrigerant, CW or steam system)
- Existing utility levels (e.g. steam header pressures, refrigeration level temperatures, etc.)
- Existing utility loads in case of retrofit problems e to assess potential savings
- Utility system constraints (such as maximum or minimum permissible flows)
- Plans regarding future investment in the utility system (e.g. plan for a new gas turbine or
cogeneration)
Cost information to identify economically attractive projects.
- Fuel and power tariff structure
- Cost of various utility levels e.g. cost of LP steam, HP steam, etc.
- Cost laws for heat exchangers (cost as a function of heat transfer area)
- Investment criterion (e.g. minimum acceptable pay-back period, etc.)
138
Chapter 5 Heat exchanger network analysis
(A)
(B)
HP
steam
HP
steam
Hot
composite
curve
T
T
Cold
composite
curve
LP
steam
Hot
composite
ΔTmin
ΔTmin
curve
Cold composite
curve
CW
CW
H
H
(C)
(D)
HP
steam
HP
steam
Grand composite
curve
T*
TLP*
LP steam
Utility pinch
Grand composite
curve
T*
Process pinch
Refrigeration
Δ H*
Tcw*
CW
Utility pinch
Refrigeration
Δ H*
FIGURE 5.9
Using Composite and Grand Composite Curve for Multiple Utility Targeting: (A), (B) Composite for single and
multiple utility targeting; (C), (D) Grand Composite for single and multiple utility targeting.
•
General process and site information to verify that the proposed scheme can be realistically
implemented.
- Key objective behind the study (e.g. energy saving, de-bottlenecking, etc.)
- Specific process constraints that need to be observed, if any
- Plant layout information (e.g. distances between key process units, etc.)
- Site-wide utilities constraints (e.g. hardware or space limitations)
5.7 Threshold problems
139
Deliverables
(a) Targets for energy saving in a process
- Potential saving in process fuel demand
- Potential saving in utility levels (e.g. replacing HP steam with LP steam use)
- Potential power savings or scope for power generation (e.g. power saving in refrigeration
system)
- Additional energy saving due to process modifications (e.g. change in the reactor
temperature, change in distillation column pressures, etc.)
(b) Targets for energy savings at site-wide level
- Potential savings in site-wide fuel demand and changes in co-generation with existing central
utility system.
- Potential benefits in fuel or co-generation due to the central utility system modifications (such
as introduction of new steam mains, changes in steam mains pressure, etc.)
(c) Capital cost targets for a process
- Approximate investment in the heat exchanger capital to achieve the targeted energy savings,
applicable for certain processes.
(d) Targets for pay-back period (economic analysis).
For certain applications (e.g. crude preheat train) it is possible to estimate approximate pay-back
period as a function of targeted energy savings.
Steps of design
a) Develop a Minimum Energy Requirement (MER) network
• Extract data from simulation, plant operations or design specification sheets and prepare
stream specification Table (Table 5.1). This involves the data extraction from the heat and
material balances of the process. The data should be consistent.
Divide problem at the Pinch
• Start at the pinch and move away
• Start with biggest stream “IN”
• Observe CPOUT CPIN, splitting streams where necessary following Fig. 5.8
• Place all pinch matches first
• Maximise loads on all pinch matches to minimise number of units (“tick-off” heuristics)
• Fill in the rest
• Merge hot end and cold end design
b) Evolve the MER network for network simplicity and capital-energy trade-off
• Analyse and act on heat load loops and heat load paths
c) Estimate further reduction of operating cost by (i) replacing high cost utility by lower cost ones
(e.g. high pressure steam with low pressure steam, refrigerant with cooling water, etc.) e using
grand composite curve and (ii) process modification
5.7 Threshold problems
In any problem, a pinch does not occur if ðDTmin Þ is below a threshold value ðDTthreshold Þ. Such
problems are called “threshold problems”. These can be understood from the composite curves
presented in Fig. 5.10. In Fig. 5.10A both hot and cold utility are required but as the composite curves
are moved closer to each other, the requirements of both utilities decreases until at
140
Chapter 5 Heat exchanger network analysis
ðDTmin Þ ¼ ðDTthreshold Þ, the composite curves are aligned at the hot end, indicating zero demand for
hot utility. The situation is depicted in Fig. 5.10B. Moving the curves still closer (Fig. 5.10C) decreases
the cold utility demand at the cold end but opens up a new demand for the same utility at the hot end,
the decrease at the cold end being equal to the new demand at the hot end. Thus the utility usage
is the same for ðDTmin < DTthreshold Þ There can be analogous cases where the cold utility disappears at
the end for ðDTmin Þ ¼ ðDTthreshold Þ.
(A)
(B)
(C)
T
T
Hot utility
T
Cold
utility
Cold
utility
Cold
utility
Cold
utility
H
H
H
FIGURE 5.10
Composite curves for threshold problems: (A) Both hot and cold utility required for ðDTmin > DTthreshold Þ
(B) No hot utility for ðDTmin ¼ DTthreshold Þ (C) Cold utility requirement at both ends for ðDTmin < DTthreshold Þ.
5.8 Data extraction
Data extraction for real plants involve several alternative sets of data as most plants are designed to
cater to different modes of operation e.g. operation on low and high purity feedstock. A comprehensive
view is required for proper extraction of data. Few related issues are discussed in the following sections
to serve as guidelines.
5.8.1 Composite curve for non-linear CP
To apply the method of composite curves when the stream enthalpy varies non-linearly with temperature, e.g. phase change of multicomponent vapours, the curve is approximated by a set of linear
segments for which the CP values differ as shown in Fig. 5.11.
Single conservative values of CP for each linear segment is
used
to closely mimic the “actual” hot and cold composite
Composite curve for non-linear CP
curves. It is safer to consider a linearisation where the composite stream temperature is underestimated. In case of the hot
composite curve, no portion of the linearised segment should be at a higher temperature than the actual
5.8 Data extraction
141
stream. With the same logic, a safely linearised cold composite curve should not allow the temperature
to be below the actual stream temperature.
To summarise
•
•
The actual hot stream must be hotter than the linearised hot stream
The actual cold stream must be colder than the linearised cold stream
Fig. 5.11 shows the safe linearization results for the composite curves.
T
Actual
Linearised
H
FIGURE 5.11
Stream linearisation to remain on the safe side.
5.8.2 Avoid mixing of streams at different temperatures
Sometimes mixing of process streams at different temperatures is shown on flowsheets where the
mixing junction appears as a direct contact heat exchanger. Let us consider streams 1 and 2 at temperatures T1 and T2 shown on a flow sheet to mix and result in temperature T3 (T1 > T3 > T2) before
being utilised. Then the data extraction should consider the start and target temperature of the streams
to be (T1, T3) and (T2, T3), respectively, and isothermal mixing of the streams should be contemplated
at T3. In addition, if any of the streams has passed through one or more exchangers before attaining T1
or T2, then the temperature of the streams upstream of the exchanger(s) should be considered as its start
temperature.
5.8.3 Use effective temperatures
As an example, for a cold stream changing phase from sub-cooled state, the effective temperature
driving force must consider the driving force due to sensible as well as latent heat transfer.
142
Chapter 5 Heat exchanger network analysis
5.8.4 True utility streams
A true utility stream i.e., steam, cooling water, refrigerant, etc., is one that can in principle be replaced
by any other stream (process or utility) for heat exchange purposes. Some streams like the live stream
used for stripping in strippers that provide energy as well as reduce the partial pressure in the column
are to be treated as process streams. Live stripping stream is not considered as ‘true’ utility as it cannot
be replaced with any other thermal fluid supplying the heat.
5.9 Applications
In a nutshell, the applications of pinch technology are
(a) Improvement of energy efficiency of a system/process
(b) Process debottlenecking where utility system is the main bottleneck by reducing utility
consumption and providing additional scope for increasing production.
(c) Significant reduction in process water demand and waste
water generation via improved re-use of water within the
process
Importance of Pinch Analysis
(d) For low temperature processes, pinch technology in
combination with energy analysis allows the designer to
assess the impact of various design changes on refrigerator power consumption
5.10 Design illustration
Problem 5.1. A chemical process involves 4 streams, the details of which are provided in Table P5.1A
(the last column in the Table refers to heat Transfer Coefficient).
Design the optimum heat exchanger network when (a) hot utility, high pressure steam and cold
utility, refrigerated brine are available at 220 and 12 C, respectively. (b) Utilisation of utilities at
multiple levels is suggested to reduce operating cost. Consider that the cheaper utilities e MP steam
and cooling water are additionally available at 170o C and at 35o C.
Table P5.1A Stream details.
Stream no.
Type
TS ( C)
TT ( C)
CP ¼ mCp (kW/ C)
h (kW/m2 C)
1
Hot
180
40
2.0
h1
2
Hot
150
40
4.0
h2
3
Cold
60
180
3.0
h3
4
Cold
30
105
2.6
h4
HU
Hot utility
220
e
e
hh
CU
Cold utility
12
20
e
hc
5.10 Design illustration
143
Solution (A)
It is assumed that the heat exchangers involved are shell and tube type with counter-current flow
(FT ¼ 1) and DTmin is adopted as 20 C based on the information in Table 5.2 for chemical industry.
From the aforementioned data, the stream specification table is constructed as shown in Table P5.1B.
Table P5.1B Stream specification table.
TS( C)
TT
( C)
CP
(kW/
C)
DH (kW)
TS [
TSLðDTmin =2Þ
for hot stream
TS [
TSDðDTmin =2Þ
for cold stream
( C)
Hot
180
40
2.0
280
170
30
2
Hot
150
40
4.0
440
140
30
3
Cold
60
180
3.0
þ360
70
190
4
Cold
30
105
2.6
þ195
40
115
HU
Hot
utility
220
e
e
CU
Cold
utility
12
e
e
Stream
no.
Type
1
TT [
TTLðDTmin =2Þ
for hot stream
TT [
TTDðDTmin =2Þ
for cold stream
( C)
The pinch point can be located either by using the ‘problem table algorithm’ or graphically by construction of composite curves
(Section 5.4.1).
Composite curves
Fig. P5.1A shows the composite curves. The hot and the cold curves are drawn as already outlined
in Section 5.3. The cold composite curve is shifted along the enthalpy axis to create the minimum
temperature difference (minimum gap between the curves parallel to the temperature axis) of
DTmin ¼ 20 C. The shifted composite curves are shown as dotted lines that are drawn by lowering
the temperatures in the hot composite curve by DTmin =2 and increasing the temperatures in the cold
composite curves by the same amount i.e. DTmin =2. The shifted curves now touch at 140 C, which
is read off as the pinch temperature. The hot and the cold pinch temperatures are noted to be 150oC
and 130 C, obtained by adding and subtracting DTmin =2 (¼10 C) to the pinch temperature,
respectively.
144
Chapter 5 Heat exchanger network analysis
200
180
Tpinch (140°C)
T (°C) →
160
140
Hot composite
120
Shifted
composite
curves
100
80
Cold composite
60
40
20
0
100
200
300
400
500
600
700
800
900
H (kW) →
FIGURE P5.1A
Composite curves and shifted composite curves for DTmin ¼ 20 C.
Problem table algorithm
Table P5.1C shows the temperature interval heat balance as well as the problem table heat cascade.
The surplus/deficit heat in each temperature interval is calculated first. With ‘0 kW’ heat supplied at
the highest temperature, the heat leaving the highest temperature interval and entering the next lower
temperature interval is found by subtracting the DH1 (þ60 kW) from the heat entering the interval
(‘0 kW’) at its higher temperature. This heat (-60 kW) cascades and enters the second interval and the
heat leaving the second interval ( 60 30 ¼ 90kW) is calculated in the same way. This is
continued for the rest of the intervals. In this problem (90) kW is the highest magnitude of heat that
cascades down to a lower temperature with hot utility of ‘0’ kW. Therefore, in the next column the heat
cascade figures are altered by adding hot utility of 90 kW at the top. This result in no heat transfers
across the temperature of 140 C in the network and establishes the same as the process pinch. The cold
utility requirement in the network is the 255 kW leaving the lowest temperature interval.
Thus we see that whether the problem is solved by composite curve method or by the problem table
method, the result is the same. i.e. the pinch point is 140 C and the hot and cold pinch temperatures are
150 and 130 C, respectively. One may note that the problem table algorithm is more elegant and is
easily implementable as a computer program. Therefore large problems involving several streams are
normally solved by this method.
5.10 Design illustration
145
Table P5.1C Temperature interval heat balance and problem table cascade.
(∑CPC – ∑CPH)
∆Hinterval
Surplus/
Deficit
3
+60
Surplus
190°
20°
1
170°
40°
+60
+60
CP = 2
+30
Surplus
+30
90
–3
CP = 3
25°
–75
Deficit
–75
–15
3
–0.4
45°
CP = 2.6
70°
1
2
CP = 4
T*
115°
+90 kW
HU
–60
30°
140°
‘0’ kW
HU
–18
Deficit
–18
+3
–3.4
30°
–102
Deficit
–102
+105
4
–6
10°
–60
Deficit
–60
+165
kW
30°
+30
+30
0
–75
+75
–18
+93
–102
+195
–60
+255
kW CU
Tpinch = 140°, Th,pinch = 140 + 20/2 = 150°C
Tc,pinch = 140 – 20/2 = 130°C
QHU = 90 kW, QCU = 255 kW
After estimation of Tpinch, the entire temperature interval is divided into the hot section above the
pinch temperature and the cold section below the pinch temperature. In the hot section, the hot streams
terminate at Th, pinch while the cold streams originate from Tc,pinch and in the cold section, the cold
streams terminate at Tc,pinch while the hot streams originate from Th,pinch.
The tick off heuristics (Section 5.4.4) is employed to generate the grid diagram for the hot and cold
section. Since feasibility criteria for stream matches at the pinch as per Table 5.5 i.e. (Nout ¼ Nin) and
(CPout CPin) is satisfied, stream splitting is not required. The CP table shows that criteria 3 of
Table 5.5 is satisfied as can be seen from Table P5.1D.
Table P5.1D CP table for hot/cold section.
CPh £CPc ; Nh £Nc ðhot sectionÞ
CPh ‡CPc ; Nh ‡Nc ðcold sectionÞ
Stream no.
Hot
1
2.0
2
4.0
.
.
Total
Cold
Stream no.
.
3.0
1
.
P
CPh ¼ 6
2.6
P
CPc ¼ 5.6
2
146
Chapter 5 Heat exchanger network analysis
Tick off heuristics – Cold Section
150°C
220 kW
1
C
40°C
101∙25°C 48∙75°C 35 kW
150°C
2
40°C
C
195
kW
130°C
210
kW
60°C
3
30°C
105°C
4
S = 4+1 = 5, Nmin = 4 (Eq. 5.13)
Nactual = 4
Tick off heuristics – Hot Section
180°C
150°C
1
90 kW
180°C
60 kW
130°C
150°C
H
3
S = 2+1=3, Nmin = 2 (Eq. 5.13)
Nactual = 2
FIGURE P5.1B
Grid diagram for the cold section and hot section using tick off heuristics.
Combined network – Maximum energy recovery
– Minimum no. of units
Pinch
150°
180°C
40°C
1
C
150°C
180°C
150°C
101.25°C 48.75°C
220 kW
40°C
2
C
130°
35 kW
60°C
H
3
90 kW 60 kW
210 kW
105°C
30°C
4
195 kW
FIGURE P5.1C
Grid Diagram for combined Network Design.
5.10 Design illustration
147
One may note that for the 210 kW HE between stream 2 and 4 in the cold section, DTmin ¼ 20 C is
not respected. However, this exchanger operates away from the pinch temperature and the temperature
difference is above 10 C, which is acceptable for such services.
Another alternate network design is shown in grid diagram form in Fig. P5.1D. We note DTmin
condition is marginally violated in E1 but it eliminates the requirement of a cooler on stream 2 and also
reduces the heat load on the heater on stream 3. Thus it alters the capital and operating costs at the cost
of cross pinch heat transfer.
180°C
CP = 2
1
60 kW
150°C
E1
220 kW
40°C
C
195 kW
150°C
E2
2
180°C
245 kW
101.25°C
55 kW
161.67°C
E1
H
CP = 4
40°C
E3
CP = 3
141.67°C
E3
3
CP = 2.6
105°C
60°C
E2
30°C
4
Th, pinch = 150°C
Tc, pinch = 130°C
Tpinch = 140°C
FIGURE P5.1D
Grid Diagram for combined Network Design e alternative 1.
Another alternate design respecting DTmin ¼ 20 C across all exchangers is shown in Fig. P5.1E. It
has two cross-pinch heat transfers and has increased the cold utility requirement on stream 1 from 220
to 255 kW.
180°C
1
25 kW
255 kW
E1
C
CP = 2
40°C
195 kW
245 kW
101.25°C
CP = 4
E2
E3
150°C
2
180°C
90 kW
150°C
E1
H
CP = 3
141.67°C
E3
CP = 2.6
105°C
E2
40°C
60°C
3
30°C
4
Th, pinch = 150°C
Tc, pinch = 130°C
Tpinch = 140°C
FIGURE P5.1E
Grid Diagram for combined Network Design respecting DTmin ¼ 20 C and cross-pinch heat transfer for
streams 1 and 3.
148
Chapter 5 Heat exchanger network analysis
Area requirement: The area required for each exchanger can be estimated if the numerical values of
the heat transfer coefficients in the last column of Table P5.1A are available. The procedure for area
calculation is provided in Chapter 4.
Solution (B)
Considering multi-level utilities e HP and MP steam are available at 220 and 170 C, respectively,
and cooling water is available at 30 C.
We use the grand composite curve to estimate utility consumption at different levels. As described
in Section 5.5, the grand composite curve is constructed with ordinate T and abscissa as the DH crossing the corresponding T. The values of ordinate and abscissa are obtained in problem table
cascade (Table P5.1C) and are reproduced in Table P5.1E. The grand composite curve is obtained by
joining the consecutive points in Table P5.1E by straight lines as shown in Fig. P5.1F. The figure shows
that the total hot utility requirement is 90 kW, out of which a maximum of 20 kW can be provided by
MP steam at T ¼ 160 C (corresponding to T ¼ 170 C) and similarly out of the cold utility
requirement of 255 kW, a maximum of 195 kW can be provided by cooling water at T ¼ 40 C
(T ¼ 30 C), thus reducing the brine refrigerant requirement to 60 kW).
Table P5.1E T and DH crossing the corresponding T.
T ( C)
190
170
140
115
70
40
30
DH (kW)
90
30
0
75
93
195
255
90 kW
70 kW
HP Steam
200
180
160
20 kW
→T*
140
Total HU = 90 kW
Total CU = 255 kW
Hot utility pinch @ T * = 160°C
Cold utility pinch @ T * = 40°C
MP Steam
Process pinch
120
100
80
60
60 kW
Refrigerated
Brine
195 kW
Cooling Water
40
255 kW
20
0
50
100
150
200
→ ΔH (Heat flow)
FIGURE P5.1F
Grand composite curve for Problem 5.1B.
250
300
5.10 Design illustration
149
Problem 5.2. Thermal design of a petrochemical process with 2 cold and 3 hot streams and no phase
change needs to be optimised for minimum utility consumption. The starting and target temperatures
of the streams as well as the product of their specific heat and flow rate (CP) are shown in Table P5.2A.
Referring to Table 5.2, we consider DTmin ¼10 C.
Solution
Table P5.2A Stream specification table.
Stream
no.
Type
TS
( C)
TT
( C)
CP (kW/
C)
DH
(kW)
TS [
TSLðDTmin =2Þ
for hot stream
TS [
TSDðDTmin =2Þ
for cold stream
( C)
TT [
TTLðDTmin =2Þ
for hot stream
TT [
TTDðDTmin =2Þ
for cold stream
( C)
1
Cold
140
230
0.2
18
145
235
2
Cold
20
180
0.8
128
25
185
4
Hot
300
230
0.2
14
295
225
5
Hot
300
40
0.3
78
295
35
6
Hot
200
30
0.1
17
195
25
Hot and cold utilities are available at temperatures above the highest and the lowest temperatures in the process.
Hot and cold utilities are available at temperatures above the highest and the lowest temperatures in
the process.
DTmin ¼ 10 C
Temperature interval heat balance and problem table cascade is shown for this case in Table P5.2B.
The pinch temperature based on the cascade is at the lowest temperature (25 C) of the cascade,
indicative of a threshold problem requiring only a hot section design.
150
Chapter 5 Heat exchanger network analysis
Table P5.2B Temperature interval heat balance and problem table cascade.
( ΣCPc–ΣCPH) ΔHInterval
kW
kW/ °C
295°C
235°C
CP = 0.2
TM
195°C
60°C
–0.5
–30
Surplus
–30
+30
–30
+67
10°C
–0.3
–3
Surplus
–3
–3
30°C
–0.1
–3
Surplus
–3
–2
Surplus
–2
10°C
–0.2
+24
Deficit
CP = 0.1
CP = 0.8
35°C
40°C
+24
+14
110°C
+0.4
+44
Deficit
+44
–30
10°C
25 °C
+0.6
+0.7
+7
Deficit
+7
Tpinch = 25°C, Only HU required,
Th,pinch = 30°C, QHU = 37 kW, QCU = nil
+75
+24
+51
+44
+7
+7
–37
2
+73
–2
+ 38
1
+70
–3
+36
6
185°C
145°C
37 kW
HU
+33
CP = 0.3
225°C
‘0’ kW
HU
5
CP = 0.2
4
Surplus/
Deficit
0 kW
CU
Since feasibility criteria for stream matches at the pinch as per Table 5.5 is not satisfied (Nh > Nc)
stream splitting is done as per Fig. 5.8. The CP table (Table P5.2C) is used to check CP feasibility
criteria and the corresponding grid diagram is drawn in Fig. P5.2A.
Table P5.2C CP table for hot and cold sections.
Stream no.
Hot
Cold
1
0.2
2
0.8
4
0.2
5
0.3
6
0.1
P
P
CPh (¼0.6) < CPc (¼1.0) is satisfied.
Nh Nc is not satisfied. Hence stream splitting
required.
Total
5.10 Design illustration
151
Network required only hot utility - Maximum energy recovery
- Minimum no. of units.
300°C
230°C
CP = 0.2
4
300°C
E3
40°C
CP = 0.3
5
E2
200°C
6
230°C
CP = 0.1
E1
225°C
17 kW
CP = 0.2
H1
E1
1 kW
180°C
30°C
140°C
1
20°C
CP = 0.4875
E2
2
78 kW
CP = 0.3125
H
E3
36 kW
14 kW
FIGURE P5.2A
Grid diagram using tick off heuristics.
In the figure, S ¼ 6 and N ¼ Nmin ¼ 6 e 1 ¼ 5, satisfies Eq. (5.13).
One may work out to see that by increasing DTmin to 20 C, converts the problem from ‘threshold
problem’ to a ‘pinch problem’ with the pinch temperature at 30 C. This gives Th,pinch ¼ 40 C and
Tc,pinch ¼ 30 C and increases the hot utility requirement to 38 kW and opens up cold utility
requirement of 1 kW in the cold section. Stream splitting in the same proportion for stream 2 gives a
balanced hot section design.
Problem 5.3. The thermal details of streams extracted from the flow sheet of a plant in a petroleum
refinery are shown in the stream specification Table P5.3A. Design the optimum heat exchanger
network considering DTmin ¼ 10 C. The stream 14 is a liquid stream that is being vaporised at 121 C
and no phase change is involved in the rest of the streams. Consider the hot and the cold utilities to be
available at sufficiently higher than the highest and lower than the lowest process stream temperatures,
respectively.
152
Chapter 5 Heat exchanger network analysis
Table P5.3A Stream specification table.
Stream
no.
Type
TS
( C)
TT
( C)
CP (kW/ C)
DH (kW)
TS [
TSLðDTmin =2Þ
for hot stream
TS [
TSDðDTmin =2Þ
for cold stream
( C)
2
Cold
175
182
128.1
896.7
180
187
4
Cold
61
106
8.95
402.75
66
111
Cold
94
122
53.34
1493.52
99
127
19
TT [
TTLðDTmin =2Þ
for hot stream
TT [
TTDðDTmin =2Þ
for cold stream
( C)
14
Cold
121
121
l ¼ 2268 kJ/kg
3780
126
126
3
Hot
156
40
8.28
960.48
151
35
13
Hot
175
40
22.3
3010.5
170
35
16
Hot
243
158
29.1
2473.5
238
153
a
Hot and cold utilities are available at temperatures above the highest and the lowest temperatures in the process.
a
Stream (1.667 kg/s) being vaporised.
Solution
Consider DTmin ¼ 10 C
Based on the information in Table P5.3A,
X
X
DHh ¼ 6444.48;
DHc ¼ 6572.97;
X
X
X
DHnet ¼
DHc þ
DHh ¼ 128.49 ðDeficit heat; net heating load requiredÞ;
The temperature interval heat balance and the problem table cascade are as shown in Table P5.3B.
The cascade shows that the pinch temperature is at 99 C i.e. the hot and the cold pinch temperatures
are 104 and 94 C, respectively. The hot and the cold section stream details are tabulated in Table P5.3C
and Table P5.3D. The grid diagram with tick off heuristics for the hot and the cold section are in
Fig. P5.3A. The reader is asked to combine the two sections and draw the complete heat exchanger
network
5.10 Design illustration
Table P5.3B Temperature interval heat balance and problem table cascade.
238
1790.26
kW
0 kW
16
ΔH = (–) 1484.1 kW
187
170
CP
= 128.1
CP = 29.1
180
1484.1
3274.36
(+) 693
791.1
2
2581.36
(–) 291
13
1082.1
2872.36
(–) 873.8
153
T* (°C)
1955.9
3746.16
(–) 44.6
151
2000.5
3
3790.76
99
CP = 53.34
CP = 8.95
111
2734.42
CP = 8.28
126
CP = 22.3
(–) 733.92
127
4524.68
3780 + 364.16 = 4144.16
14
ΔH = 3780
(–) 1409.74
380.52
19
(+) 380.52
(–) 1790.26
0
(–) 713.79
66
4
(–) 1076.47
713.79
(–) 947.98
35
(–) 128.49
Tpinch = 99°C
Th, pinch = 99+5 = 104°C
Tc, pinch = 99–5 = 94°C
1661.77
153
154
Chapter 5 Heat exchanger network analysis
Table P5.3C Hot section stream details.
Stream
Type
TS ( C)
TT ( C)
CP (kW/ C)
DH (kW)
2
Cold
175
182
128.1
896.7
4
Cold
61
106
8.95
107.4
19
Cold
94
122
53.34
1493.52
14a
Cold
121
121
l ¼ 2268 kJ/kg
3780
3
Hot
156
104
8.28
430.56
13
Hot
175
104
22.3
1583.3
16
Hot
243
158
29.1
N
P Nh <PNc is obeyed. At pinch, cold streams go in and hot streams go out
Ph ¼ 3; Nc ¼ 4; Hence
CPc ¼ 190.39; CPh CPc;
P
2473.5
CPh ¼ 59.68;
a
Stream (1.667 kg/s) being vaporised.
Table P5.3D Cold section stream details.
Stream
Type
TS ( C)
TT ( C)
CP (kW/ C)
DH (kW)
4
Cold
61
94
8.95
295.35
3
Hot
104
40
8.28
529.92
13
Hot
104
40
22.3
Nh ¼ 2; Nc ¼ 1; P
Hence Nh >
PNc is obeyed. At pinch, cold streams go in and hot streams go out
P
CPh CPc ;
CPc ¼ 8:95;
P
1427.2
CPh ¼ 30:58;
5.10 Design illustration
155
Tick off heuristics – Hot Section
430.56 kW
156°C
CP = 8.28
3
E2
107.4 kW
1475.69 kW
175°C
170.18°C
CP = 22.3
13
E1
E3
104°C
104°C
2473.5 kW
243°C
CP = 29.1
16
121°C
121°C
466.28 kW
182°C
H2
106°C
1306.5 kW
121°C
178.36°C
E2
158°C
E4
ΔHTotal = 3780 121°C
kW
E4
14
H1
E1
107.4 kW
122°C
H3
121.67°C
E3
CP = 128.1
175°C
2
CP = 8.95
94°C
4
CP = 53.34
94°C
19
Nunits = 4+3 = 7
S=7
Nmin = S-1 = 6
Tick off heuristics – Cold Section
104°C
3
295.35 kW
104°C
CP = 22.3
E5
13
94°C
529.92 kW
CP = 8.28
E5
C1
90.76°C
1131.85 kW
C2
CP = 8.95
40°C
40°C
Nunits = 3
S=4
Nmin = S-1 = 3
61°C
4
FIGURE P5.3A
Grid diagram using tick off heuristics e Hot and Cold Sections.
Problem 5.4 (With heat load loop). A chemical process with two hot and two cold streams without any phase
change are to be networked for energy savings. Details of the streams are shown in Table P5.4A. Steam
and cooling water are available at 220 C and 25 C, respectively. Design the optimised network
considering DTmin ¼10o C.
156
Chapter 5 Heat exchanger network analysis
Table P5.4A Stream specification table.
CP
(kW/
C)
DH(kW)
TS [
TSLðDTmin =2Þ
for hot stream
TS [
TSLðDTmin =2Þ
for cold stream
( C)
TT [
TTLðDTmin =2Þ
for hot stream
TT [
TTDðDTmin =2Þ
for cold stream
( C)
Type
TS
( C)
TT
( C)
1
Hot
170
60
2.5
275
165
55
2
Hot
150
30
1
240
145
25
3
Cold
20
135
1.5
172.5
25
140
4
Cold
80
140
4
280
85
145
Stream
no.
Hot and cold utilities are available at temperatures above the highest and the lowest temperatures in the process.
Solution
The temperature interval heat balance and the problem table cascade as shown in Table P5.4B is
created using the information in Table P5.4A. The heat flow across 85 C is ‘0’and therefore for the
process, the pinch temperature is 85 C. Since the pinch is based on DTmin ¼ 10 C, the hot and the cold
pinch temperatures are 90 C and 80 C, respectively.
Table P5.4B Temperature interval heat balance and problem table cascade.
CP = 2.5
165°C
1
CP = 1.0
145°C
20°
( ΣCPC–ΣCPH)
ΔHInterval
–2.5
–50
0 kW
2
–50
50
5°
0.5
2.5
140°C
112.5
2.5
47.5
55°
85°C
5.5–3.5 = 2.0
110
–60
55°C
30°
1.5–1.0 = 0.5
15
HU = 62.5 kW ; CU = 45 kW
Tc, pinch = 80°C, Tpinch = 85°C, Th, pinch = 90°C
60
15
–17.5
CP = 1.5
0
–60
–2.5
3
110
110
–62.5
4
CP = 4.0 30° 1.5–3.5 = –2.0
25°C
62.5 kW
45
5.10 Design illustration
157
The stream details and the CP table for the cold section are shown in Table P5.4C and Table P5.4D,
the information being collected from Table P5.4B.
Table P5.4C Cold section stream details.
Stream no.
Type
TS ( C)
TT ( C)
CP (kW/ C)
DH (kW)
1
Hot
90
60
2.5
75
2
Hot
90
30
1
60
3
Cold
20
80
1.5
90
Table P5.4D CP table for the cold section.
Stream no.
Hot
1
2.5
2
1.0
3
1.5
P
P
P
P
CPh ¼ 3.5; CPc ¼ 1.5; DCPov ¼ CPc CPh ¼ 2.0
Total
Cold
Heat exchange scheme in the cold section is arrived at by using the ‘tick off heuristics’ already
outlined in the text and starting off from the pinch and moving away from there. The cold section
design is shown in Fig. P5.4A.
90°C
CP = 2.5
1
90°C
30 kW
45 kW
E1
C1
60 kW
CP = 1.0
60°C
30°C
E2
2
80°C
60°C
E1
E2
CP = 1.5
3
Nh = 2, Nc = 1, Nh > Nc satisfied
FIGURE P5.4A
Tick off heuristics e Cold section design.
Similarly for the hot section Tables P5.4E and P5.4F show the stream details and the CP table.
Exchanger configurations in the hot section are set in a similar way as the cold section starting from the
pinch and moving away as per the tick off heuristics principle. The hot section design arrived at is
shown in Fig. P5.4B.
158
Chapter 5 Heat exchanger network analysis
Table P5.4E Hot section stream details.
Stream no.
Type
TS ( C)
TT ( C)
CP (kW/ C)
DH (kW)
1
Hot
170
90
2.5
200
2
Hot
150
90
1
60
3
Cold
80
135
1.5
82.5
4
Cold
80
140
4.0
240
Table P5.4F CP table for the hot section.
Stream no.
Hot
1
2.5
2
1.0
Cold
3
1.5
4
4.0
P
P
P
P
CPh ¼ 3.5, CPc ¼ 5.5 DCPov ¼ CPc CPh ¼ 2.0
Total
170°C
200 kW
CP = 2.5
150°C
90°C
E3
1
60 kW
CP = 1.0
2
22.5 kW
135°C
CP = 1.5
120°C
H1
140°C
90°C
E4
40 kW
H2
80°C
3
E4
CP = 4.0
80°C
4
E3
Nh = 2, Nc = 2, Nh = Nc
∑ CPC – ∑ CPH = 5.5 – 3.5 = 2.0
FIGURE P5.4B
Tick off heuristics e Hot section design.
Further reading
159
The complete network for the process is arrived at by combining the cold and the hot section
designs as shown in Fig. P5.4C. This involves a total hot utility of (22.5 þ 40 ¼) 62.5 kW and cold
utility of 45 kW that corroborates the problem table algorithm. This network however involves
exchanger E4 and E2 across the same pair of streams (2 and 3) and thus contains a heat loop. The
reader is advised to continue the exercise and eliminate either of the exchanger by shifting its heat load
to the other, recalculate the intermediate temperatures and the load of the hot and the cold utility. Such
options are practised in real problems involving cross-pinch heat transfer that leads to an overall
optimum as it affects the capital as well as the utility costs.
170°C
200 kW
1
E3
90°C
60 kW
2
E4
22.5 kW
E4
45 kW
60°C
C1
60 kW
90°C
30°C
E2
80°C
H1
78°C
E1
150°C
135°C
30 kW
20°C
60°C
E1
E2
3
Heat load loop
140°C
40 kW
H2
80°C
130°C
E3
4
Hu = 62.5 kW; Cu = 45 kW
Tc, pinch = 80°C, Tpinch = 85°C, Th, = 90°C
FIGURE P5.4C
Complete Network Design showing heat loop.
Further reading
Smith, R. (2005). Chemical process: Design and integration. John Wiley & Sons.
Serth, R. W. (2007). Process heat transfer principles and applications. Amsterdam: Elsevier.
Nag, A. (2015). Distillation & hydrocarbon processing practices. PennWell Books.
CHAPTER
Evaporators
6
6.1 Introduction
Evaporation is a common unit operation used in chemical, food, and pharmaceutical industries and
also in desalination, water treatment, and power plants. In the process, a solvent is boiled out of a
solution to concentrate a product. In most cases, the solvent is water, and the product is a concentrated
solution, or in some cases, it can be a slurry. The product can also be solid, as in the case of evaporative
crystallizers used for the production of salt and ammonium sulfate crystals from their solution.
Concentrating solutions like caustic soda lye, sugar syrup, fruit juice, paper mill effluents, etc., employ
evaporators.
Heat transfer to a solution or slurry distinguishes the evaporator from a dryer where heat is transferred
to a solid to vaporize the accompanying volatile liquid. The
vapor from an evaporator is not separated into components as in
the process of reboiling in the reboiler of a distillation column.
Evaporator, Dryer, and Reboiler
In the latter case, the purpose is to generate a vapor stream that is
returned back to the column for component-wise separation.
Although evaporators involve simultaneous heat and mass transfer, they are classified as heat
transfer equipment, as the process rate is governed by the rate of heat transfer. A substantial amount of
heat energy is consumed in the evaporation systems, possibly next to distillation.
6.2 Components of an evaporation system
The basic evaporator unit is comprised of the evaporator body (vessel), arrangements for supplying the
heat, and also the auxiliaries for pulling of vacuum, recirculation of liquid if required, and condensing
the spent vapors. Tubes have traditionally been used as heat exchange surface. The heat transfer
arrangement can be internal to the body or an external heat exchanger. When internal, the tube bundle,
called calandria, has a pair of tube sheets. The central tube in calandria has a larger diameter so that it
acts as “downtake,” leading to the circulation of liquid in the body. Rest of the tubes having a smaller
diameter act as “risers.” A typical short tube calandria type evaporator is shown in Fig. 6.1. Evaporators
with an external heating surface have the advantage that the heat transfer area is not limited by the size
of the evaporator body. Circulation through the external heater in most cases is by forced circulation, as
shown in Fig. 6.2. Plate type exchangers are also used as external heaters in recent designs. Circulation
of the liquid past the heating surface may be induced by boiling or by pumps. In the latter case, boiling
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00006-3
Copyright © 2020 Elsevier Inc. All rights reserved.
161
162
Chapter 6 Evaporators
may or may not occur at the heating surface. Since either the vapor or the concentrate stream or both,
maybe the desired product, the evaporator has provisions for separation of the vapors from the
concentrate and the feed. The vapor-liquid separator prevents entrainment, contamination of the
condensed vapor and fouling/corrosion of surface on which the vapor condenses. The vapor outlet in
the separator is usually connected to a vacuum system or a condenser, as shown in Fig. 6.2.
vapour
Evaporator body
central downcomer
Feed
Steam
Calandria
Condensate
Concentrate
FIGURE 6.1
Short tube evaporator with calandria.
CW out
CW in
Condenser
Condensed
vapour
Steam
Condensate
Pump
Heater
Feed
Concentrate
FIGURE 6.2
Evaporator with external heating e forced circulation.
6.2 Components of an evaporation system
163
Some phenomena affecting the performance and operation of evaporators are discussed. These
depend both on the process fluid and affect the choice and design of evaporator.
Salting, Scaling, and Fouling e These are three distinct phenomena to be minimized/eliminated
in evaporators. The choice of the material of construction of evaporators often depends on these.
Salting is deposit and growth of material on cooler surfaces in an evaporator. This is common in
crystallizing evaporators as the crystal solubility increases with temperature. Salting is reduced by
keeping the liquid in contact with a large surface of the crystallizing solid.
Scaling is also deposition and growth of a solid on heat transfer surface and happens for solutes
whose solubility decreases with increase in temperature. It may also be the result of an irreversible
chemical reaction in the evaporator. It is managed in the same manner as salting. Forced circulation
evaporators are preferred over evaporators with boiling induced circulation for processes having highscale formation tendency.
Fouling is deposition other than salts and scales on the heat transfer surface that can be due to
corrosion, solid matter entering with feed and deposits from condensing vapors.
Foaming and Entrainment: Foaming is caused by colloids, surface tension depressants, finely
divided solids and dissolved air or gases in the liquid. Defoaming techniques use chemical, thermal, or
mechanical methods. Correct choice and dosage of chemical antifoams (vegetable oil, fatty acid,
sulfonated castor oil, etc.) are quite effective and drastically reduce/eliminate foaming. Thermal
defoaming causes foam collapse by increasing or decreasing the temperature. At a high temperature,
foams may collapse due to a decrease in surface tension, solvent evaporation, or chemical degradation
of the foam-producing agents. This is often effected by the use of steam jets impinging on the foam
surface or operation at a low liquid level so that the hot surface can break the foam on contact.
A reduction in surface elasticity may be responsible for foam breakage by lowering the temperature.
Mechanical methods use tensile shear, or compressive forces to destroy foams, for example,
impingement at high velocity against a baffle as done in a long vertical tube, agitated film, and forced
circulation evaporators. The choice of defoaming technique depends on the process to which it is
applied and the convenience with which it may be applied.
Entrainment is carryover of liquid droplets by the exiting vapor and is considerably reduced by
providing sufficient disengagement height of say 1.8 m, above the boiling liquid. In spite of this, the
addition of some form of de-entrainer is common. The upturned pipe, deflector, and the tangential
separator shown in Fig. 6.3 are mechanical contraptions for reducing entrainment. An upturned pipe
has the simplest construction and is normally for adopted small equipment. Deflector type is most
common in use. Climbing-film evaporators are fitted with tangential separators. A good entrainment
separator will limit liquid carryover to 10e20 kg/106 kg of vapor.
Corrosion and erosion are common in evaporators due to (A) the high liquid and vapor velocities
encountered, (B) presence of solids in suspension and (C) necessary concentration differences.
Splashing losses are usually insignificant if a reasonable disengagement height is provided above
the liquid level. This height depends on the vigor of boiling and is usually 2.4e3.5 m in short-tube
vertical evaporators and less in forced circulation and long-tube vertical evaporators where liquid
motion is retarded by baffle or by centrifugal motion.
164
Chapter 6 Evaporators
(A)
(B)
(C)
Drip
Drip
Drip
FIGURE 6.3
Mechanical methods of reducing entrainment (A) upturned pipe, (B) deflector, (C) tangential separator.
6.3 Evaporator types
The design criteria for evaporators are the same regardless of the industry involved. However, many
types of evaporators with several variations take care of different product characteristics and range of
operating parameters for different industries and processes. Depending on the requirements of the
process, the right options for each service is chosen and configured to a functional system.
The classification tree for evaporators is presented in Fig. 6.4.
Heating
method
Mode of
operation
Direct
Batch
Indirect
Continuous
• Nature of
liquid
circulation
• Movement of
Evaporating
film
• Type of heat
transfer
surface
Nature of
liquid
circulation
over
heating
surface
Natural
Circulation
(Short tube)
• Horizontal
• Vertical
• Basket
Forced
circulation -
Movement
of the
evaporating
film
Type of
heat
transfer
surface
Climbing
film
Tubular
Plate
Falling film
Climbing Falling film
Wiped film
• Boiling in
tube
• Submerged
type
Film type
(Long
Tube)
FIGURE 6.4
Evaporator classification basis and types.
6.3 Evaporator types
165
Heating may be either direct or indirect. Direct heating is provided by solar evaporation (production of Glauber’s salt) and submerged combustion of a fuel. The advantages of this technique are
the ability to handle corrosive liquors, a large amount of heat release per unit volume (typically
70 MW/m3) in submerged combustion and the almost instantaneous transmission of heat to the liquid.
Generally, the most widely used mode of indirect heating is by condensing steam or vapor on the heat
transfer surface.
Evaporators can be batch or continuous. Batch evaporators, also called batch pans are the simplest
and one of the oldest designs. It consists of a steam jacketed vessel heated
with vapor or liquid heating medium as shown in Fig. 6.5. The batch is
heated to its boiling point, and the vapors are removed until the desired
Batch Evaporator
concentration is reached. The concentrate is drained or pumped out of the
tank through a nozzle. These are particularly suitable for products that are
clean, viscous, and not heat-sensitive, and are used for small-scale
applications like concentrating jam, jelly, syrup, and some pharmaceutical products. Its limitations
are (A) long residence time, (B) low heat transfer coefficient, (C) low heat transfer area per unit
volume occupied by the feed, (D) high tendency of fouling (as the product movement is by natural
circulation only) and (E) high boiling point of the product at the tank bottom (due to the liquid head).
Some designs incorporate agitator to improve the heat-transfer coefficient. Batch pans can be operated
under vacuum to reduce the boiling point.
Condenser
Water
Evaporator
Steam
to
jacket
To drain
Steam trap
for condensate
Product
FIGURE 6.5
Batch Pan evaporator.
166
Chapter 6 Evaporators
6.3.1 Types of continuous evaporators
Continuous evaporators are further classified based on (i) the method of agitation or the nature of liquid
circulation over the heating surface, (ii) movement of the evaporating film, (iii) type of heat transfer
surface.
Evaporators may be divided into three main types on the basis of nature of circulation:
(a) Natural circulation units
(b) Forced circulation units
(c) Film-type units
In natural-circulation evaporators, the circulation of the liquid is effected by employing a short
length of the tube. These evaporators are further classified as horizontal tube and vertical tube type.
Horizontal tube evaporators (Fig. 6.6A) have the tube bundle fitted horizontally into the lower
part of the body. Above the heating section is a cylindrical portion in
which vapor-liquid separation takes place. Some form of deentraining device is usually fitted (not shown in the diagram) to
Horizontal tube Evaporator
prevent carryover of liquid droplets with the vapor stream. The
horizontal tube evaporator is the only type with the heating medium
inside the tubes. Steam is fed to one steam chest wherefrom it enters
the tubes and reaches the opposite chest. From here, the condensate leaves through a steam trap (not
shown). A small vent is provided at the top location of the opposite chest to bleed out any condensable
component accompanying the condensing vapor/steam. Horizontal tube evaporators are relatively
cheap and easy to install, require low headroom, and are suitable for handling liquors that do not
crystallize. They can be used either as batch or as continuous units. Typically, the shell diameter is in
the range 1e3.5 m and the height is 2.5e4 m. These units are not used for viscous liquors as the natural
recirculation rate is poor. Difficulty in cleaning the outer surfaces of the tubes render this design
unsuitable for liquids that form scales or deposit salts.
(A)
(B)
Vapour
Vent
Feed
Steam
Steam
condensate
Thick liquor
FIGURE 6.6
Natural circulation evaporator with (A) horizontal tubes, (B) vertical tubes.
From Richardson, J.F., Harker, J.H., & Backhurst, J.R. Particle technology & separation processes (5th ed.). Coulson and
Richardson’s chemical engineering (Vol. 2). Butterworth-Heinemann.
6.3 Evaporator types
167
Arrangement in a vertical tube evaporator is illustrated in Fig. 6.6B. The tube bundle (calandria)
is vertical and has a large central downtake with an area between 75%
and 150% of the total tube cross-sectional area. The liquid flows
inside the tubes with steam condensing outside. The boiling liquid
Vertical Tube Evaporator
flows up the tubes and returns through the central downtake. The
condensate is removed from a suitable location on the bottom tubesheet, and the noncondensed gases are vented from heating (steam)
chest through the vent nozzle. The vent nozzle is located close to the upper tube-sheet, where the
noncondensable gases tend to accumulate. Fig. 6.6B shows the typical location of the feed and
concentrate discharge. The heating tubes are 37e75 mm in diameter and 1e2 m long, with a length to
diameter ratio between 20 and 40. The liquid level in the evaporator has a significant influence on
circulation and heat transfer. The highest heat-transfer coefficients are achieved when the level is about
half-way up the tubes. Lower than the optimum level results in incomplete wetting of the tube wall,
increase in fouling and rapid reduction in capacity. With a salting or scaling product, this type of
evaporator is usually operated with the liquid level appreciably higher than optimum and usually above
the top tube sheet. It is not used for temperature-sensitive materials and is unsuitable for crystalline
products unless agitation is provided. Due to better circulation of liquor in the tubes, the vertical tube
evaporator is widely used in sugar and salt industries, where throughputs are very large.
The advantages of short-tube vertical evaporator include
•
•
•
•
low head-space
fairly high heat-transfer coefficients with low viscous liquids (up to 5e10 cP)
relatively inexpensive to manufacture
suitable for liquids with moderate scaling tendency since the product is in the tube side, which is
accessible for cleaning
In the basket-type evaporator (Fig. 6.7), the tube bundle is centrally suspended in the body, thus
forming an annular downtake. This allows the heating unit to be easily removed for cleaning and
repairs and ensures that crystals formed in the downtake do not break up.
In Forced Circulation Evaporators, a propeller or other type of impeller is mounted in the
central downtake, or a circulating pump is mounted outside the
evaporator body to provide higher liquor velocity through
the tubes, which result in high liquid-film heat transfer coefficient.
Forced Circulation Evaporator
Typically, velocity in the tubes is maintained at 1 m/s for salt
evaporators containing less than 5% solids and around 3 m/s for
lower concentration. Higher velocity operation reduces fouling,
thereby maintaining capacity and reducing downtime. Fig. 6.8 shows an arrangement with an external
circulating pump. Centrifugal pumps are used when crystals are present; otherwise, vane types may be
used. The liquor is introduced either at the bottom and pumped through the calandria, or introduced in
the separating section. In most units, the hydrostatic head of liquid suppresses boiling in the tubes and
boiling (flashing) occurs only in the separator.
The heating element is located at a lower elevation, much below the liquid level or the return line to
the flash chamber to avoid vaporization. This makes the heating surface relatively immune to salting
and scale formation. Nevertheless, the highest heat transfer coefficients are obtained when the liquid is
allowed to boil in the tubes, but these are seldom used except for headroom limitations or where the
liquid neither salts nor scales.
168
Chapter 6 Evaporators
Vapour
Steam
Vapour head
Deflector
Gas vent
Feed
Annular
downtake
Steam
condensate
Basket type
heating element
Thick liquor outlet
Salt filters
where required
FIGURE 6.7
Basket-type evaporator.
From Richardson, J.F., Harker, J.H., & Backhurst, J.R. Particle technology & separation processes (5th ed.). Coulson and
Richardson’s chemical engineering (Vol. 2). Butterworth-Heinemann.
Forced circulation evaporators ensure high heat transfer rates even with increasing viscosity of the
liquid, thus enabling the formation of a more concentrated product.
Since pumping costs increase roughly as the cube of velocity, the
added cost of operation may make it uneconomical. Nevertheless,
Advantages and Limitations
many forced circulation evaporators operate with a liquor velocity
of 2e5 m/s through the tubes, which is significantly higher than
that obtained in natural circulation. These units can be made
smaller and cheaper than those relying on natural circulation and are preferred where stainless steel or
expensive alloys, such as Monel are used. Forced circulation evaporators are suitable for the widest
variety of evaporator applications. The main applications are in (A) crystallizing evaporators,
(B) concentration of solutions where solubility decreases with temperature and (C) for thermally
degradable materials, which result in a solid deposition. It is suitable for concentrating meat extracts,
salt, caustic soda, alum, and other crystallizing materials and also with glues, alcohols, and foaming
materials. In all cases, recirculation ratio as high as 100 to 150 kg of liquor per kilogram of water
6.3 Evaporator types
169
evaporated is maintained to ensure that the temperature rise across the tube bundle is kept low
(2e3 C). The high liquor velocity through the tube also helps to minimize the build-up of deposits or
crystals on the heating surface. Forced circulation evaporators normally are more expensive than film
evaporators because of the need for large-bore circulating pipework and large recirculation pumps.
Operating costs of such a unit are also considerably higher. For certain applications, multipass arrangements may be used.
These are often constructed from a host of inert materials for the handling of corrosive fluids.
Graphite is usually preferred due to its unique combination of chemical inertness and excellent thermal
conductivity.
Separator
Vapour out
Liquor head
to prevent boiling
at heating surface
Low temperature
rise across
Calandria
Concentrated
liquor
Steam
Condensate
Dilute
liquor
Circulating
pump
FIGURE 6.8
Forced circulation evaporator with an external pump.
Film-type units resemble the vertical tube evaporator in that the liquid is inside the tube and steam
is outside. The liquor level is maintained low, not more than 0.6e1 m
above the bottom tube sheet. The product forms a thin film only on the
heat transfer surface and does not occupy the entire tube cross-section.
Film Type Evaporator
The low holdup significantly reduces the residence time within the heat
exchanger. It also allows operation with as low as 3.5 C steam-toproduct temperature difference and minimizes the hot spots. Film type
evaporators are, thus, ideal for heat-sensitive materials like pharmaceutical, food, and dairy products.
Film evaporators can have rising film, falling film, or a combination of rising and falling film
design. Both tubular and plate configurations are used.
The long-tube vertical or rising-film evaporator is one of the most widely used tubular evaporators.
These are simple to build as a large single once-through unit with high
heat-transfer performance. It is basically a shell-and-tube heat
exchanger mounted with a vapor/liquid separator. The tubes are usuRising Film Evaporator
ally 38e50 mm OD and 4e10 m long. The dilute feed enters at the
bottom of the tube-sheet and flows upward through the tubes with the
heating medium on the shell side. The bottom bonnet of the evaporator
feeding the tubes runs full with liquid. The annular flow or climbing-film regime is present in almost
the entire tube length; the film climbs due to the drag induced by the vapor core moving at a high
170
Chapter 6 Evaporators
relative velocity. The vapor and entrained liquor leaving the top bonnet of the evaporator enters a
separator tangentially to break any foam. This enables handling of foamy liquids. The feed enters the
tubes at nearly its boiling point. Subcooled feed makes the initial section act merely as a feed heater
that reduces the overall performance of the unit.
Fig. 6.9 shows the schematic of a rising film evaporator with a 1e2 S&T exchanger for feed
preheating. Preheating ensures early initiation of vaporization that reduces the liquid film thickness
and increases the liquid film velocity.
The rising-film evaporator requires high head-room but little floor space. The pressure drop
through the tubes, contributed by the static head of the single-phase and two-phase regions and losses
due to friction and acceleration of the vapor phase, is higher as
compared to falling film type. In addition, the hydrostatic head at
the bottom of the tubes increases product boiling temperature,
Advantages and Limitations
which poses to be a problem for temperature-sensitive materials.
Viscous materials are not well handled as a thicker film hinders heat
conduction through it and deters the vapor generation rate. This
limits the use of such evaporators to products that do not have high viscosity, for example, the concentration of cane sugar syrup, black liquor in paper plants, nitrates, and electrolytic tinning liquors.
Typically, around 14 C temperature difference between the vaporizing liquid and the condensing
steam ensures sufficient vaporization rate in the tube to force the liquid film against gravity. This limits
the maximum number of effects in the forward feed configuration. Say, if steam is available at 108 C
and the product boiling temperature is 52 C under a suitable vacuum condition in the last stage, the
total available temperature driving force is 56 C. If forward feed is used, a maximum of four effects
can be employed with rising (climbing) film evaporators.
Vapor
Steam
Product
Vent
Condensate
Feed
FIGURE 6.9
Climbing film evaporator with a 1e2 S&T preheat exchanger.
From Towler, G., & Sinnott, R. (2012). Chapter 16 - Separation of fluids. In: Chemical engineering design: principles, practice and
economics of plant and process design (2nd edn.). Elsevier.
6.3 Evaporator types
171
In a falling film evaporator, the liquid flows under gravity as an evaporating thin film on the inside of
heated vertical tubes. The resulting vapor also flows co-currently with
the liquid. This results in a thinner film with a short contact time with
the heating surface. Part of the concentrated liquid may be recycled
Falling Film Evaporator
back to the evaporator inlet to ensure that the tubes are sufficiently wet.
The configuration is similar to placing a climbing film evaporator
turned upside down. A typical falling film evaporator with a preheat
exchanger is shown in Fig. 6.10. The liquid distribution system is a critical aspect in a falling film
evaporator as the feed needs to be uniformly distributed in all tubes to form a continuous film at the
inner tube surface. Most distributor designs are some type of perforated plate placed over the top tubesheet. In some designs, liquid spreading to different tubes is enhanced by flash evaporation at tube entry.
The design of the vapor-liquid separator depends greatly on the properties of the material being processed and the operating conditions. The ratio of the liquid vaporized to the feed rate is a critical
parameter of falling film evaporator. High vapor fraction in a single-pass may lead to inadequate flow of
liquid to keep the tubes wet near the bottom. This leads to fouling by degraded product.
The advantages of falling film evaporators include high heat transfer coefficients (2000e5000
W/m2K for aqueous material and 500e1000 W/m2K for organics) at reasonable
temperature difference, short residence time on the heated surface (5e10 s
without recirculation), low pressure drop (0.2e0.5 kPa), suitability for vacuum
Advantages
operation, high evaporation ratios (70% without and 95% with recirculation),
wide operating range (up to 400% of the minimum throughput), low susceptibility to fouling and minimum cost of operation. Falling film evaporator is
often chosen when the driving force is small (<8.5 C). This allows a significant number (even 10 or
more) of effects within the same overall temperature driving force for multiple-effect evaporators.
Further, since vapor flow is assisted by gravity, falling film evaporator produces thinner films and
Steam
Feed
Steam
Separator
Vacuum
Condensate
Product out
FIGURE 6.10
Single-effect falling film evaporator with preheat exchanger.
172
Chapter 6 Evaporators
shorter residence time as compared to rising film evaporators for any given set of conditions. The
temperature is also more uniform in falling film types as there is no problem of hydrostatic head, and the
only critical concern is the feed distribution system.
Due to the combined feature of functioning at the low-temperature difference and short residence
time, the falling film evaporator is highly suitable for temperature-sensitive products. Typical applications include the concentration of dairy products, sugar solutions, urea, phosphoric acid, and black
liquor.
The Climbing-and-Falling film Evaporator (Fig. 6.11) combines the configuration of the rising-film
and the falling film evaporators and offers the advantages
of both. When a high ratio of evaporation to feed is
required resulting in a viscous product, a tube bundle can
Climbing and Falling Film Evaporator
be divided into two sections, in which, the first, functions
as a climbing-film evaporator and the second as a falling
film evaporator. Feed enters at the bottom of the tubesheet of the climbing-film portion. Boiling starts as the liquid rises through the tubes. A mixture of
liquid and vapor is discharged and redistributed over the top of the tubes for the falling film pass. The
vapors from the climbing-film aid in the distribution of liquid in the tubes and increase the velocity of
the liquid, which increases heat transfer. The discharge from the falling film tubes go to a vapor-liquid
separator located at the bottom of the calandria, and the vapor outlet is connected to a vacuum system
or a condenser.
Heating
steam
Upflow
tubes
Downflow
tubes
Vapour to vacuum
system/condenser
Demister
pad
Condensate
Vapour-Liquid
separator
Feed
Product
FIGURE 6.11
Climbing & Falling film evaporator.
6.3 Evaporator types
173
They are best suited for handling clear liquids, or foamy liquids with large evaporation load and
their advantages are
•
•
• low residence time
• high heat transfer rate
Advantages and Limitations
• lower cost
• low hold-up
• smaller floor space requirements
good heat transfer over a wide range of services
large units can be manufactured
However, these evaporators require high head-room. In some cases, they also require recirculation
of the liquid to ensure wetting of the tube surface. These are not suitable for salting or severely fouling
fluids.
Thin-layer or wiped-film evaporators, also known as thin-film evaporators are expensive and used
specifically for highly viscous liquids and for solvent removal down to
very low concentration. It consists of a vertical tube, with a lower
jacketed part containing the heating medium and the upper part acting
Wiped Film Evaporator
as a separator. An external motor drives a shaft with blades mounted
with a small clearance (w1.5 mm) between blade tips and the inner
surface of the tube, thus extending nearly to the bottom of the tube. The
liquor to be concentrated is picked up by the rotating blades as it enters and gets thrown against the
tube wall to form a thin, well-agitated liquid film even with very viscous liquids. The film gets
concentrated as it flows down by gravity. The concentrated liquor is drawn off from the bottom by a
pump and the vapor leaves the top of the unit to a condenser. Scale formation is minimal on the scraped
heating surface. Large units are uneconomic, and therefore, these are used in laboratory-scale or for
highly valued products.
Plate Type Evaporator consists of a series of plates spaced by gaskets, the entire unit mounted
within a support frame. These can be climbing-film, falling film or a
combination of both and can be operated under vacuum, as well as at
under pressure. Fig. 6.12 shows the flow and plate arrangement of a
Plate Type Evaporator
falling film plate evaporator. Each unit has a product plate and a steam
plate, and the required heat transfer area is provided by multiple such
units. Capacity augmentation by addition of units, if required, is a
major flexibility for plate type evaporators. Product flowing down each side of the plate in series is
adopted when this is advantageous in terms of wetting rates. Both the vapor evaporated from the
boiling film, and the concentrated product is discharged from the evaporator to a vaporeliquid
separator. The product is pumped, and the vapor passes to the next effect (or to the condenser from the
last effect). They also have lower residence time, that is, they operate with high velocity and achieve
high heat transfer coefficient. This allows heating with a low-temperature difference across the heating
surface and makes the plate type evaporators particularly suitable for heat-sensitive materials like fruit
juice, milk, and pharmaceutical products. Low concentration ratios between feed and product normally
require single-pass, while higher ratios require recirculation of part of the exit stream. Satisfactory
mixing of the recycled and the fresh feed stream often use static in-line mixers.
Compared to tubular evaporators, the plate evaporators offer advantages in terms of headroom,
floor space, accessibility, and flexibility. They also have lower residence time. In plate units, boiling on
the heating surfaces is avoided by increasing the pressure on the heating surface. A “restriction orifice”
between the plate pack and the separator ensures this. Plate type evaporators are, therefore, (A) well
174
Chapter 6 Evaporators
Steam
Product
section
Steam
section
Steam
section
Feed
Product
from
separator
Vapour &
product to
separator
Condensate
outlet
Final product to sump
FIGURE 6.12
Plate type evaporator (Falling film).
suited for evaporating heat-sensitive, viscous and foamy materials, (B) compact with low headroom,
and (C) easy to clean and modify. Typical applications are stripping applications, removing monomers
from polymers and deodorization. Nevertheless, there are large gasketed areas that are weak and may
be prone to leakages. Gasket material also limits the maximum temperature of the equipment.
Flash evaporators suppress evaporation on the heat transfer surface. The superheated liquor enters
a separator where flashing occurs due to reduced pressure. Scheme of a typical flash evaporator system
is shown in Fig. 6.13.
7
9
CW out Seal water
CW in
5
8
Condensate
Steam
4
6
1
Condensate
2
3
Condensate
FIGURE 6.13
A flash evaporation system.
Product
6.4 Evaporator performance
175
The scheme shows feed mixed with recycled product from a tank (1) being fed by a pump (2) to the
evaporator (4) via preheating heat exchanger (3). The vapor and liquid from evaporator separate in the
separator (5). Vapor leaving the separator condenses in the condenser (8). The system vacuum is
created by the liquid-ring pump (9) pulling out the noncondensable from the condenser shell. The
product, under vacuum, is drawn by a pump (6), part of which is recycled back with feed.
Evaporative crystallizer enables product formation as crystalline solid instead of thick liquor.
Crystals of salts like sodium chloride and ammonium sulfate whose solubility does not change much
with temperature are economically produced in this equipment. These are also used for crystallizing
solutes, whose solubility decreases with increasing temperature (solutes with inverted solubility
curves). Most evaporative crystallizers use an external heat transfer surface. In some cases, further
cooling may lead to the formation of additional crystals. Uniformity of crystal size is ensured by using
forced circulation. Problems of salting, scaling, and fouling are more common in crystallizing
evaporators and these are minimised by providing sufficient submergence and suitable body geometry.
Evaporators without heating surfaces
The submerged-combustion evaporator comprises a tank, where the liquid is heated by direct contact
with combustion gases. A burner and gas distributor is immersed into the liquid, thus eliminating the
need for heat transfer surface. This makes the equipment suitable for severely scaling and corrosive
liquids and for nonheat-sensitive thermally stable materials, where contamination by combustible
gases is acceptable. Since the vapor is mixed with large quantities of noncondensable gases, it is
impossible to reuse the heat in this vapor. Therefore, these units are economical, where the fuel cost is
low. High entrainment loss is a concern. These evaporators cannot be used when control of crystal size
is important.
Disk or cascade evaporators consist of a rotating horizontal shaft on which disks perpendicular to
the shaft or bars parallel to the shaft are mounted. These are primarily used in the pulp and paper
industry for a final concentration of the black liquor before it is burnt in the boiler and to recover heat
and entrained chemicals from boiler stack gases. The assembly is partially immersed in the thick black
liquor, so liquor film is carried into the hot-gas stream as the shaft rotates.
6.4 Evaporator performance
The thermodynamic efficiency of an evaporator is very low. This is because the useful work, equal to
the heat that would be liberated by mixing the product and the liquid solvent to reconstitute the feed
(heat of mixing) is very low compared to the energy input to create the vapor phase (the latent heat of
vaporization). One may recall that thermodynamic efficiency for distillation is also very low due to the
same reason.
Evaporator performance is, therefore, not measured by thermodynamic efficiency but by “steam
economy,” also known as “economy.”
Economy for an evaporator is defined as kg solvent evaporated per kg steam used. This can be
improved by the use of (A) multiple effects and (B) vapor recompression. In this chapter, we refer to
the heating medium as “steam” and the product of evaporation as “vapor.” Thus, in multiple-effect
evaporators, one effect produces vapor, which becomes steam for the next effect. Customarily,
steam refers to water vapor and vapor refers to vapor from any liquid, not necessarily water.
176
Chapter 6 Evaporators
6.4.1 Multiple-effect evaporators
In multiple-effect evaporators, the effects are arranged in order of decreasing operating pressure that
results in lowering of the boiling temperature of the liquid in succeeding effects. This enables vapor
generated in one effect (at a higher temperature) to be used as the heating medium for the next effect,
thus utilizing the latent heat of vapor generated in all effects except the last. Steam from an outside
source is required only for the first effect. Accordingly, the steam economy improves with an
increasing number of effects. On some large duty evaporation systems, it is economical to utilize as
many as seven effects. At the same time, for any particular duty, increasing the number of effects
significantly increases the capital cost. The optimum number of effects is decided by an economic
balance between saving in steam and added investment cost, as discussed in Section 6.6.2. In general,
when the evaporation load is above 1400 kg/hr, multieffect evaporation is considered.
Feeding arrangements
There are different configurations of multiple-effect evaporators, depending on the flow arrangement
of feed and heating vapor. As shown in Fig. 6.14, these include forward feed, backward feed, mixed
feed, and parallel feed. In all cases, the effects are numbered (Roman numerals in this book) in the
direction of steam flow irrespective of the feed flow direction. The inter-effect transfer pumps are only
shown in the figures and the feed and product pumps required in all cases are not shown. A comparison
of the four configurations is discussed below and summarized in Table 6.1.
(A)
Vapour to
condenser
I
II
(B)
I
III
Steam
II
III
Vapour to
condenser
Steam
Condensate
Feed
Condensate
Product
Feed
(C)
I
II
III
Vapour to
condenser
Steam
Condensate
Feed
Feed
Feed
Product
Product
Product
Product
(D)
I
II
III
IV
Vapour to
condenser
Steam
Condensate
Product
Feed
FIGURE 6.14
Different configurations of multiple-effect evaporators e (A) Forward feed, (B) Backward feed, (C) Parallel
Feed, (D) Mixed feed.
In the forward feed configuration, the dilute feed and the heating steam enters the first effect, and
the liquor flow is parallel to the steam flow. A feed pump is required to introduce
the feed to the first effect (often at about atmospheric pressure) and also to
withdraw a product from the last effect mostly operating under vacuum. Intermediate liquor transfer pumps are not needed as the flow occurs due to pressure
Forward feed
differential between successive effects. Control valves on these transfer lines
control the liquor level in the effects. This configuration exposes feed to the
6.4 Evaporator performance
177
highest temperature steam and is advantageous for a hot feed or a thermally sensitive concentrated
product that would be damaged/deposit scale at high temperature. Low steam economy with cold feed
can be improved by preheating feed, in stages, with vapor bled from intermediate effects.
In the backward feed, the feed enters the last (coldest) effect, and the product is discharged from the
first effect. Intermediate liquor pumps are essential to transfer liquor to
destination effect at a higher pressure. The backward feed is advantageous for
cold feed or viscous products and usually has the highest steam economy.
Backward feed
When product viscosity is high, but a hot product is not needed, the liquid
from the first effect is sometimes flashed to a lower temperature in one or
more stages, and the flash vapor is added to the vapor of the latter effects.
Thus, for hot feed, forward feeding possesses greater economy while for cold feed, backward
feeding is more economical.
Mixed feed combines the advantages of higher steam economy of backward feed arrangement and
also permits the final evaporation to be done at the highest temperature. This
reduces the number of intermediate liquor pumps and is used for special applications, for example, when liquor at an intermediate concentration and a
Mixed feed
certain temperature is desired for additional processing.
In a parallel feed arrangement, feed is pumped, and liquor is withdrawn from each effect while the
steam flow is similar to the previous cases. Primarily, this is used when the feed
is substantially saturated and the product is a slurry or a solid; for example, the
saturation of brine to make common salt. They are employed in services with a
Parallel feed
higher tendency to scale and foul. Fresh feed entering the effects provides a
washing effect for the deposits. This arrangement is also useful when more than
one product concentration is required to be produced.
A comparison of the four configurations is presented in Table 6.1.
Use of vapor as a “hot stream” in the plant
Vapor from the multiple-effect evaporator system can also be viewed by the designer as a cheap source
of heat (low pressure steam). Part of vapor from an effect can be utilized elsewhere after it has already
generated i times its own weight of vapor (i is the effect number from where the vapor is withdrawn).
This is an important aspect of improving the general economy of a plant and is fully exploited in the
beet sugar industry. No special provision in the design is necessary if such withdrawals are small. For
substantial withdrawals, additional area has to be provided in subsequent effects to ensure a reasonable
temperature difference.
6.4.2 Vapor recompression
In this scheme, vapor from an effect is compressed to increase its condensation temperature, and the
heat of condensation released at this higher temperature is utilized for heating the same or some other
effect of the same evaporator. The extra heat energy available in vapor recompression thus involves
input energy for compressing the vapor to the required pressure. The compression may be by mechanical means (mechanical vapor recompression) or by steam jet ejector (thermocompression).
178
Chapter 6 Evaporators
Table 6.1 Comparison of multiple effect evaporator arrangements.
Arrangement
Forward feed
Backward feed
Parallel feed
Mixed feed
Entry of
Feed
Steam
·
·
First effect
First effect
Last effect
First effect
Each effect
First effect
Intermediate effect
First effect
Liquor flow
Parallel to steam
flow
Opposite to steam
flow
Independently in
each effect
Forward feed for
some effects and
backward feed for
rest
Product
withdrawal from
Last effect
First effect
Each effect
First effect
Advantages
Needs no intereffect transfer
pump
-
Higher steam
economy
Suitable for
viscous
products
-
-
-
-
Simplest in
construction
Feed washes
deposit/scales
More than one
product
concentration
obtained
-
Eliminates
some
intermediate
liquor pumps
Allows product
draw from the
highest
temperature
stage
Limitations
Low steam
economy for cold
feed
-
Needs inter
effect transfer
pump
Low steam
economy
Low steam
economy
Applications
-
-
Cold feed
High product
viscosity
-
-
-
General
observation
Hot feed
Product with
scaling
tendency at a
higher
temperature
Product
sensitive to a
higher
temperature
Greater economy
for hot feed
Used as
crystallizing
evaporator
(e.g., Brine
evaporation to
make common
salt)
Used when
liquor at
intermediate
concentration
is also a
product
Greater economy
for cold feed
Thermocompression (TC) is attractive when steam is available at pressures much higher than can
be used in evaporators, (>3 kg/cm2(g)) and preferably over 7 kg/cm2(g)).
Usually, a portion of the steam evaporated from the product is compressed
by a steam ejector and returned to the steam chest. The ejector also serves
Thermocompression
as a reducing valve. Due to its low first cost and ability to handle large
volumes of vapor, this method is an attractive option to improve the
economy of evaporators that must operate at low temperatures, and hence,
cannot be operated in the multiple-effect configuration. TC units do not operate well outside the design
6.4 Evaporator performance
179
Thermocompression ejector
Steam
I
II
III
Vapour to
vacuum
Feed
Product
FIGURE 6.15
Use of thermocompression to improve the steam economy in a forward feed triple effect evaporator.
conditions and are not recommended if the product is known to foul severely so that the heat transfer
coefficient is significantly reduced over time. The increase in temperature as a result of compression is
usually too small for materials that have high boiling point elevation. This can also be used in
conjunction with the multieffect for further improvement in the economy, as shown in Fig. 6.15, where
it is used in conjunction with the forward feed. Part of the vapor generated from the second effect is
thermo-compressed and used for heating the first effect.
Thermodynamically, mechanical vapor recompression (MVR) is the most efficient technique
and is common in desalination evaporators. The vapor
compression is carried out by a radial type fan or a
compressor. A fan provides a relatively low compression ratio
Mechanical vapor recompression
which results in the requirement of high heat transfer surface
area but is an extremely energy-efficient system. Although
higher compression ratios can be achieved with a centrifugal
compressor, the fan is conventionally used due to its high reliability, low maintenance cost, and low
RPM. The input energy is required only for compressing the vapor vis-a-vis the recovery of latent
heat of condensation. In practice, due to inefficiencies in the compression process, the equivalent
number of effects is in the range 30e55 depending on the compression ratio. The compressor can be
driven by an electric motor, steam turbine, gas turbine, or an internal combustion engine. The high
cost of mechanical compression equipment makes MVR evaporators significantly costlier than the
multieffect option. However in most cases, for medium to large evaporators, the payback time for the
additional capital cost is 1e2 years. Like TC, MVR system is also not suitable for high fouling duties
or for high boiling point elevation. Entrainment is especially detrimental as apart from the erosion
effect of the droplets, the entrained liquid droplets evaporate at a higher temperature and deposit
dissolved solids on the rotary equipment.
180
Chapter 6 Evaporators
6.4.3 Heat recovery systems
The following heat recovery schemes are considered during design to increase the economy
•
•
•
Heat exchange between outgoing (product and evaporator condensate) and incoming streams to ensure
the minimum possible temperature of outgoing and maximum possible temperature of incoming
fluids. This often requires additional liquid-liquid exchangers which are justifiable only in large plants.
Condensate flash system in which the condensate from each except the first effect is flashed in
successive steps to the pressure of the heating element of the succeeding effect. Some amount of
condensate flash may also be used for feed preheating. Product flash tanks may be used in
backward or mixed feed evaporator.
In the forward feed evaporators, the principal means of heat recovery is by using feed preheaters
heated by vapor blend from each effect. A feed preheated by last effect vapor also reduces
condenser water requirements.
6.4.4 Evaporator selection
The selection of evaporator type best suited for a particular service is governed by (A) heat transfer
considerations, (B) characteristics of feed and product, such as (high) viscosity or (high) solid content,
throughput, fouling tendency and foaming tendency, (C) product quality and (D) corrosion.
However, for simple applications, several types may serve equally well. In such cases, the choice
may be dictated by factors like capacity, small batch production, past plant experience, available space,
operating manpower requirement, utility requirement, maintenance required, and/or cost.
Typical guidelines for selecting evaporator type and configuration are listed below and a
comparison between the different types is presented in Table 6.2.
➢ Batch or stirred batch evaporator preferred for low capacity or multiproduct batch production.
Although it may require more cleaning time, it is typically a low maintenance system. For a high
capacity system, a continuous process is usually used.
➢ Tubular evaporators are the first choice where applicable and are usually the choice for very large
systems operating above 0.7 kg/cm2(g) and handling suspended solids.
These require less floor space and have fewer gasket limitations as compared to plate evaporators.
➢ Vertical short tube evaporators occupy lower headspace, and rising-falling film type requires
smaller floor space.
➢ Plate evaporators are often the choice for heat-sensitive products and viscous products.
They require lower headroom, less expensive building and installation costs and are also easier to clean.
They allow flexibility as modules can easily be added or removed.
➢ Film evaporators assure a high product quality for heat-sensitive products since they offer the
dual advantage of low residence time and low-temperature difference
• Falling film evaporators (plate or tubular), provides the highest heat transfer coefficient but
are not suitable for heavy fouling products and products with viscosities above 300 cP.
• Falling film plate evaporator ensures the shortest residence time.
• Agitated thin film type is uneconomic for large scale and is used only for a highly valued product
➢ Plate-and-frame and agitated thin-film evaporator are preferred for products that are highly
temperature-sensitive, very viscous, high fouling, or have high solids content.
➢ Forced circulation evaporators can be operated up to 5000 cP viscosity and significantly reduce
fouling. Although capital and operating costs are high, a higher heat-transfer coefficient offsets the
capital cost in some cases. In the case of crystallizing evaporators, the requirement for producing
crystals of a definite uniform size usually limits the choice to forced circulation evaporators.
Table 6.2 Criteria for evaporator selection based on product characteristics.
Product
characteristics
Clean
Batch
Horizontal
tube
Vertical
short
tube
Vertical
long
tube
Falling
film
Rising and
falling film
Forced
circulation
Plate
type
Agitated
thin film
X
X
x
x
x
x
x
x
x
x
x
High capacity
Solids/Crystals
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
High
High
Fouling
Foamy
x
Temp Sensitive
x
Viscous
x
x
Corrosive
Heat transfer
coefficient
x
High
High
High
6.4 Evaporator performance
x
x
181
182
Chapter 6 Evaporators
In some cases, the evaporator type is selected based on material of construction, e.g. for a sulfuric
acid evaporator where the acid concentration can reach 50% uses graphite tubular heat exchangers and
nonmetallic separators and piping.
Typical materials of construction for common evaporator applications are shown in Table 6.3.
Table 6.3 Material of construction for different services.
Product
Material of construction
Most dairy and food products
304/316 stainless steel
Most fruit juices
316 stainless steel
Sugar products
Carbon steel/304/316
Foods containing high salt
(NaCl)
Titanium/Monel
High alloy stainless steels
Duplex stainless steels
Caustic soda <40%
Stress relieved carbon steel
Caustic soda high concentration
Nickel
Hydrochloric acid
Graphite/rubber lined carbon
steel
6.5 Evaporator accessories
The auxiliary system associated with an evaporator include:
a) Vapor condensation and the associated vacuum system
b) Condensate removal system to remove the condensate from each effect
The different common accessories are presented in Fig. 6.16.
6.5.1 Condensers
In surface condensers, the heat transfer surface (usual tubes) separates the condensing vapor and the
coolant. These are mostly shell and tube heat exchangers with vapor in the shell and cooling water
running in the tubes. A vacuum pump or steam ejector is required to remove air/noncondensable gases
from surface condensers operating below atmospheric pressure. Direct contact condensers allow
mixing of the coolant and vapor inside the condenser body. This is a cheaper option and commonly
employed with most aqueous systems. These may be classified as wet or dry, or barometric and low
level. A wet condenser removes noncondensed gases and cooling water by the same pump while
separate pumps are employed in a dry condenser. In practice, parallel flow condensers are almost
always wet condensers while counter-current condensers are always dry.
6.5 Evaporator accessories
183
Evaporator
accessories
Condenser
Condenser and
vacuum system
Condensate
removal
system (pumps
and taps)
Vent/ Catchall
Vacuum system
(vacuum pump
or ejector)
Direct contact
Surface
Jet (wet)
condenser
Countercurrent
Barometric
(dry)
FIGURE 6.16
Evaporator accessories.
The most common type of direct contact condensers is the counter-current barometric condenser.
Here vapor is condensed while rising against a shower of cooling water,
and the condenser is located at an elevation allowing gravity discharge
of water from vacuum in the condenser through the barometric leg.
Barometric condenser
Such condensers are inexpensive and economical on water consumption. They can usually be used to maintain a vacuum corresponding to a
saturated vapor temperature within 3 C of the water temperature
leaving the condenser. The ratio of water consumption to vapor condensed can be determined from
enthalpy balance.
Jet or wet condensers use high-velocity water jets both for condensation of vapor and also to force
noncondensable gases out of the tailpipe. This type of condenser is placed at
a lower elevation (below barometric height) and requires a pump to remove
the mixture of water and gases. Jet condensers consume more water than
Jet Condenser
common barometric type condenser and cannot be throttled conveniently to
conserve water at low evaporation rates.
184
Chapter 6 Evaporators
6.5.2 Vent systems
Noncondensable gases are invariably present in the vapor as a result of air in-leak, dissolved air in feed
or reaction during evaporation. When the vapor is condensed in a succeeding effect, the concentration
of noncondensable gases increases and impedes heat transfer. Therefore, noncondensable gases should
be vented well before their concentration reaches 10%. Since gas concentrations are difficult to
measure, the usual practice is to overvent and an appreciable amount of vapor can be lost in poorly
designed systems.
Venting is usually done from the upper part of the steam chest of one effect to the steam chest of the
next, which is at a lower pressure. This line is provided with a throttling valve to limit the flow and
ensure that the excess vapor in one vent performs useful evaporation at a steam economy only about
one less than the overall steam economy. When there are large amounts of noncondensable gases
present as in beet-sugar evaporation, it is desirable to pass the vents directly to the condenser to avoid
serious losses in heat-transfer rates. In such cases, it can be worthwhile to recover heat from the vents
to preheat the entering feed in separate heat exchangers.
The noncondensable gases eventually reach the condenser (unless vented from an effect above
atmospheric pressure to the atmosphere or to auxiliary vent condensers) and will be joined by the
dissolved air in case of direct contact condenser. A water-jet-type condenser or a separate vacuum
ejector may be used to remove these gases. Reciprocating pumps or water-ring (Hytor) pumps may
also be used if high-pressure cooling water or steam is unavailable.
Salt removal
In crystallizing evaporators, salt crystals are to be removed along with a minimum quantity of mother
liquor. In installations with sufficiently high headroom, the body is often located above the barometric
height, and the lower part of the body provides a settling zone, where salt concentration builds up. Large
diameter drains, at convenient locations drain the salt by gravity in short periodic cycles with only a
small risk of plugging. In situations, where the headroom is limiting, and the salt removal rate is up to
1000 kg/hr, a salt trap vessel is connected at the bottom of the effect where the salt settles. The trap vessel
is periodically isolated from the effect and emptied. The air in the trap must be displaced fully with feed
liquor before reconnecting the trap, or else this creates problem in condensation of vapor.
6.6 Evaporator design
A properly designed evaporator must, at a minimum:
•
•
•
•
•
•
•
effectively transfer heat at a high rate with the minimum surface area so that it is economical for
installation, operation, and maintenance
effectively separate vapor from liquid concentrate
meet solvent evaporation capacity
meet product quality (concentration)
be energy efficient by effective use of steam in multiple-effect evaporation or vapor
recompression, wherever possible
minimize fouling of heat transfer surface
be constructed of materials which minimize corrosion
6.6 Evaporator design
185
There are three principal elements in evaporator design e heat transfer, vapor-liquid separation,
and energy utilization. Among these, heat transfer is the most important factor since the heat transfer
surface represents the largest component of evaporator cost.
6.6.1 Single-effect evaporation
The surface area of a continuous single-effect evaporator is obtained from the heat transfer equation as
q
A¼
(6.1)
UDTeff
Where q is obtained from energy balance neglecting condensate subcooling and radiation losses. It is
important to have a clear understanding of the basis of definitions of DTeff and its corresponding U.
The effective temperature driving force for heat transfer (DTeff) is given as e
DTeff ¼ Tcon T
(6.2)
Where Tcon is the temperature at which the heating vapor (steam) condenses and T is the bulk liquid
temperature, which is estimated by adding the boiling point elevation (BPE) of the liquid leaving the
effect to the boiling point (Ts) of pure solvent (water in most cases) at the operating pressure (P) in the
effect, i.e.,
T ¼ TS þ BPE
(6.3)
BPE is a function of the solute concentration x in the thick liquor leaving and is available from
literature and TS is found from steam table as saturation temperature corresponding to pressure P.
Feed to the evaporator can be at a lower temperature than the effect but quickly attains the bulk
liquid temperature (T) due to well-mixed liquid phase in evaporators. The heating steam enters at a
temperature Tsteam with a few degrees of superheating and quickly cools to its saturation (condensing)
temperature (Tcon). Therefore the effective temperature driving force for heat supply to the effect is
considered as DTeff ¼ TconT, and the heat transfer coefficient (U) is defined with respect to this
temperature driving force.1 In an evaporator, the average boiling point of liquid is higher than the
boiling point corresponding to the pressure in the vapor space due to the effect of hydrostatic head.
This reduces the DT across the heating surface, thereby causing a decrease in evaporator capacity.
Fig. 6.17 shows the parameters of material and energy flows around a single effect with the
notations F, L, V, S corresponding to feed, liquor, vapor, and steam mass flow rate, respectively. Solute
concentration (x,xF in % w/w), enthalpy per unit mass (h) and temperature (T) and pressure (P) values
are marked therein. Subscripts L, V, steam, and con denote thick liquor, vapor leaving, supply steam,
and condensate generated. hsteam is obtained from the steam table at steam supply pressure Psteam and
temperature Tsteam. Enthalpy of feed and thick liquor are respective functions of solute concentration
(xF and x) and temperature. These are found from enthalpy charts (see Fig. 6.22) for different solutesolvent systems. In absence of such charts or experimental data, information can be obtained from
solution rules with or without considering the heat of solution.
1
Earlier practice was to define U corresponding to the apparent temperature difference DTapp ¼ (TconTs). One must be
careful while employing data reported in literature and check whether the value of reported U is based on true or apparent
temperature difference as DTapp DTeff.
186
Chapter 6 Evaporators
Vapour
V
hV
T
P
T = Ts (P)
+BPE (x)
P
Steam
S
hSteam
Thick liquor
TSteam
L
PSteam
x
Feed
hL
F
T
xF
hF
TF
Condensate
S
hcon
Tcon = Ts (PSteam )
PSteam
FIGURE 6.17
Parameters related to material and energy flow around a single effect.
Using the notations specified in Fig. 6.17, the mass and energy balance equations are e
F¼L þ V
(6.4)
FxF ¼ LxL
(6.5)
FhF þ Shsteam ¼ LhL þ VhV þ Shcon
(6.6)
Equipment costs are usually correlated as a function of heating surface area, the material of
construction, and evaporator type. Other things being equal,
the evaporator type is selected on the basis of highest heat
transfer coefficient under the desired operating condition. U is
Overall heat transfer coefficients
governed primarily by the boiling liquid coefficient as it is
much lower than the the steam side coefficient. The boiling
liquid side coefficient is influenced by the velocity and viscosity of the evaporating liquid and cleanliness of the heating surface. Higher overall heat transfer
coefficient allows a lower temperature difference between the heating fluid and the product. This can
be achieved by mechanical agitation.
6.6 Evaporator design
187
Usually overall heat transfer coefficients are used in evaporator design. The curves of Fig. 6.18 as
represented by Eq. 6.7 can be used for vertical tube evaporators.
"
#
ða bÞ
U ¼ 5:6783 b þ
(6.7)
1 þ ð0:5556 DTeff =cÞd
Where U and DTeff are in W/m2K and oC, respectively, and the constants a, b, c and d for different
boiling points in the effect are given in Table 6.4.
Table 6.4 Constants to be used in Eq. 6.7 for predicting U.
Boiling Point ( C)
a
b
c
d
100
0.4530
720.2609
12.7327
0.9524
75
0.4856
684.4337
22.3611
1.1038
60
0.2090
509.0018
26.5472
1.2798
50
0.3641
687.8854
83.2172
1.0207
3000
U (W/m2k)
2000
1000
BP 100°C
BP 75°C
BP 60°C
BP 50°C
0
0
20
40
ΔTeff (°C)
FIGURE 6.18
Relationship between boiling point (BP), temperature drop (DTeff) and overall heat transfer coefficient in
vertical tube evaporators.
These curves are derived from the experimentally generated curves by Badger and Shepard (AIChE
Trans. 13(I):101e137(1920)) for 3000 diameter evaporator with 24 numbers of 200 diameter 4800 long
tubes.
While DTeff and condensing temperature (Tcon) are fixed by operating conditions and not by
evaporator construction, the removal of noncondensable gases depends on the evaporator construction.
188
Chapter 6 Evaporators
Removal of noncondensable gases in vertical tube evaporator is not very efficient. Noncondensable
gases are transferred to the condensate steam chest in horizontal tube, long tube vertical and forced
circulation evaporators.
6.6.2 Multiple effect evaporation
The equations for a single effect are valid for the individual effects of the multiple-effect evaporator.
The rate of heat transfer for any effect ‘i’ is thus, given by
qi ¼ Ui Ai DTeff ;i
(6.8)
Assuming that the feed enters the first effect at its boiling point and the condensate leaving effect
2 is at the temperature of vapor obtained from the boiling liquid in the first effect (T1), the entire heat
used in generating vapors in the first effect must be given out when the same vapor condenses in the
second effect and so on.
Mathematically,
qi ¼ qi1 ¼ qiþ1
(6.9)
Ui Ai DTeff ;i ¼ Ui1 Ai1 DTeff ;i1 ¼ Uiþ1 Aiþ1 DTeff ;iþ1
(6.10)
or
Where DTeff,i for each effect is given by Eq. 6.2.
In ordinary practice, to obtain economy of construction, all Ais are preferred to be equal, which
gives e
Ui DTeff ;i ¼ Ui1 DTeff ;i1 ¼ Uiþ1 DTeff ;iþ1
(6.11)
Therefore, the temperature difference across the heating surface in each effect (DTeff,i) of a
multiple-effect evaporator is inversely proportional to the heat transfer coefficient.
Optimum number of effects in a multiple-effect system
Assuming that the latent heat is not significantly influenced by pressure, it can safely be considered
that the latent heat required to evaporate 1 kg steam is same in each effect and for every 1 kg steam
supplied to the first effect, N kg water will be evaporated in an N-effect evaporator while the evaporator
capacity remains substantially constant.
Total amount of heat required to achieve the evaporator capacity (total evaporation per hour) for N
effects is
qtotal ¼
N
X
i¼1
qi ¼
N
X
Ui Ai DTeff ;i
(6.12)
i¼1
For all effects having equal area (Ai ¼ Ai1 ¼ Aiþ1) and an average coefficient Uav
qtotal ¼ Uav ADTov
(6.13)
Where DTov, the overall temperature difference in the evaporator system is given by
DTov ¼ Tsteam TV
(6.14)
6.6 Evaporator design
189
Tsteam is the heating steam supply temperature and TV refers to the vapor saturation temperature from
the last (Nth) effect (including BPE).
For a single-effect evaporator of area A, operating at DTov with a heat transfer coefficient Uav
q ¼ Uav A DTov
(6.15)
Thus for constant DTov, the total capacity of the system remains substantially unchanged by varying
the number of effects while the capital cost increases. Thus a N effect evaporator will cost about N
times a single-effect evaporator. Therefore, the choice of the proper number of effects is dictated by an
economic balance between savings in steam obtained by multiple-effect evaporation and added investment costs due to addition of each additional effect.
The total annualized cost, computed as the sum of the annualized fixed cost (calculated based on
the prevailing interest rate) and the annual cost of steam, water, and labour is the economic parameter
that is optimized. The number of effects that correspond to the minimum annualized fixed cost is the
optimum number of effects for the design case. Fig. 6.19 shows a typical graph for finding the
optimum.
It is needless to say that if the optimum number of effects thus obtained is a fraction, it is rounded
off to the next higher number.2
30
25
Total annualised cost
Cost
20
Optimum
15
Annual steam cost
Annualized fixed cost
10
Annual water cost
5
Annual labour cost
0
1
2
3
4
No. of Effects
FIGURE 6.19
Plot for arriving at the optimum number of effects.
2
Annualized fixed cost (Rs/year) ¼ (Interest % per annum/100) Fixed cost (Rs).
5
190
Chapter 6 Evaporators
6.6.3 Design data
Elevation of boiling point (BPE)
Usually evaporators deal with concentrated solutions whose specific heat, latent heat of vaporization
and boiling point deviate from water. There may be other thermal phenomena (e.g., heat of crystallization) that need to be considered. The elevation in boiling point for different solute percentages at
different pressures is estimated from Duhring plot and the change in other thermodynamic properties
are estimated from enthalpy-concentration plots.
Duhring plots: These are plots of boiling point of pure solvent (usually water) in the abscissa and
the corresponding boiling point of the solution in the ordinate at the same pressure. Different lines are
for solutions at different concentrations. The points on a particular line are for a solution of same
concentration but different pressures. These are straight lines for practical purposes that make interpolation and extrapolation easier. Boiling point elevation (BPE) of a solution at a particular concentration is thus obtained from the difference between the ordinate and abscissa at that concentration
where the abscissa corresponds to the pure solvent boiling point at the effect pressure. The linearity of
the lines suggests that the boiling point elevation is primarily a function of solute concentration and
does not change much with pressure and temperature. This is a fact that is often used for simplifying
calculations. Although linear, the lines are not parallel and in general have a steeper slope for more
concentrated solution, i.e., boiling point elevation (BPE) increases faster with increasing pressure for
more concentrated solution than for dilute solutions. Fig. 6.20 presents a typical Duhring plot for
sodium chloride solution.
FIGURE 6.20
Duhring Plot for sodium chloride solution.
6.6 Evaporator design
191
Boiling point elevation is usually small and can be neglected for (i) very dilute solutions and
(ii) solutions of materials with extremely high molecular weight.
Information on boiling point elevation not only provides an estimate of the boiling point of
concentrated solutions but also gives an idea whether low pressure steam can provide a proper temperature difference (DT) for concentrating solutions under atmospheric pressure.3
Boiling point elevation in multiple effect evaporators
The effect of boiling point elevation is more pronounced in multiple-effect evaporators. This is
illustrated in Fig. 6.21 for a single-, double- and a triple-effect evaporator operating under the same
terminal conditions, that is, same steam pressure to the first effect and same saturation temperature of
vapor to condenser. Total height of each column in the figure represents DTov, the total temperature
spread from steam temperature to saturation temperature of vapor in last effect. The shaded portions
represent loss of DT due to boiling point elevation in each effect The figure reveals that in the extreme
case of a large number of effects or very high BPE, the sum of the BPEs may be equal to or even more
than DTov, the total temperature drop available. Operation is impossible under this condition.
ΔTeff,1
BPE1
Single Effect
T1
Ts(P1)
T1
Ts(P1)
ΔTeff,1
BPE1
ΔTeff,2
BPE2
Double Effect
Ts (Psteam)
T1
Saturation
temperature
of supply
steam
Ts(P1)
ΔTeff,2
BPE2
Effect 3
Effect 2
BPE1
Effect 1
(C)
Effect 2
Effect 1
(B)
ΔTeff,1
Temperature
(A)
T2
Ts(P2)
ΔTeff,3
T2
BPE3
Ts(P2)
Triple Effect
T3
Ts(P3 )
Saturation
temperature
of vapour
effect
Ts (Psteam) = Saturation temperature of steam
supplied at pressure Psteam
Ts (P3 ) = Saturation temperature of vapour
from last (3rd) effect at pressure P3
BPE1, BPE2, BPE3 = Boiling point elevation of solution
in effect 1, 2, 3.
FIGURE 6.21
Comparison of temperature driving forces in (A) single (B) double and (C) triple effect evaporator with same
terminal conditions.
3
When the boiling point elevation is not (accurately) known, it has been a customary practice to use an apparent temperature
difference, DTapparent(¼ Tsatd steam Tsatd vap).
192
Chapter 6 Evaporators
Enthalpy plots
Evaporator design calculations involve enthalpy balance around the effects that require solution
enthalpy to be evaluated. Enthalpy of the solution is a function of solute concentration and solution
temperature and pressure. This data is presented as enthalpy plots, for example, in Fig. 6.22, where
lines of constant solution boiling temperature are drawn on graphs with solute concentration in abscissa and enthalpy of solution in ordinate. Pressure is not included as a parameter in the enthalpyconcentration plot as the solution boiling point and its solute concentration defines it implicitly.
The pure solvent boiling point corresponding to the solution (boiling) temperature and solute concentration can be found from the Duhring plot for the system and the corresponding pressure is the
vapor pressure of pure solvent. In some cases, the same information may also be available as separate
plot of solution vapor pressure.
In absence of enthalpy-concentration charts, the enthalpy of feed and thick liquor can be calculated
from specific heats of components. Heats of dilution are usually neglected. The latent heat of
vaporization of water from an aqueous solution may be taken from steam tables at the actual boiling
temperature of the solution rather than the equilibrium temperature of pure water.
Tsteam & Tcon
Among pressure and temperature, pressure can be measured more easily and in the temperature range
involved in evaporators, it can be measured more accurately than temperature. Therefore, the pressure
in the steam chest is measured and the saturated temperature is obtained from steam tables. The same
applies to the vapor space. The saturation temperature is obtained from steam tables corresponding to
the measured pressure in the vapor space and the boiling point elevation added to this gives the actual
temperature of the steam space.
(148.9°C)
250
30
200
250
°F
(121.1°C)
200
°F
(93.3°C)
150°
F
(65.6°C)
100°F
(37.8°C)
150
100
0°F
600
500
400
300
200
50
Enthalpy (kJ/kg solution)
Enthalpy (btu/lbm solution)
300
100
(10°C)
50°F
0
0
0.10
0.20
0.30
0.40
0.50
0.60
Concentration (wt fraction NaOH)
FIGURE 6.22
Enthalpy plot for NaOH solution.
Geankoplis, C. J., (2003). Transport processes and separation process principles (unit operations) (4th ed.). Reprinted by
permission of Pearson Education, Inc., New York, NY.
6.6 Evaporator design
193
Steam pressure
Although steam at a higher pressure leads to a higher DT and a consequent decrease in the heat transfer
area (and cost) of an evaporator, it is rarely used as heating medium for evaporation because
•
•
•
High pressure steam is much more valuable as a source of power than a source of heat. It is much
cheaper to generate power using high pressure steam and use the exhaust steam in evaporator than
to use boiler steam directly.
Steam at higher pressure has a higher enthalpy but a lower latent heat of vaporization. So low
pressure steam can deliver more latent heat per kg steam.
The construction of an evaporator to hold high pressure steam would be more expensive.
The disadvantage of low pressure steam is that it exists at a lower temperature and so provides
lower DT between steam and evaporating liquid. Usually the steam pressure is between 1 and
0.7 atm(g) and in some case can be up to 2.5e3 atm(g).
Pressure in the vapor space
It is important to note that evaporators do not necessarily have to work under vacuum. A vacuum is
necessary solely for the purpose of obtaining a larger DTov. Vacuum also ensures that heat-sensitive
products and feeds do not decompose or alter during evaporation and entails cheaper construction
(lower capital cost).
One may use steam at 10 e 15 kg/cm2(g) and take off vapor at 3.5e5.5 kg/cm2(g) if there is a use
for such vapor in the plant but such cases are not common.
Influence of feed, steam and condensate temperature
The feed temperature usually has no effect on evaporator calculation. This arises because the volume
of liquid in evaporator is very large compared to the amount/rate of feed addition and the liquid is
always at the final concentration at the boiling point of the final solution. Moderate amounts of superheat in the steam used for heating and subcooling of the condensate also has negligible effect on the
mean temperature of steam. Therefore, temperature of feed, temperature of condensate and (in most
practical cases) any possible superheating of steam are neglected in evaporator design calculations and
a practical working temperature difference is the temperature difference between temperature of
saturated steam and boiling liquid.
However, if the feed is at a temperature much below its boiling point and the amount of evaporation
is small, there would be areas where the liquid temperature is below the temperature of the thick liquor.
Since it is impossible to estimate the extent of these areas and their mean temperature in advance, the
only practical temperature that can be used in calculations is the boiling point of thick liquor.
Therefore, it is desirable to use a feed preheater to heat the feed to nearly its boiling point in the
evaporator.
6.6.4 Design algorithm for multiple-effect evaporator
The evaporator schematic is depicted in Fig. 6.23 with key variables shown. Steam is supplied to the
first effect on the left and the vapor boil up in effects are used to heat the subsequent effect. The final
vapor stream is condensed. To compute the energy balance for the units, information on enthalpy and
boiling point elevation are required. Heat transfer coefficient data or correlation are required for each
effect. The pressure, at which the last effect is operated, often at vacuum, must be known.
194
Chapter 6 Evaporators
2nd Effect
1st Effect
Vi-1
V1
V2
hV1
hV2
hVi-1
T1 Vapour 1 T2 Vapour 2 Ti-1
P1
P2
Pi-1
S
hsteam
Tsteam
Psteam
F
xF
hF
TF
P1
T1=Ts(P1)
+BPE(x1)
ith Effect
Vi
hVi
Vapour T
Vapour i
i
i-1
Pi
P2
T2=Ts(P2)
+BPE(x2)
Pi
Ti=Ts(Pi)
+BPE(xi)
Steam
Feed
L2
x2
hL2
T2
L1
x1
hL1
T1
VN-1
Li
xi
hi
Ti
Li-1
xi-1
hLi-1
Ti-1
S
Vi-1
hcon1
Condensate 1
Condensate 2
V1
Tcon,1 = T (P
hcon,i-1
hcon2
s steam)
Tcon,i =Ts(Pi-1)
Tcon,2 = T (P )
Psteam
s 1
Pi-1
P
Nth Effect
VN
hVN
TN Vapour N
PN
To vacuum/
Condenser
PN
TN=Ts(PN)
+BPE(xN)
LN-1
Condensate i
i
VN-1
hcon,N
Product
LN
XN(=Xp)
hL
T = TS(PN)
Condensate N
Tcon,N =Ts(PN-1)
PN-1
FIGURE 6.23
Generalized configuration of N-effect forward feed evaporator.
The following convention is used in Fig. 6.23.
F
Feed mass flow rate entering Effect 1
xF
Mass fraction of solute in F
TF
Temperature of feed stream
hF
Enthalpy of F at TF
S
Mass flow rate of heating steam entering 1st effect
Psteam,
Tsteam
Temperature and pressure of S
hcon,steam
Enthalpy of condensate (saturated) water at pressure Psteam
hcon,i
Enthalpy of condensate (saturated) water at pressure Pi1 (in effect i1)
Li, Vi
Liquid and vapor mass flow rate leaving ith effect
Ti, Pi
Temperature and pressure in ith effect
hLi, hVi
Enthalpy of Li and Vi at Ti, Pi
xi
Mass fraction of solute in Li
xP
Mass fraction of solute in product liquid (LN) leaving Nth effect (last effect)
BPEi
Boiling point elevation in ith effect with respect to saturation temperature of pure solvent (Ts(Pi)) in
the same effect
6.6 Evaporator design
195
Design input
Process design of evaporator with N effects starts with known
(i) feed rate (F), feed conditions (xF, TF) and desired product concentration (xP)
(ii) Pressure (PN) in Nth stage (last effect).
(iii) System properties e calculation procedure and/or tables for saturation temperature of solvent
(water: steam tables), BPE, enthalpy of solution and solution properties (may be available in the
form of Figs. 6.20 and 6.22 as already discussed).
(iv) Steam supply pressure and temperature (Psteam and Tsteam). Usually Tsteam will have a few
degrees of superheat.
(v) Evaporator type and configuration and the estimated heat transfer coefficient of each effect (U1,
U2, . UN). This is usually known from past experience of design and operation. It is important
to note that for evaporators, Ui is based on the temperature difference of condensing vapor/
steam in the steam chest (Ts(Pi1)) and the (saturation) temperature of vapor leaving ith effect.
In case of the first effect, Ts(Pi1) ¼ Ts(Psteam).
Process design output for the chosen type of multiple-effect evaporator includes:
(i) Heating steam requirement e estimated from mass and energy balance
(ii) Heating surface requirement e estimated from heat transfer equations
(iii) Estimated temperature in each effect
(iv) Amount of vapor leaving the last effect and going to the condenser
The design solution involves trial and error.
Design objective
Meeting the final product concentration with high steam economy is the foremost objective. The
multiple-effect evaporator design aims to arrive at a design with (nearly) same heat transfer area for
each effect. This is an indirect way to economize on fabrication cost and minimize inventory cost by
holding common spares.
Design deliverables
To summarize, process design output gives the heat transfer areas (Ai, i ¼ 1, .,N) and also includes
values of all variables shown on Fig. 6.23, whose values are not specified as design input.
Design algorithm
i) Note the inputs: N, F, xF, TF, PN, U1, U2, . UN
ii) Find the value of Ts(PN) from steam table
iii) LN ¼ F xF/xP
iv) Vtotal ¼ F LN
N1
P
v) Assume: Vi: i ¼ 1, .,N 1; Calculate VN ¼ Vtotal Vi ; Initial guess can be Vi ¼ (F LN)/N,
i¼1
for i ¼ 1,...,N.
vi) L1 ¼ F e V1 and Li ] Li1 Vi for i ¼ 2, .,N1
vii) BPEi ¼ BPE(xi), for i ¼ 1, .,N e this can be found from the Duhring plots (Fig. 6.20) that are
linear and pass through the origin.
196
Chapter 6 Evaporators
viii) SBPE ¼
N
P
BPEðxi Þ
i¼1
ix) DTov ¼ Ts(Psteam) Ts(PN)
and for all the effects put together DTeff,total ¼ DTov SBPE
x) Assume: DTeff,i, i ¼ 1, .,N1 and estimate DTeff ;N ¼ DTeff ;total N1
P
i¼1
DTeff ;i ;
Initial guess can be from assuming same heat transfer rate in each effect which gives
DTeff ;total
DTeff ;i ¼ N
ð1 =Ui Þ
P
ð1=Ui Þ
i¼1
xi) TN ¼ Ts(PN)þBPE(xN);
Tcon;1 ¼ Ts ðPsteam Þ
Tcon;i ¼ Ts ðPi1 Þ ¼ Ti þ DTeff ;i
and Ti1 ¼ Tcon;i þ BPEðxi1 Þ;
i ¼ N; .; 2
xii) S ¼ {V1hV,1(T1)þhcon,steamFhF(TF)}/hsteam(Tsteam, Psteam)
hF ¼ hF ðTF Þ
hV;i ¼ hs Tcon;iþ1 þ CP;steam Ti Tcon;iþ1 ; i ¼ 1; .; N 1
hV;N ¼ hs Tcon;N1 þ CP;steam ðTN Ts ðPN ÞÞ
hcon,i ¼ hw(Tcon,i), i ¼ 1, .,N1, [hw(Tcon,i) stands for saturated water enthalpy at Tcon,i
obtained from steam table.]
hL,i ¼ hL(xi,Ti), i ¼ 1, .,N, [Enthalpy of solution with solute concentration xi at Ti from table/
chart similar to Fig. 6.22 applicable for the system.]
xiii) Calculate heat load and area required for each effect
q1 ¼ S hsteam ðTsteam ; Psteam Þ Tcon;1
qi ¼ Vi1 hV Tcon;i ; i ¼ 2; .N
Ai ¼ qi = Ui DTeff ;i
If max ABS Ai SNi¼1 ðAi Þ = N > 0:05; i ¼ 1; .; N; then
re-estimate
DTeff
ðqi = Ui Þ; go to step xi
DTeff ;i ¼ N
P
ð1=Ui Þ
i¼1
xiv) Recalculate V from the following set of N equations formed by energy balance around each
effect e 1st Effect
V1 ¼ F hF hL;1 þ S hsteam ðTsteam ; Psteam Þ hcon;1 = hV;1 hL;1
6.7 Design illustration
197
2nd to Nth Effect
Vi ¼ Li1 hL;i1 hL;i þ Vi1 hV;i1 hcon;i = hV;i hL;i ; i ¼ 1; .; N
xv) Check validity of Vi estimates in step v
If max ABS Vi SNi¼1 ðVi Þ N > 0:01, i ¼ 1, .,N, then re-estimate Vi ¼ values from step
(xiv), i ¼ 1, N 1,
VN ¼ Vtotal N
1
X
Vi
i¼1
go to step v.
xvi) Report e
Overall steam economy ¼ (F LN)/S.
1st Effect steam economy ¼ V1/S.
iih Effect steam economy ¼ Vi/Vi1, i ¼ 2, .,N.
Capacity: Feed processed per unit mass steam required ¼ F/S.
Product produced per unit mass steam required ¼ LN/S.
6.7 Design illustration
Design example 1
Design a forward feed triple effect evaporator to concentrate 14% w/w caustic soda solution to a
product with 40% w/w NaOH. Feed liquor is available at 6 kg/s at 75 C. Last effect of the evaporator
can be connected to an existing vacuum system and operated at a pressure of 7 kPa (abs). Steam with
negligible superheat is available at 120 C. Estimated overall heat transfer coefficients for the effects
are 3000, 2000 and 1250 W/(m2C), defined with respect to the difference in temperature of the liquid
in the effect and the condensing temperature of steam/vapor heating it.
Process design deliverables
i) Steam consumption (S kg/s)
ii) Heat load (q W); Heat transfer area (A m2); Operating temperature (Ti C) and pressure (Pi kg/
cm2(g)) and condensate temperature (Tcon,i C) in each effect.
iii) Flows rate of all streams (S,V,L kg/s); Concentration of NaOH in each liquor stream (x fraction
w/w)
iv) Enthalpy of all streams (hs, hv, hcon, hF, hL kJ/kg)
Data
N ¼ 3; F ¼ 6 kg/s; xF ¼ 0.14; x3 ¼ 0.4; TF ¼ 75 C;
P3 ¼ 7 kPa ¼ 7/101.3 e 1.03,323 ¼ 0.964 kg/cm2 (g)
198
Chapter 6 Evaporators
BPE table for NaOH.
X,
fraction,
w/w
0
0.1
0.2
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
BPE, C
0
2.2
7.8
13.9
19.4
26.1
36.1
41.7
48.9
55.6
66.7
76.7
Tsteam ¼ 120 C; U1 ¼ 3000; U2 ¼ 2000; U3 ¼ 1250; Psteam ¼ Saturation pressure corresponding
to (Tsteam ¼ 120 C) ¼ 0.9926 kg/cm2 (g)
Tcon,4 ¼ Saturation temperature of steam at pressure P3 ¼ 38.4 C
L3 ¼ FxF /x3 ¼ 2.1; Vtotal ¼ F L3 ¼ 3.9
Trial 1: V1, V2, V3 are assumed equal to one third of Vtotal
V1 ¼Vtotal/3 ¼ 3.9/3 ¼ 1.3; V2 ¼ 1.3; V3 ¼ 1.3;
Step - A
L1 ¼ F e V 1 ¼ 6 e 1.3 ¼ 4.7; L 2 ¼ L 1 e V2 ¼ 4.7 e 1.3 ¼ 3.4; x 1 ¼ FxF /L 1 ¼ 0.1787;
x 2 ¼ FxF /L 2 ¼ 6(0.14/3.4) ¼ 0.2471; Estimating BPE corresponding to x 1, x 2 and x 3 in the
effects from BPE table, in C: 6.49, 10.4 and 26.1.
Total BPE ¼ 42.99
Total DTav ¼ 120 e 38.4 ¼ 81.6 C
DTeff,total ¼ 81.6 e 42.99 ¼ 38.61 C
Estimating individual contribution by assuming same q and Ai in all effects
DTeff,1 ¼ 38.61 (1/3000)/(1/3000 þ 1/2000 þ 1/1250) ¼7.89
DTeff,2 ¼ 38.61 (1/2000)/(1/3000 þ 1/2000 þ 1/1250) ¼ 11.82
DTeff,3 ¼ 38.61 e 7.89 11.82 ¼ 18.9
T3 ¼ Tcon,4 þ BPE3 ¼ 38.4 þ 26.1 ¼ 64.5
Tcon,3 ¼ 64.5 þ 18.9 ¼ 83.4
T2 ¼ Tcon,3 þ BPE2 ¼ 83.4 þ 10.4 ¼ 93.8
Tcon,2 ¼ 93.8 þ 11.82 ¼ 105.62
T1 ¼ Tcon,2 þ BPE1 ¼ 105.62 þ 6.49 ¼ 112.11
Tcon,1 ¼ saturation temperature of steam ¼ 120 C
Estimation of effect pressure (g)
P1 ¼ saturation pressure corresponding to 105.62 C ¼ 0.2263 kg/cm2(g)
P2 ¼ saturation pressure corresponding to 83.4 C ¼ L0.4792 kg/cm2(g)
6.7 Design illustration
199
Enthalpies
hsteam(Tsteam, Psteam) ¼ 2705.9; hcon,1 ¼ hsat steam(Tcon1) ¼ 503.9
hV,1 ¼ hsteam(T1,P1) ¼ 2697.1; hcon,2 ¼ hsat steam(Tcon2) ¼ 442.9
hV,2 ¼ hsteam(T2,P2) ¼ 2669.5; hcon,3 ¼ hsat steam(Tcon3) ¼ 349.3
hV,3 ¼ hsteam(T3,P3) ¼ 2676.1;
Enthalpy of solution found by neglecting heat of solution and considering NaOH (Specific heat of
solid ¼ 1.4915 kJ/kg) to have enthalpy “zero” at 0 C.
hF ¼ hF (75,0.14) ¼ 285.7
hL,1(112.11,0.1787) ¼ 416.2
hL,2 (93.8,0.2471) ¼ 330.5
hL,3 (83.4,0.4) ¼ 200.5
S ¼ (V1 hV,1 þ L1 hL,1 FhF)/(hsteam hcon,1) ¼ 1.703
q1 ¼ S.(hsteam hcon,1) ¼ 1.701(2705.9 503.9) ¼ 3735.5
q2 ¼ V1.(hV,1 hcon,2) ¼ 2931.5
q3 ¼ V2.(hV,2 hcon,3) ¼ 3016.4
A1 ¼ q1 / [U1 (Tcon,1 T1)] ¼ 0.1580
A2 ¼ q2 / [U2 (Tcon21 T2)] ¼ 0.1240
A3 ¼ q3 / [U3 (Tcon,3 T3)] ¼ 0.1276
Aavg ¼ (A1 þ A2 þ A3) / 3 ¼ 0.1365
% deviation from Aavg ¼ 5.2433, 3.0596 and 2.1837.
Recalculating DTeff,1, DTeff,2 and DTeff,3
X
ðqi = Ui Þ ¼ 5.124
i¼1;3
DTeff ;1 ¼ DTeff ;total ðq1 = U1 Þ=5:124 ¼ 9.3829
DTeff ;2 ¼ DTeff ;total ðq2 = U2 Þ=5:124 ¼ 11.0451
DTeff ;3 ¼ DTeff ;total ðq3 = U3 Þ=5:124 ¼ 18.1835
Recalculated A values with new values of DTeff,1, DTeff,2, DTeff,3: 0.1315, 0.1329 and 0.1328. These
are within 5% from Aavg.
Re-estimating V values
V1 ¼ q1 þ F $ hF L1 $ hL;1 =hsteam ðT1 ; P1 Þ ¼ 1.3000
V2 ¼ q2 þL1 $ hL;1 L2 $ hL;2 =hV;2 ¼ 1.3269
V3 ¼ q3 þ L2 $ hL;2 L3 $ hL;3 =hV;2 ¼ 1:2731
Recalculated Vi values differ from corresponding V values by more than 1%. Hence, new assumed
values for are V are replaced by Vi values and calculations from Step A are repeated till the Vi and V
values differ within 1% and the design calculation converges.
200
Chapter 6 Evaporators
The final converged results
Parameter
Effect 1
Effect 2
Effect 3
Feed/liquor entering, kg/s
6
4.7
3.3731
Steam/heating vapor entering, kg/s
1.6901
1.3
1.3269
Solute in feed/liquor entering, (wt fraction)
0.14
0.1787
0.2490
Vapor leaving, kg/s
1.3
1.3269
1.2731
Liquor leaving, kg/s
4.7
3.3731
2.1
Solute in liquor leaving, (wt fraction)
0.1787
0.2490
0.40
BPE, C
6.49
10.51
26.1
Effect temperature, C
110.7
93.3
64.5
Condensing temperature in steam chest, C
120
104.2
82.8
Condensing temperature of vapor leaving effect 3, C
2
38.4
U, W/m .s
3000
2000
1250
q,W
3704.7
2936.3
3080.9
Area, m2
0.1333
0.1346
0.1345
Feed/liquor entering
285.67
410.98
328.31
Liquor leaving
410.98
328.31
200.46
Enthalpy, kJ/kg
Vapor leaving
2695.9
2668.8
2675.2
Steam/heating vapor entering
2705.9
2695.9
2668.8
Condensate leaving
503.8
437
346.8
Design example 2
Design a feed forward evaporator system to concentrate 50,000 kg/hr feed of 7% w/w glycerol
available in storage tank at 27 C, to 80% w/w finished product. Steam is available at 103.6 kPa(abs)
and the vacuum utility can generate 92.5 mm Hg (abs.) pressure in the last effect. The overall heat
transfer coefficients in W/m2. C1 are estimated to be 2350, 1250, 1120, if a 3-effect system is used. If
more effects are used, then conservatively the first three effects be considered to have the same U and
the later ones to have 1120 W/m2. C1.
Specific heat of pure glycerine is 2.42 kJ/(kg. C).
Deliverables
Designs with 3, 4 and 5 effects along with a comparison table.
Please see Example of 1 for the deliverable items.
Data.
For 3-effect design.
U1 ¼ 2350; U2 ¼ 1250; U3 ¼ 1120;
6.7 Design illustration
201
Boiling point of glycerol solutions.
Pressure
(mm Hg)
Boiling point of liquor ( C)
Boiling
point of
water
( C)
Weight fraction of glycerol in liquor
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.9564
92.3
50
50.2
50.9
52.1
53.4
55.2
57.6
61
66.2
80.1
103.1
149.19
60
60.3
61
62.2
63.5
65.5
68.1
71.5
77.3
92
117.6
233.53
70
70.4
71.2
72.4
73.7
75.6
78.5
82.2
88.3
104
132.1
355.1
80
80.5
81.4
82.6
84
86
88.8
92.8
99.3
116
146.5
525.8
90
90.6
91.5
92.8
94.2
96.3
99.3
103.5
110.3
127.8
161.1
760
100
100.7
101.6
102.9
104.5
106.7
109.6
114
121.5
139.8
175.8
The BPE table prepared based on the above table is e
Boiling point elevation of liquor ( C)
Pressure
(mm Hg)
Weight fraction of glycerol in liquor (x)
Boiling point of
water (Tw) ( C)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.9564
92.3
50
0.2
0.9
2.1
3.4
5.2
7.6
11
16.2
30.1
53.1
149.19
60
0.3
1
2.2
3.5
5.5
8.1
11.5
17.3
32
57.6
233.53
70
0.4
1.2
2.4
3.7
5.6
8.5
12.2
18.3
34
62.1
355.1
80
0.5
1.4
2.6
4
6
8.8
12.8
19.3
36
66.5
525.8
90
0.6
1.5
2.8
4.2
6.3
9.3
13.5
20.3
37.8
71.1
760
100
0.7
1.6
2.9
4.5
6.7
9.6
14
21.5
39.8
75.8
The above table will be interpolated based on x and T. However we note that in last effect with
92.5 mm Hg, Boiling point of water is Tw ¼ 50 C and for x ¼ 0.8, the BPE is 16.2 C in the last effect.
The first effect heating steam is at 103.6 kPa(abs) with saturation temperature of 100.6 C. If we
consider three effects, the DTav ¼ 100.6 e 50 ¼ 50.6; T(3) ¼ 50 þ 16.2 ¼ 56.2 C. BPE for x ¼ 0.07
will be max 0.6 C. If we consider a driving force of w15 C in the first effect, the effect will operate at
85 C.
A look at the BPE table suggests that with this range of Tw and x, the BPE estimation based only on
x can entail w1 C maximum error and we decide to go for the approximation.
Data
N ¼ 3; F ¼ 50,000/60 ¼ 833.3 (kg/s); x F ¼ 0.07; x 3 ¼ 0.8; T F ¼ 27;
P steam ¼ 103.6 kPa(abs) ¼ 103.6 .010,197 e 1.03,323 ¼ 0.02,318 kg/cm 2 (g)
P3 ¼ 92.5 mm Hg(abs) ¼ (92.5/760 e 1) 1.03,323 ¼ 0.90,748 kg/cm2(g)
U1 ¼ 2350; U2 ¼ 1250; U3 ¼ 1120; Tsteam ¼ saturation temperature corresponding to
(0.02,318 kg/cm2(g)) ¼ 100.6 C
202
Chapter 6 Evaporators
Tcon,4 ¼ saturation temperature of steam at pressure P3 ¼ 50 C
L3 ¼ FxF/x3 ¼ 72.92; Vtotal ¼ F L3 ¼ 760.41;
Trial 1: V1, V2, V3 are assumed equal to one third of Vtotal
V1 ¼ Vtotal/3 ¼ 253.47; V2 ¼ 253.47; V3 ¼ 253.47;
Step e A
L1 ¼ FeV1 ¼ 579.86; L2 ¼ L1 e V2 ¼ 326.39;
x1 ¼ FxF/L1 ¼ 0.1007; x2 ¼ FxF/L2 ¼ 0.1787
Step e B
Roughly estimating BPE in effects from BPE table, C: 0.5, 1 and 16.2.
Total BPE ¼ 17.7
Total DTav ¼ 100.6 e 50 ¼ 50.6 C
DTeff, total ¼ 50.6 e 17.7 ¼ 32.9 C
Estimating individual contribution by assuming same q and Ai in all effects
DTeff,1 ¼ 32.9 (1/2350)/(1/2350 þ 1/1250 þ 1/1120) ¼ 6.61
DTeff,2 ¼ 32.9 (1/1250)/(1/2350 þ 1/1250 þ 1/1120) ¼ 12.42
DTeff,3 ¼ 32.9 e 7.89 11.82 ¼ 13.87
T3 ¼ Tcon,4 þ BPE3 ¼ 50 þ 16.2 ¼ 66.2
Tcon,3 ¼ 66.2 þ 13.87 ¼ 80.07
T2 ¼ Tcon,3 þ BPE2 ¼ 80.07 þ 1 ¼ 81.07
Tcon,2 ¼ 81.07 þ 12.42 ¼ 93.49
T1 ¼ Tcon,2 þ BPE1 ¼ 93.49 þ 0.5 ¼ 93.99
Tcon,1 ¼ saturation temperature of steam ¼ 100.6 C
% Checking if assumed BPE values match x and Tcon,2, Tcon,3, Tcon,4 values
Recalculated BPE values e
BPE1 ¼ BPE(93.49,0.1007) ¼ 0.6412 against 0.5
BPE2 ¼ BPE(80.07,0.1787) ¼ 1.21 against 1
BPE3 ¼ BPE(50,.80) ¼ 16.2 against 16.2
Check if for each effect, the recalculated BPE value differ from the previous value by more than
0.1 C. If the difference is more that 0.1 C, new assumed values are the recalculated values and calculations from Step B are repeated till the previous and values differ by less than 0.1 C.
Further reading
1. Badger, W. L., & Banchero, J. (1997). Introduction to chemical engineering. Bombay: Tata McGraw-Hill
Edition.
2. Kern, D. Q. (1990). Process heat transfer. New York: McGraw-Hill.
CHAPTER
Industrial cooling systems
7
7.1 Introduction
All process industries require streams and equipment to be cooled. Process cooling up to ambient
temperature is carried out with cooling water and also with ambient air. Cooling water (CW) is the
most common process utility used for picking up this heat. Once-through systems use water from a
source like river, sea, or canal and after heat exchange, the warm water is returned back to the same
source or some other stream. Such systems in industrial scale are less popular due to limitations like
the unavailability of sufficient quantity of acceptable quality water throughout the year. Any chemical
added to this water for reducing algal growth or scale reduction also leaves along with the water
discharged.
Circulating cooling water system is the alternative to the once-through system. Many of the industries have changed over from their older “once-through cooling water system” to circulating
cooling water system and installed cooling towers. Air-cooled exchangers, also termed as fin fan
coolers, are frequently used for cooling and condensing process streams with ambient air as the
cooling medium. Fluid coolers are a case of circulating water surface cooler and cooling tower
combined as a single unit.
Drift and evaporation loss put together in a cooling tower (CT) is around 0.2% of the circulation
rate. In a 10,000 m3/hr system, the same will be 20 m3/hr
or 3360 m3 in a week, which is close to the size of a small
pond. The operation of this tower will dry up one such
Cooling Tower vs ‘Once through system’
pond full of water every week. As an alternative, if it is
possible to use a once-through system, 10,000 m3/hr of
water would have been returned to the environment at a
temperature, which would be higher than its initial temperature by around 12 C. In the case of a
flowing stream, the warm water returned mix with the rest of the water and the stream temperature,
usually, rises by around 4e6 C that subsides within a reasonable distance downstream e say after
flowing 500 m and becomes almost imperceptible.
The foregoing analysis suggests that although the CT option is possibly more attractive from the
point of economy for the industry, it may not always be so from the environmental aspect.
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00007-5
Copyright © 2020 Elsevier Inc. All rights reserved.
203
204
Chapter 7 Industrial cooling systems
The present chapter discusses the design of cooling towers (CT) in which the circulating cooling
water comes in direct contact with air. The quality specification of cooling water is available in
Chapter 18 (Table 18.8).
7.2 Cooling tower
Wet Cooling Tower is the most common form of industrial cooling arrangement. The circulating
cooling water picks up heat from the plant and rejects it in the cooling tower. Hot water entering at
the top is distributed within the tower structure in a manner that exposes a large water surface to the
air passing through. Water distribution is achieved by spray nozzles or distribution pans. In most
cases, various types of fill media are used to increase the air-water contacting surface. Airflow can be
due to natural draft or by fans forcing in or sucking out the air. As water trickles through the fill
media, the air is blown across the fill to have direct contact with the falling water. A small part of the
water evaporates in the tower with its heat of vaporization (latent heat) being supplied from the rest
of the water that gets cooled. The cold water is circulated back to the plant. Since water comes in
direct contact with air in a cooling tower, this type of cooling system is called an open recirculating
cooling system.
Advantages of cooling tower includes •
•
•
•
•
•
Can achieve lower water temperatures compared to other cooling methods. Achieved temperature
can be lower than the ambient air dry-bulb temperature if the air is relatively dry and typically to a
temperature around 4 C above the ambient air wet-bulb temperature.
Relatively cheap and efficient option for rejecting low-grade heat1 from the warm cooling water
returned from the process.
Minimal freshwater requirement to make up water losses, thus promoting water conservation
Lower environmental impact due to cut down on chemicals added to cooling water (as only a
small amount of chemical is lost with the water leaving the circulating water system).
Close control and improved water quality that reduce fouling and corrosion tendency in process
equipment.
Occupy a smaller plot space as compared to a fin fan air cooler used to remove the same heat duty.
7.2.1 Classification
Cooling towers are classified based on build, heat transfer method, airflow pattern, and the principle
used in creating the air draft. Fig. 7.1 shows the basis of classification and the different types of wet
cooling towers.
1
Low-grade heat refers to the heat energy associated with a hot stream that has a relatively low temperature. Removing this
“low-grade heat” would involve a lower temperature difference (DT) with the cooling media. This calls for a large value of
“U A” for the heat exchange process designed to remove heat Q (Q ¼ U A DT). In Indian condition cooling water
returned from the processes is typically at a temperature of 45e47 C and the average ambient temperature is around 33 C.
Therefore, the warm water is cooled by direct contact with air in cooling towers that have high “U A.”
7.2 Cooling tower
(A)
205
Cooling
Tower
Classification
based on Build
Classification
based on Heat
Transfer method
Classification
based on air
draft
Classification
based on air
flow pattern
Natural
draft
Mechanical
draft
Package
type
Wet
Field
erected
Dry
Counterflow
Induced
draft
Fluid
Crossflow
Forced
draft
Atmospheric
(B)
Air
Air
Drift
eliminators
Fan
Drift
eliminators
Nozzles
Hot water
Redwood
sheath
and fill
Fill
Hot
water
Nozzles
Fan
Air
Air
Louvers
Air
Basin
Cold
water
INDUCED DRAFT
Basin
FORCED DRAFT
Nozzles
Hot water
Louvers
Air
Basin
Cold
water
ATMOSPHERIC
FIGURE 7.1
(A) Cooling tower classification and (B) schematic of different types of cooling tower.
Cold
water
206
Chapter 7 Industrial cooling systems
Classification by build
Packaged Towers: These are common facilities for low heat rejection requirements, such as food
processing plants, textile plants, hospitals, hotels, malls, chemical processing plants, automotive
factories, etc. The preassembled towers are transported and fixed at an appropriate location. Due to
their intensive use in domestic areas, sound level control is an important issue.
Field erected towers: These are larger compared to the packaged type and common in petroleum
refineries, petrochemical complexes, power plants, steel plants, fertilizer plants and other process
industries.
Classification based on air draft
Atmospheric Towers: These are rectangular chambers with fills having two opposite louvered walls for
entry of atmospheric air driven by its own velocity. The air inside is moist and is also warmer than the
ambient air due to contact with hot water. The presence of water vapor (molecular weight-18) makes
moist air lighter than dry air (molecular weight-28.8) at the same temperature. This creates an updraft
in the tower due to the buoyancy of moist and warmer air. As hot air moves upwards through the tower,
fresh cool air is drawn in. These towers are cheap but inefficient and are not economical for high
capacities. Its performance depends upon the direction and velocity of wind.
Natural Draft Tower: Natural draft cooling towers are tall, up to 200 m and have a hyperbolic
shape. The draft is generated by the difference in density between the ambient air and the moist,
warmer air inside the tower. Atmospheric air flowing at an altitude across the top of these tall towers
creates an additional draft. Fresh cool air is drawn in through the air inlet at the bottom. These towers
use very large concrete chimneys to direct air through the fill media. The natural draft created is
sufficient and no fan is required. There is almost no recirculation of hot air that could affect the
performance in these tall towers.
Natural draft towers can be crossflow type or countercurrent flow type. In crossflow configuration,
the packing is external to the tower and the ambient air drawn through the fill is in crosscurrent flow to the
falling water. In counterflow towers, the fill is inside and an updraft of air flows through it. Concrete is
used for the tower shell supported on a set of reinforced concrete columns. The hyperbolic shape allows
more packing to be fitted in the bigger area at the bottom of the shell. This shape also provides greater
structural strength and also directs the air to flow smoothly towards the center, thus aiding the upward
draft. The pressure drop across the tower is low and the air velocity above the packing may vary from 1 to
1.5 m/s. These cooling towers are for large heat duties and are generally used for water flow rates
above 45,000 m3/hr because large concrete structures are expensive. Natural draft cooling towers are
usually economical for substantially large cooling requirements in industries like steel plants.
Because of their large size, construction difficulties and cost, natural draft towers have been
replaced by mechanical draft towers in many installations when economics favor such an option.
Mechanical Draft Towers: These employ large fans to force or draw air through the water stream.
The water falls downwards over fill surfaces, which increases the contact between the water and the air.
Cooling rates of mechanical draft towers depend upon various parameters, such as fan diameter and
speed, fill characteristics, etc.
The two different classes of mechanical draft cooling towers are e
Forced draft: These have one or more fans located at the air entry to force air into the tower. The
vertical fans force air at a low velocity horizontally through the packing and then vertically against the
downflow of water. The drift eliminators located at the tower top disengages the water droplets
entrained in the air. The fans handle mostly dry air, significantly reducing erosion and water
condensation problems.
7.2 Cooling tower
207
Induced draft: The draft of hot, moist air is created by fans mounted at the air exit/tower top. This
produces low entering and high exit air velocities, reducing the possibility of moist air recirculation
into the air intake. This is the most common type for moderate-sized cooling towers where the liquid
load is around 12e20 m3/m2 $ hr.
Classification based on airflow pattern
Crossflow Towers: These have airflow perpendicular to water downflow. Air enters through one or
more vertical faces of the tower to meet the fill material and flowing water (perpendicular to the air)
that descends through the fill by gravity. Water distributor in these towers consists of a deep pan with
holes or nozzles in the bottom. The exiting air in larger towers usually flows into an open plenum area.
Crossflow towers are thermodynamically less efficient and are mostly for small capacity. These
generally use induced draft, but crossflow natural draft towers are also in use.
Counterflow Towers: These have airflow opposite to water flow. Air first enters an open area below
the fill media and then moves up vertically through water, which flows downward by gravity through
the fill. Counterflow configuration ensures higher thermodynamic efficiency and is used for large
capacity towers. These can have either forced or induced draft configuration.
Classification based on the heat transfer method
Wet Cooling Towers: These lower the water temperature by evaporative cooling. A small part of the
water evaporates in the tower by absorbing the heat of vaporization (latent heat) from the remaining
water, which gets cooled in the process. Thus cooling in a wet cooling tower is a combined heat and
mass transfer process and the heat transfer is predominantly by latent heat. These are the most common
types of cooling towers and shall, henceforth, be referred to as cooling towers.
Dry Cooling Towers: These are basically air-cooled exchangers used for cooling circulating water by
the transfer of sensible heat. Since air and water are not in direct contact, there is no evaporation loss or
contamination of water, and this is particularly advantageous in areas having water shortage. The cooling
water recirculates in a closed loop between the process equipment/heat exchanger and the cooler.
Fluid Coolers: In these coolers, the circulating cooling water passes through a tube bundle, upon
which water is sprayed and a fan-induced draft is applied to cool the external surface of the tube. This
is a case of circulating water surface cooler and the cooling tower combined as a single unit. The
resulting heat transfer performance is close to a wet cooling tower with the advantage of protecting the
circulating cooling water from air exposure and picking up dirt. Fluid coolers avoid cooling water
contamination due to exposure to atmospheric air and are used when the cooling water quality is
important.2
7.2.2 Components of a typical cooling tower
The schematic diagram of a typical “induced-draft countercurrent” cooling tower is shown in Fig. 7.2.
The basic components are described below e
Cell: Mechanical cooling towers are constructed with one or more square cells. The cells are
placed side by side, sharing a common partition. Air entry/exit is through the opposite sides. The cell
2
More on the quality specification of cooling water is available in Ch. 18.
208
Chapter 7 Industrial cooling systems
FIBERGLASS FAN STACK
DRIVE SHAFT
FAN
GEAR
REDUCER
MOTOR
DRIFT
ELIMINATORS
PERIMETER
HANDRAIL
FAN DECK
HOT WATER INLET
DISTRIBUTION
SYSTEM
PVC
FILM
FILL
CORRUGATED
CASING PANEL
AIR INLET
COLD WATER BASIN
FIGURE 7.2
A typical induced draft counterflow cooling tower with film fill.
size is limited to 20 20 m to avoid nonuniformity of airflow throughout the cell section. Partitioning
the tower in cells also helps in achieving energy-efficient tower operation at a lower load when only the
required number of cells in a tower is run at their optimum rated capacity. During construction of
multi-cell cooling towers, usually, a provision is kept for adding one extra cell. This takes care of
increased future demand or imperfections in design that may show up as limitations in cooling.
Frame and casing: Frame and casing are partitioned into cells. The structural frames support the
exterior enclosures (casings), motors, fans and other components. The casing contains the water within
the tower, provides an air plenum for the fan and transmits wind loads to the tower frame.
Cold-water basin: The cold-water basin, located below the tower, receives the cooled water that
flows down through the tower and fill. The basin, also termed as a sump, used to be underground in
older installations but nowadays, it is an overground concrete tank. In some cases, there can be an
additional storage sump to collect water. Thus the cold water basin has two important functions:
collecting the cold water after its flow through the tower and acting as the tower’s primary foundation.
Louvers: Every well-designed crossflow tower is equipped with inlet louvers whereas counterflow
towers occasionally require louvers. Their purpose is to retain circulating water within the confines of
the tower, as well as to equalize airflow in the fill. Louvers slant towards the inside of the tower to
return any escaping water droplet into the tower.
Nozzles: Nozzles are a part of the water distribution system that distributes water to wet the fill.
Uniform water distribution at the top of the fill is essential to achieve proper wetting of the entire fill
surface. Nozzles can be fixed and spray in a round or square pattern, or they can be part of a rotating
assembly as found in some towers with a circular cross-section.
7.2 Cooling tower
209
Air inlet: It is the area of air entry into the tower. This may take up an entire side of a tower for
crossflow design or be located low on the side or the bottom of the tower in counterflow design.
Fans: Cooling tower fans must move large volumes of air efficiently and with minimum vibration.
Generally, propeller fans are used in induced draft towers and both propeller and centrifugal fans are
found in forced draft towers. Propeller fans have ability to move vast quantities of air at the relatively
low static pressure encountered. They are comparatively inexpensive, may be used on tower of any size
and can develop high overall efficiencies. Compared to propeller fans, the centrifugal fans can work
against higher head load and are usually used in cooling towers designed for indoor installations.
However, their inability to handle large volumes of air and high input horsepower requirement limits
their use to relatively small applications. Airflow in propeller fans can be adjusted by varying the blade
pitch and RPM in order to provide the required airflow with minimum input fan power. The optimum
speed of a cooling tower fan seldom coincides with the most efficient speed of its motor and a gear
reducer is often installed between the motor and the fan.
Drift eliminators: Drift eliminators remove entrained water from the exiting air by forcing it to
undergo sudden changes in direction. The centrifugal force separates the water drops as these hit the
surface. The collected water is returned to the tower.
Fill: Most towers employ fills (made of plastic or wood) to facilitate heat transfer. Fill is used to
increase contact area, as well as turbulence that promotes intimate vaporeliquid contacting. This
determines the efficiency of the tower. An efficiently designed fill media with appropriate water
distribution, drift eliminator, fan, gearbox and motor results in lower fan power consumption as the
airflow requirement is lowered.
There are two types of “Fill”- Splash fill (Fig. 7.3A) and Film fill (Fig. 7.3B). In Splash fill, water
falls over successively stacked “splash bars” and breaks into fine droplets, increasing
the heat and mass transfer area. The surface of these bars made of wood or plastic is
wet and add to the water-air contact area. These fills have low-pressure drop and are
Fill types
less prone to clogging but are very sensitive to inadequate support. The Film fills
consist of thin, closely spaced vertical plastic surfaces, which may be flat,
FIGURE 7.3
Fill types: (A): Splash Fill, (B) Film Fill.
© 2020 SPX Cooling Technologies, Inc. All Rights Reserved.
210
Chapter 7 Industrial cooling systems
corrugated, honeycombed, or may have other patterns. Water spreads over it and forms a thin film in
contact with air. This provides maximum air-water interface.
Film fill is more efficient since it can result in significant power savings due to lower airflow requirements. Nevertheless, its performance is affected in the case of mal-distribution of water. These
are chosen for applications where the circulating water is generally free of debris that could block the
fill passageways. Low-clog film fills with larger flute sizes are employed to handle water with high
turbidity. This is considered a preferred option over conventional splash type fills for seawater for
power savings and better performance.
Originally, cooling towers were constructed primarily with wood, including the frame, casing,
louvers, fill and cold-water basin. Sometimes the cold-water basin was made of
concrete. Today, manufacturers use a variety of materials to construct cooling
towers. Materials are chosen to enhance corrosion resistance, reduce mainteTower material
nance and promote reliability and long service life. Galvanized steel, various
grades of stainless steel, glass fiber and concrete, are widely used in tower
construction and aluminum and plastics are adopted for some components. Frame and casing are
usually made of glass fiber, while PVC, polypropylene, and other polymers are widely used for fills.
When water conditions require the use of splash fill, treated wood splash fill is still used in wooden
towers, although plastic splash fill is mostly used. Nozzles are usually made of PVC, ABS, polypropylene and glass-filled nylon. Aluminum, glass fiber and hot-dipped galvanized steel are commonly
used fan materials. Centrifugal fans are often fabricated from galvanized steel. Propeller fans are made
from galvanized steel, aluminum, or molded glass fiber reinforced plastic.
7.2.3 Cooling tower parameters
The factors influencing the performance of the cooling tower are capacity, heat load, range, wet-bulb
temperature, approach temperature.
For a cooling tower intended to cool hot water received from the process plant at temperature Th
( C) to the cold water temperature Tc ( C), at which it is returned to the plant, the parameters of interest
are described below. A diagrammatic representation showing the relationship between the various
parameters is depicted in Fig. 7.4.
Cooling range (R) is the difference between the inlet hot water (Th ) and outlet cold water temperature (Tc ) in ð CÞ.
Rð CÞ ¼ ðTh Tc Þ
The range is decided not by the cooling tower but by the process it is serving.
FIGURE 7.4
Diagrammatic representation of the cooling tower
system and various parameters.
(7.1)
7.2 Cooling tower
211
There are two possible causes for an increase in range:
- The inlet (to the cooling tower) water temperature is increased (and the cold-water temperature at
the exit remains the same). In this case, it is economical to invest in removing the additional heat
picked up.
- The exit water temperature is decreased (and the hot water temperature at the inlet remains the
same). In this case, the tower size would have to be considerably increased because the approach
is also reduced (discussed later), and this is not always economical.
Capacity - Heat rejected (Q kcal/hr), and water circulation rate (C m3/hr) indicates the capacity of
cooling towers. Q in kcal/hr is a product of mass flow rate of water, specific heat (Cp ¼ 1000 kcal/
mt. C for water) and temperature difference (R) in C.
Q ¼ C m3=hr Cp R ¼ C m3=hr Cp ðTh Tc Þ
(7.2)
Heat load imposed on a cooling tower is determined by the process being served. Typical numbers
used to estimate cooling load for some common equipment/devices are presented in Table 7.1.
Table 7.1 Typical cooling capacity requirement for different equipment.
Equipment
Cooling load requirement
Air compressor
-
Single-stage
130 kcal/kW$hr
-
Single-stage with aftercooler
860 kcal/kW$hr
-
Two-stage with intercooler
518 kcal/kW$hr
-
Two-stage with intercooler and aftercooler
860 kcal/kW$hr
Refrigeration, compression
65 kcal/min/ton refrigeration load
Steam turbine condenser
555 kcal/kg of steam
Diesel engine, four stroke
880 kcal/kW$hr
Natural gas engine, four stroke
1525 kcal/kW$hr (for 18 kg/cm2 compression)
Wet-bulb temperature e The amount of cooling that can be obtained from a cooling tower depends on the relative humidity or the wet-bulb temperature of the air. Irrespective of the size of cooling
tower, range or heat load, it is not possible to cool water below the wet-bulb temperature of air with
evaporative cooling. Thus, the wet-bulb temperature of air entering the cooling tower determines the
minimum operating temperature for the process or system that uses cooling water. In practice Tc is
always a few degrees above Tamb;WBT , typically a minimum of 4 C. However, it is theoretically
possible to cool water to temperatures below the wet bulb temperature of the ambient air since air on
entering the cooling tower gets heated and can hold more moisture.
212
Chapter 7 Industrial cooling systems
It is important to note that the specified wet-bulb temperature is generally the ambient air wet-bulb
temperature, but in reality, this is often affected by the discharged moist air recirculating into the tower.
Hence the ambient wet-bulb temperature (the temperature in the cooling tower area) may not be same
as the inlet wet-bulb temperature (the wet-bulb temperature of the air entering the tower) and the
designer may adjust the wet-bulb temperature used for sizing the tower upward to account for any
potential recirculation. In general, the design wet-bulb temperature selected is close to the average
maximum wet-bulb temperature in summer. The design WBT (Tamb;WBT , C) should not be exceeded
for more than 5% of the time, and it is necessary to evaluate the effects of increased wet-bulb temperatures on the tower performance.
Approach to wet-bulb temperature (A) is the difference between Tc and Tamb;WBT .
Að CÞ ¼ Tc Tamb;WBT
(7.3)
The lower the approach, the better is the cooling tower performance, but this leads to designing a
more expensive cooling tower due to its increased size. An approach lower than 2.8 C is not
economical, nor will it be certified by the Cooling Technology Institute (https://www.cti.org/ and see
7.2.5). Cost-effective selections are based on a criterion using an approach close to 4 C. This is not
because towers are unable to achieve lower than this, but any error in measurement becomes very
significant when performance is calculated at the design point. Approach temperature above 4 C
results in higher cooling water temperature in process plants and reduced efficiency of heat exchange
using cooling water without much savings on cooling tower.
While both range and approach should be monitored, “Approach” is a better indicator of cooling
tower performance. When the size of the tower has to be chosen, the approach is the most important
parameter, closely followed by the flow rate. The range and wet-bulb temperature are of lesser
importance.
As the water gets cooled during its downflow in contact with air, the required depth of fill over
which the contact takes place is governed by the range of cooling while the plan area of the fill section
increases with increasing water flow rate. In simple words, the tower height is decided by the cooling
range, whereas the tower cross-section is decided by the water flow capacity.
Liquid/Gas ðL=GÞ ratio of a cooling tower is the ratio of the mass flow rates of inflow water ðLÞ
and dry air (G).
From enthalpy balance, heat removed from water must be equal to the heat absorbed by surrounding air or
ðL=GÞ ¼
ðhvo hvi Þ
R
(7.4)
Where hvo and hvi are the enthalpy (kcal/kg dry air) of air-water vapor mixture at exhaust wet-bulb
temperature and inlet wet-bulb temperature respectively in ( C).
Effectiveness ðEf Þ is the ratio (expressed as %) between the actual range and the maximum range.
Ef ð%Þ ¼ 100 ðTh Tc Þ
R
¼
RþA
Th Tamb;WBT
(7.5)
As discussed above, a cooling tower can never be 100% effective. Moreover, in summer, the
ambient wet-bulb temperature is higher as compared to winter, and this limits the CT efficiency.
7.2 Cooling tower
213
Cooling towers have certain design values, but the best cooling tower effectiveness requires
adjustment for seasonal variations and tuning of water and air flow rates. Adjustments can be made by
water box loading changes or blade angle adjustments.
7.2.4 Cooling water circuit in a process plant
A schematic diagram of a typical cooling water system with an induced draft cooling tower is shown in
Fig. 7.5. Pumps supply water (at a recirculation rate C m3/hr) from the basin to the cooling water
supply header that goes to the process plant. The cold water picks up heat in the heat exchangers in the
process installation and joins the cooling water return header. The “warm” cooling water return header
reaches the cooling tower top by its own pressure. As shown in the figure, there is only one set of pump
in the flow circuit. It develops sufficient pressure to overcome the pressure drop in supply header,
exchangers, return header and also the hydrostatic head to reach the cooling tower top. The cooling
water supply and the return header pressure in the processing unit usually depend on the layout, i.e.,
system pressure drop. However, the return header pressure should not be less than 1.5 kg/cm2(g) to
reach the tower top and the supply header pressure is typically around 3.5 kg/cm2(g).
The major water loss from the system is the water evaporated
for cooling duty (E). Theoretically, evaporation from a cooling
tower is pure water, while all of the dissolved ions are left
Water losses from cooling tower
behind in the system. If the water loss is only due to evaporation, the concentration of the dissolved ions in the recirculating
water would continue to rise until the solubility limit of each
ion is reached. Further evaporative loss would start salt deposition on the heat transfer surfaces as
scales. To avoid this, the concentration of critical scaling-prone ions in the circulating water is usually
FIGURE 7.5
Schematic showing a circulating cooling water system with an induced draft cooling tower.
214
Chapter 7 Industrial cooling systems
controlled by a combination of (a) bleeding off a certain portion (B m3/hr) of the recirculation water
with make up of the same quantity of water having low solid concentration, and (b) adding antiscaling
additives. The blowdown stream (B) leaves either the sump or the pump delivery header. The figure
also shows the droplets of water entrained in the exiting air. This is called drift loss (D). There is also
some water loss (L) within the process due to leakages, draining, etc. The possible sources for leakages
(uncontrolled water loss from a system) are from pump seals, valves, overflow, exchanger draining,
splash out, etc. Drifts and leaks are nonblowdown water losses. One may note that the loss streams take
out dissolved solids and suspended solids to some extent.
The makeup water stream (M) joins the sump to
compensate for the water losses from the system and to
Make-up water & added chemicals
keep its level steady. Dissolved and suspended solids present in the makeup water stream (M) get added to the system. Solids also enter during contact of the water with air in
the tower and the sump. It may also be picked up from the contacting heat transfer surfaces and piping.
The rate at which (blowdown) water is bled from a system (B in m3/hr) compared with the amount of
makeup water (M in m3/hr) determines the concentration ratio. This is called cycles of concentration
(COC). To check the concentration ratio in a system, a soluble ion (such as silica or magnesium) that is
present in sufficient quantity and is stable and easily tested is selected and monitored in the makeup
water (XM) and in the recirculating water (XC). At steady state, the rates at which the solids enter are the
same as the total rate of the solids leaving with blowdown stream, process plant leakage, draining and
drift loss. The blowdown streamflow is increased whenever the concentration approaches the
maximum tolerable limit.
Chemicals for preventing corrosion, fouling, and biological growth are added directly in the
cooling water sump/pump delivery header (as shown in the figure), and the pH control chemicals are
added to the CT sump. Antiscaling and corrosion control chemicals are generally added in the pipeline
(pump delivery header). In some installations, chlorine is dosed in the cooling water supply line daily
for about an hour to control biological growth. This is called “shock dosing” of chlorine. The concentration of chlorine in the return line is closely monitored during chlorine dozing and is never
allowed to exceed 1 ppm to prevent corrosion due to chorine overdose.
The stream parameters to and from the cooling tower (as mentioned above and shown in Fig. 7.5)
are estimated as follows.
Evaporation loss (E) e Although it varies with temperature and
humidity, a general rule is that for every 6 C drop in water
temperature across tower, approximately 0.85% of recirculation
rate (C) will be evaporated. Accordingly, the following empirical
Estimation of Stream Parameters
formula can be used to estimate evaporation loss: (Reference:
Perry’s Chemical Engineers Hand Book)
E m3 =hr ¼ 0:0085 ðR=6Þ C m3 =hr
(7.6)
7.2 Cooling tower
215
The evaporation loss can also be estimated from heat balance
the cooling tower, i.e., the
across
amount of heat to be removed from circulating water (Q ¼ C m3 hr Cp R) and the amount of
heat removed by evaporative cooling (Q ¼ E l)
On equating the two, we get:
C Cp R
E ¼
(7.7)
l
Where, l ¼ latent heat of vaporization of water ¼ 2260 kJ/kg
Cp ¼ specific heat of water ¼ 0.238
C;
kJ/kg
C is water recirculation rate in m3 hr and R is in C
A more rigorous way of calculating E based on humidity difference of inlet and exit air and its flow
rate is illustrated in the design example at the end of this chapter.
Drift loss (D) is usually estimated as a percentage of recirculation (C). Splash fill towers tend to
have higher drift rates than film fill towers. Drift eliminator design, unit maintenance and airflow also
have an influence on the amount of drift from a cooling system. In the absence of manufacturer’s data,
D may be assumed to be:
(i) 0.3%e1.0% C for a natural draft cooling tower
(ii) 0.1%e0.3% C for an induced draft cooling tower
(iii) about 0.01% C or less, if the cooling tower has drift eliminator
Makeup water (M) is estimated from a water balance around the entire system
M¼E þ B þ D þ L
(7.8)
M¼E þ B þ D
(7.9)
Ideally with negligible leakage,
Cycles of Concentration e The quantities of blowdown and makeup water are optimized by the
Cycles of Concentration (COC).
Any of the following ion concentration or even the conductivity can be used to calculate COC.
(i) COC ¼ Silica in Recirculating Cooling Water/Silica in Makeup Water
(ii) COC ¼ Calcium hardness in Cooling Water/Calcium hardness in Makeup water
(iii) COC ¼ Conductivity of Cooling Water/Conductivity of Makeup water
From a chloride balance around the system and considering that the evaporated water (E) has no
salts,
COC ¼ XC =XM ¼
M
E
¼1þ
ðB þ DÞ
ðB þ DÞ
Where,
XM ¼ Concentration of chlorides in makeup water (M), in ppm by weight
XC ¼ Concentration of chlorides in circulating water (C), in ppm by weight
(7.10)
216
Chapter 7 Industrial cooling systems
COC usually, range from three to seven in petroleum refinery cooling towers and may be much
higher in some large power plants. While a high COC reduces the makeup water requirement of
the cooling tower, it allows higher dissolved solids concentration in circulating cooling water,
which results in scaling and fouling of heat transfer surfaces.
Holding Capacity or System Volume (HC) is the amount of water held up in the cooling water
system expressed in cubic meters. This includes the holdup in the basin, additional sump if any, and all
associated equipment and circulating water piping.
Time per cycle is defined as the time taken for all the water held up in a system (HC) to make one
trip around the recirculating loop (from the discharge side of the recirculation pump back to the suction
side of the pump). Mathematically,
Time per cycle ¼ HC=C
(7.11)
Holding Time Index or Half-Life index (HTI) indicates the time required to reduce the chemical
or makeup water added to a system to 50% of its original concentration. It is essentially the half-life of
a chemical added to the system and is estimated based on the assumption that the rate of decrease in
concentration of the chemical at any instant is proportional to its concentration. The expression for
calculating the holding time index usually reported in hours is e
HTI ¼ 0:693
HC
.
ðB þ DÞ
(7.12)
The HTI is important for a chemical treatment program and is also used to determine the
requirement of some biocides to achieve proper control of microorganisms.
7.2.5 Codes and standards
Cooling Technology Institute (CTI), USA, established in 1950, is a body that has standardized the
cooling tower design (Industrial Cooling Tower Standard - STD-203), testing (STD-202), and several
other aspects. CTI codes are among the most popular codes used these days. To properly select a tower,
the designer should consider towers with CTI certified listing as this is the most widely accepted
standard.
7.2.6 Thermal design
Quantitative treatment of cooling tower performance by separately dealing with mass and heat transfer
is laborious. Therefore, the simplifying approximation of Merkel’s total heat theory has been almost
universally adopted for cooling tower calculations.
Briefly, Merkel’s theory states that all of the heat transfer taking place at any position in the cooling
tower (dQ) is proportional to the difference between the enthalpy of saturated air at the temperature of
the water (T) at that position in the tower (h0 ) and the enthalpy of the air at the same location (h).
Mathematically,
dQ ¼ Kaðh0 hÞdV
(7.13)
7.2 Cooling tower
217
where
dQ ¼ Heat transferred by convection and evaporation for cooling of water in volume dV per unit
plan area
K ¼ Equivalent heat transfer coefficient.
a ¼ Area of contact (m2/m3) between air and water.
The contact area ‘a’ cannot be determined, and this is combined with K as Ka which refers to the
unit volume of the fill.
The transfer of heat dQ to air is equal to the loss of sensible heat by water. Mathematically,
dQ ¼ LCp dT
(7.14)
where L ¼ water flow rate per unit area of the tower (kg/m2 hr)
Cp ¼ specific heat (kJ/kg C)
dT ¼ differential change in temperature ( C) across the volume (dV, m3/m2 of plan area)
Equating Eq. 7.13 and 7.14 for Cp ¼ 1 kJ/kg C
LdT ¼ Kaðh0 hÞdV
The integrated form of the thermal balance equation is Z Th
KaV
dT
¼
0
L
Tc h h
(7.15)
(7.16)
where
V ¼ active fill volume/plan area (m3/m2) and KaV
L ¼ tower characteristic
The equation assumes L and G to be constant, but due to evaporation, this is not true in practice;
however, at normal temperature levels, the error from this assumption is not significant.
A standard psychrometric chart is shown in Fig. 7.6. Based on the data from the psychrometric
chart, the cooling tower thermal balance plot (Fig. 7.7) is drawn with temperature as abscissa and
enthalpy per unit mass of dry air as ordinate. The plot in Fig. 7.7 is based on data of the Design
Illustration in Section 7.3. Line CD is the air operating line obtained from the thermal balance of heat
lost by the cooling water (L) and the same picked up by air (G, kg/hr m2) in counterflow. This line has a
slope of ðL=GÞ and the coordinate of point C is ðTc ; hc Þ. For a known ðL=GÞ ratio, point D can be
located as ½Th ; hc þ ðL=GÞR. Assuming that the thin film of air surrounding the water droplets is
always saturated, line AB is the saturated air enthalpy (h) versus air temperature plot, which is the
same as the 100% RH curve on a humidity (psychometric) chart. One may note that the driving force at
any cross-section through the fill is the vertical distance between the two lines (BA and CD), which is
the difference between the total heat of air bulk and air film against temperature. The integral in the
right-hand side of Eq. 7.16 can be numerically evaluated from the graph.
In a design problem, the ambient wet-bulb temperature (Tamb;WBT ) is known and hc is the saturated
air enthalpy corresponding to Tamb;WBT . Cooling of water continues as long as the operating line remains below the line of saturated air.
218
Chapter 7 Industrial cooling systems
Humidity Ratio (kg of moisture pure kg of dry air)
-10
0
10
20
30
40
50
60
0.03
0.03
0.02
0.02
0.01
0.01
0.00
0.00
-10
0
10
20
30
Dry Bulb Temperature ºC
40
50
60
FIGURE 7.6
Psychrometric chart drawn at 101.325 kPa https://www.tecquipment.com/assets/documents/downloads/ECPsychrometric-Chart-poster-A3-0617.pdf.
FIGURE 7.7
Cooling tower thermal balance.
7.2 Cooling tower
219
Cooling Technology Insitute of USA has standardized the procedure for evaluating the integral
using the Chebyshev method of integration. The integral value can also be found from a nomogram
(Fig. 7.8).
FIGURE 7.8
Nomogram to estimate the RHS of Merkel equation.
In order to obtain the value of the integral i.e., the KaV
L value for known Tamb;WBT , from any two of
the parameters - Tc, Th, R, and L=G the steps are e (i) the point in the grid section corresponding to the
cooling range and Tc is joined by a line with the Tamb;WBT value on the appropriate axis. The intersection of this line with the L=G axis gives the L=G value, and the corresponding KaV
L is read out from
the intersection of the line and the KaV
scale.
Lines
drawn
parallel
to
this
line
provide
the KaV
L
L values
corresponding to different ðL=GÞ ratios.
In a design problem (refer to the problem in Section 7.3) , the L value would be known and so will
be the Th , Tc and Tamb;WBT values. It is possible for different airflow rates to achieve the same cooling
but in each case the KaV
L will be different. For any selected G, the foregoing procedure would give us the
KaV value required for the fill. Cooling tower performance is affected by the characteristics of the fill,
L
fill height (H), and the water (L), and the air (G) flow rates per unit tower area. These are combined
empirically and published by fill manufacturers in the following form of an equation or something
similar.
220
Chapter 7 Industrial cooling systems
KaV
¼ p þ q H ðL=GÞn
L
(7.17)
Where p, q and n are constants for a specific fill.
Since the equation is empirical, one needs to be careful about the units of the terms in Eq. 7.17.
Table 7.2 shows the typical design range for different fill types that may be used as design
guidelines. Characteristic curve for a typical industrial fill based on data of design Illustration in
Section 7.3 is shown in Fig. 7.9. This relates KaV
L and ðL =GÞ for 1.5 m of fill depth. The power law form
of the equation plotted on log-log axes is linear. The plot also shows a curve that is derived using
Figs. 7.7 and 7.8 for different ðL=GÞ values in the design problem. The intersection of the two lines is
Table 7.2 Typical values for different types of fill.
Fill type
Range of L=G ratio
Effective area, a
(m2/m3)
Fill height (m)
Pumping head
required (m)
Splash fill
1.1e1.5
30e45
5e10
9e12
Film fill
1.5e2.0
150
1.2e1.5
5e8
Low clog film fill
1.4e1.8
80e100
1.5e1.8
6e9
FIGURE 7.9
Tower characteristic curve- determination
of the design operating point.
7.3 Design illustration
221
the design operating point for the tower for the type of fill selected. The ðL=GÞ at the operating point is
used to find the airflow ðGÞ to be provided by the fan.
Further steps of cooling tower design are illustrated in the design illustration (Section 7.3).
7.2.7 Notes on design and operation
Effect of altitude/ambient pressure: The standard psychrometric chart given in Fig. 7.6 is drawn for
atmospheric pressure of 1000 mbar. When the atmospheric pressure differs from this, the chart loses
accuracy. For small changes in pressure, the error is small but for appreciably lower pressures, as at
high altitudes, it is necessary to apply a correction. This is because although the enthalpy of air at a
particular dry-bulb temperature and absolute humidity is independent of barometric pressure, the
moisture carrying ability of air is increased with reduced pressure and this alters the composition of the
air/water vapor mixture at saturation. The enthalpy at saturation, therefore, increases with altitude. The
effect of this increase in enthalpy improves the driving force and tends to reduce the size of the tower
needed for a particular duty. However, this is counteracted by the fan, a nearly constant volume
machine, delivering a lower mass flow rate due to the reduced density of air. CTI has an elaborate
procedure to make pressure deviation corrections to the cooling tower performance. The details are not
included in this text.
Good practices: Cooling water treatment to control suspended solids and algal growth is
mandatory for any cooling tower irrespective of fill media. With increasing costs of water, efforts to
increase COC by cooling water treatment would help to reduce makeup water requirements significantly. In large industries and power plants, improving the COC is often considered a key area for
water conservation.
Drift loss is a perennial concern in cooling towers and nowadays, most of the end-user specifications assume a 0.02% drift loss. However, improved design and material (mostly PVC) being
employed have improved drift eliminators with loss as low as 0.001%e0.003%.
Operation of cooling tower needs to be energy efficient. Energy is spent to run the circulating
cooling water system, i.e., for pumping the water and in the fans, the sum total of which should be
minimized. During cold weather months, the plant engineer should maintain the design water flow rate
and heat load in each cell of the cooling tower. If less water is needed due to temperature changes (i.e.,
the water is colder), one or more cells should be turned off to maintain the design flow in the other
cells. It is a practice to run the fans at half speed or turn them off during colder months to maintain the
desired temperature range.
7.3 Design illustration
Design a cooling tower to cool 6000 m3/hr of warm cooling water returned at 45 C from a process
plant. Cold water from the tower is circulated to the supply header at 33 C. The maximum ambient
wet-bulb temperature during summer in the area where the tower is to be installed does not exceed
29 C for more than 5% of the days.
222
Chapter 7 Industrial cooling systems
Summary of available data
C ¼ 6000 m3 =hr; Th ¼ 45 C; Tc ¼ 33 C; Tamb;WBT ¼ 29 C;
Plant pressure drop in circulating water header ¼ 2 kg/cm2
Tower selection
Water load (L) of CT usually lies between six and seven USG per ft2 (14.7e17.1 m3/m2 hr)
Based on L ¼ 15 m3/m2 hr, Tower area ¼ C/L ¼ 6000/15 ¼ 400 m2
CT cells are usually square with up to 20 m arms (Refer to Section 7.2.2). In this case, four cells of
dimension 10 10 m are chosen to provide the tower area.
This is a moderate size tower and hence, we opt for induced draft design (Refer to Section 7.2.1).
The cells are placed side by side, with air entry from opposite sides.
It is also assumed that the circulating water is fairly clean, without much debris getting entrained in
the flow.
Fill details
The fill chosen is “Film Fill” due to its higher contact efficiency compared to “Splash Fill” and “Low
Clogging Film Fill.” Typically film fill depth varies from 1.2 to 1.5 m (see Table 7.2). Among several
types of film fills we choose C19 Film Fill with 1.5 m depth. Characteristics of C19 fill with depth
1.5 m under 4 to 7 US GPM/ft2 water load is given by the equation provided by the manufacturer as
KaV
¼ 2:847 ðL=GÞ0:8621
L
Determination of operating L=G for the fill chosen
The thermal balance diagram for the tower is based on psychometric data from a standard psychometric chart (Fig. 7.6). Data relevant to the problem, as derived from the figure, is tabulated in
Table P7.1. Any intermediate value is found by interpolation.
Table P7.1 Psychrometric Data for Saturated air at 1000 mbar pressure.
Aqueous
Tension (Pa)
Absolute
humidity (kg
H2O/kg dry
air)
Specific
volume of dry
air (m3/kg)
Specific
volume of
satd air (m3/
kg dry air)
Enthalpy of
satd air (kcal/
kg dry air)
15
1704
0.011
0.816
0.83
10.263
20
2337
0.015
0.83
0.85
13.923
25
3167
0.020
0.844
0.872
18.206
30
4243
0.027
0.859
0.896
23.732
35
5623
0.037
0.873
0.924
31.124
40
7378
0.049
0.887
0.957
39.809
45
9585
0.065
0.901
0.995
51.005
50
12,339
0.087
0.915
1.042
66.005
Temperature
( C)
7.3 Design illustration
223
Steps of calculation
The saturated air enthalpy curve (AB) is drawn in Fig. 7.7 for the range 20e50 C using data from
Table P7.1.
Saturated air enthalpy (on line AB) at Tamb;WBT ¼ 29 C, is read; hc ¼ 22.479 kcal/kg dry air.
1. Point C, the air entry location on the operating line is located on the graph corresponding to
(Tc ¼ 33 C, hc ¼ 22.479 kcal/kg dry air)
2. A straight line CD0 is drawn that touches the curve AB. Slope of this line corresponds to the
theoretically minimum air requirement, i.e., ðL=GÞmax .
The slope of the operating line must be lower than ðL=GÞmax .
3. Referring to Table 7.2, we note that for “Film Fill” 1.5 < ðL=GÞ < 2 is recommended.
Accordingly, a value of ðL=GÞ is assumed as say 1.5.
4. An operating line CD is drawn with a slope of ðL=GÞ. The end point D of the operating line is
located corresponding to water temperature Th ¼ 45 C. Corresponding enthalpy (hD) of air
exiting the tower is: hD ¼ hC þ ðL=GÞðTh Tc Þ e.g., for ðL=GÞ ¼ 1.5,
hD ¼ 22:479 þ 1:5 ð45 33Þ ¼ 40:479 kcal/kg dry air
R Th dT
5. The KaV
L corresponding to the ðL=GÞ value assumed is the area CDD’B that represents Tc ðh0 hÞ.
The integral can be evaluated by the Chebeyshev’s method as suggested by CTI. For ðL=GÞ ¼ 1.5,
KaV ¼ 1.7858.
L
6. For different values of ðL=GÞ, the corresponding KaV
L is calculated following Step 5e7. The results
are presented in Table P7.2.
Table P7.2 KaV
L [
R Th
dT
Tc ðh0 LhÞ, from Merkel equation.
ðL=GÞ
1.50
1.55
1.60
1.65
1.70
1.75
1.80
1.85
1.90
1.95
2.00
KaV
L
1.7858
1.8558
1.9326
2.0181
2.1138
2.2216
2.3445
2.4861
2.6515
2.8482
3.0869
ðL=GÞop corresponds to the operating condition when the chosen fill provides the required KaV
L
i.e., the KaV
L from the Merkel equation and that from the fill characteristics match. ðL=GÞop is therefore
found by drawing the lines for ðL=GÞ vs. KaV
L from the fill characteristics equation and from Table P7.2
on the same graph (Fig. P7.1) and locating the intersection point. The lines intersect at
ðL=GÞop ¼ 1.587 in this design example.
Note: Although earlier, it has been mentioned that the tower characteristics are plotted with log-log
axes, Fig. P7.1 has been drawn with the linear axis as the range of variation is small.
Fan power calculation
For ðL=GÞop ¼ 1.587 and C ¼ 6000 mt/hr, L ¼ 15 m3/m2 hr, G ¼ 15/1.587 ¼ 9.45 mt/m2 hr dry
airflow.
224
Chapter 7 Industrial cooling systems
FIGURE P7.1
Tower characteristics curve for the design example.
r Air flow/cell ¼ 10 10 9.4518 ¼ 945 mt/hr dry air.
The induced draft fan driving the moist air needs to provide sufficient power to overcome the head
losses in
-
Air inlet and the rain zone (below the fill)
Fill and Water Distribution Level
Drift eliminator
Plenum Zone
CT manufacturers have their own empirical equations to estimate each component of the losses
mentioned. However, in industrial towers, the head loss in the fill and distributor level is the major
component and accounts for about 70% of total head loss.
Estimating head loss in the fill and water distributor level
The empirical equation for pressure drop in C 19 fill is
DPðmmWCÞ ¼ 0:63644 exp 2:445307 103 L ðVair Þ1:771 ðHÞ0:77 ðrair Þ
where,
L is water loading (m3/m2 hr)
Vair is superficial air velocity through the fill (m/s)
H is fill depth (m)
rair is the average density of saturated air (kg/m3) in the fill
7.3 Design illustration
225
In this design: H ¼ 1.5 m; L ¼ 15 m3/m2 hr.
Exit air enthalpy (hD;op ) at the operating point,
hD;op ¼ hC þ ðL=GÞop ðTh Tc Þ ¼ 22:479 þ 1:587 ð45 33Þ ¼ 41:523
Corresponding to hD;op , the saturated air temperature interpolated from Table P7.1 is 40.865 C.
Average temperature of air inside the fill ¼ (40.865 þ 29)/2 ¼ 34.933 C
Interpolating data from Table P7.1, rair (saturated at 34.933 C) ¼ 1.0827 kg dry air/m3 saturated
air and velocity of air
Vair ¼ 1000 945=ð3600 10 10 1:0827Þ ¼ 2:4249 m=s
DPðmmWCÞ ¼ 0:63644 exp 2:445307 103 15 ð2:4249Þ1:771 ð1:5Þ0:77 ð1.0827Þ
¼ 4:7 mmWC
Fan suction flow rate ¼ 945/(4 1.0827) ¼ 218 m3/hr.
Considering head loss in the fill zone to be 70% of total head loss.
Head to be developed by the fan ¼ 4.7/0.7 ¼ 6.71 mmWC, Say, 7 mmWC.
Interpolation of data in Table P7.1 corresponding to saturated air at exit temperature (40.865 C)
gives specific volume ¼ 0.96357 m3/kg dry air.
Gop (per cell) ¼ 945 mt/hr dry air ¼ (945/3600) mt/s.
Power required by fan ¼ (1000 945/3600) 0.96357 (7/1000) 1000 9.8 ¼ 17351 W.
i.e., (17351/746 ¼ ) 23.3 HP
Assuming the efficiency of fan, gearbox and the motor to be 69%, 96% and 94%,
Motor power ¼ 23.3/ (0.69 0.97 0.94) ¼ 37 HP.
Estimating make up water (M) requirement
Evaporation loss (E)
Total air inflow to tower (Gop) ¼ 3780 mt/hr dry air
From Table P7.1, corresponding to the exit air temperature (40.865 C) and the ambient wet-bulb
temperature (Tamb WB), the absolute humidity values are 0.05,141 and 0.025,365 kg H2O/kg dry air
E ¼ Evaporation loss (all cells) ¼ 3780 (0.05141e0.025365) ¼ 98.467 mt/hr, i.e., 98.467 m3/hr
(1.64% on 6000 m3/hr)
Drift loss (D)
This is based on an empirical estimation of 0.02% of circulation rate, assuming efficient drift eliminators. (Refer 7.2.3)
D ¼ 0:0002 L ¼ 1:2 m3 =hr
226
Chapter 7 Industrial cooling systems
Blowdown, including loss from the process plant (B)
COC for cooling tower normally remains between 3 and 7. We assume COC ¼ 5. Accordingly,
B ¼ E=ðCOC 1Þ D ¼ 98:467=ð5 1Þ 1:2 ¼ 23:417 m3 =hr 0:39% on 6000m3=hr
Hence, make up water, M ¼ B þ D þ E ¼ 23.417 þ 1.2 þ 98.467 ¼ 123.08 m3/hr, say 124 m3/hr,
amounting to 31 m3/hr per cell (2.07% on 6000 m3/hr), assuming negligible leakage loss.
Pump calculations
Selection of pump: We choose centrifugal pumps as per industrial practice for high flow rates, i.e.,
2 nos. 3000 m3/hr capacity. The operating point of the centrifugal pump is chosen to have maximum
efficiency. Selecting 2 3000 m3 =hr pumps will give us additional benefit of operating only 2 cells
with a single pump running if need arises. Since centrifugal pump capacity can be turned down to 50%,
even a single cell operation would be possible.
The cooling water header pipe size is chosen to be 2000 NB, Schedule 40, having ID 18:81200 . This
would entail a reasonable velocity of 2.3236 m/s, and the pressure loss estimated to be 0.0776 kg/cm2
per 100 m length.
At the tower, the header climb is the total of air inlet height (taken to be half the cell width, i.e.,
5 m), and fill and distributor height, i.e., 2 m.
Hence, the total static head of 7 m is considered.
For a static climb of 7 m, the header pressure at the base of the cooling tower, if kept at 1 kg/cm2
(g) is sufficient.
Pump discharge pressure ¼ Pressure at CT base þ Pressure drop in process plant þ Pressure drop in
header to and from CT (assumed 1 kg/cm2) ¼ 1 þ 2 þ 1 ¼ 4 kg/cm2(g), i.e., 40 mWC.
Assuming pump and motor h to be 85% and 95%,
Pump motor power ¼ (3000/3600) 40 1000 9.8/(1000 0.85 0.96) ¼ 400 kW
Cooling tower sump
Base area of tower ¼ 4 10 10 ¼ 400 m2
Sump water depth ¼ 1.75 m, Sump freeboard ¼ 0.25 m (assumed)
Sump holdup ¼ 400 1.75 ¼ 700 m3
This corresponds to holding time of ð60 700=6000Þ ¼ 7 min
Note: In case the holding time needs to be increased, additional sump may be provided. The depth
of the sump may be kept 2 m, and a space adjacent to the tower may be used in constructing the
additional sump (Table P7.3).
Further reading
227
Table P7.3 Summary of the process design.
Project name: cooling water system
Tower
Induced draft water cooling tower
Tower model
———————
Type
concrete, rectangular, counterflow
Design & Operating Conditions
Circulating water flow, m3/hr
Hot(inlet) water temp. C
6000
45
Cold(outlet) water temp. C
33
Wet-bulb temp. Inlet C
29
Ambient temp. C
–
Relative humidity %
–
3
Makeup water flow, m /hr
3
124 (31 m /hr per cell)
COC
5
Fan
1 per cell,
Suction flow rate 218 m3/hr, DP ¼ 7 mmWC
Fan motor power
23.3 HP
Number of cells
4 in a row
Plan area
40 10 m
Overall tower dimension,
L B H mm
Water sump dimension, 2 L B H mm
Casing material
Fill
Water distributor
40,000 10,000 7000
40,000 10,000 (1750 water level þ 250 freeboard)
CONCRETE
PVC C-19 fill 600 m3
Polypropylene nozzles
CW pump
2 nos 3000 m3/hr, discharge pressure 4 kg/cm2(g);
run by 400 kW motor
CW header
2000 NB ANSI schedule no. 40
Further reading
CTI Code: Tower: Acceptance Test Code for Water-Cooling Towers; Feb, 1990 revision.
CTI Bulletin TPR-121: The evaluation of Cooling Tower Performance from Field Test Data.
228
Chapter 7 Industrial cooling systems
Cooling Tower Fundamentals e Marley e SPX (https://www.google.co.in/url?sa¼t&rct¼j&q¼&esrc¼s&source¼
web&cd¼1&cad¼rja&uact¼8&ved¼0ahUKEwjohPjFxZDVAhVKxLwKHZXGB2gQFggnMAA&url¼
http%3A%2F%2Fspxcooling.com%2Fpdf%2FCooling-Tower-Fundamentals.pdf&usg¼AFQjCNH
skYtjKdM1MUkOqtkQZZfEgIM03Q).
Cooling Tower Selection and Sizing (Engineering Design Guideline) e KLM Technology group (URL¼?).
Water Purification Handbook (Chapter 31 e Open Recirculating Cooling Systems) - GE Power and Water - Water
and Proicess Technologies (1995).
Cooling Tower Efficiency Calculation (http://www.chemicalengineeringsite.com/cooling-tower-efficiencycalculations/76).
Energy Efficiency Guide for Industry in Asia (www.energyefficiencyasia.org).
Cooling Tower (https://beeindia.gov.in/sites/default/files/3Ch7.pdf).
SECTION
Mass transfer
processes
III
A good scientist is a person with original ideas. A good engineer is a person who makes a design work
with as few original ideas as possible. There are no prima donnas in engineering
eFreeman Dyson
CHAPTER
Interphase mass transfer
8
8.1 Introduction
Interphase mass transfer is the basic transport process involved in all separation processes based on
concentration difference. In practice mass transfer is seldom stand-alone and is accompanied by heat
and momentum transport and/or chemical reaction. For conventional separation processes, namely
distillation, absorption, stripping, adsorption, extraction, and leaching mass transfer governs the
overall rate and their design is based primarily on mass transfer and equilibrium considerations. On the
other hand, in processes like drying, humidification, dehumidification, evaporative water cooling (in
cooling towers), and membrane separation, the respective overall rates are not limited by mass transfer
and their design is dealt with other transport processes (commonly heat transfer) as the controlling
phenomena. Heterogeneous reaction systems which may involve mass transfer that sometimes maybe
the rate-limiting step. Design of such reaction systems uses a different approach based on apparent/
overall reaction kinetic rate that includes the effect of mass transfer.
In this section of the book, we focus only on the design of traditional mass transfer processes, that is,
absorption, stripping, distillation, adsorption and extraction. Three steps are always involved in these
processes - (i) creation of a two-phase system, (ii) mass transfer between phases and (iii) separation of
the phases. Each mass transfer system in its basic configuration is built around an arrangement for
contacting the phases and auxiliary systems for supply/removal of heat and handling the fluids.
Distillation exploits the difference in volatility of the components to be separated, while absorption and
stripping are separation processes based on the difference in solubility of the gaseous constituent(s) in the
contacting liquid phase. Absorption refers to the transfer of one or more components from the gas to the
liquid phase in which it is soluble. Stripping is the reverse operation, where the component transfer is
from the liquid to the gas phase. In distillation, the vapor and the liquid phases of the same component(s)
are contacted, and separation occurs by the transfer of the more volatile component(s) from the liquid to
the vapor phase and the less volatile component(s) from the vapor to the liquid phase. Accordingly, all
the components are present in both vapor and liquid phase during distillation. Extraction involves mass
transfer between two immiscible liquid phases. An external stream, which is a liquid solvent, is added (to
the feed) to create the immiscible phases. It is often used when the breaking of an azeotrope is difficult,
or the volatilities of the components are too close, making the separation by distillation nearly impossible
or uneconomical. An example is the separation of aromatic and paraffinic hydrocarbons of nearly the
same molecular weight present in kerosene. Industrially, these aromatic compounds are separated by
extraction using liquid sulfur dioxide as a solvent. Both adsorption and leaching involve solid-fluid
(liquid/gas) mass transfer and are governed by fluid-solid equilibria. Adsorption is a surface
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00008-7
Copyright © 2020 Elsevier Inc. All rights reserved.
231
232
Chapter 8 Interphase mass transfer
phenomenon, and it involves the transfer of specific component(s) from the gas/liquid phase to the
surface of the solid adsorbent, where it adheres due to preferential affinity. Leaching is the preferential
dissolution of one or more components from a solid mixture by contact with a liquid solvent. The
appropriately chosen solvent dissolves specific components so that the desired solute can be removed.
Creation of the phases: In case of distillation, the contacting vapor and liquid phases are (normally)
derived from the same source, that is, the process feed by addition of heat. The other mass transfer
processes use a stream different from the feed to create the additional phase. The additional phase is
created by the introduction of a liquid stream (absorbent/solvent) in case of absorption, leaching, and
extraction; an external vapor stream that is referred to as the inert stream in case of stripping and a solid
adsorbent contacting the fluid (liquid/gas) in case of adsorption. Thus, for separation of a binary
mixture, the minimum number of components is two for distillation and three for the other operations
(see Table 8.1), while the number of contacting phases involved is two for all the cases.
Recovery and recycle: Design of systems for processes using an external stream to create the
second phase (as outlined above) will usually include an additional facility for recovery/regeneration of the said stream for reuse/recycling. This is done to improve the economy of the process.
Thus, while the distillation system may be complete in itself, the other processes in order to be
economic will have absorbent/solvent recovery section or adsorbent regeneration section, as the
case may be.
8.2 Processes and equipment
Distillation separates the feed to streams that are relatively pure. This gives the distillation process an
edge over the other processes, where the substance to be separated is collected in a dilute form in the
auxiliary phase(s) and may require a costly recovery step. Distillation requires energy to be supplied in
the form of heat that can subsequently be easily recovered/removed from the streams.
Distillation, absorption, stripping, and extraction, normally use the contacting columns. The two
phases are brought into intimate contact either in a batch or a continuous flow device where the two
phases exhibit cross (extraction) or countercurrent flow (absorption, stripping). Several stages of
interphase mass transfer are present in the same physical column with counterflowing phases. Interphase mass transfer occurs because the contacting phases are not in thermodynamic equilibrium. The
column may be fitted with internals (packings and trays) to promote contacting and also to improve
separation of phases (chimney trays and demister pads) for the streams leaving the equipment.
The contacting equipment can also be broadly classified based on the phase dispersed. The gas
phase is dispersed as bubbles in bubble columns (sparged vessels), mechanically agitated vessels
and tray towers. Liquid phase is dispersed as thin films in wetted wall columns, packed bed, and as
droplets in spray towers and venturi scrubbers. Tray and packed towers are the most common industrial equipment for gas-liquid and liquid-liquid contacting. They are used for both continuous
and batch processes. Stirred tanks followed by settler vessels are used for extraction and leaching
and also for solid adsorbents being contacted with the liquid phase. The phase that has the higher
mass transfer resistance is chosen as the dispersed phase. This is done to reduce the diffusion length
in the controlling phase and also to increase its interfacial area. Bubble columns are, therefore,
used when the resistance is gas-phase controlled and spray towers for larger resistance in the liquid
phase.
Typical features of the different mass transfer processes are shown in Table 8.1. It may, however, be
kept in mind that the entries in the table are only for general information and deviations/variations are
possible for specific applications.
Table 8.1 Typical features of different Mass Transfer Processes
Feature
Nature of contacting
equipment
Options
Single stage
Processes
Distillation/
Rectification
Absorption/
Stripping
Extraction
Leaching
Adsorption
x
x
x
x
x
x
x
x
Cross flow multistage
cascade
Counter current flow
multistage cascade
x
x
x
x
x
Established Design
Approach
Equilibrium based
x
x
x
x
x
Rate based
x
x
x
Mode of operation
Batch
x
x
x
Continuous
Countercurrent with
cross flow over trays
x
Usually
countercurrent
Usually cross flow /
Countercurrent
Semi continuous
Crossflow /Cocurrent
(fluidised bed)
x
x
Involved phases
V -L
G-L
L-L
S-L
S-L
S-G
Minimum no of
components
2
3
3
3
3
x
x
x
Common Equipment
Tray column
Wetted wall column
x
Bubble column
x
Packed bed (column)
Spray tower
x
x
x
x
x
Mixer (with agitation)settler
Venturi scrubber
Mechanically agitated
continuous contactors
(Rotating Disc
Contactor etc.)
x
x
x
x
x
x
Continued
Table 8.1 Typical features of different Mass Transfer Processesdcont’d
Feature
Options
Processes
Distillation/
Rectification
Absorption/
Stripping
Extraction
Leaching
Fluidised Bed
x
Percolating leaching
equipment: Open tanks
and vats, Diffusion
batteries, Bucket
elevator contactors,
Screw conveyer
contactors
x
Dispersed solid
leaching: Agitated
vessels e simple
vessels and Pachuka
tanks, Gravity
thickeners, Continuous
centrifuges
x
Vapour refers to gas phase below its critical temperature
Used when heat of absorption is large e.g. absorption of hydrochloric acid vapour
Used for absorption of sulphur dioxide from furnace gas with slurry of limestone, lime or magnesia
Adsorption
8.2 Processes and equipment
235
Most equipment used for these continuous processes involve multistage contacting.
There are two different design approaches for mass transfer equipment.
Equilibrium Stage approach: The number of equilibrium contacting stages (NIdeal) required for
achieving the desired separation is estimated. Additional stages are provided to account for
nonequilibrium effects by considering a stage efficiency parameter h such that the actual number of
stages, Nactual ¼ NIdeal/h. This ensures that the equipment is designed to achieve the desired performance. The detail of the procedure and a discussion on stage efficiency is provided in Chapter 11 on
Distillation. This approach is adequate for binary mixtures and also for nearly ideal multi-component
mixtures.
Rate-based approach: The contacting efficiency (h) of a stage depends on the physical and
transport properties of the phases and the species getting transferred. It also depends on the hydrodynamic conditions (turbulence and mixing) resulting from the contactor geometry and flow
conditions (velocity, etc.) influencing the mass transfer coefficient (k) in the equipment. This
variation in k is taken care of in the rate-based approach. Unlike the equilibrium stage approach, it
considers nonequilibrium stages based on the physical details of the contacting stages (type, dimensions. etc.) and determines the number of actual stages (number of trays or packing height)
required for the desired separation. Accordingly, the mass and energy balances around each
equilibrium stage are replaced by separate balance equations for each phase around a stage.
Although the same equilibrium and enthalpy relations are used, phase equilibrium is considered to
exist only at the vapor-liquid interface on trays/packing and the enthalpies, concentrations, etc., are
evaluated at the conditions of phases exiting. Entrainment, occlusion, chemical reaction(s), etc.,
can also be added to the model. Rate-based approach is superior to the equilibrium-based models
particularly for nonideal systems and multicomponent mixtures. This is implemented in the
RATEFRAC module of the process simulator ASPENþ and also in others like ChemSep Release 3.1
and CHEMCAD.
The Design Problem: The common form in which a problem is posed states the requirement for
designing a separation system for an available feed stream. The feed stream composition and quantity
(in case of batch processing) or flow rate (in case of a continuous system) are known. Separation
performance target for the design is specified in terms of parameters, such as
(i) purity limits in terms of concentration of specific component(s) in the separated streams
(ii) recovery % of the desired component(s) from feed
(iii) limit of specific property values of the separated streams
The client often imposes additional constraints that may include but are not limited to:
(i) using a specific process or equipment (contactor) type
(ii) using specific solvent/inert/adsorbent
(iii) limitations on availability of hot and cold utilities
(iv) maximum limit of solvent/inert/adsorbent and/or utilities per unit of feed processed
(v) specified range of feed throughputeturndown ratio limit
(vi) maximum limit on investment required to build and operate the facility
236
Chapter 8 Interphase mass transfer
In most real life situations, the problem posed is usually ill defined, with incomplete information
that the designer fills in through discussions with the client, his own experience, and literature
survey. Experience of the designer is an invaluable component that helps to quickly conceive the
initial system configuration. This step is primarily based on heuristics. Technical information gaps
are filled later.
Complete Design Solution: A complete design solution to the problem comprises of the specification of the system, process design of equipment with their details and the hydraulics of the complete
plant. It should also contain the instrumentation and control scheme, as well as settings for any safety
device (say, pressure safety valve)/arrangements for trips/interlocks.
Execution of the following steps leads to the final design:
•
•
•
•
•
Configuring the overall system. This includes the contactor and the arrangement of the auxiliary
equipment/facilities, such as solvent regeneration in the case of absorption and adsorption, etc.
Selection of appropriate contacting equipment among the available options and performing the
process design calculations that generate the information to estimate the cost.
Deciding the economically optimum design choice. Minimizing only the cost of the separation
equipment may increase the cost of the rest of the system, and hence, the complete system,
including accessories/auxiliary system is optimized. This is illustrated in the optimum design of
distillation column.
Working out the mechanical details to generate the complete specifications and fabrication
drawings.
Detailing the plant hydraulics
8.3 Process design and detailed design of the equipment
Once a contacting equipment type for a mass transfer process is chosen, its detailed design depends on
the properties of the phases, their flow rates and process conditions. The detailed design of the contacting equipment can then be carried out independently. An example of this is in the design of the
tower internals; the tray design is carried out in the same way irrespective of the process being absorption or stripping or distillation. However, in order to optimize the process, while carrying out the
process design, some shortcut/quick estimation of the equipment parameters are done to estimate their
costs.
Designs dealt in this section of the book covers the process aspects of mass transfer equipment with
the deliverables primarily being the height and diameter of the tower. The details of packed and tray
towers for contacting the phases are dealt separately in Chapter 14 entitled Column and Column
Internals.
Since the process designs, in this section, pivot around phase equilibria, the same is briefly covered
in Chapter 9. Subsequent chapters (Chapters 10e14) cover the process design of (i) absorption and
stripping, (ii) distillation, (iii) adsorption and (iv) extraction systems. In order to deliver the design
solution of mass transfer processes, one may be guided by the above chapters and Chapter 14 on
Column and Column Internals. Inputs from sections V and VI of the book will be required for a
complete design of the process system/plant.
8.3 Process design and detailed design of the equipment
Chapter 9: Phase Equilibria and Equilibrium staged separation.
Chapter 10: Absorption and Stripping.
Chapter 11: Distillation.
Chapter 12: Adsorption.
Chapter 13: Extraction.
Chapter 14: Column Internals.
237
CHAPTER
Phase equilibria
9
9.1 Introduction
Phase equilibrium data pertaining to the transferable component(s) is essential for design of any mass
transfer process. Interphase mass transfer between immiscible phases occurs in the direction required
to attain equilibrium, and its rate depends on the departure from equilibrium, i.e., how far away is the
concentration of species i from the equilibrium concentration. Equilibrium concentration is independent of the amount/relative proportion of the two phases, and the locus of equilibrium concentration data generates the equilibrium distribution curve for each distributed component. The data can
be presented either at constant temperature (isothermal data) or at constant pressure (isobaric data).
Equilibrium distribution of the transferable component(s) represents the limiting composition(s) of the
phases in each ideal stage of contact. The designer calculates the separation attainable in a mass
transfer process consisting of one or more ideal contacting stages by estimating the equilibrium
concentration(s) from phase equilibrium thermodynamics.
Generally speaking, whenever a dynamic equilibrium is established between phases, the concentration of the species within individual phases (equilibrium
concentration) is uniform and is fixed by the system temperature
and pressure. In case of steady state, the species concentrations
Equilibrium and Steady State
and the thermodynamic parameters (temperature, pressure, etc.)
may not essentially be the same at all locations within a phase,
but at every location, these do not vary with time. Hence, the
equilibrium condition encompasses a steady-state condition, but the converse is not true.
9.2 Representation of concentration
The concentration of species i in a phase can have different representations. Usually, mole fraction or
a quantity proportional to it, e.g., partial pressure of component in gas-liquid or gas-solid system is
used to denote concentration in the gas phase. Traditionally the concentration of more volatile
component in the liquid phase is x, and the same in vapor or another liquid phase richer in the
component is denoted by y. In most situations, x and y denote mole fraction of the transferable
species. Mole ratios X and Y may be used to represent moles of i per mole of phase free of component
i, i.e., X ¼ x / (1 x) and Y ¼ y / (1 y).
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00009-9
Copyright © 2020 Elsevier Inc. All rights reserved.
239
240
Chapter 9 Phase equilibria
The same symbols (x, y, X, Y) are also employed at times to represent concentrations in terms of
mass (weight fraction) instead of moles. Other units of concentration, such as normality, molarity,
molality, or even a property value directly related to the concentration, e.g., absorbance or conductivity
as may be appropriate, can also be used. The partial pressure of the ith component (symbol: pi) is also
used to represent the concentration in the vapor phase. The symbol ci is used to represent concentration
of species i in the liquid. It is expressed as mg/gm or ppmw (in liquid phase) or ppmv (in liquid phase)
or something similar. The symbol ci can also be used to represent the concentration in the immiscible
liquids or in the solid phase. Table 9.1 shows typical symbols used and what they conventionally
represent.
Table 9.1 Representation of species concentration in phases.
Symbol for concentration
of component i
Conventionally represents
xi , yi
Mole fraction of species i
Xi, Yi
Mole ratio of species i
Xi ¼ xi / (1 xi), Yi ¼ yi / (1 yi)
pi
Partial pressure of species i in vapor/gas phase
qi, ci or Ci
Concentration (mg/gm, ppmw or any other w/w unit), (ppmv or any other w/v unit)
etc. Sometimes it may also be a property, e.g., color intensity of a dye solution,
related to the concentration of component i.
Usually q refers to concentration in the solid and c or C refers to concentration in the
liquid e generally expressed as weight fraction
9.3 Representation of equilibrium
Phase equilibrium is the condition at which each species has the same chemical potential in
different phases; ideally, this is in the absence of chemical reaction. However, for practical purposes, the equilibrium representation in some systems is extended to cases where usually, a single
species is transferred, and it reacts chemically with the components present in the destination
phase. This is the case of the chemical equilibrium in a heterogeneous system. Examples of such
cases are absorption of NH 3 in water or absorption of H2S or CO2 in aqueous alkanolamine (monoethanol amine, di-ethanol amine, etc.) solutions. In the case of adsorption on solids, the adsorbate
molecules can be held on the adsorbent surface by van der Waals forces, as is the case of physisorption. In chemisorption, a stronger chemical bond (electron sharing) is formed. A further
discussion on the two mechanisms of adsorption is provided in Chapter 12.
9.3.1 Graphical representation of equilibrium
Several manual computational procedures are based on geometric constructions on the graphical
representation of equilibrium. Typical graphical representations called equilibrium curves and their
relevance are listed in Table 9.2. Few typical equilibrium curves are shown in Fig. 9.1.
Table 9.2 Graphical representation of equilibrium relationships.
Drawn at
Special feature
Txy (Fig. 9.1A)
Constant total pressure
Tie lines join the equilibrium
composition of the phases.
Binary VLE e distillation
x y (Fig. 9.1B)
Constant total pressure
Temperature information
unavailable.
Points on the curve relate
equilibrium compositions.
Binary VLE e distillation
Gas solubilitya e absorber
X Y (Fig. 9.1C)
Constant total pressure
Temperature information
unavailable.
Points on the curve relate the
equilibrium compositions on
solute free basis.
Gas solubilitya e absorber, stripper
LLEa e extraction
LSEae adsorption, leaching
Px y (Fig. 9.1D)
Constant temperature
Tie lines join the equilibrium
composition of the phases.
Binary VLE e distillation
Hxy (Enthalpyconcentration)
diagram
(Fig. 9.1E)
Constant total pressure
Tie lines join the equilibrium
composition of the phases.
Binary VLE e distillation
pi x (Fig. 9.1F)
Constant temperature
Points on the curve relates the
equilibrium compositions.
Gas solubilityae absorber, stripper
VSEa e adsorption
q c (Fig. 9.1G)
Constant temperature
Points on the curve relate the
equilibrium compositions.
LSEa e adsorption, leaching
Ternary diagram
(Fig. 9.1H)
Constant temperature
Tie lines join the equilibrium
composition of the phases.
Ternary system.
LLE e extraction
LSE e leaching
VSEa e adsorption
Multicomponent systems at
times represented.
V, vapor, L, liquid, S, solid, E, equilibrium.
a
for single component transfer.
Application/Use
9.3 Representation of equilibrium
Representation
241
Chapter 9 Phase equilibria
Min boiling
azeotrope
P = constant
V+L V
T
V+L
L
0.0
0.5
x, y
T
No azeotrope
P = constant
V
L
1.0 0.0
0.5
x, y
(D)
Max boiling
azeotrope
P = constant
V
L
1.0 0.0
T = Constant
L
V+L
0.5
x, y
P
(A)
T
242
V+L
1.0
V
0.0
0.5
x, y
(B)
1.0
P = Constant
(E)
P = Constant
V
x
=
y
y
L+V
Tie line
A
L
T
V
0.0
L
1.0
x, y
1
0.8
0.6
0.4
0.2
0
V
λa
V+L
Y
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x
250
200
150
100
50
0
0
10 20 30 40 50 60 70 80 90 100
X
FIGURE 9.1
Cont’d
Enthalpy (HV, HL)
y
(C)
0.5
x
L
HV
A
Tie line
λb
HL
x, y
9.3 Representation of equilibrium
(F)
(G)
qmax
50°C
(Partial pressure of
solute over liquid)
pi
60°C
243
Adsorbate loading
q
40°C
30°C
x
(mol. fraction of solute gas in liquid)
Adsorbate conc. in solution, c
(H)
B
20
80
60
40
60
80
Plait point
40
20
Tie lines
S
A
20
40
60
80
FIGURE 9.1
Equilibrium Curves (A) Txy (B) x y (C) X Y along with corresponding x y diagram (D) Pxy
(E) Hxy and corresponding Txy diagram with tie lines (F) pi x diagram (Hydrocarbon solubility in
poly-alkene glycol) (G) q c plot for adsorption (H) Ternary diagram for LLE with tie lines.
9.3.2 Mathematical representation of equilibrium
Mathematical expressions relating equilibrium composition of components in different phases are
derived by equating the expressions for chemical potential of a species present in different phases.
The system may be binary or multi-component. In the simplest form, the phases are considered to
be ideal mixtures. A more realistic representation is obtained by considering nonideal thermodynamics for the condensed (liquid and solid) and the vapor phase using activity coefficients and
fugacity coefficients, respectively. In most cases of low-pressure systems, correcting only for
nonideality in the liquid phase results in fairly accurate equilibrium relationships. Liquid phase
nonideality often appears due to association of molecules, presence of ions, interaction between
species, etc. The behavior of hydrocarbons in the gas phase may be considered “ideal” up to
10 atm pressure for most engineering calculations.
VLE: Distillation
Ideal solutions obey Raoult’s law:
pi ¼ xi psat
i
(9.1a)
244
Chapter 9 Phase equilibria
where pi is the equilibrium partial pressure of component i present in solution, xi is the mole fraction in
the liquid phase, and psat
i is the vapor pressure of the pure component at the same temperature.
Raoult’s law is valid for chemically similar liquids or for components in large excess, i.e., as xi / 1
the prediction accuracy improves.
Inclusion of activity coefficient (gi ) accounts for nonideality of the liquid phase and modifies the
expression as:
pi ¼ gi xi psat
i
(9.1b)
The equilibrium vapor-phase mole fraction (yi ) for both phases ideal is
yi ¼ pi =P ¼ xi psat
i =P
(9.2a)
and for nonideality in the liquid phase is
yi ¼ pi =P ¼ gi xi psat
i =P
(9.2b)
where P is the total system pressure.
Data on activity coefficients/equations to evaluate the same can be obtained from any standard
textbook on phase equilibrium thermodynamics.
Equilibrium data are also presented in the form of equilibrium constant Ki for component i. It is
termed distribution coefficient and is commonly used in case of hydrocarbon systems.
Ki ¼ yi =xi
(9.3)
Up to moderate pressure for dilute mixtures, some common expressions of Ki are shown in
Table 9.3.
For ideal solutions, Ki values can be obtained from pure component vapor pressure using Raoult’s
law (Table 9.3). However, in reality, they vary with total system pressure, temperature, and composition due to nonideal behavior of the phases. Extensive charts, nomograms, and correlations are
available for predicting K values for various components, particularly those associated with natural gas
and oil refining industries.
Table 9.3 Expressions of distribution coefficient (Ki ).
Basis
Raoult’s law
Modified Raoult’s
law
Expression
Ki ¼ psat
P
i
Ki ¼ gi psat
P
i
Henry’s law
Ki ¼ Hi =P
Solubility
Ki ¼ psat
i
xi P
Applicability
Ideal solution and solute at subcritical temperature
Moderately nonideal solution when activity coefficients (gi ) are
known
Solutes at supercritical temperature and also for sparingly soluble
solutes at subcritical temperature
When solubility data in mole fraction (xi ) is available
P, total pressure; psat
i , saturation pressure of pure component i; Hi , Henry’s law constant for component i in solution.
Another way to express vapor-liquid equilibrium data is by using relative volatility (ai;j ) of
component i with respect to another component j. Relative volatility is related to distribution coefficient of the two components i and j as:
ai;j ¼ Ki =Kj ¼
yi =xi yi =yj
¼
yj =xj xi =xj
(9.4)
Solubility: absorption and stripping
Solubility data of a gaseous component in the liquid phase needs to be known for absorber and stripper
design. Equilibrium solubility of components of a gas mixture over a liquid is often expressed in terms
of partial pressure of the component (Table 9.3). An ideal dilute solution is described by Henry’s law:
pi ¼ Hi xi , for components in minute quantities (xi /0). Hi , the Henry’s law constant for
component i depends on temperature but is relatively independent of system pressure at moderate
pressure levels. xi 0:1 is considered as the upper limit for applicability of Henry’s law within engineering accuracy.
The solubility of gas decreases with increasing temperature, and hence, the equilibrium (solubility)
curves are steeper at higher temperatures, as is evident from Fig. 9.1F. Gas solubility increases with
pressure, and it is possible to produce any gas concentration in the liquid by applying sufficient
pressure as long as the liquefied form of the gas is completely soluble in the liquid. Solubility of a gas
is affected by presence of other gases in the system and also by the presence of nonvolatile solute.
The aforementioned relationships are applicable to nonreactive systems only and cannot be used
for systems where the absorbed gas reacts with the solvent.
Considering the advantages of linear interpolation/extrapolation, experimental solubility data
are often presented as a reference substance plot. These are plotted
with the pure solvent boiling point along the x-axis and the partial
pressure of the solute gas along the y-axis; each line on the graph
Linear equilibrium plots
corresponds to a specific solute concentration. At times, the vapor
pressure of pure liquid is also marked in lieu of its boiling point.
This representation connects xi , T, and pi . Fig. 9.2 shows the reference substance plot for the
ammoniaewater system.
100
80
60
Partial pressure ammonia, mmHg
40
Mole fraction
H2O in liquid = 1.0
20
0.90
0.60
10
0.75
8
6
4
2
4
6
8 10
20
40
60
Vapor pressure H2O, mmHg
FIGURE 9.2
Reference substance plot for NH3eH2O system.
100
246
Chapter 9 Phase equilibria
GSE and LSE: adsorption
The amount of substance adsorbed at equilibrium depends on:
•
•
•
•
Temperature e Since adsorption is an exothermic process, higher temperature reduces adsorbate
loading at constant solute partial pressure for gas adsorption. The same is also true for liquid
adsorption, but the effect is much less. The temperature effect is neglected in water treatment and
ambient vapor phase applications.
Solute partial pressure e for gas adsorption, higher pressure increases loading at a constant
temperature
Specific surface area/porosity of adsorbent - Higher porosity ensures higher specific surface and
larger adsorption capacity per unit adsorbent weight.
Nature of solute - vapors and gases with higher molecular weight and lower critical temperature
are more readily adsorbed. Chemical differences as the extent of unsaturation also influence the
extent of adsorption. Permanent gases are usually adsorbed to a relatively small extent. Molecules
with higher polarity are adsorbed more readily than nonpolar molecules due to which water is
more readily adsorbed than hydrocarbons.
For gas adsorption, equilibria can be expressed as e fðq; p; TÞ ¼ 0; or q ¼ f ðp; TÞ where “q”
represents the concentration of an adsorbed component in the solid.
Adsorption equilibria are usually represented by keeping one of the aforementioned parameters
constant, i.e.
•
•
•
Adsorption isotherms: q ¼ f ðpÞ; at constant T
Adsorption isobars: q ¼ f ðTÞ; at constant p
Adsorption isostere: p ¼ f ðTÞ; at constant q
Isotherms are the most common form of reporting equilibrium data for adsorption and are plotted
or tabulated as capacity or loading (equilibrium concentration of the adsorbed component on the solid)
versus the equilibrium concentration in the fluid phase. The solid is generally referred to as adsorbent
or substrate and the adsorbed component as adsorbate/solute. Loading in the solid phase is usually
expressed as adsorbed mass per unit mass of (solute free) adsorbent. It can also be represented as the
amount adsorbed or the number of molecules adsorbed per unit area.
For commercial adsorbents used in air driers, this is usually specified as static adsorbent capacity at
10% and 60% relative humidity, often denoted as E0.1 and E0.6.
At room temperature, when gas pressure does not exceed atmospheric, adsorption isotherms for
most gases are linear. The nonlinearity arises due to concentration dependence of activity coefficient of
adsorbate in the fluid and the solid phase.
Fluid phase adsorbate concentration is expressed as partial pressure (p) or relative humidity in the
vapor phase and mass (or mole) fraction per volume (mol/m3, kg/m3 or ppm, etc) for the liquid phase.
Adsorption isotherms for vapor with partial pressure as ordinate can obviously extend only up to
the saturation vapor pressure at the isotherm temperature. Beyond this pressure, the vapor liquefies.
This characteristic is not shown for gases above their critical temperature. Adsorption isotherms of
vapors often exhibit hysteresis at least over a part of an isotherm. This phenomenon is discussed in
greater detail in Chapter 12.
It is interesting to note that unlike solubility curves, adsorption isotherms are not always concave to
the pressure axis.
9.3 Representation of equilibrium
247
The simplest adsorption isotherm expresses loading (q) as proportional to fluid phase concentration,
resulting in an expression similar to Henry’s law.
q ¼ b c
Isotherm equations
(9.5)
c is the equilibrium concentration of the solute in the mixture.
There are three commonly used mathematical expressions e
Langmuir, BET (BrunauereEmmetteTeller), and Freundlich isotherms to describe vapor/gas
adsorption equilibria as q vs p, the equilibrium partial pressure.
Table 9.4 provides the details of the equations.
Table 9.4 Vapor/Gas-solid adsorption isotherms.
Assumptions/
Considerations
Isotherm
Corresponding equation
Langmuir
isotherm
q ¼ b1 p =ð1 þ b2 p Þ
b1 e Slope of the isotherm
at zero coverage (Henry’s
law coefficient)
b2 e Constant
p e equilibrium pressure of
the solute
Accounts for surface
coverage, i.e., for high
fluid concentration,
adsorbate monolayer
forms on the adsorbent
surface
BET
equation
1
¼
q ½ð psat =p Þ 1
k1
p
1
þ
qm k
qm k
psat
Multilayer adsorption
theory based on
Langmuir model
Special features
· linear in the range
0.05 < ð p = p Þ < 0.35
applicable for
· not
supercritical conditions
used for data
· seldom
correlation and representation
sat
qm e loading corresponding
to complete monolayer
adsorption
k e BET equation constant
psat e Saturation pressure of the
solute
Freundlich
isotherm
Timken
isotherm
q ¼ KF ð p ÞKc
KF, Kc - constants for each
solute-adsorbent pair at a fixed
temperature
KF depends on nature of
adsorbent and adsorbate
q ¼ b1 ln KT þ b1 ln c ,
KT ,b1 e constants
Empirical fitting of
isotherm data to a linear
equation in log-log
coordinates
commonly used
· most
isotherm, although the
·
·
equation is
thermodynamically
inconsistent
works well for heterogeneous
surfaces
limited application range as it
does not describe isotherm
over a wide range of pressure
Chemical bonding with
adsorbate
While Langmuir isotherm is theoretically justified, Freundlich isotherm is of a purely empirical character since it does not have
a finite Henry’s law constant.
As is evident from equation, Freundlich isotherms are linear for Kc ¼ 1, concave upward for Kc > 1 and concave downward for
Kc < 1. Generally 2 < Kc > 10 represents good and 1 < Kc > 2 represents moderately difficult adsorption characteristics. Kc < 1
depicts poor adsorption characteristics and requires impractically large adsorption dosage for appreciable solute removal.
248
Chapter 9 Phase equilibria
When one component of a gaseous mixture is appreciably adsorbed over others, the adsorption
isotherm for the pure adsorbate is applicable, with the equilibrium pressure being the partial pressure
of the said vapor. In the case of comparable extent of adsorption of
both components from a binary gaseous mixture, the equilibrium
data are represented as triangular plots, similar to those used in
Multicomponent adsorption
liquid-liquid extraction and elaborated later in this chapter. Unlike
liquid solubility, adsorption is strongly influenced by both temperature and pressure and the equilibrium diagram in these cases
are typically plotted under isothermal-isobaric conditions.
The reference substance method of plotting for gas-liquid solubility is also applicable to adsorption
data where the adsorbate is the reference substance, provided the gas temperature is less than the
critical temperature.
Adsorption isostere is the relation of equilibrium concentration of adsorbate in the fluid with temperature at constant adsorbent loading. Partial presLinear plots
sure, dew point, or some other form of concentration is plotted against
temperature or inverse absolute temperature at specific extents of loading. The
abscissa of inverse absolute temperature makes the plots near-linear, and this
improves the accuracy of interpolation. A typical example is shown in Fig. 9.3.
Equilibrium partial pressure of acetone, mm Hg
400
200
kg acetone
0.30
adsorbed
per
kg
carbon
100
0.25
0.20
0.15
80
0.10
0.05
60
40
20
30
10
200
40
50 60
400 600
1000
80
2000
100
Temperature, °C
120 140 160 180 200
4000 6000
10,000
20,000
Vapor pressure of acetone, mmHg
FIGURE 9.3
Acetone adsorption on activated carbon with loading marked on the isostere lines.
9.3 Representation of equilibrium
249
Loading (mg/g/)on activated carbon adsorbate -->
Single component liquid adsorption refers to the adsorption of a single adsorbate (solute) from a
solution of inert solvent(s) in which the activity of the solvent(s) is constant. While contacting fresh
adsorbent (solid) with liquid, there is an uptake of adsorbate, as well
as occlusion of liquid into the pores of the solid. This occlusion also
leads to an apparent level of adsorption and must be carefully
Adsorption from a liquid
considered by the designer as this reduces the volume of liquid
recovered after contacting with solid as compared to the volume of
the original contacting liquid in batch processes. The apparent adsorption depends upon the concentration of solute, temperature, nature of the solvent and adsorbent. The extent of adsorption
practically always decreases at increased temperature and increased solubility in the solvent.
For dilute solution, the adsorption isotherm is plotted as equilibrium solute concentration in liquid
versus net solute apparently adsorbed per unit weight of adsorbent (Fig. 9.4).
102
101
100
10–2
10–1
100
101
Concentration (mg/L) in liquid phase -->
FIGURE 9.4
Isotherm of phenol from aqueous solution on activated carbon at ambient temperature.
The customary procedure to determine the apparent weight of solute adsorbed is to treat a known
volume of solution (v) with a known weight of adsorbent (W). As a result of preferential adsorption of
solute, the solute concentration in liquid falls from cIinitial to final equilibrium value c , both expressed
as mass solute/volume of liquid. The apparent adsorption of solute is calculated as
fðv =WÞ ðcInitial c Þg mass solute adsorbed per unit mass of adsorbent. This is a satisfactory
measure of true loading in case of dilute solutions when the fraction of original solvent adsorbed
(occluded) is small. With the apparent adsorption of solute determined over the entire range of concentrations from nearly pure solvent to nearly pure solute, curves, as shown in Fig. 9.5 result. One may
250
Chapter 9 Phase equilibria
1.0
E
a
Solute concentration in solution
b
D
0.0
c
–
0
+
Apparent weight of solute
adsorbed / weight of
adsorbent
FIGURE 9.5
Equilibrium curves when both solute and solvent are adsorbed on the adsorbent.
note that for pure solvent and pure solute contacting the adsorbent, the apparent loading would be “0.”
Curve “a” is the apparent adsorption isotherm in the case of a dilute solution e with negligible
adsorption of the solvent on the adsorbent solid. Curve “b” results when there is appreciable apparent
adsorption (removal) of the solvent from the solution. In the range D to E, the solvent is more strongly
adsorbed that results in the solution getting more concentrated than the original, i.e., c > cInitial and
the apparent loading becoming negative.
The isotherm expressions for the gas phase can also be extended for the liquid phase adsorption
with the partial pressure being replaced by a suitable measure of concentration and the units of the
constants modified accordingly. Thus, over a small concentration range particularly for dilute solutions, the isotherms are frequently described by Freundlich empirical equation
c ¼ K1 ½v ðcInitial c ÞK2 .
(9.6)
Where “v” is the volume of liquid treated per unit mass of adsorbent, cInitial and c are the initial and
final concentration of solute in the liquid, and thus, the product within the bracket represents “apparent
loading.” While K1 is influenced by the concentration units, the value of K2 is unaffected for dilute
solutions.
LLE: extraction
Unlike gases, which are miscible in all proportions, liquid solutions (binary or higher) often display
partial immiscibility at least over a certain range of temperature and composition. Also, there is
negligible effect of pressure on liquid-liquid equilibria provided a sufficiently high pressure is
9.3 Representation of equilibrium
251
maintained to ensure that only the liquid phase is involved. Liquideliquid extraction involves
systems composed of at least three substances (components) and two phases and although the
insoluble phases are chemically very different, all three components generally appear to some extent
in both the phases. In such ternary systems, the equilibria are depicted by triangular diagrams, in
their simple form with equilateral triangular coordinates. The advantage of using a ternary plot for
depicting composition is that the three variables can be conveniently plotted in a two-dimensional
graph. In the triangle, the apices denote pure components and the sides denote compositions of
binary mixtures. This is illustrated in Fig. 9.6A for components A, B and S where the original binary
mixture contains A and B and the partially miscible solvent “S” is added to preferentially extract B.
Apices A, B and S represent pure (100% molar or mass composition) A, B and S respectively and the
scales on the three sides BS, SA and AB are the respective percentages of the binary solutions, e.g., B
in a solution of B and S, S in a solution of S and A, and B in liquid solution of B and A. On addition of
S to a mixture of A and B, the overall composition shifts from side AB to a point M inside the triangle
such that the sum of the perpendiculars from the point to the three opposite sides denote the
respective % of the components in the mixture, and their sum is 100%. The concentration of each
species decreases linearly with distance along the perpendicular line drawn from M to the opposite
side of the triangle. An important property of the diagram is that if lines are drawn from an apex
through the point M and meeting the opposite side, the marking on the axis on the opposite side is the
composition of the two components in the mixture.
P
A
R
E
M
0.8
O
Q
0.8
0.6
0.4
0.2
0.8
P
0.6
0.6
1.0
0.4
R
0.6
M
E
0.2
S
Solute
fraction in
extract
E,R
P
0.4
Solute
fraction in
raffinate
0.2
S
0.0
0.0
0.2
0.4 0.6
xS , yS
0.8
1.0
x
0.8
0.4
0.4
0.2
Extract
curve
xB , yB
Raffinate
curve 0.6
0.2
=
1.0
0.8
(C)
B
y
(B)
B
yB
(A)
0.0
0.0
0.2
0.4 0.6
xB
0.8
1.0
FIGURE 9.6
Ternary equilibrium plot: (A) Equilateral triangular plot (B) Rectangular plot (C) Distribution curve.
In relation to extraction, B is the solute that, along with “feed solvent” A, constitutes the feed
phase. The extraction solvent S, often referred to as “solvent,” is partially miscible with the feed
solution, i.e., the addition of a suitable amount of S to the feed generates two distinct phases that
are in equilibrium. In the triangular diagram for the system (Fig. 9.6A), the zone of partial
miscibility is the area of the dome-shaped region OPQ. Solute B is miscible in all proportions with
both A and S. The dome, thus, bound by the two equilibrium curves, which are the solubility curves
with high and low concentration of the solvent S. Any point within the triangle ABS represents a
252
Chapter 9 Phase equilibria
ternary composition and when the point is outside the dome OPQ, it represents composition of a
homogeneous mixture phase. A mixture with a composition corresponding to the point M
within the partial miscibility region splits into two phases that are in equilibrium. Composition of
the two phases in equilibrium are E and R that lie on the equilibrium curves. The line RE is a
typical “tie line” that passes through the point M with the endpoints corresponding to the equilibrium compositions in the two liquid phases. The phase composition represented by E has a
higher proportion of solvent S and is termed extract phase, and R represents the “raffinate phase”
composition.
Tie lines are rarely parallel and gradually change their slope in one direction. As evident from
Fig. 9.6A, the tie lines become shorter in length as one approaches the top part of the dome until it
reduces to a point at “P.” This point of inflection near the top of the two-phase envelope is termed the
plait point. It signifies the condition at which the compositions of the two liquid phases in equilibrium
become identical and transform into a single phase. Thus, the “plait point” composition is obviously
the limit of composition where no phase separation takes place. The plait point is ordinarily not at the
maximum value of B on the solubility curve.
Henceforth, the equilibrium solubility curve of the extract and raffinate phase will be referred to as
the “extract curve” and the “raffinate curve,” respectively. In this book, the composition in the raffinate
phase is denoted by x and that in the extract phase by y, with subscripts denoting the components. The
composition can be expressed in terms of mass, mole, or any other quantity basis of each substance.
The curves are different for different physical quantity selected, but the material balance, equilibrium
principles, and the results obtained are the same in all cases.
One may note that the composition M actually results from mixing the feed and the solvent streams,
and it splits into two phases with the compositions represented by E and R. On removing S from the
ternary mixture M, the binary solution regains its original composition, which lies on line AB.
It is often more useful to plot LLE data in rectangular coordinates with the concentration of solute
(B) plotted against the concentration of solvent (S), and the concentration of feed solvent (A) is the
remaining fraction, such that all weight fractions sum to unity. Similar to triangular plots, the twophase region and single-phase homogeneous liquid region are demarcated by the extract and raffinate curves, as shown in Fig. 9.6B. Tie lines connecting the two equilibrium phase compositions are
also shown.
The distribution of the solute in the two phases can also be conveniently shown as a distribution
curve (Fig. 9.6C) of solute B In this case, the concentration of B in the extract phases is plotted on the
y-axis and that in the raffinate on the x-axis. The equilibrium curve lying above the diagonal (y ¼ x)
denotes that the distribution of B favors the S-rich phase (% of B in E is more than that in R). The slope
of the curve is quantitatively expressed as the distribution coefficient KDi , for component i.
KDi ¼ yi =xi
(9.7)
Similar to vapor-liquid systems, KDi is found from the thermodynamic considerations by equating
the chemical potential of each component in the two phases.
Often distribution curves are plotted with concentration of solute in raffinate and extract phase
expressed on solvent-free basis denoted as XB ¼ xB =ð1 xS Þ and YB ¼ yB =ð1 yS Þ respectively.
Further reading
253
There are two main classes of liquid-liquid equilibrium in extraction:
(i) One immiscible pair of species that produces the familiar envelope shown in Fig. 9.6 and is
discussed above. In the system shown, species AB and SB are completely miscible while
AS is partially miscible, and the mutual saturation limits are denoted by the envelope ends
(O,Q) on line AS. The more insoluble the liquids A and S, the closer will be the points to the
triangular apices. This nature of LLE is more common and is preferred for extraction with
solvent S. Solvents are often selected to get this. Nevertheless, the type can change with
temperature, and this needs to be considered.
(ii) Two pairs of immiscible species exist, and so the two-phase envelope crosses the triangular
diagram like a bridge. The ternary diagram drawn at 25 C in Fig. 9.7 shows this nature e AB is
completely miscible in all proportions, but there is only partial miscibility between AS and
BeS. BeS becomes completely miscible at 3.5 C. At 50 C, the miscibility improves further, and
we note that the two-phase envelope shrinks to a single immiscible pair.
B
A
25°C
B
S
A
35°C
B
S
A
50°C
S
FIGURE 9.7
Effect of temperature of equilibrium solubility on the ternary system.
Further reading
Treybal, R. E. (1980). Mass-transfer operations. McGraw-Hill Classic Textbook Reissue Series.
Reid, R. C., Prausnitz, J. M., & Poling, B. E. (1987). The properties of gases and liquids. New York: McGraw-Hill.
Prausnitz, J. M., Lichtenthaler, R. N., & de Azevedo, E. G. (1998). Molecular thermodynamics of fluid-phase
equilibria. Pearson Education.
CHAPTER
Absorption and stripping
10
10.1 Introduction
Absorption and stripping involve gas and liquid streams which
transfer components from gas feed to a liquid stream in case of
absorbers and from liquid feed to a gas stream in strippers. Such
Absorption and Stripping
contacting in a flow system can be countercurrent or cocurrent.
Countercurrent contacting has the well-discussed advantage of utilizing a higher average driving force for mass transfer that results in
more compact equipment in most cases of absorption and stripping. Cocurrent flow design is rarely
useful in absence of reactions or when only about one stage of contacting suffices due to high
solubility of the component being transferred.
Nevertheless unlike countercurrent flow, the capacity of the cocurrent contactor is not limited by
flooding. This allows processing at high throughput as in venturi scrubbers. Cocurrent downward gasliquid flow through packed bed is used for catalytic chemical reactions in trickle bed reactors. It is also
used for situations where
(i) a rapid, irreversible chemical reaction accompanies the mass transfer process, e.g., absorption of
hydrogen sulfide into aqueous sodium hydroxide,
(ii) an exceptionally tall tower is built in two sections, with the second section operated in cocurrent
flow to save on the large diameter gas pipe connecting the two.
This chapter deals with the design of continuous absorbers and strippers where the desired function
is achieved through countercurrent contacting of gas and liquid in staged contactors (tray columns) and
continuous contactors (packed towers).
Industrially, the more economical option between a tray column and a packed column is chosen
for the specific design task. The maximum attainable separation is governed by the equilibrium
concentration between the phases that are affected by the process conditionsdprimarily the
operating temperature and pressure, the number of stages of contacting, and the liquid to gas flow
rate ratio.
Inputs to the process design in case of absorber/stripper are:
•
•
•
Inlet flow rates of gas and liquid
Composition of the inlet gas and liquid in case of absorption and stripping respectively
Minimum target of recovery of the component(s)
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00010-5
Copyright © 2020 Elsevier Inc. All rights reserved.
255
256
•
•
Chapter 10 Absorption and stripping
Operating pressure and maximum permissible pressure drop across the column
The chosen solvent (in case of absorber)/inert gas (in case of stripper)
The last two are often decided based on economic considerations, and are, therefore, left to the
choice of the designer.
The design decisions are usually based on the following considerations:
1) In the case of absorbers, the solvent is selected, such that, it has a high solubility for the solute.
This reduces the amount of solvent. In addition, it should be relatively cheap, stable, nonvolatile,
noncorrosive, nontoxic, nonviscous, nonfoaming, and preferably nonflammable. Since the exit
gas is saturated with solvent, a part of the solvent is lost. A low-cost solvent is often preferred over
a costly one with higher solubility or lower volatility. The availability of suitable material of
construction also influences the choice to a large extent. Recovery of the solvent, usually by
distillation and at times by chemical means, is almost always necessary and needs to be included
in the design and cost analysis. The more effective the regeneration process, the less costly the
absorber, as the regenerated solvent is left with a lower concentration of residual dissolved solute.
Water is the most commonly used solvent, oils are used for hydrocarbons, and special chemical
solvents for acid gases like H2S, CO2, and SO2.
There is always a loss of solvent with the exiting streams, and the designer needs to specify
the equivalent make up rate. In case the solvent has several components, the loss of lighter
components from the solvent is more, and therefore, the makeup stream needs to be richer in
lighter component(s). A light, lean oil solvent for absorbing light hydrocarbons will have higher
loss but has the advantage of high absorption capacity (moles/m3 circulated) compared to heavier
lean oil. The selection of a solvent close in carbon number to the components absorbed has a higher
absorption capacity, but the closeness of volatility makes the separation difficult. Therefore,
optimization of the absorber needs to be done by considering the absorber and the regenerator
together. As an example, lean oil with three carbon numbers heavier than the lightest component is
usually common in petrochemicals/refineries, whereas a lean oil heavier by about 10e14 carbon
numbers is adopted in natural gas processing units.
The considerations for deciding on the stripping gas (inert) are also similar and largely dictated by
the availability and economics. Steam and nitrogen are common industrial stripping agents, and as
in the case of solvent selection, the overall cost of the stripper operation and the cost of recovery
need to be considered for arriving at the optimum choice.
2) Height of the tower and its components, e.g., the depth of packing or the number of trays
3) The optimized liquid flow rate through the absorber and regenerator
4) Inlet and outlet temperatures of the stream(s) and amount of heat required to be removed to
account for heat of solution, etc.
5) Operating pressure of the column
6) Mechanical design
10.2 Tray column
257
10.2 Tray column
Fig. 10.1 shows the schematic diagram of a countercurrent absorber column with N trays and a single
component being transferred from the gas to the liquid phase. The mole fraction of the component in the
liquid and vapor phases are x and y, respectively, and the total molar flow rates are L for the liquid phase
and G for the gas phase, as marked in the figure. L0 and G0 denote the corresponding flow rates of the
nonabsorbable (solute free) components, and these remain unchanged along the column. The subscripts
correspond to the tray number which the stream exits. Trays are numbered from top to bottom.
Accordingly, subscripts Nþ1 and 0 are used for the external gas feed and the liquid entering the column.
G1
y1
L0
x0
1
2
n
Gn+1
yn+1
Ln
xn
n+1
N-1
N
GN+1,
yN+1
LN,
xN
FIGURE 10.1
Schematic diagram of an absorber column with N trays.
258
Chapter 10 Absorption and stripping
10.2.1 Graphical determination of the number of contacting stages
Assuming that no chemical reaction occurs and a single component is absorbed from the gas to the
liquid phase, the number of ideal stages is determined from a graphical construction using the operating and equilibrium curves.
The operating curve relates the mole fraction of the transferable component in the outgoing vapor
from a tray (say nth tray) with the composition of the liquid falling on the
same tray and is arrived at by species balance across the dashed control
volume marked in Fig. 10.1. It extends from the point representing the
Operating curve
streams entering the column to that representing the exiting streams from the
nth tray and thus passes through the point having coordinates (xn, ynþ1).
The linearity of the operating curve depends on the units in which the concentrations of the material
balance are expressed and the graph axes. When expressed in terms of
mole fractions (moles solute/mole solution) or in any concentration ratio
proportional to mole fraction (partial pressure, say), the operating line is
Linear operating curve
nonlinear.
A straight line is obtained
(i) for very dilute solutions
(ii) when the total quantity of each phase remains constant while composition changes owing to the
diffusion of several components (binary distillation)
- This forms the basis of the McCabe-Thiele method of estimating the number of trays.
(iii) when the concentration is expressed as the mole ratio (moles solute/mole solute free solution) as
the solute free flow rates remain unchanged throughout the column. This facilitates
interpolation and extrapolation. Referring to Fig. 10.1, the equation of the operating line in
terms of L0 and G0 (mol/hr flow rates of nonabsorbable components) is obtained from the species
balance across the dashed control volume as
x0
ynþ1
xn
y1
L0
þ G0
¼ L0
þ G0
1 x0
1 ynþ1
1 xn
1 y1
and in the generalized form
L0
x0
y
x
y1
¼ L0
þ G0
þ G0
1y
1x
1 x0
1 y1
(10.1)
where x and y are the compositions in the respective liquid and vapor phases leaving and entering a tray.
In terms of mole ratio denoted as X and Y for composition in the liquid and gas phase, respectively,
Eq. 10.1 reduces to
L0 X0 þ G0 Y ¼ L0 X þ G0 Y1
(10.1a)
Note: Eq. 10.1 is nonlinear on the mole fraction plot (x-y plot), i.e., the operating line is a curve
plotted on x-y axes while it is linear in the XeY plot.
In an absorber design problem, the feed gas flow rate (G, G0 ) and concentration (yNþ1) are known,
and so is the exit gas composition (y1). The component concentration in the absorbent liquid (xo) is also
knowndit is zero for fresh liquid and can have a small value in the case of regenerated solvent. Hence,
for a known value of L [L0 ¼ L(1 x)], the operating line (Eq. 10.1) can be drawn on the graph. On the
10.2 Tray column
259
same graph, the equilibrium solubility data for the solute gas in the solvent liquid can also be plotted in
terms of the same concentration units. Each point on the equilibrium curve represents the gas concentration in equilibrium with the liquid at its local concentration and temperature. The position of the
operating line with respect to the equilibrium curve depends on the choice of abscissa and ordinate visà-vis the direction of mass transfer. The line is above the equilibrium curve if the mass transfer occurs
from gas to liquid phase (absorption), and the composition in the gas phase is represented in the y-axis.
In the case of a stripper, the operating curve is below the equilibrium curve for the same choice of axes.
The number of ideal contacting stages for a design problem can be determined graphically from the
operating and equilibrium curves, as discussed below.
x-y plot
0.35
FIGURE 10.2
Graphical determination of the number
of ideal trays.
0.3
y (mole fraction)
0.25
Operating Line
with L = 1.5 Lmin
0.2
(0.0035,0.2)
(0.00503,0.2)
4
Operating Line
with Lmin
0.15
3
0.1
(0,0.02)
0.05
2
1
0
0
(x2,y2)
0.0035
(x1,y1)
1
2
3
4
x (mole fraction)
5
6
7
×10–3
A typical example is shown in Fig. 10.2 for a SO2 absorber where freshwater (xo ¼ 0) is used as an
absorbent to reduce SO2 concentration (mixed with air) from 20 mol% SO2 to 2 mol%. The operating
line generated using Eq. 10.1 corresponds to molar flux (molar flow rate/column cross-section) on a
solute free basis L0 ð¼ L0 =At Þ and G0 ð¼ G0 =At Þ of 333 and 5.18 kg mol/m2.hr, respectively, where At
denotes the cross-sectional area of the column. The horizontal line drawn in the figure through (0, 0.02)
corresponding to the top tray (Tray no. 1) intersects the equilibrium line at “1.” The abscissa of this
point denotes the equilibrium composition (x1) of the liquid leaving tray 1, and the vertical line through
“1” intersects the operating line whose ordinate corresponds to the gas composition (y2). This process
of drawing the horizontal and vertical lines are continued to obtain a sequence of near triangular steps
till the next horizontal line has to be drawn above yNþ1. The two corner points at the base of the lowest
triangular step are, therefore, (xo, y1) and (x1,y1). The corresponding lower corner points in the next
upper triangular step are (x1,y2) and (x2,y2), and so on. Corresponding to the known gas and liquid flow
rates (G, G0 and L, L0 ), the figure, therefore, depicts the number of theoretical trays required to enrich
260
Chapter 10 Absorption and stripping
the gas concentration from yNþ1 to y1 or more. From Fig. 10.2, this absorber requires 2.4 ideal trays. If
the overall tray efficiency of 40% is considered, the actual number of trays required is 2.4/0.4 ¼ 6
trays.
It is important to note that the enrichment per tray is lower at the dilute end, as separation is more
difficult. Therefore, the standard practice of graphical construction that produces a more accurate
estimation of the number of trays is to start from the dilute end and continue up to the final
concentration.
Minimum required liquid flow rate (Lmin) in case of absorber for a given gas rate (G,G 0 )
The foregoing geometrical construction to determine the number of ideal stages of contacting could be
done, only because (1) the point on the operating line corresponding to yNþ1 is situated above the
equilibrium line, (2) the operating line and the equilibrium lines neither touch nor intersect below
yNþ1.
The geometric condition of the minimum liquid flow rate Lmin ; L0min for a given gas flow rate
would correspond to the operating line touching the equilibrium line. Thus, the minimum theoretical
liquid flow rate (Lmin) is found from the material balance
equatione Lmin ¼ G.(yNþ1 y1)/(xN xo)
and leads to an operating line passing through (xo,y1) and xNþ1 ; yNþ1 , where xNþ1 is the liquid-phase
composition in equilibrium with the vapor composition yNþ1. In the construction of Fig. 10.2, this
corresponds to xN ¼ 0.0063 and the (Lmin/At) ¼ 147.3 kg mol water/m2. hr, where At is the crosssectional area of the tower.
Optimum (economic) operating liquid flow rate (L, L0 ) is usually around 1.5 to 3 times the minimum liquid flow rate.
It is important to realize that in the case of the equilibrium line touching or intersecting the
operating line at some point P, the gas composition enrichment limit is yP. This point is the “pinch
point” for the system, and if yP <yNþ1, enrichment up to yNþ1 is not possible with the liquid flow rate
(L, L0 ) considered.
Approximations for low concentration system
When the concentrations are low, xo<<1 and yNþ1<<1, the mole ratio (X, Y) and mole fraction (x,y)
can be approximated to be equal over the entire concentration range. In this case, the partial pressure of
the inert gas remains constant throughout the column length, and the solute concentration in the liquid
and gas phase is sufficiently small.
The operating line equation reduces to the following linear expression with a slope of (L/G).
y ¼ ðL = GÞ:x þ y1 ðL = GÞ$xo
(10.2)
Also, the equilibrium relationship at low concentrations is usually well approximated by Henry’s
Law that has the linear form
y ¼ Hx
(10.3)
When the operating and equilibrium relationships are both linear, an analytical solution for the
number of stages (N) exists in the form of the following equation known as the Kremser equation.
In the case of absorber,
N ¼ log½ðyNþ1 m:xNþ1 Þ = ðy1 m:x1 Þ=logðAÞ
(10.4)
10.3 Packed column
261
and in the case of stripper,
N ¼ log½ðx1 y1 = mÞ = ðxNþ1 yNþ1 = mÞ=logð1 = AÞ
(10.5)
where, A[ ¼ L/(m.G)] is the absorption factor.
When the equilibrium line is in the linear approximation of a curve with the value of m
being m1 and m2 at the column bottom and the top conditions, A1 ¼ L/(m1.G), A2 ¼ L/(m 2.G) and
A¼ (A1.A2)1/2 is used in Eqns. 10.4 and 10.5.
The problem shown in Fig. 10.2 can also be solved using Eq. 10.4. After constructing tangents
at the top and bottom of the equilibrium curve, the slopes are: m1 ¼ 20 and m2 ¼ 43; also
L0 ð¼ L0 =At Þ ¼ 333 and G0 ð ¼ G0 =At Þ ¼ 5:18; A1 ¼ L/(m1.G) ¼ 3.21, A2 ¼ L/(m2.G) ¼ 1.5 and
A ¼ (A1.A2)1/2 ¼ 2.19;
Using Eqn.10.4, N ¼ 2.59, which is slightly different from 2.4, the value found from the graphical
procedure described earlier.
10.2.2 Absorption factor
The Absorption Factor (A ¼ L/(m.G)) in Eqns. 10.4 and 10.5 is the ratio of the operating line slope to
the equilibrium curve slope. For A<1, there is limited absorption of solute even for an infinite number
of theoretical trays. For A>1, any degree of separation is possible if a sufficient number of trays are
provided. When A is unity, i.e., the equilibrium and operating lines are parallel, Eqns. 10.4 and 10.5
become indeterminate, and the number of stages is the overall concentration change per unit driving
force, which is a constant.
In absorbers, where the solute concentration is not very dilute, heat of solution causes a rise in
temperature, and the value of m is greater at the column bottom than at the top. When the L/(m.G)
value is not constant for this reason or for others, the choice of L/G ratio is more difficult. The conditions at the dilute end are usually more important for the design since, in case of nearly complete
absorption, most of the transfer units are required in the dilute region.
In the case of packed columns, the absorption factor is needed to decide the height of a transfer unit,
the number of transfer units, and also the column diameter.
10.3 Packed column
The operating line in the case of packed bed relates the bulk concentrations (y and x) of the gas and
liquid phases at any section of the column between which the
mass transfer takes place. Figs. 10.3A and B show the typical
operating line and the equilibrium curve for absorbers and
Absorption/Stripping in packed bed
strippers, respectively. They also show the operating line corresponding to the minimum required liquid flow for absorber,
and the minimum required gas flow for stripper. This line
touches the respective equilibrium lines at a point termed as the pinch point. As pinch point is
approached, the concentration difference (driving force) tends to zero. Thus an infinite number of
contacting stages is required to approach the concentration at pinch point. This then represents the
limiting L/G ratio denoted as (L/G)min.
262
Chapter 10 Absorption and stripping
The same operating line equation holds for the stripper column, but due to the column top and
bottom concentration values, the equilibrium line lies below the operating line in absorbers and above
it in case of strippers. This can be seen from the typical cases shown in Fig. 10.3A and B. Subscripts 1
and 2 in the figure denote the bottom and the top position of the tower.
Since the equilibrium curve frequently concave upward, (L/G)min is usually calculated based on
equilibrium at the column bottom, where both liquid and gas have the highest concentration of solute.
However, the equilibrium curve can be shaped, such that, the pinch point exists not at the end but
somewhere in the middle, as shown in Fig. 10.3C for an absorber. Then, the operating line shown in the
figure represents (L/G)min. Such a situation may be a result of heat effects that alter the equilibrium
conditions within the column.
y2
(A)
y1
x2
(B)
Operating line (min.
liq. flow)
y2
Operating
line (actual
liq. flow)
Equilibrium
line
Optg.
line
(min.
gas flow)
max
y2
Equilibrium
line
Optg.
line (actual
gas flow)
y2
y1
x2
x1
y1
x1
x1
x2
(C)
y1
Operating
lines
P
y2
Equilibrium
line
x2
x1
x1*
FIGURE 10.3
Equilibrium curve, operating line, and minimum (L/G) operating line for (A) absorber, (B) stripper,
(C) absorber with pinch point P between y1 and y2.
For the cases of very soluble gases or operation under vacuum, Lmin may not be sufficient to wet the
entire packing surface, leading to poor liquid distribution. In such cases, it is desirable to recirculate
the liquid over the packing at the expense of a reduced concentration driving force and operate the
10.3 Packed column
263
packing above the minimum irrigation rate. The operation, in this case, is carried out at or above a
“minimum wetting rate” computed as qL =a where qL is the volumetric liquid flow rate in m3/(hr.m2)
of tower cross-section, and a is the packing surface area in m2/m3.
10.3.1 Packed column design based on mass transfer coefficient
The rate of mass transfer in the column depends on the concentration difference driving force across the
interphase, the liquid-phase and gas-phase mass transfer coefficients (kx, ky), and the interfacial area a for
mass transfer provided by the packing. Active volume of packing required to achieve the design target
of concentration change, say, from y1 (or x2) to y2 (or x1) of a stream depends on the volumetric mass
transfer coefficient, which is the mass transfer coefficient (kx, ky) times the interfacial area (a) per unit
volume of the packing (m2/m3 bed). A higher volumetric mass transfer coefficient requires a lower bed
volume. As the bed diameter is (primarily) decided by the flooding considerations at the design liquid
and the gas flow rates, the bed height is lower when the volumetric mass transfer coefficient is higher.
Procedure to estimate the height of the active section of an absorber bed needed to achieve a given
separation uses (i) rate expression for representing interphase mass transfer and (ii) material balance to
represent the change in the composition of the two phases. The rate expression involves the interphase
mass transfer coefficients. Combining these expressions leads to an integral expression for the number
of transfer units that is very similar and closely related to equations for the number of theoretical
plates. Fig. 10.4A schematically shows the bulk (xAL, yAG) and interphase (xAi, yAi) concentrations at
any section of an absorber bed while component A is transferred from the gas to the liquid phase.
Interphase concentrations in a packed bed are difficult to measure, and grossly, the overall driving
force for mass transfer can be expressed in terms of the difference in the overall composition.
Relationships represented on the concentration axes for the contacting liquid and gas streams at any
point (P) in the bed (Fig. 10.4B) are:
(i) the operating curve relating the respective bulk average concentrations (yAG, xAL)
(ii) the equilibrium curve relating the respective interface concentrations (yAi, xAi)
(iii) the driving force line (PM) joining the points on the operating curve (yAG, xAL) and the
equilibrium curve (yAi, xAi) for the same position in the packed bed
(A)
(B)
Interface
Liquid phase
yAi
yAG
P
D
Slope = m"
NA
xAi
Distance from
interface
Equilibrium
line
Gas phase
yAG
xAL
Operating
line
Slope = –
yAi
Distance from
interface
kx
ky
Slope = m'
M
yA*
xAL
xA*
FIGURE 10.4
(A) Bulk and Interphase concentrations with component (A) transfer from gas to liquid phase; (B) Operating
curve, equilibrium curve, and the driving force line for an absorber.
264
Chapter 10 Absorption and stripping
10.3.2 Driving force line
Line PM is termed as the driving force line since it identifies the bulk (x,y) and the corresponding
interface concentrations (xi,yi) at a point P in the bed, and the difference (y yAi) gives a measure of
the driving force. The slope of the driving force line is a function of the relative diffusional resistance
in the two phases.
The equation for line PM is deduced as follows
Molar flux of A at steady state in case of equimolar counterdiffusion:
NA ¼ ky ðyAG e yAi Þ ¼ kx ðxAi e xAL Þ
(10.6)
and when A diffuses into nondiffusing B:
ky ¼
kx ¼
ky0
ð1 yA ÞiM
kx0
ð1 xA ÞiM
(10.7a)
(10.7b)
Where
ð1 yA ÞiM ¼
fð1 yAi Þ ð1 yAG Þg
lnfð1 yAi Þ=ð1 yAG Þg
(10.7c)
ð1 xA ÞiM ¼
fð1 xAL Þ ð1 xAi Þg
lnfð1 xAL Þ=ð1 yAi Þg
(10.7d)
and
Equating the flux of A in the two phases relates yAG and xAL asNA ¼ ky0
ðyAG e yAi Þ
ðxAi e xAL Þ
¼ kx0
ð1 yA ÞiM
ð1 xA ÞiM
(10.8)
Eq. 10.8 relates the bulk and the interphase concentrations and is the equation of the driving force
line passing through P (xAL,yAG) and M (xAi,yAi).
Only a single component diffusing across the interphase is mostly considered in designing for
absorption, as well as stripping columns, and in such a case, the slope of PM in case of only A diffusing
in stagnant B is given by
Slope ¼
ðyAG e yAi Þ
k0 =ð1 xA ÞiM
k0
¼ x0
¼ f x0
ðxAL e xAi Þ
ky =ð1 yA ÞiM
ky
(10.8a)
where,
f¼
ð1 yA ÞiM
ð1 xA ÞiM
The slope of PM is ( kx0 ky0 ) in case of equimolar counterdiffusion.
(10.8b)
10.3 Packed column
265
When kx0 , ky0 , P(xAL,yAG) are known, construction of the driving force line PM allows us to determine the corresponding interphase concentration xAi and yAi at point M on the equilibrium curve. As an
engineering assumption, the system may be considered dilute and ð1 xA ÞiM and ð1 yA ÞiM are
nearly unity if the concentration
is below 10%. In this case, the line can be straightaway drawn through
P with its slope as ( kx0 ky0 ).
The following iterative procedure is needed to draw the line PM for concentrated systems as the
expression of slope contains the interphase concentrations (xAi and yAi) that are not known initially
ð1y Þ
(i) Assume f ¼ ð1xAA ÞiM value to be unity as the first trial
iM
k0 (ii) Draw line PM with slope kx0 and locate M on the equilibrium curve
y
k0 (iii) The coordinates of M (xAi,yAi) are used to recalculate f and the slope f kx0 which is used to
y
refine the location of M. Three trials usually suffice.
10.3.3 Overall mass transfer coefficient
Overall mass transfer coefficient is obtained from the individual coefficients by addition of interphase
resistances
1
1 m0
¼ þ
K y ky kx
(10.9)
1
1
1
¼ þ 00
K x kx m ky
(10.10)
In Eqs. 10.9 and 10.10, m0 and m00 are the slope of the chords (Fig. 10.4B). They are equal only for a
linear equilibrium curve.
If kx z ky, the slope of equilibrium curve (m0 ), at the point in question, decides the rate of mass
transfer. If m0 is small, K1y zk1y and when m0 is very large, K1x zk1x .
When kx z ky the relative size of (kx/ky) and m0 determines the location of mass transfer resistance.
Since superficial mass velocities vary slightly throughout the tower, mass transfer coefficients also
vary slightly. Fig. 10.3 shows that the smallest driving force occurs at the (column) top. Therefore, the
mass transfer coefficients are calculated for rates at top of the column as a conservative estimate.
The designer needs to know whether the mass transfer in the system is gas-phase or liquidphase controlling. Usually, for commercial processes, absorption
is gas-phase controlling, especially for highly soluble gases or
when the gas reacts with the liquid. Since the resistance to mass
Mass transfer coefficient
transfer essentially resides in the gas film, calculating only the gasphase mass transfer coefficient is sufficient. For stripping, the
liquid phase is usually controlling, and only the mass transfer
coefficient in the liquid phase is calculated.
In most diffusion operations, e.g., in packed and spray towers, the estimation of available interfacial area for mass transfer is not possible. It is also difficult
to measure the film coefficients kx0 and ky0 and Kx0 and Ky0 . In
such
cases it is customary to report experimentally observed
Volumetric mass transfer coefficient
rates of transfer in terms of transfer coefficients based on unit
volume of bed (volumetric mass transfer coefficient) rather
266
Chapter 10 Absorption and stripping
than unit interfacial area. The volumetric mass transfer coefficient (Kxa, Kya, etc.) is the product of the
mass transfer coefficient and the specific area of mass transfer per unit volume of tower packing. This
can be defined for
(i) equimolar mass transfer for the gas and the liquid phases, as kya and kxa
(ii) component A diffusing into a stagnant B in liquid and the gas phases as kx0 a and ky0 a
(iii) overall mass transfer coefficient Kx0 a and Ky0 a based on the liquid and the gas phases
It may be noted that for stripping and absorption, the mass transfer is one component diffusing into
a stagnant phase, and therefore, coefficients kx0 a and ky0 a, as well as Kx0 a and Ky0 a are used in the design
equations.
The volumetric mass transfer in each case will have the unit (kg mole of A transferred)/(s. m3 of
packing. mol fraction difference of A as driving force).
The mass transfer coefficients of each phase are estimated from available correlations reported
in literature. In packed beds, the coefficients have
been reported to increase with square root of
mass velocity and two-thirds power of diffusivity.
Estimation of individual mass transfer coefficients
Nevertheless, correlations proposed by different
researchers differ appreciably. As the coefficient is
related to turbulence and fluid properties, these are
usually correlated in terms of Sherwood number, Reynolds number, and Schmidt number.
10.3.4 Estimation of active bed height
The design equation for the bed height hbed(m) may be obtained from any of the following expressions
Z hbed
Z y2
G$dy
hbed ¼
dz ¼
(10.11)
0
ky aAt
0
y1
ð1 yÞðy yi Þ
ð1 yÞiM
Z hbed
Z y2
L$dx
(10.12)
dz ¼
hbed ¼
0 aA
k
t
0
y1
x
ð1 xÞðxi xÞ
ð1 xÞiM
using film coefficients and
hbed ¼
hbed ¼
Z hbed
0
y1
Z hbed
Z y2
0
using overall coefficients.
dz ¼
Z y2
dz ¼
y1
G:dy
Ky0 aAt
ð1 yÞM
(10.13)
ð1 yÞðy y Þ
L:dx
Kx0 aAt
ð1 xÞðx xÞ
ð1 xÞM
(10.14)
10.3 Packed column
267
In the above expressions, G and L are the total molar flow rates, and At is the cross-sectional area of
the column.
Since the individual coefficients of mass transfer vary rapidly with the flow rate, the quotient of
each coefficient divided by the phase flow rate to which it
applies is more nearly constant than the coefficient itself.
Height of a transfer unit (HTU) and
L
The quantity obtained by this division k0 GaAt or k0 aA
is
t
Number of transfer units (NTU)
y
l
the height of one transfer unit (HTU), which is the bed
height required to accomplish one unit of separation. The
HTU based on gas phase HTOG ¼ k0 GaAt is more commonly used.
y
Z y2
dyð1 yÞiM
The corresponding driving force term NTOG ¼
ð1
yÞðy yi Þ
y1
where ð1 yÞiM ¼
ð1 yi Þ ð1 yÞ
ð1 yi Þ
ln
ð1 yÞ
This is the number of overall gas-phase transfer units required for changing the composition of the
gas phase from y1 to y2 and hbed ¼ HTOG.NTOG.
It is important to note that for packed towers, the column height depends not only on the operating
and equilibrium lines but is also inversely proportional to the mass transfer coefficients that play a
relatively minor role in determining the plate efficiency.
Although the processes are similar, in the case of packed column distillation, the difficulty is
encountered in the integration to evaluate NTOG and hbed. This is
because the assumption used for gas absorption is not valid.
Although L and V (moles/hr) are constant, the corresponding
Absorption versus distillation
mass rates in kg/hr may vary appreciably due to the variation of
molecular weight with composition. Since the present mass
transfer coefficients are functions of mass flux (flow rates per unit
area), considerable variation in these coefficients may occur along the tower. In addition, the fluid
physical properties may vary significantly due to changes in both temperature and pressure.
Accordingly, the theory of distillation is not very satisfactory in packed towers.
If the x and y values for the gas and the liquid streams are below 0.1, the system is considered as a
“dilute” or “low concentration” system in the engineering sense.
The low concentration and its small change leads to only a limited
change in the volumetric flow rate of the two phases in the tower.
Design of dilute systems
Hence, it is considered that there is only a limited change in turbulence along the tower, and the mass transfer coefficients are
fairly constant over the entire tower.
The design Eqs (10.11e10.14) for the dilute system thus simplifies to e
"
# Z
Z hbed
y2
G ð1 yÞiM
dy
hbed ¼
(10.15)
dz ¼ 0
ky aAt ð1 yÞ
0
y1 ðy yi Þ
av
268
Chapter 10 Absorption and stripping
"
# Z
x1
L ð1 xÞiM
dx
hbed ¼
dz ¼ 0
ky aAt ð1 xÞ
0
x ðxi xÞ
av 2
"
#
Z y2
Z hbed
G ð1 yÞM
dy
hbed ¼
dz ¼ 0
K
ðy
y Þ
aA
ð1
yÞ
t
0
y1
y
Z hbed
(10.16)
(10.17)
av
Zhbed
hbed ¼
0
L ð1 xÞM
dz ¼ 0
Kx aAt ð1 xÞ av
Zx1
dx
ðx xÞ
(10.18)
x2
Additionally, for a dilute system, the operating line is nearly straight, and the log mean driving
force is used:
Z y2
dy
ðy1 y2 Þ
ðy1 yi1 Þ ðy2 yi2 Þ
¼
(10.19)
; where ðy yi ÞM ¼
ln½ðy1 yi1 Þ=ðy2 yi2 Þ
y1 ðy yi Þ ðy yi ÞM
and
Z y2
y1
y1 y1 y2 y2
dy
ðy1 y2 Þ
¼
; where ðy y ÞM ¼ ðy y Þ ðy y ÞM
ln y1 y1 = y2 y2
(10.20)
For relating the performance of packed towers with tray towers, the packing performance is defined
in terms of the height equivalent to a theoretical plate (HETP).
Although the HTU concept is theoretically
more correct for packed towers in which mass
transfer is accomplished by a differential action
rather than a series of discrete stages, the concept
Height equivalent to a theoretical plate (HETP)
of HETP is more convenient.
For linear equilibrium and operating curves,
the two concepts are related as
HTOG
mðG=LÞ 1
¼
lnðmðG=LÞÞ
HETP
(10.21)
Where G and L are the respective molar flow rates of the gas and liquid phase, and m is the slope of the
equilibrium curve.
For the special case when the equilibrium and operating lines are parallel (mG/L ¼ 1),
HTOG ¼ HETP and bed height hbed may be estimated from either HTU or HETP concepts, i.e.,
hbed ¼ HTOG NTOG ¼ HETP N
(10.22)
where N is the number of theoretical plates (stages).
10.3.5 Design based on liquid-phase resistance
The number of liquid-phase transfer units (NTOL) is not the same as the number of gas-phase transfer
units (NTOG) unless the operating and equilibrium lines are straight and parallel. For absorption, the
operating line is usually steeper than the equilibrium line, which makes NTOG> NTOL, but this
10.4 Design illustration
269
difference is compensated by the difference between HTOL and HTOG, and the column height can be
determined by either approach.
Even if the individual coefficients (kGa) and (kLa) are relatively constant for any given case, the
overall coefficients vary with m for nonlinear equilibrium curve. Therefore, the overall coefficients
should be used only when m and molar density of the phase (rm) are nearly constant.
10.3.6 Absorption accompanied by chemical reaction
In many commercial absorption processes, a chemical reaction between the solute and the solvent
provides a more complete removal of solute, e.g., removal of CO2 from the air by using mildly alkaline
solutions or scrubbing of ammonia using a dilute acid solution. The chemical reaction is employed to
favorably alter the gaseliquid equilibrium relationship for the enhancement of mass transfer rate. The
reaction in the absorbent phase affects the liquid-phase mass transfer coefficient (kL), which is
influenced by reaction kinetics, as well as by factors influencing physical mass transfer at the interphase. The enhanced rate due to chemical reaction also occurs from a greater effective interfacial area
since absorption can take place in the nearly stagnant regions, as well as the dynamic liquid hold up
and is usually incorporated by introducing an enhancement factor (E) in the rate expressions where
kL
E¼ o
kL
(10.23)
kL is the actual mass transfer coefficient and kLo is the mass transfer coefficient in the absence of reaction under the same circumstances.
When absorption is accompanied by a very slow chemical reaction, the apparent values of kGa may
be lower than with absorption alone, e.g., in the absorption of chlorine in water followed by hydrolysis
of dissolved chlorine, the slow hydrolysis reaction essentially controls the overall rate of absorption. In
the “slow reaction regime,” there is no enhancement effect, and we assume kL ¼ kLo and E ¼ 1. In this
case, the only effect of the chemical reaction is to enhance the driving force from the interface to the
bulk, which is kept higher due to the low concentration of solute in the bulk liquid.
In the case of a fast chemical reaction (instantaneous reaction regime), the mass transfer rate is
independent of chemical kinetics and depends on factors affecting the physical transfer of reactants
and reaction products. E can be very large, particularly when the concentration of the reactant in the
liquid is high. Between the “slow reaction” (E ¼ 1) and “instantaneous reaction” EzN (mass transfer
independent of reaction rate) regimes, there is a broad range of conditions termed as the fast reaction
regime. In this case, kL depends on the reaction rate, and while both kL and kLo are affected by the
hydrodynamic conditions, E is relatively independent of these factors. Based on the value of E, the
effective mass transfer coefficient can be estimated and used in the design calculations. In many cases,
the effective equilibrium data with chemical reaction are obtained from experimental and pilot plant
data. This data can be directly used for the process design.
10.4 Design illustration
Problem 10.1. Design a packed bed absorber to remove at least 90% of the ammonia present in an
airstream by scrubbing with water. The air stream containing 10% ammonia (by volume) has a flow
rate of 1500 Nm3/hr and is available at 30oC and a pressure slightly above atmospheric. Ceramic
270
Chapter 10 Absorption and stripping
Raschig rings (100 size) available in the plant stores may be used for random packing. The equilibrium
data (mole fraction) for ammoniaeairewater system at 30oC is given (below) in Table P10.1a.
Table P10.1a Equilibrium data (mole fraction) for ammoniaeairewater system at 30 C.
x
0
0.0126
0.0167
0.0208
0.0258
0.0309
0.0409
0.0503
0.0739
y
0
0.0151
0.0201
0.0254
0.0321
0.0390
0.0527
0.0671
0.1050
Basis: 1 hr.
It is assumed that if any water vaporizes into the gas stream, the quantity is small, and hence, the
same is neglected. NH3 removed exits along with the liquid exit stream. The gas flow and mole
fractions are derived from the inflow data considering 90% removal of NH3 from inlet gas.
For (L/G)min condition.
Exiting liquid stream composition x1 is in equilibrium with y1 (¼ 0.1).
Hence based on equilibrium data in Table P10.1a.
x1 ¼ 0.0708 and Lmin ¼ (6.7 e 0.67) / (0.0708 e 0) ¼ 79.14 kmol.
Fig. P10.1A shows the component flow rates and stream compositions for operation at (L/G)min.
kmol
kg
mf
NH3 0.67 0.011(y2)
Air 60.26 0.989
11.39
1747.54
60.93 1.0
1548.93
(2)
30°C
∼1atm
L
G
kmol
mf
kg
NH3
–
H2O 79.14
0(x2)
1
0
1424.52
1.0
1424.52
79.14
min
kmol
NH3 6.03
H2O 79.14
(1)
85.17
Nm3
kmol
NH3 150
Air 1350
6.7
60.26
0.1(y1) 113.9
1747.54
0.9
1500
66.96
1.0
ρ30° =
mf
mf
kg
0.0708 102.51
0.9292 1424.52
1.0
1527.03
kg
ρL ≈ 1000 kg/m3
1861.44
1861.44
1500 × (303/273)
= 1.118 kg/m3
FIGURE P10.1A
Material balance for operation with (L/G)min.
10.4 Design illustration
271
Usually, the economic use of solvent flow varies from 1.5 to 2.5 times Lmin. We consider the factor
to be 1.5 times minimum water flow rate. This needs to be verified later.
rLop ¼ 1.5 Lmin [ 118.71 kmol/hr ¼ 2136.78 kg/hr.
For this flow rate of water, y1 ¼ 0.1, y2 ¼ 0.00189, x2 ¼ 0, x1 ¼ (6.7 e 0.67) / 118.71 ¼ 0.048.
The entry and exit flow rates and compositions for the present operating case is shown in
Fig. P10.1B. It also shows an arbitrary control volume where the entering gas and exiting liquid has
flow rates Gop and Lop (kmol/hr) with the corresponding solute concentration of yop and xop.
kmol
mf
kg
kmol
mf
kg
NH3 0.67
Air 60.26
0.011
0.989
11.39
1747.54
NH3
0
H2O 118.71
0
1
–
2136.78
1.0
1758.93
118.71
1.0
2136.78
60.93
(2)
30°C
∼1atm
Control volume
L
1.5 x
G min
Gop Lop
yop
xop
(1)
kmol
NH3 6.7
Air 60.26
66.96
mf
kg
0.1(y1) 113.9
0.1
1747.54
1.0
1861.44
kmol
NH3 6.03
H2O 118.71
124.74
mf
kg
0.048 (x1) 102.51
0.952
2136.73
1.0
2239.29
FIGURE P10.1B
Material balance for operation with 1.5(L/G)min.
Operating line: Any point on the operating line is (xop,yop). The operating line equation is formed
by solute transfer balance across the phases in the section of the bed within the said control volume, viz
60:26 yop = 1 yop y2 = ð1 y2 Þ ¼ 118:71ðxop = ð1 xop Þ x2 = ð1 x2 ÞÞ
where y2 (¼ 0.011) yop y1(¼ 0.1)
Table P10.1b lists the operating line points generated from the above equation, for plotting the
same on the xey axis along with the equilibrium line in Fig. P10.1C.
Table P10.1b Operating line points.
xop
0
0.0051584
0.010366
0.015626
0.020937
0.026302
0.03172
0.037193
0.042721
0.048306
yop
0.011
0.020889
0.030778
0.040667
0.050556
0.060444
0.070333
0.080222
0.090111
0.1
272
Chapter 10 Absorption and stripping
L
Empirical correlations for HTOG ¼ kyGaAt and HTOL ¼ kl aA
are available for 100 Raschig ring
t
as dumped packing for absorption of NH3 in water and considering the system to be dilute.
These correlations are taken from Table 10.8-2 of “Transport Processes and Unit Operation” by
C. J. Geankoplis, Pg. 633, third Edition, 2000 (Prentice Hall India) and the correlations are valid for
0.271 < mV (kg/m2.s) < 0.95, and 0.678 < mL (kg/m2.s) < 6.1 respectively.
This requires estimation of tower diameter, which has been done following the procedure elaborated in Chapter 14, Section 14.5.
We estimate tower diameter (d) based on the upper limit of mL [ 0.95 kg/m2.s, leading to a
smaller tower diameter. This gives for At (m2) ¼ p d2/4 ¼ (1861.44/3600)/0.95, d [ 0.832 m which
is greater than the minimum diameter specified in Table 14.20.
Adopting d ¼ 0.835 m, At (m2) ¼ 0.5476.
which gives the revised mV ¼ 0:95 ð832=835Þ2 ¼ 0.9432 kg/m2.s.
and mL ¼ (2239.29/3600)/0.5476 ¼ 1.136 kg/m2.s. Both the values lie within the limits specified
for the correlations.
The adopted diameter and mass fluxes are used to estimate the % approach to flooding and the
pressure drop in the bed and the tower, following the methodology discussed in Section 14.4.4 (not
shown here). These are found to be well within limits.
Driving force lines
Assuming this to be a dilute system, the flow rates of the phases will not differ much at the top and
bottom of the bed.
So the G and L are considered at the bottom.
Driving force line passing through
a typical operating point (xop,yop) intersects the equilibrium
yop e yi
k0 að1 xÞiM
k0 a
curve at (xi,yi) and its slope ¼
¼ x0
¼ f x0 ,
ky a
ðxop e xi Þ
ky að1 yÞiM
where,
ð1 yi Þ 1 yop
lnfð1 xop Þ=ð1 yi Þg
f ¼ 1 yop iM=ð1 xop ÞiM ¼
fð1 xop Þ ð1 xi Þg
ln ð1 yi Þ= 1 yop
In order to generate kx0 a and ky0 a values for the system, we use the correlations available for finding.
L
.
HTOG ¼ kyGaAt and HTOL ¼ kl aA
t
For random packing of 100 Raschig rings, these values areeIn gas phase,
b g
1=2
HTOG ¼ a mV mL NSc ¼ 0:557 ð0:943Þ0:32 ð1:136Þ0:51 0:6691=2 ¼ 0:419 m
10.4 Design illustration
273
where a ¼ 0.557, b ¼ 0.32, g ¼ (0.51) - from Table 10.8e1, 3rd Edition, 2000 (Prentice Hall India),
“Transport Processes and Unit Operation” by C. J. Geankoplis
NSc ¼ 0:669
The solute (NH3) is highly soluble in water, and hence, the mass transfer resistance is considered in
the gas phase.
Estimating mass transfer coefficients
The expression and the constants for the liquid phase are taken from the same source.
This gives,
!h
mL
1:136 0:22
0:5
HTOL ¼ q NScL
¼ 0:00235 ð303:1Þ0:51 ¼ 0:214 m
0:0008
ml
Where NScL is the Schmidt Number for the liquid phase
mV =MWG
ð0:943=27:8Þ
¼ 8:1 kmol = m3 $s
¼
ky0 a ¼
0:419
HTOG
mL =MWL
ð1:136=17:95Þ
¼ 0:253 kmol=m3 $s
kx0 a ¼
¼
0:25
HTOL
Where MWG and MWL refer to the average molecular weight of the gas and the liquid phase
respectively.
The procedure to find interphase concentration (xi,yi) corresponding to a point (xop,yop)
on the operating line is as follows
(1) Choose yop such that y2 <yop <y1 and note the corresponding xop on the operating line
(2) Assume f ¼ 1 in Eq. 10.8. This is the initial guess.
k0 a
(3) Draw driving force line through (xop,yop) with slope m ¼ ð fÞ kx0 a
y
(4) Note coordinate (xi,yi) at the intersection point of driving force line and equilibrium line.
ð1 xop Þ
ln
ð1 yi Þ 1 yop
ð1 xi Þ 9
8
(5) Recalculate f as fRecalculated ¼
ð1 xop Þ ð1 xi Þ
< ð1 y Þ =
i
ln : 1 yop ;
(6) If fand fRecalculated differ by only a small amount, say 0.0001, note (xop,yop) and (xi,yi). Proceed
with calculations for a new set of (xop,yop) starting from Step (2)
Else, substitute f with fRecalculated and go to Step (3).
274
Chapter 10 Absorption and stripping
Fig. P10.1C shows a set of driving force lines along with the operating line and the equilibrium
curve.
0.12
Driving
force
line(s)
0.1
y
0.08
Operating
line
Equilibrium
curve
0.06
0.04
0.02
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
x
FIGURE P10.1C
NH3 absorption - driving force lines.
The procedure is followed to generate a table with columns (xop,yop) and (xi,yi) with y2 < yop < y1.
The values in the table are used to evaluate e
Z y1
ð1 yi Þ 1 yop
dy
8
9
¼ 4:1
NTOG ¼
Þ
yop yi
ð1
y
<
=
i
y2
ð1 yi Þ
ln : 1 yop ;
and hbed ¼ HTOG NTOG ¼ 0:419 4:1 ¼ 1.72 m; say 1.75 m.
Hence the bed packed randomly with 100 ceramic Raschig ring should have a diameter of 0.835 m
and a depth of 1.75 m. One needs to note that this is the effective bed depth. There will be layers of
bigger size packing above and below the bed to have better fluid distribution and to keep the bed
mechanically stable.
Bed pressure drop ¼ 900 1.75 ¼ 1575 Pa/m ¼ 155.5 mm WC. This is small compared to the
assumed constant bed pressure (w760 mm Hg). Hence, the assumption is fairly ok. However, there
will be additional minor pressure drop in the absorber equipment across the top and bottom layers of
bigger size packing, bed supporting perforated plate/grid, contraction and expansion loss at entry and
exit of gas. The total pressure drop is expected to be below 2 155.5 ¼ 311, say 350 mm WC
(w26 mm Hg).
3
Problem 10.2. 4000 Nm /hr of air mixed with SO2 (10%) is to be scrubbed by water in a packed bed
absorber to remove 95% of the SO2 entering. The water is at room temperature (around 30oC) and
10.4 Design illustration
275
pressure slightly above the atmospheric pressure. Design the scrubber with 1 1200 Raschig rings,
randomly packed. The equilibrium data (mole fraction) for SO2e air - water system at 30oC is given in
Table P10.2a.
Table P10.2a Equilibrium data (mole fraction) for SO2eairewater system at 30 C.
x
0
5.62e e 5
14.03e e 5
28.0e e 5
42.2e e 5
56.4e e 5
84.2e e 5
140.3e e 5
196.5e e 5
279.0e e 5
y
0
0.79e e 3
2.23e e 3
6.19e e 3
10.65e e 3
15.5e e 3
25.9e e 3
47.3e e 3
68.5e e 3
104.0e e 3
Basis: 1 hr.
The equilibrium curve is drawn on the xey axis.
For minimum L/G operation.
Gas inlet: y1 ¼ 0.1; kmol SO2 at inlet ¼ 400/22.4 ¼ 17.86; kg SO2 at inlet ¼ 64 17.86 ¼ 1143.04.
Water inlet: x2 ¼ 0.1, kmol SO2 at inlet water ¼ 0; kg SO2 at inlet ¼ 0.
To use minimum water, exit concentration of SO2 in exiting liquid (x1) should be maximum. This is
possible when x1 is in equilibrium with y1. Hence, x1 ¼ 0.0027, read from the equilibrium curve
obtained from Table P10.2a.
r Minimum water inflow ¼ Lmin ¼ (17.86 e 0.893) / (0.0027 e 0) ¼ 6267.103 kmol.
It is checked that a straight line joining (x1,y1) and (x2,y2) does not touch/intersect the equilibrium
curve at any intermediate point within ordinate limit y1 to y2. This confirms that there is no pinch point
in this case, and the reduction of concentration from y1 to y2 is possible.
The parameters are shown in Fig. P10.2A.
kmol
SO2 0.893
Air 160.71
161.603
kmol
mf
0.00553(y2)
0.99447
–
SO2
H2O 6267.103
6267.103
1.0
mf
kg
0(x2)
1
0
112807.85
1.0
112807.85
(2)
30°C
1atm
L
G min
(1)
Nm
3
kmol
SO2 400
17.86
Air 3600 160.71
4000 178.57
mf
kmol
16.967
SO2
H2O 6267.103
kg
6284.07
0.1(y1) 1143.04
0.9
4640.59
1.0
5803.63
FIGURE P10.2A
Material balance for operation with (L/G)min.
mf
0.0027(x1)
0.9975
1.0
276
Chapter 10 Absorption and stripping
We decide Lop ¼ 1.5 Lmin ¼ 9400.65 kmol ¼ 169,211.7 kg, as usually the economic optimum is
in the limit: 1.5 Lmin Lop 3 Lmin
At this operating point, x1¼ (17.86 e 0.893) / 9400.65 ¼ 0.001802.
x2, y2 and y1 have the original values, as shown in Fig. P10.2B. The flow rates and the concentrations are also shown in the figure along with a control volume cutting across an arbitrary elevation in
the bed where the entering gas and the exiting liquid have compositions of yop and xop mole fraction
respectively.
kmol
SO2 0.893
Air 160.71
161.603
mf
kg
0.00553(y2)
0.99447
57.15
4660.59
1.0
4717.74
30°C
1atm
L
1.5x
G
yop
178.57
mf
–
SO2
H2O 9400.65
9400.65
0(x2)
1.0
1.0
Control volume
min
kmol
SO2
H2O
xop
mf
kg
16.967
9400.65
0.00182(x1)
1085.89
169211.7
0.99818
9417.617
1.0
mf
kg
0.00553(y1)
0.99447
1143.04
4660.59
1.0
5803.63
kmol
SO2 17.86
Air 160.71
kmol
170297.59
FIGURE P10.2B
Material balance for operation with 1.5(L/G)min.
Operating line equation based on the solute balance across the control volume shown in
Fig. P10.2B is e
!
yop
xop
y2
x2
160:71 ¼ 9400:65 1 yop 1 y2
1 xop 1 x2
or,
or,
xop
¼ 0:0171 1 xop
yop
0:005561
1 yop
p
xop ¼
1þp
!
¼ p; say
10.4 Design illustration
277
Table P10.2b lists the operating line points generated from the above equation, for plotting the
same on the xey axis along with the equilibrium line in Fig. P10.2C.
Table P10.2b Operating line points generated in the range 0.00,553 £ yop £ .1
xop
0
18.339ee5
37.068ee5
56.197ee5
75.74ee5
95.711ee5
116.12ee5
136.99ee5
158.34ee4
180.17ee5
yop
0.00553
0.016027
0.26523
0.03702
0.047517
0.58013
0.06851
0.079007
0.089503
0.1
The tower diameter is estimated based on bottom flow rates that are the highest mass flow rates.
The procedure based on bed flooding given in Section 14.5 is followed using the following values.
rG ¼ ð5803:63 = 4000Þ ð273 = 303Þ ¼ 1:307; rL z 1000
kg=m3 at 30o C; 1 atm
and mL ¼ 0.0008 Pa.s.
The estimated tower cross section for around 70% flooding is: At ¼ 3.205 m2, and
d ¼ ð3:205 4=pÞ1=2 ¼ 2:02 m
Finding kx0 a and ky0 a
Empirical correlations valid for SO2 (in air)-water system at 20 C with 100 Raschig ring random
0:7 1=4
0:82
packing are - kx0 a ¼ 0:0594 mV
mL
, and kx0 a ¼ 0:152 mL
kmol/s.m2 per
mole fraction.
Correction for operating temperature of 30 C are incorporated by correcting for the change in gas
and liquid phase diffusivities as follows
0:7 1=4
0:7 1=4
kx0 a ¼ 0:0594 mV
mL
ð303=293Þ1:5 ¼ 0:06247 mV
mL
;
and
0:82
0:82
ð303 = 293Þ ¼ 0:157 mL
kx0 a ¼ 0:152 mV
Due to transfer of solvent, the mass flow rates of the phases vary along the tower. This shall render
the mass transfer coefficients to be calculated for each section of the tower. Considering the system to
be a concentrated system, we include this change in the values of mV and mL . This is again based on
solute balance around the said control volume and appear as
3
2
1
1
64 yop þ 29 1 yop 5 ;
mV;op ¼ 4160:7 3600 3:205
1 yop
278
and
Chapter 10 Absorption and stripping
"
#
1
1
f64 xop þ 18 ð1 xop Þg mL;op ¼ 9400:65 ð1 xop Þ
3600 3:205
Finding (xi,yi) for a typical (xop,yop) e
1. Choose a point on the operating line (xop,yop), y2 < yop < y1
2. Assume f ¼ 1
0
0
3. Calculate mV;op and mL;op from the above expressions. Calculate kxa and kya from their
expressions at 30 C as discussed above.
0
0
4. Draw driving force line through operating point (xop,yop), with slope ¼ f (kxa/kya)
5. Locate (xi,yi) as the intersection of the equilibrium curve and the driving force line drawn.
9
8
<ð1 y Þ 1 y = lnfð1 x Þ=ð1 x Þg
i
op
i
op
Find fcalc ¼
: ð1 xi Þ ð1 xop Þ ; ln ð1 yi Þ= 1 yop
6. If fxfcalc,
Then.
0
0
Record (xop,yop), (xi,yi), mV;op , kxa and kya.
If the entire range of yop has been covered.
then stop computing, else Go to Step 1.
Else.
Replace f with fcalc, Go to Step 3.
End of If statement
x-y plot
0.12
Driving force line(s)
0.1
y (mole fraction)
0.08
Operating line
0.06
Equilibrium curve
0.04
0.02
0
–0.5
0
0.5
1
1.5
x (mole fraction)
FIGURE P10.2C
SO2 absorptioneDriving force lines.
2
2.5
×10–3
3
Further reading
279
Eq. 10.11 gets modified by replacing (G/AT) with mV;op as e
Zhbed
hbed ¼
Zy2
dz ¼
0
y1
ky0 a
mV;op :dy
ð1 yÞiM
ð1 yÞðy yi Þ
Numerical integration of the above gives hbed ¼ 2.67 m.
Bed dimension-Active bed: Diameter ¼ 2020 mmf, H ¼ 2670 mm. The L/D ratio (1.32) is
slightly low. However, the active bed will have additional larger size packing layers below and above
for fluid distribution and bed stabilization. The total L/D is expected to be reasonably OK. For details
see Chapter 14.
Some specific terms with symbol and typical units used in this chapter:
mL ¼ Liquid mass flow rate (kg/s)
mV ¼ Vapor/Gas mass flow rate (kg/s)
mL ¼ Liquid mass flow rate per unit tower cross sectional area (kg/s$m2)
mV ¼ Vapor/Gas mass flow rate per unit tower cross sectional area (kg/s$m2)
qL ¼ Liquid volumetric flow rate (m3/s)
qV ¼ Vapor/Gas volumetric flow rate (m3/s)
L ¼ Liquid molar flow rate (kmol/s)
L ¼ Liquid molar flow rate per unit tower cross sectional area (kmol/s$m2)
G ¼ Gas/Vapour molar flow rate (kmol/s)
G ¼ Vapour/Gas molar flow rate per unit tower cross sectional area (kmol/s$m2)
L 0 ¼ Solute free Liquid molar flow rate (solvent component only) (kmol/s) or (kmol/hr)
G 0 ¼ Solute free Vapor/Gas molar flow rate (nonabsorbable component only) (kmol/s) or (kmol/hr)
Further reading
1. Treybal, R. E. (1981). Mass transfer operations (3rd ed.). McGraw Hill.
2. Geankoplis, C. J. (2003). Transport processes and separation process principles (4th ed.). PHI Learning Pvt
Ltd.
3. B.D. Smith. Design of equilibrium stage processes. McGraw Hill Book Company. NY.
4. Towler, G., & Sinnott, R. (2013). Chemical engineering design (2nd ed.). Elsevier Limited.
CHAPTER
Distillation
11
11.1 Introduction
Distillation is employed to separate a miscible binary or a multicomponent feed to two or more
fractions utilising the difference in volatility of the components. Distillation equipment ensures intimate contact between the vapour and the liquid phase to achieve transfer of components (lighter
component(s) from liquid to vapour and the heavier one(s) from vapour to liquid) across the phase
boundary. This results in the vapour phase getting richer in more volatile component(s) and the liquid
phase richer in less volatile component(s).
The process can be carried out in batch or in continuous mode. It can involve one or more stages of
vapoureliquid contact in tray/plate columns, packed columns or just a heated still providing a single
stage of contact. The equipment, their configuration arrangements and operation differ in these cases.
‘Flash distillation’ is distillation in its simplest form. This involves flashing or partial vaporisation
of a feed stream in a flash drum to a vapour stream richer in more volatile component(s) and a liquid
stream that has lower concentration of more volatile components. Such systems are always continuous.
The other options of the distillation system are (a) batch distillation with or without reflux and
(b) continuous staged distillation (also called fractionation or rectification). The reboiled stripper is a
variation of the latter.
Typical configuration of flash distillation, batch distillation, fractionator and reboiled stripper are
schematically shown in Fig. 11.1. General features of these distillation arrangements are presented in
Table 11.1.
11.2 Conceptual design
Prior to design, the configuration of the system is conceived based on available knowledge and information in line with the general strategy of process design that has been discussed in Chapter 1. The
information contains the details of the problem and the solution options available with the designer.
At this stage, the options to be considered and their corresponding configurations are e Batch
versus Continuous. The batch process goes through cycles of start-up, production run and shutdown
that makes the productivity low compared to a continuous plant of same equipment size or same
investment. Substantial loss of heat energy makes the process inherently less thermally efficient
compared to continuous distillation. The batch distillation equipment is bigger in size since the still has
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00011-7
Copyright © 2020 Elsevier Inc. All rights reserved.
281
282
Chapter 11 Distillation
V, y
F, zF
L, x
(A)
Condenser
Condenser
QC
QC
Accumulator
Tray
Product
cuts
D, xD
Steam
QR
Accumulator
Product
cuts
1
Column
D, xD
5
Still
Steam
QR
Condensate
Condensate
(B)
(C)
CONDENSER
Strip out
ENRICHING
(RECTIFICATION)
SECTION
FEED
REFLUX DRUM
Feed
REFLUX
1
DISTILLATE
STRIPPING
SECTION
HEATING OIL
IN
REBOILER
N
HEATING OIL
OUT
Stripped
product
BOTTOMS
(D)
(E)
FIGURE 11.1
(A) Flash distillation, (B) batch distillation, (C) Batch distillation with trays and reflux, (D) Fractionator and
(E) Reboiled stripper.
11.2 Conceptual design
283
Table 11.1 General Features of different Distillation arrangements.
Distillation
type
Nature of
operation
Number of
contacting
stages
Fractionator
Continuous
Reboiled
stripper
Vapour
Reflux at
bottom
Feed entry
location
Feed
phase(s)
Top
Reflux
Multiple
Between top
and the
bottom stage
V or L or
VþL
Yes
Yes
Continuous
Multiple
Top stage
L
No
Yes
Flash
distillation
Continuous
One
Above the
drum liquid
level
L or V or
VþL
No
No
Multistage
batch
distillation
Batch
Multiple
At the still
before start
of distillation
L
Yes
No
Single-stage
batch
distillation
Batch
One (see
Section 11.6)
At the still
before start
of distillation
L
No
No
to accommodate the entire feed per batch and the investment for a moderate to higher capacity plant is
higher as compared to continuous distillation for the same average daily processing capacity. In
addition, the long time of exposure of the mixture to high temperature increases the risk of thermal
degradation or decomposition of substances. However, in small scale, batch distillation plant may be
cheaper than continuous distillation due to its simplicity. It is therefore resorted to only for low capacity plants; say processing about 1e2 m3 per day of feed produced in batches in any upstream unit or
in pilot plant operations.
In spite of being thermally less efficient and requiring relatively higher capital investment, batch
distillation provides much more flexibility in operation; a single column can produce any number of
products. To achieve the same result using a continuous plant, (Ne1) columns would typically be
required for N product streams. It is an attractive option when the purity of product is a major concern
and any off specification product is undesirable especially when the cost of energy is not prohibitive
compared to value addition in this separation step. This is often the case for speciality, high value
products in small volume, as in pharmaceutical industry and in manufacture of speciality chemicals. It
is also used when the batch size as well as the feed quality (composition) may vary over wide ranges or
the product quality (composition) requirements may vary from time to time and possibly from batch to
batch. When the feed has a tendency to leave deposits in the equipment that requires frequent cleaning
and maintenance, a batch process is often opted.
Continuous processes make almost full utilisation of the plant facility except short phases of startup, shutdown and plant emergencies and therefore have high productivity. Large plants like refineries,
petrochemicals, fertilisers and other medium to large chemical industries go for continuous distillation
processes.
284
Chapter 11 Distillation
Configuration options for continuous distillation systems
In case of continuous distillation which has to split a feed into two streams, a distillate and a product,
there is not much to decide on the configuration. However, when a feed has to be split into three or more
streams, there can be several competing alternative options. Fig. 11.2 shows the common options for three
product streams using two columns in sequence as well as using a single column with side stream draw.
(A)
(B)
A
(C)
A
A
B
F
F
B
F
B
C
C
(D)
C
A
B
F
(E)
A
F
C
C
B
FIGURE 11.2
Product fractionation schemes e (A) side stream draw, (B) side stream draw with stripper,
(C) prefractionation, (D) direct sequencing and (E) indirect sequencing.
A configuration option could also incorporate a flash stage or a prefractionator column before the
main fractionator (Fig. 11.2C). This reduces the loading of the main distillation column. Also if much
of the lighter components are removed in a prefractionator, the vapour volume to be handled in the
fractionator comes down along with lowering of its operating pressure. The optimum is struck between
the additional costs due to the prefractionation column and lowered costs of the main column. Use of
prefractionator column is common when the feed has a large fraction of volatiles in large-scale processes like crude oil distillation.
Among the plausible configuration alternatives synthesised during the conceptual design, the final
configuration is selected based on heuristics and economic considerations, wherever possible. A set of
heuristics rules stated below helps in synthesising and short-listing the design alternatives:
•
•
Small capacity usually calls for batch distillation.
Batch distillation is preferred when the product quality needs frequent changes.
11.2 Conceptual design
•
•
•
•
•
•
•
•
285
Batch distillation is usually best for separation of volatile product or volatile impurities.
If purity is not a major concern for the lighter or the heavier stream, flash distillation is a cheap
alternative.
Optimum based on economic calculations must be evaluated for all alternative configurations to
choose the best option. For this, all competing conceptual designs are compared based on some
chosen economic criterion. Selection and computation of the economic optimisation function is
based on available cost data. Shortcut design procedures are normally used to quickly estimate the
size and cost of different configuration options. The optimum for each competing configuration
option needs to be calculated separately and the best among those are selected for overall
comparison.
Practical considerations like ease of operation, proven/reliable design, existence of a similar plant
in the same complex, ease of maintenance due to simplicity of design or common spare
equipment, etc., may override the computed economic optimum consideration in choosing plant
configuration.
Separation by distillation at lower pressures is easier. The number of stages found by
McCabeeThiele construction for the same change of composition in the stripping or in the
enriching section is lower at lower pressure as the binary equilibrium (x-y diagram) curve shifts
further away from the 45 degree (x ¼ y) line with reduction in pressure. Reboiler and the
condenser temperatures are also lower at lower pressure. Hence, the lowest practical operating
pressure is used for design. On the other hand, deciding on column pressure lower than necessary
increases the volumetric vapour flow rate that may lead to a larger diameter (more expensive)
column.
A practical distillation column will always have some leakages through flanges, fittings, valve
glands, etc. Thus, a vacuum column will suck in ambient air and pressurised column will bleed
vapour to the atmosphere, however small the quantity may be. In case of hydrocarbon columns,
accumulation of air inside results in potential explosion hazard. Even when distillation is feasible
at atmospheric pressure, columns handling hydrocarbons are designed and operated slightly
above atmospheric pressure. This practical positive gauge pressure may vary from few cm of
water column in small systems to 0.1e0.4 kg/cm2 (g).
Vacuum columns are preferred mostly when the components have high boiling point and/or are
heat sensitive, i.e., they may crack, decompose, polymerise or get denatured. Operation under
vacuum allows the column to operate at lower temperature.
The temperature of the bottom product may be limiting for heat-sensitive materials.
An example of optimisation can be the design of a continuous distillation facility to split a binary
component feed stream to an overhead and a bottom product. The design
needs to be done for a particular feed flow rate in order to meet the composition requirements of the product streams. Optimum design is obtained by
Optimum design
minimising the total annualised cost for the system. Annual operating cost for
the system includes the cost of cooling in the overhead condenser, reboiler
energy input and the energy for pumping the streams. The total annualised cost is arrived at by adding
to this term, the annual financial cost of the fixed capital investment required for the erection, fabrication and commissioning of the system. The reflux ratio for the column is taken as the independent
286
Chapter 11 Distillation
parameter to be varied to minimise the annualised cost of the system. Increasing the reflux ratio
monotonically increases the operating cost while the annualised fixed cost passes through a minimum.
The reflux ratio corresponding to minimum total annualised cost (fixed þ operating) is the optimum
reflux ratio and the corresponding process details of the equipment, e.g., number of trays, height and
diameter of column, etc., is the optimum design. As ballpark estimates, optimum reflux ratio is 1.2 to
1.35 times minimum reflux ratio (Rm). For refrigerated systems, Ropt ¼ 1.1 to 1.2 times Rm can be
used. Use of shortcut design procedures, approximate empirical correlations, etc., are often used in lieu
of detailed design at this stage as long as the accuracy of these are better than the accuracy of cost
estimation. Once the optimum is fixed, the detailed design of the system for the optimum case is
generated using rigorous process design calculations. If the annualised fixed cost recalculated for the
detailed design is within 5%e10% of the initial estimate, the design may be taken as the optimum
design.
11.3 Detailed design
Deliverable from conceptual design is the gross details of the optimum process option. This includes
features/facilities for safe start-up, normal operation, shut down and any special requirement during
plant maintenance like flushing or cleaning with flushing oil, etc. Instrumentation and control scheme
and the plant hydraulics are also covered.
The optimum design option is detailed based on input design specifications and applicable design
codes.
Process design
Process design starts with defining the battery limit. The battery limit is set depending on the scope
of the design problem posed. Stream conditions at the battery limit are firmed up, the process functionality targets and constraints are identified and documented. Examples of such a target and constraints can be fractionating a feed to three streams of specified quality and availability of steam and
cooling water as hot and cold utility at specified pressure and temperature, respectively.
The deliverable in this phase, for a distillation plant, is the ‘process package document’ that includes a brief process description, start-up and shutdown procedures, emergency handling notes,
potential/approved vendors for the equipment and any other specific information. It includes BFD/
PFD, P&ID, general arrangement drawing for the column and auxiliary equipment and summarises the
salient features of the distillation system. The column configuration, dimensions and other details are
schematically represented at this stage. The scope of design may however remain limited only to the
design of the column and its auxiliaries, i.e., condenser and reboiler, the associated piping, pumps,
instrumentation scheme and safety devices.
Process design generates the design operating parameters and gross specification of the equipment
including the tower internals. This forms the basis of generating the mechanical details.
Mechanical design
Detailing the mechanical design of the equipment, auxiliaries and the hydraulic circuits is carried
out by following the applicable code of practice as already discussed in Chapter 1. The output from this
step is the set of fabrication drawings for the equipment. In case of a complete distillation facility, it
11.4 Fractionator
287
also includes the set of isometric drawings showing exact location and orientation of the equipment
and piping.
We discuss the design of a fractionator in the next section, followed by design of flash and batch
distillation in Sections 11.6 and 11.8, respectively. Details of the column and its internals are covered
in Chapter 14. Associated piping design features are covered in Chapter 16. Column shell and fittings
are detailed in Chapter 17.
11.4 Fractionator
The fractionating column/fractionator (Fig. 11.1D) with plates/trays and/or packed section(s) offer
multiple stages of vapoureliquid contact. Feed is
introduced at an intermediate point in the column at
the feed tray or the feed zone in case of a packed
Fractionator configuration and components
column. Contacting sections above and below the
feed entry are the enrichment and the stripping
sections of the column. Reboiled stripper
(Fig. 11.1E) is a special configuration, where feed enters the top stage. Fig. 11.3 shows a fractionator
with trays. P&ID of a fractionator with a side stream draw is shown in Fig. 11.4. The figure depicts
the following:
•
•
•
•
column with its feed entry arrangement, enriching section and stripping section with trays/
packing.
overhead system comprising of the overhead vapour line, condenser and the reflux drum
(accumulator vessel) and arrangements for overhead product draw, reflux flow to top tray and
venting of noncondensable vapour.
side stream draw.
column bottom system, with the reboiler providing the vapour reflux to the column and
arrangement for bottom product draw.
Thus, the simplest fractionator has a feed stream, a distillate and a bottom product stream. More
complex configurations may include multiple feed, one or more side stream draw and external
refluxing arrangement. Fig. 11.5 shows the configuration of an atmospheric distillation column for
crude oil with prefractionator column, side stream (kerosene, light gas oil and heavy gas oil) draws and
steam stripping columns for the side streams from the main column. The figure also shows three
circulating refluxes for the main column. These are provided in addition to the overhead reflux on the
top tray. This column does not include a bottom reboiler but uses stripping steam supplied at the
bottom for the same purpose. Such design configurations are decided based on technical requirements,
economics and requirements of operational flexibility.
288
Chapter 11 Distillation
Condenser
Reflux drum
Reflux
R
Vapour
upflow
through
tray
Distillate Draw
Liquid flowing down
through downcomer
F
Column
Vapour reboil
Reboiler
Steam
Condensate
Bottom Product Draw
FIGURE 11.3
A simple fractionator with trays/plates.
Vent for non
condensables
Overhead vapour line
LC
R
Distillate
SP
Enriching Section
17
TC
Side stream Draw
SP
Feed
2
Stripping Section
LC
Bottoms
FIGURE 11.4
Fractionator with a side stream draw.
11.4 Fractionator
289
FIGURE 11.5
Crude oil distillation column with prefractionator column.
The components/subsystems shown in Figs. 11.3e11.5 are elaborated in the following section.
Column overhead system
The total condenser in Figs. 11.3 and 11.4 is expected to condense the entire vapour reaching it
through the overhead vapour line(s) from the column top. The condensed liquid drains by gravity to the
reflux drum located at a lower elevation. The drum is provided with a bleed for releasing the
noncondensable gases which will always exist in however small quantity it may be. This vent line is
shown only in Fig. 11.4. Dissolved gas (or air) in the feed is a source of noncondensable entering the
system. In vacuum towers, there is always some air leaking into the system through flange connections,
valve glands and instrument connections. This may constitute a substantial part of the noncondensable
stream that gets carried over to the reflux drum. Venting arrangement for these noncondensables is
essential to avoid any pressure build up. Vacuum columns often use ejector or vacuum pumps to create
vacuum as well as to remove the noncondensable vapour.
Throttling the noncondensable stream flow is also a means to regulate the pressure in the accumulator and this in turn fixes the column pressure as the overhead vapour line is always highly
290
Chapter 11 Distillation
oversized offering only a small pressure drop. The condenser pressure drop is also small. Column top
pressure is controlled by manipulating the noncondensable venting rate from the reflux drum.
The distillate product and the reflux streams are drawn out either by common or by individual
pumps. The distillate flow is manipulated to control and maintain the liquid level in the reflux drum as
shown in Fig. 11.4. The pressure developed by the product pump has to overcome the pressure drop in
piping, fittings, heat exchanger(s) and the liquid head of the product storage tank. Flow rate of reflux is
regulated as per the required purity of the top product and hence the line is fitted with a control valve.
The column top temperature is the dew point of the overhead product at the column pressure. Since the
column top temperature directly relates to the quality of the distillate and is easily monitored, the
overhead temperature is controlled by manipulating the reflux flow. This in turn fixes the distillate
quality purity).
Partial condensers are used when the top product stream is withdrawn as vapour and it is considered
as one vapoureliquid contacting stage. In such cases, the column may or may not have any liquid
distillate product stream drawn from the accumulator and the entire liquid from the condenser may be
refluxed to the column. The vapour withdrawal from the top of the reflux drum is similar to that for
venting noncondensable. In industry parlance, when no distillate product stream is drawn as liquid
from the accumulator, it is referred to as a ‘total reflux column’. Only a vapour overhead product is
drawn in this case and the entire liquid is refluxed back to the column. Strictly speaking, this is a
misnomer as under ‘total reflux’ condition, no net top product (either as vapour or as liquid) is drawn
from the column.
In most plants, the specified battery limit temperature is 40 C for liquids that are not very viscous
and in case of viscous streams, the temperature may be 90 C or higher.
The overhead condenser system may have variations, some of which are
•
Condenser-subcooler: This is used to reduce the reflux flow requirement by subcooling the same.
A subcooled reflux achieves the same column top temperature with a lower reflux flow rate. For
this, (horizontal) condensers are designed with partial submergence of the tubes that achieve
subcooling of the condensed liquid.
Operating reflux for total condenser is often subcooled at column pressure particularly if the
condenser is overdesigned or there is significant heat loss in condenser. When the bubble temperature
at condenser pressure is much higher than the cooling water inlet temperature, the condenser outlet
temperature may fall below the bubble point due to the ‘cold’ cooling water. If the condenser is partial
(liquid reflux, vapour distillate/top product) or mixed (liquid reflux, both liquid and vapour as top
product), reflux stream is a saturated liquid unless heat losses cause it to sub-cool. With the condenser
outlet pressure being less than the column top pressure, reflux is subcooled for all condenser types.
This needs to be considered for an accurate prediction of the number of equilibrium stages required,
or else the number of equilibrium stages is slightly overestimated. The procedure to incorporate the
correction in the McCabeeThiele construction for binary mixtures is elaborated in Section 11.4.2
(Eq. 11.9).
•
Hot reflux configuration: In this case (Fig. 11.6) the reflux provided is not subcooled. A subcooled
reflux may condense some components that form a separate liquid phase (on condensation) on the
top tray. In crude distillation columns, this is done to avoid moisture condensation in contact with
11.4 Fractionator
•
291
cold reflux stream that may lead to corrosion in presence of H2S and chloride ion. Only the
warmer hydrocarbon liquid is refluxed back. Two sets of exchangers are provided in series. After
the first set, part of the hotter liquid is refluxed to the column and the rest is subcooled in the
second set of exchanger.
Condenser with hot (vapour) bypass: This is used in some naphtha debutaniser columns with
flooded condenser. The column pressure is manipulated to change the submergence of the
condenser tubes. Opening of the hot bypass valve varies the differential pressure between the
column top and the reflux drum. One may note that the reflux drum pressure is slightly lower than
the column pressure.
Column
Air cooled
condenser
Reflux drum with
water boot
Non-condensable
gases
Hot reflux
#1
Water cooled
exchanger
Condensate
(water)
Top product
FIGURE 11.6
Schematic showing hot refluxing in a crude distillation column.
Column bottom section
Supply of vapour reflux stream below the bottom tray is essential for fractionation to take place in
the stripping section. The reboiler generates this vapour stream from the liquid falling from the bottom
tray. The reboiler is essentially a heat exchanger where a hot fluid supplies the latent heat of vaporisation. The reboilers shown in Figs. 11.1D and 11.3 are ‘kettle type’. Liquid from the column flows to
the reboiler by gravity and the vapour is returned below the bottom tray and above the column bottom
liquid level. The hot fluid for heating the reboiler may be condensing steam or some other hot stream
available in the plant. Utilisation of such hot stream adds to the plant economy by saving both hot and
cold utility. Use of small fired heaters (furnaces) as reboiler is also possible, though not very common.
In some configurations, a pump circulates the column bottom liquid through the reboiler and the hot
liquid flashes, releasing reboiled vapour inside the column on its return. Such forced circulation
reboilers are needed for viscous bottom product.
For cases where the bottom product is unstable, i.e., it has a tendency to crack at temperatures
slightly above the bottom temperature, reboilers cannot be used as it exposes the material to higher
temperature for a long time. Crude distillation column (Fig. 11.5) is an example of such a fractionator
without a reboiler. Bottom product ‘Reduced Crude Oil (RCO)’ from the column starts cracking at
292
Chapter 11 Distillation
about 400 C, whereas the bottom temperature is around 365 C. Using a reboiler would require its
heating tube surface temperature close to the cracking temperature and this would lead to coke
formation in the equipment and the associated pipelines. So instead of bottom reboiler, crude
distillation columns use superheated stripping steam injected below the bottom tray and above the
bottom liquid level to reduce the partial pressure and supply heat of vaporisation to strip out vapour
from RCO.
Feed zone
The feed enters the column through the feed nozzle on the column shell. This zone of the column is
also called ‘flash zone’ as part of the entering feed usually vaporises here. The pipeline carrying the
feed is called transfer line, particularly if it is carrying the feed heated in a furnace. Feed can be vapour,
liquid or a mixture of both. The temperature of the feed as it enters the column is not necessarily equal
to the temperature in the column at the feed tray location although such equality is desirable to increase
thermodynamic efficiency of the process. It is desirable to avoid a subcooled liquid or a superheated
vapour feed. Supply of a partially vaporised feed at the column temperature is desirable and is
commonly achieved by preheating the feed in a heat exchanger by the bottom product stream and/or
some other process stream available at a sufficiently high temperature. The spacing above the feed tray
is kept higher than that of other trays to reduce liquid entrainment with vapour. In case of packed
columns, the feed enters in between two consecutive sections of packing with arrangement for
distributing the liquid and the vapour across the column section. Feed entering the column from the
nozzle may be made to hit a splash baffle or a false downcomer for efficient vapoureliquid separation.
This is elaborated in Chapter 17. In large columns, the feed may have a tangential entry.
Side draws
Fractionators may be designed with one or more side stream draw with composition in between the
top and the bottom product stream. Such draws are from chimney trays. Chimney trays are not mass
transfer trays. Fig. 11.7 shows schematic of a chimney tray in a column. The vapour approaching the
chimney tray from the bottom passes through the chimney structures on the tray without coming in
contact with the liquid on the tray. The tray receives liquid from the upper section of the column and
routes it to the draw off pan. The side stream is drawn from the draw off pan through the (side stream)
draw off nozzle. The excess liquid overflows from the seal as internal reflux to the lower section of the
tower.
Circulating reflux streams, if provided to remove heat from a column, are drawn from an intermediate tray in the column (usually between two side-stream draws or the overhead and the first side
stream draw). Arrangement for circulating reflux draw is similar to side stream draw. The stream is
cooled and returned two trays above its draw tray and the return tray arrangement is similar to the feed
tray section. Circulating reflux, common in crude distillation columns, increases the internal reflux
flow in the trays below draw-off trays and reduces vapour flow above the trays on which it is returned.
Trays involved in circulating reflux are ineffective as fractionating trays due to mixing of liquid in the
upper and the lower trays. The set of trays across which the reflux circulates is considered equivalent to
a single stage of contacting. The scheme shown in Fig. 11.5 includes three circulating refluxes for the
atmospheric distillation column.
11.4 Fractionator
293
Hat
Vapour
Chimney
Draw off
pan
Chimney
tray
Vapour
Column
shell
Side draw
nozzle
Internal reflux
to lower tray
FIGURE 11.7
Schematic diagram of a chimney tray in a column.
Tower and tower internals
The vapoureliquid contacting inside the distillation column is effected either in the trays or in the
packed sections. These are detailed in Chapter 14.
11.4.1 Process design of fractionating tower e equilibrium stage approach
Process design with equilibrium stage approach is traditional and is carried out in two phases:
•
•
Estimation of the number of theoretical stages of contact required for the desired extent of
separation.
Calculating the actual number of contacting stages (trays/plates) or the actual packing depth
required in case of packed columns for realising the estimated number of theoretical stages of
contact. This is accounted for by considering an efficiency of contacting to approach equilibrium.
The next step is sizing of tower height and diameter.
Typical output of process design contains the details mentioned in Table 11.2.
294
Chapter 11 Distillation
Table 11.2 Process design output e fractionator.
Process equipment parameters
Column
Composition, pressure and temperature profile
Flow rates, pressure, temperature, phase (V, L, V þ L) of feed, reflux, distillate and bottom product; vapour boil up
rate and noncondensable vapour stream rates
·
·
Trays
Number of theoretical stages and efficiency, number of actual trays, feed tray location
Type of tray, tray diameter and tray layout
% flooding and pressure drop across tray
·
·
·
Packed sections
· NTU or number of theoretical stages/plates
or HETP
· HTU
section (column) diameter, depth, % flooding at design condition and pressure drop
· Packed
· Packing material and specifications
support and top cover arrangement
· Packing
· Distributor/redistributor
Reboiler and condenser
· Type, pressure, temperature, heat duty
Cold and hot utility
· Flow rates, inflow and outflow conditions
Dimension-related parameters
Column
Height, diameter, support type and height
Nozzle sizes, elevation and orientation e all services (process fluid, sampling, instrumentation, utilities, vent,
drain, safety)
Location of trays, packing support, packed section
Design pressure drop for overhead line, vapour return from reboiler, etc.
Location (elevation and orientation) of instrument tapping on column shell for measurement of temperature,
pressure, level
Size and location of manholes
·
·
·
·
·
·
Column pressure
Conventionally the term operating pressure of a column refers to the pressure on the top tray. This
pressure needs to be kept steady since even a small pressure fluctuation of 0.01 kg/cm2 across a tray in a
1.5 m diameter column will generate force in the order of 0:01 ðp =4Þ ð1:5 100Þ2 z 177 kg, which
is sufficient to dislodge trays. Trays are designed to be loaded from top and usually fail due to pressure
surges below the tray. Pressure surges in packed columns are notorious for disarraying the packed bed.
General heuristic considerations relating to column pressure have already been presented under
conceptual design (Section 11.2).
During design, the column top pressure is estimated by estimating the reflux drum pressure and then adding a small margin to
Estimating column pressure
account for the pressure drop in the overhead vapour line and
11.4 Fractionator
295
condenser. Overhead condensers are typically designed to have 0.15e0.25 kg/cm2 pressure drop and
the vapour line with w15 m/s vapour velocity culminating to 0.1e0.15 kg/cm2 pressure drop in
superatmospheric columns. Vapour line pressure drop is kept much lower in vacuum columns, e.g., in a
vacuum column with 80 mm Hg(abs.) column top pressure, the condenser may operate at around
70e75 mm Hg(abs.).
The liquid exit temperature attainable in the condenser depends on the coolant temperature. In
Indian condition, cooling water from cooling tower is available at around 33e35 C and is returned
back to the tower at 45e47 C. Accordingly, in a condenser cooled by cooling water, the temperature
of the exiting liquid shall be 53e55 C for a realistic minimum approach of around 20 C. The reflux
drum receives liquid from the condenser that is at its bubble point temperature. Therefore, the
bubble pressure of the liquid corresponding to the condenser exit temperature is the reflux drum
pressure. Adding the condenser pressure drop to the reflux drum pressure sets the condenser inlet
pressure. Column top pressure is arrived at by further adding to it the pressure drop in the overhead
vapour line.
However, in case of heat recovery from the overhead vapour, exchangers are installed in the
overhead vapour line and in such case, the pressure difference between the column top and reflux drum
can be up to 0.8 kg/cm2. Also in case of large columns, there can be more than one set of overhead
vapour line and condensers working in parallel. This is often seen in large vacuum distillation columns
where the pressure drop limits are lower as the column operating pressure is low and the vapour
volumetric flow rate is high due to the pressure being low. The overhead vapour line is sized for this
maximum allowable pressure drop.
Vapour flows through the packed beds/trays from the bottom to the top at a lower pressure. Once
the column (top) pressure is fixed, the feed zone and the bottom pressures are
estimated from the actual number of trays and/or the packed bed depth that are
arrived at through approximate calculations.
Pressure profile
The column pressure profile is required for detailed fractionation calculations. Thereafter, the column internals are designed (Chapter 14) ensuring that
the pressure profile in the column is close to that considered at this stage.
Table 11.3 shows the typical height equivalent to a theoretical plate (HETP) values for packing of
various nominal sizes. A first estimate of the required depth (hbed in m) of
packing for typical packed tower distillation systems can be arrived at by
multiplying HETP and the number of theoretical stages/plates. Depending on
Packed column
the gaseliquid traffic, ðDP=hbed Þ typically varies between 5 and 125 mm
water column per m of packing depth and this information can judiciously be
used to estimate the pressure drop across the active packed bed. However,
there are other components of pressure drop due to the presence of an extra top layer, redistributor(s),
etc., that may be added to improve the estimation. Detailed estimation and calculations related to
design of packed section is covered in Chapter 14.
296
Chapter 11 Distillation
Table 11.3 Height equivalent to a theoretical plate (HETP) for packing of different nominal size.
Nominal packing size, mm (inch)
19
300 4
HETP (m)
0.28 to 0.41
25 (100 )
00 38 112
0.46 to 0.67
50 (200 )
0.56 to 0.86
00 75e90 (3e312
0.36 to 0.51
0.79 to 1.14
The major component of pressure drop across a tray is contributed by the static head of liquid on it.
The height of the outlet weir governs the liquid level on cross-flow trays. In case of
sieve trays without downcomer it depends on liquid and vapour load, liquid
properties, orifice size and number. The liquid depth is typically around 50 mm
Tray tower
(w200 ). Including other losses, a fair and conservative estimate of pressure drop per
(actual) tray is 55e60 mm of liquid head. This does not vary much with vapour
flow. It is important to emphasise that the pressure drop is in terms of liquid head having the
composition on the tray. An estimate of average liquid density in the column is often used for estimating the average pressure drop in mm of water column per tray.
Often for columns operating at atmospheric pressure or above, the trays are designed with pressure
drop w5 mm Hg/tray. The figure is w2.5 mm Hg/tray for vacuum columns with column pressure
around 40e80 mm Hg absolute. Design figures for cryogenic columns for air separation, where the
liquid surface tension and viscosity both are lower than most other systems are typically w30 mm
water column (WC)/tray for small plants and w20 mm WC/tray for lager columns.
In many cases, particularly when the column pressure is high, the total pressure drop across the
column is small compared to the column pressure. This often prompts the designer to use average
pressure in the column for a quick design approximation. Vacuum columns or tall columns operating at
low pressure may be treated as exceptions.
Effect of pressure variation in the column on equilibrium data
The number of ideal stages/trays required for separation of the feed to specified products is
commonly estimated from equilibrium data (x-y diagram/T-x-y diagram/H-x-y diagram) at constant
pressure.
Since the pressure increases from top to bottom of a column, it is necessary to decide the pressure
(top, feed, bottom or a derived combination) at which the equilibrium data is to be considered. As
mentioned earlier, the separation is easier and requires lesser number of stages at lower pressure.
Therefore, for a more conservative design, the equilibrium data at higher pressure may be adopted for
design calculations.
As an example, let us consider the following
Number of trays ¼ 19; Feed tray: ninth from top; Top pressure: PTop, atm.; Average density of
liquid on trays: 0.8 gm/cc;
11.4 Fractionator
297
The pressure estimated on the feed tray (PFd) and the column bottom (PBtm) are
PFd ¼ PTop þ (9 0.8 60 / 10000) ¼ PTop þ 0.0432 atm.
PBtm ¼ PTop þ (19 0.8 60 / 10000) ¼ PTop þ 0.091 atm.
If this column is expected to be operating at around 7 atm, then
PTop ¼ 7 atm; PFd ¼ 7.043 atm; PBtm ¼ 7.091 atm.
The closeness of the pressure values (within 1.3%) suggests that the selection of the pressure for the
equilibrium data does not make much practical difference in computing the number of stages.
On the other hand, if the separation is carried out under vacuum with say
PTop ¼ 120 mm Hg(abs.),
PFd ¼ PTop þ (9 0.8 60/13.6) ¼ PTop þ 31.8 mm Hg(abs.) ¼ 151.8 mm Hg(abs.)
and
PBtm ¼ PTop þ (19 0.8 60 / 13.6) ¼ PTop þ 87.4 mm Hg(abs.) ¼ 207.4 mm Hg(abs.)
In this case the estimated variation of pressure (36.6%) within the column is large, and a more
conservative (higher) pressure may be adopted for the equilibrium data.
While predicting equilibrium data, it is wise to determine the possibility of azeotrope formation of
a given system. In such cases, both the minimum and maximum boiling azeotrope compositions can be
modified by changing the system pressure and/or addition of a third component which forms a minimum boiling azeotrope with one of the original pair and the new azeotrope boils well below or above
the original azeotrope. By this, one of the original components can often be recovered as a nearly pure
product, while the second azeotrope obtained needs to be separated in an additional step.
Such thermodynamic calculations are not included here.
Number of ideal stages/trays
Most real systems are multicomponent. Compared to multicomponent systems, the analysis and
design calculations for binary systems are much simpler and fairly well developed. In order to understand the fundamentals of distillation, binary distillation is discussed first.
11.4.2 Binary fractionation
The number of theoretical stages required for separating a feed into a distillate and a bottom product of
specified composition depends on the reflux ratio.
Binary fractionator design based on equal molar counterflow
McCabeeThiele graphical procedure is drawn on the equilibrium x-y diagram at the design column
pressure. This method is applicable when both components have nearly the same molar heat of
vaporisation. It does not include any detailed thermal balances and neglects sensible heat change, heat
of mixing and heat losses from the column. Energy balances are needed only to determine condenser
and reboiler duties.
298
Chapter 11 Distillation
Inputs to and outputs from the McCabeeThiele method for design of a simple binary distillation
column comprising of a single feed and two products are listed in Table 11.4.
Table 11.4 Input and output items for McCabeeThiele method.
Inputs
Outputs
flow rate (F) and composition (z )
· Feed
pressure (P) (assumed uniform
· Column
throughout the column)
(phase) of feed at column pressure
· Condition
curve for binary mixture at column
· V-L-E
pressure
· Overhead condenser type (total/partial)
type
· Reboiler
and bottoms composition (x and x )
· Distillate
· Ratio of reflux to minimum reflux (R/R )
and bottoms flow rate (D, B)
· Distillate
number of equilibrium stages (N )
· Minimum
· Minimum reflux ratio (R )
up rate in reboiler (V)
· Boil
and reboiler heat load (Q
,
· Condenser
)
Q
· Number of equilibrium stages (N)
stage location (N )
· Feed
vapour and liquid composition (y ,
· Stagewise
x)
F
D
min
min
Condenser
Reboiler
F
B
n
min
n
Flow rates (F,D,B,V) are in mol/hr; Compositions (zF, xD, xB, yn, xn) are in mole fraction of the more volatile component. N is the
total number of theoretical trays and n denotes the tray number. Conventionally trays are numbered from top to bottom.
The McCabeeThiele construction for design of a benzene-toluene distillation system at near atmospheric column pressure is shown in Fig. 11.8.
1.0
0.9
#1
(xD,yD)
#2
0.8
(xe,ye)
#3
#4
0.7
#6
0.6
#7
0.5
#8
q–line
q
slope =
q–1
y
(xF,yF)
0.4
0,
xD
#9
R+1
0.3
#10
0.2
#11
0.1
(xB,yB)
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x
FIGURE 11.8
McCabeeThiele construction.
0.8
0.9
1.0
11.4 Fractionator
299
The figure shows that besides the equilibrium curve, the graphical construction of the diagonal
(45 degrees reference line), feed line (q-line or f-line), and operating lines for the rectifying and
stripping section for operating reflux ratio (R ¼ 1.5 Rmin). The operating line relates the liquid
composition (xn ) on stage ‘n’ with the composition of vapour (ynþ1 ) approaching tray n from below as
shown in Fig. 11.9. For the rectifying/enriching section, the equation is
x R
D
ynþ1 ¼
xn þ
(11.1)
Rþ1
Rþ1
yn
xn–1
Stage ‘n’
yn+1
yn+2
xn
Stage ‘n+1’
xn+1
FIGURE 11.9
VapoureLiquid traffic across trays.
The construction steps are
(i) Locate the feed ðzF Þ, distillate ðxD Þ and bottom ðxB Þ stream compositions on the x-axis of the x-y
diagram.
(ii) Find the fraction ðf Þ of feed vaporizing/flashing on the feed tray.
q is the fraction remaining as liquid: q ¼ 1 f , where q by definition is the ratio of the heat
required to convert 1 mole of feed to saturated vapor and the molar latent heat of vaporisation at feed
condition.
In case of
(a) Liquid feed at its bubble point q ¼ 1
(b) Vapour feed at its dew point q ¼ 0
(c) Partially vaporised feed: q ¼ 1 f
q or f can be found from a flash calculation at the feed tray pressure.
Cold liquid feed below its bubble point temperature TBPF
q ¼ 1 þ CpL ðTBPF TF Þ=l ¼ 1 f
(11.2)
Superheated vapour feed above dew point temperature TDPF
q ¼ CpV ðTF TDPF Þ=l ¼ 1 f
where
CpL; CpV ¼ specific heat (molar) of liquid and vapour
TF ¼ feed temperature
(11.3)
300
Chapter 11 Distillation
TBPF ; TDPF ¼ bubble and dew point of feed having composition zF at column pressure
l ¼ molar heat of vaporisation(nearly same for both components)
Þ
q
(iii) Compute the feed line slope ¼ ð1qÞ
¼ ð1f
and draw the feed line (also called q-line or
f
f-line) passing through the point (zF, zF). Equation of the line is
q
zF
xþ
y¼ ð1 qÞ
ð1 qÞ
(11.4)
(iv) Construct operating lines for the rectification and the stripping
sections. The operating line in
xD the rectification section will have a y-intercept of
, i.e., it passes through the points
Rþ1
xD
0;
and ðxD ; xD Þ. The stripping section line is drawn through ðxB ; xB Þ and the
Rþ1
intersection of the rectification section operating line with the feed line.
xD The easy way to draw the rectification section operating line is to locate the point 0;
on
Rþ1
y-axis and join it with the point ðxD ; xD Þ on the 45 ðx ¼ yÞ line. Intersection point of this operating
line and the feed line marks the location of the feed tray. Stripping section operating line is drawn
by joining this intersection point with the point ðxB ; xB Þ on the 45 ðx ¼ yÞ line.
(v) Construction to find the number of stages is carried out by constructing triangles starting either
from the distillate or the bottoms composition as shown in Fig. 11.8. Usually the staircase is
stepped off between the operating line and the equilibrium curve from the point ðxD ; yD Þon the
45 degrees line and continues all the way to the bottom composition similar to the construction
described in Section 10.2. The construction step crossing the feed line locates the feed tray.
Counting the number of steps above and below the feed line gives the respective number of
rectification and stripping stages required. The number of stages in the rectification section is
obtained directly from the construction in case of a total condenser. A partial condenser provides
a stage of contacting and the number of rectification section stages to be provided within the
column in that case will be lower by one. Since the reboiler generally acts as an additional
equilibrium stage, the number of stages in the stripping section is less than the number of steps
below feed stage by one. In case of steam stripping in place of a reboiler, the number of stripping
stages obtained from the McCabeeThiele plot gives the number of ideal stages in the stripping
section of the column.
Usually an integral number of stages are not obtained and a fractional stage appears which is
rounded off to give the next higher number of stages.
Often close to the top and the bottom of the column the number of stages (steps of construction) is
more as the operating line and the equilibrium curve get closer to the 45 degrees line. A more
accurate estimate of the number of stages may even require constructions on these portions in
magnified scale. Improved accuracy is achieved by starting constructing of stages from the section
which has a smaller angle between the equilibrium line and the operating line, i.e., the construction
from the distillate as well as the bottoms end of the fractionator may be done simultaneously for
achieving better accuracy.
11.4 Fractionator
301
(vi) Finding the actual number of trays in the column
Vapour and liquid leaving a real tray do not attain equilibrium, i.e., in reality yn and xn will not be
located on the equilibrium curve. This is accounted for by inclusion of Murphree tray efficiency
ðhM Þ, in the McCabeeThiele construction procedure.
The Murphree tray efficiency ðhM Þ, i.e., the efficiency on individual trays is defined for a given
component and is equal to the change in composition in the phase divided by the change predicted
by equilibrium.
Mathematically,
hM ¼
Enrichment in vapour composition achieved in the actual tray
Maximum possible enrichment based on equilibrium being achieved
yn ynþ1
¼ yn ynþ1
(11.5)
where, on the nth tray, hM is the Murphree vapour efficiency, yn is the vapour mole fraction in
equilibrium with liquid composition xn and yn is the actual vapour mole fraction leaving tray n. The
component subscript in the equation is dropped because hM values are taken to be equal for the two
components of a binary mixture.
Considering the Murphree stage efficiency, the actual exit phase compositions are located at hM
fraction of the vertical distance from the operating line to the equilibrium curve and the actual
number of stages is obtained by stepping off between the curve for actual exit phase composition
and the operating lines. The construction is shown in Fig. 11.10. The left hand side figure illustrates
how the vapour composition yn ordinate is to be located for a known xn and hM . The dotted line on
the figure shows the locus of yn .
1.0
equilibrium line
#n
yn*
q–line
yn
KM x yn*–yn–1
yn–1
y
yn*–yn–1
0.0
0.0 xB
xF
x
FIGURE 11.10
McCabeeThiele diagram for trays with Murphree Efficiency (hM ).
xD 1.0
302
Chapter 11 Distillation
The actual number of trays may also be obtained by introducing an overall efficiency defined as
h0 ¼ ðNo. of equilibrium stagesÞ=ðNo. of actual traysÞ
(11.6)
The number of actual trays, calculated (separately for the enriching
section and the stripping section ¼ (Number of equilibrium stages in the
section)/ðh0 Þ.
In general, most practical separation problems involve 4 to 45 trays.
h0 is a complex function of the geometry and design of contacting trays, flow rates and flow paths
of the vapour/gas and liquid streams as well as their composition and properties. Tray efficiency increases with
Overall tray efficiency
•
•
•
•
•
•
decrease in liquid viscosity
decrease in relative volatility for distillation/increase in gas solubility (lower K-value) for
absorption/stripping
increase in flow path until it causes channelling
reduction in fractional area of holes
liquid level on tray, that is directly decided by the weir height. This is particularly true for
absorption of hydrogen sulphide/carbon dioxide with amines, caustic scrubbers, etc.
higher pressure since this increases the tray temperature (bubble temperature) and lowers the
viscosity as well as relative volatility of tray liquid
Tray efficiency data in industrial columns are determined from data collected during test runs under
total reflux condition. However, the efficiency measured under total reflux can differ significantly from
that at design reflux ratio. Designers use empirical correlations to estimate efficiency.
Typical conservative values of h0 used in designing of different columns are shown in Table 11.5. It
may be noted that values of h0 for absorbers and strippers are typically low ( 50%).
Minimum reflux and total reflux condition
The limits of design of distillation column for a specific separation target are operations under
minimum reflux and total reflux conditions.
Under total reflux condition, neither any distillate nor a bottom product stream is drawn from the
column. The entire liquid from the condenser is refluxed back to the column and the entire liquid from
the bottom tray is vaporised in the reboiler and sent as vapour reflux (vapour reboil). Accordingly, both
the rectifying and stripping operating lines coincide with the 45 degrees line, their respective ends
being at ðxD ; xD Þ and ðxB ; xB Þ. As both distillate and bottom product flow rates are zero, the feed rate to
the column is also zero. This explains the lack of influence of feed condition and neither the feed
composition nor the feed line influences the staircase construction. With the operating lines located as
far as possible from the equilibrium curve under this condition, a minimum number of stages (Nmin) are
required for achieving the desired top and bottom tray compositions.
A column is brought to total reflux only for test such as measurement of tray efficiency. Operation
at total reflux is sometimes used as an alternative to temporarily stopping production from the plant for
a short time as this is usually more convenient and requires less time and energy (in the form of reboiler
heat and coolant) as compared to shutdown and reestablishing operating conditions.
One may note that a total condenser is a practical device, whereas a total reboiler is not. This is
because complete vapourization at steady state will deposit any nonvaporized impurity present and
foul the heat transfer surface. In addition, the high heat transfer resistance of vapour films on the heat
11.4 Fractionator
303
Table 11.5 Typical conservative values of h0 (%) for industrial columns.
Process
Service
Enrichment section
Stripping section
Amine absorber
DEA or MDEA
e
50
Regenerator column for amine
absorption system
Sour gas e DEA
e
10
Sour gas e MEA or MDEA
e
15
Sour water stripper
WatereH2S
e
25e35
Solvents
Hexane/Heptane
75
80
Light hydrocarbon separation
Demethanizer/Deethanizer
100
100
Ethylene fractionator
95
95
Depropanizer
90
75
Propyleneepropane
fractionator
95
90
Debutaniser/naphtha
stabiliser
90
75
Benzene column
70
70
Toluene column
65
60
Xylene column
80
80
Aromatic separation
Others
C8eC9 splitter
80
70
Ethanol e water
60
60
Isopropanol e water
70
70
transfer surface during complete vaporisation can lead to overheating of the tubes. Therefore total
reboil if at all resorted to must be for a very short period.
At minimum reflux condition the operating lines of the rectification and the stripping section meet
the feed line (q-line or f-line) on the equilibrium curve as shown in the McCabeeThiele construction in
Fig. 11.11. Accordingly, the column requires infinite number of trays to effect the required separation.
It is important to determine the minimum reflux ratio (Rmin) since it forms a basis for establishing
the design R. This is done by using the ratio (R/Rmin) as an independent variable for optimising the
design of a distillation system. Typically this ratio lies between 1.1 and 1.5.
Analytical expression for Rmin in case of a binary distillation with saturated liquid feed and the
relative volatility being a is given by
Rmin ¼
xD ½1 þ ða 1Þ xF a xF
.
a xF xF ½1 þ ða 1Þ xF This is derived from the geometrical properties of the McCabeeThiele diagram.
(11.7)
304
Chapter 11 Distillation
The design reflux for a column is required to lie between the limiting conditions of total and
minimum reflux. It has already been shown that the minimum reflux ratio Rmin for a separation
problem is fixed.
1.0
Rectification Operating
line at minimum
reflux
0.8
q-line
y
0.6
slope =
Stripping Operating
line at
minimum
reflux
q
q–1
0.4
0.2
0.0
0.0
xB
0.2
xF
0.4
0.6
0.8
xD
1.0
x
FIGURE 11.11
McCabeeThiele construction for finding minimum reflux ratio.
A third limiting condition of interest involves the degree of separation. As a perfect split (xD ¼ 1
and xB ¼ 1) is approached for a reflux ratio at or greater than Rmin, the number of stages required near
the top and near the bottom of the column increases rapidly and without limit until pinch points occur
at xD ¼ 1 and xB ¼ 0. Hence, a prefect separation of a binary mixture that does not form an azeotrope
requires infinite number of stages in both sections of the column. However, the value of R is finite for a
perfect separation. For example, if the feed is saturated liquid, the minimum reflux for a perfect binary
separation is
Rmin ¼
1
xF ða 1Þ
(11.8)
where a is the relative volatility at the feed condition.
Hot and subcooled reflux
The McCabeeThiele construction considers the reflux stream to be generated by totally
condensing the overhead vapour, i.e., the reflux stream is at the bubble temperature corresponding to
the top tray pressure.
11.4 Fractionator
305
In case of subcooled reflux, the reflux stream on reaching the tray heats up to its bubble point,
consuming latent heat of vaporisation from the vapour approaching the tray and causing it to condense.
This causes the internal reflux ratio (Rint) within the rectifying section of the column to be higher than
the reflux ratio (R) from the reflux drum. The number of equilibrium stages is slightly overestimated if
this is ignored.
The Rint value for the McCabeeThiele construction in such a case can be estimated from R by an
approximate energy balance around the top tray as
cpL DTsubcooling
Rint ¼ R 1 þ
(11.9)
l
where cpL is the molar specific heat of reflux liquid, l is the molar latent heat of vaporisation and
DTsubcooling is the degree of subcooling in the external reflux, i.e., the difference between the actual
reflux temperature and the bubble point of same at the column top pressure.
Accordingly, Rint should be used instead of R in Eq. 11.1 and the rectifying section operating line
equation becomes
Rint
xD
y¼
xþ
Rint þ 1
Rint þ 1
Effect of increasing the ratio ðR=Rmin Þ
Capital cost: A tower theoretically requires infinite number of trays at minimum reflux ðR=Rmin ¼ 1Þ
and hence the corresponding capital investment for the system comprising of the column, condenser,
reflux drum, reflux pump and reboiler is infinite. Higher ðR=Rmin Þ ratio reduces the number of trays and
consequently the column height but increases the column diameter due to increased vapour and liquid
traffic in the column. The corresponding reboiler and condenser heat duties also increase. Thus, increase
in (R/Rmin) from its minimum value of 1 decreases the capital cost for the system from a very large value
due to the effect of lowering of tower height overriding the opposite effect of diameter increase. This
reduction goes on up to a limit, beyond which the capital cost increases again due to the effect of increase
in tower diameter and also due to increased heat duty and corresponding bigger sizes of the condenser
and the reboiler.
Operating cost: Operating cost includes costs for manpower, maintenance, depreciation and taxes
and the cost of coolant in the condenser and heat energy added to the reboiler. If the coolant is cooling
water and the heat supplied to the reboiler is by condensing steam, then the cost of these utilities
constitute the corresponding component of operating cost expressed in Rs/year. Except manpower, the
remaining components of operating cost increase with increase in the ratio (R/Rmin).
Optimum (economic) design
Optimum design is arrived at by minimising the annualised total cost. Fixed investment cost and
the annual operating cost are added to give the annualised total cost in Rs/year. If borrowed capital is
used for the investment, the interest per annum to be paid thereon is the annualised fixed investment
cost. Information on the market borrowing (interest) rate is required in this case. In case of investment
of own capital, the interest revenue loss from the alternative of keeping the same (investment) amount
as deposit in bank is considered.
306
Chapter 11 Distillation
The annualised total cost is a function of ðR=Rmin Þ. The curve of annualised total cost versus
ðR=Rmin Þ starts from infinity at minimum reflux ðR=Rmin ¼ 1Þ and passes through a minimum (at
R ¼ Ropt) for specified composition of feed, distillate and bottom product. Usually ðRopt =Rmin Þ lie
between 1.1 and 1.5, with the lower value applying to a difficult separation and the higher value to an
easy separation. However, optimal reflux ratio is not sharply defined in most cases and for greater
operational flexibility, columns are mostly designed for reflux ratios slightly higher than the optimum.
In an existing plant, a decrease in reflux ratio can save only the utility cost and a reflux sufficient to
obtain the desired product yield and purity should be used. Usually the total annual cost is dominated
by the cost of reboiler energy input except at close to minimum reflux condition. Also, in reality, often
the credit for additional separation overshadows the utility savings. In such cases of existing columns,
the operating ðR=Rmin Þ used is as high as possible without causing flooding or entrainment in the
column. Thus, the optimum reflux for an column depends upon the product values and the desired
degree of separation.
11.4.3 Multicomponent distillation
There are two approaches for multicomponent distillation design:
(i) Rigorous approach: This considers multicomponent thermodynamics and mass transfer along
with heat transfer and involves tray-to-tray/stagewise heat and mass balances.
(ii) Short cut approach based on similarities with binary system: This starts with identifying a pair of
key components whose separation represents the separation target of the distillation process
being designed.
Prior to a discussion of the aforementioned approaches, it is necessary to get acquainted with a few
definitions relevant to multicomponent distillation.
Definitions
Volatility is the tendency of a component to vaporise. At a temperature T, it is the ratio of the pure
sat
component vapour pressure (psat
i ) to the total system pressure (P), i.e., ai ¼pi ðTÞ P
Relative volatility (ai;j ) of component i with respect to component j is the quantitative comparison
of the volatilities of two components. In case of an ideal system,
sat
ai;j ¼ psat
i ðTÞ=pj ðTÞ
(11.10)
sat
where psat
i ðTÞ and pj ðTÞ are the pure component vapour pressures at temperature T.
ðyi =xi Þ Ki
¼
In case of a non-ideal system; ai;j ¼ Kj
yj =xj
where Ki ¼ yi =xi is the distribution coefficient of component i. The VLE relationship in terms of ai;j is
yi ¼
a xi
i;j
1 þ ai;j 1 xi
(11.11)
Since ai;j is a function of temperature, which is different at the top and the bottom of the column,
their geometric mean is used for designing the column.
Top 1=2
Bottom
aavg
¼
a
a
(11.12)
i;j
i;j
i;j
11.4 Fractionator
307
Light key and heavy key components
All components may not be present in the top as well as the bottom product of multicomponent
distillation columns. An example of this is splitting of the debutaniser feed to produce LPG as the top
product. LPG is primarily a mixture of C3 and C4 hydrocarbons. The lightest component C2H6 does not
condense in overhead condenser and is bled out from the reflux drum vapour space. Some small amount
of C3H8 is lost along with C2H6 leaving. This is inevitable but should be kept to a minimum. The feed
composition is shown in Table 11.6 with the components arranged in decreasing order of volatility.
Table 11.6 Splitting of a multicomponent feed.
Adjacent key case
Presence in
distillate
stream
Split key case
Presence in
distillate
stream
Component
% mole in
feed
Presence in
bottom stream
Presence in
bottom stream
C2H6
0.8
X
X
C3H8
6.61
X
X
iC4H10
8.67
X
X
nC4H10
14.77
X(LK)
X
X(LK)
X
iC5H12
11.61
X
X (HK)
X
X
nC5H12
10.06
X
X
X (HK)
C6
20.84
X
X
C7
14.4
X
X
C8
8.77
X
X
C9
3.47
X
X
Total
100
LK, Light key; HK, Heavy key.
The distillate liquid, i.e., LPG is a high valued product. It should accommodate as much of C3 and
C4 components as possible to have higher yield. This requires focussing on the split between the liquid
distillate (LPG) and the column bottom streams.
Maximum yield of LPG can be achieved with the ideal split having all of nC4H10 and lighter
components in distillate and all of iC5H12 and heavier components in the bottom product. In reality,
nC4H10 and iC5H12 will be partially separated and will appear in the top as well as the bottom product.
These components nC4H10 and iC5H12 are therefore termed as the light key (designated as LK) and the
heavy key (HK) components based on which the separation target is defined. The light and the heavy
key components are in decreasing order of volatility. The other components are termed non-keys. Nonkey components more volatile than the light key are termed light non-keys (i-C4H10 and lighter) and
those less volatile than the heavy key are heavy non-keys (e.g., C7 and heavier).
In the example case, the light and the heavy key components appear consecutively in the volatility
sequence list. This is a case of adjacent key components. When the light and the heavy keys are
308
Chapter 11 Distillation
separated by other components, the group of non-key components which have their volatility between
the light and heavy key are termed as split key components.
As a split key example we may consider the same feed being separated into LPG as top product
having an allowable maximum limit of 5% total C5 (nC5H12 þ iC5H12) content. Such a limit actually
exists to limit heavy components in LPG and ensure that empty LPG cylinders contain no residual liquid.
In this case the separation target needs to be set in terms of separation between nC4H10 and nC5H12 (the
heavier of the two pentanes). Therefore, the light and the heavy keys are nC4H10 and nC5H12,
respectively. The keys in this case are separated by iC5H12 (split key) having an intermediate volatility.
To summarise, one may state that the selection of key components depend on the separation targets
for the design problem and the features of key components are
•
•
•
•
Both light and the heavy keys will be present in distillate and the bottom stream
Split key components will also be present in both the streams
None of the components lighter than the light key will be present in the bottom product
None of the components heavier than the heavy key will be present in the top product
Separation sequencing for multicomponent system
The question of sequencing arises only when the feed has to be separated into more than two
streams. Different options for separating a feed to three different streams have already been presented
in Fig. 11.2. The correct way to arrive at the most appropriate sequence for separation is through
economic analysis. The economic criterion can be the minimum total annualised cost, i.e., the summation of the annualised cost of investment and the annual operating cost. This is often a complicated
and difficult procedure as the configurations to be compared are with optimally designed individual
columns. Procedure for optimum design of individual column configurations for binary fractionation
has already been discussed (Section 11.4.2) and the same approach is valid for multicomponent
system.
As a preliminary/quick evaluation alternative, the following heuristic rules are often applied for
non-heat integrated distillation columns:
(i) Separations where the key components have relative volatility close to 1 or form azeotrope
should be performed in absence of nonkey components. In other words, the easier separation
should be performed in the first column.
(ii) Sequences that remove the lightest components one by one in order of decreasing volatility may
be favoured. This means that the direct sequence is preferred.
(iii) A component present as a large fraction in feed should be removed first.
(iv) Column configurations with as similar as possible molar flow of the top and bottom products are
favoured.
Shortcut design methods
The steps in shortcut design of multicomponent distillation column involves a few empirical
equations, namely the Fenske equation, Underwood equation and the Gilliland equation, each being
known with their proposer’s name. The method is called F-U-G method in short and is shown in
Fig. 11.12 in the form of a flow chart. In addition, Kirkbride equation is used to decide the location of
the feed tray in the column.
11.4 Fractionator
Start
Specify feed
Specify split of light and heavy key
Estimate split of non-key components
Decide condenser type. Estimate column pressure
Flash feed at column pressure
[Adiabatic flash calculation]
Re-estimate split of non-key
components and column
pressure
Calculate minimum no. of ideal stages
[Fenske equation]
Calculate split of non-key components
[Fenske equation]
Yes
Estimated and
calculated split of nonkeys differ considerably
No
Calculate minimum reflux ratio (Rmn)
[Underwood equation]
Calculate no. of stages for specified reflux
ratio (R). (R>Rmn) [Gilliland correlation]
Calculate feed stage location
[Kirkbride equation]
Calculate reboiler and condense duties
[Energy balance]
Stop
FIGURE 11.12
Flow chart for multicomponent distillation column design by F-U-G method.
309
310
Chapter 11 Distillation
Minimum number of total trays in a column
The minimum number of trays in a column with total condenser under condition of total reflux is
given by Fenske’s equation (Eq. 11.13).
log xLK;D =xHK;D xHK;B =xLK;B
Sm ¼ ðNmin þ 1Þ ¼
(11.13)
log aavg
LKHK
where Nmin is the minimum number of trays in the column and Sm is the minimum number including
the reboiler. xLK;D and xHK;D are the mole fraction of the light and heavy key in the distillate and xLK;B ,
xHK;B denote the corresponding mole fractions in the bottoms product. aavg
LKHK is the average relative
volatility between the key components and is given by Eq. 11.12.
Since vapoureliquid contacting on the feed tray is expected to be poor, one more tray is added to
give Sm ¼ ðNmin þ2Þ.
Further, in case of a partial condenser due to the additional stage of vapoureliquid contacting, it
provides Sm ¼ ðNmin þ3Þ.
Eq. 11.13 shows that the minimum number of equilibrium stages depends on the degree of separation of the key components and their relative volatility. It is independent of the feed phase and
composition. This is expected as the operating lines for rectification as well as the stripping section
under total reflux coincide with the 45 degree line on the x-y plane, making the location of feed
composition irrelevant. The non-key components influence Nmin only by their effect on aLKHK . The
Fenske equation needs to be used with caution when (i) the relative volatility varies appreciably over
the column and (ii) the mixture forms a nonideal liquid solution. Once Nmin is known, the split for all
non-key components is calculated using Eq. 11.13 by substituting ‘LK’ with component ‘i’.
Minimum Reflux e Algebraic expression for the minimum reflux ratio (Rmin) given by the Underwood’s equation is valid for ideal or near-ideal systems.
When feed is at its bubble point (q ¼ 1),
"
#
avg
1
xLK;D aLKHK 1 xLK;D
Rmin ¼ avg
(11.14a)
1 xLK;F
aLKHK 1 xLK;F
When feed at its dew point (q ¼ 0),
2
3
avg
1
x
a
x
LK;D
LK;D
4 LKHK
5 1
Rmin ¼ avg
yLK;F
aLKHK 1
1 yLK;F
1
(11.14b)
In the general case 0 < q < 1, the explicit algebraic expression for Rmin does not exist and the
implicit relationship between the parameters is
a ðRmin þ 1ÞyLK;F þ ðq 1ÞxLK;D
Rmin xLK;F þ qxLK;D
¼
ðRmin þ 1Þ 1 xLK;F þ ðq 1Þ 1 xLK;D
Rmin 1 xLK;F þ q 1 xLK;D
(11.15)
Eqs. 11.14 and 11.15 show that Rmin depends mainly on the feed condition and relative volatility
and to a lesser extent on the degree of separation of the two key components.
11.4 Fractionator
311
Theoretical number of trays at actual reflux
The actual reflux ratio (R) and the corresponding number of trays for a particular separation
problem are related to Rmin and Nmin by the Gilliland’s correlation fairly well represented by
S Sm N Nmin
R Rmin 0:5124
¼
¼ 0:7591 0:7532 (11.16)
S
N þ1
Rþ1
Where N is the total number of equilibrium stages in the column including partial reboiler, but
excluding partial condenser, if any. Nmin is also defined in the same way. The correlation is to be used
for the RHS range from 0.02 to 0.98.
Feed tray location
Feed tray location can be estimated by the ratio of the total number of theoretical stages in the
rectification (Sr) and the stripping section (Ss) from the Fenske equation at total reflux
Sr Nr þ 1 log xLK;D =xHK;D zHK;F =zLK;F
¼
¼
(11.17)
Ss Ns þ 1 log zLK;F =zHK;F xHK;B =xLK;B
where Nr and Ns are the respective number of trays in the rectification and stripping section.
This equation is solved for ðSr =Ss Þ. This is not an exact answer as the feed tray composition hardly
ever matches the exact composition of the feed. Locating the feed tray utilising this ratio may be off by
two or three theoretical trays. Multiple feed tray option may be kept with three alternative feed nozzles
provided on alternate trays. Feed tray location is much more exact in case of tray to tray calculation
procedure.
Actual number of trays in the rectification section (Nactual;r ) can be found as
Nactual;r ¼ Sr ho for total condenser and Nactual;r ¼ ðSr 1Þ ho for partial condenser.
Where ho stands for overall tray efficiency and
Ss ¼ Sm =ð1 þ ðSr = Ss ÞÞ; Sr ¼ Sm Ss
(11.18)
In case of systems with large variation in relative volatility,
log xLK;D =xHK;D
Sr ¼
log aTopFeed
LK;HK
and
Ss ¼
log xLK;F =xHK;F
FeedBottom
log aLK;HK
(11.19)
1=2
1=2
TopFeed
Feed
FeedBottom ¼ aFeed aBottom
¼ aTop
and aLK;HK
.
where aLK;HK
LK;HK
LK;HK
LK;HK aLK;HK
For some problems the above approach fails to generate meaningful result. The Kirkbride equation
can also be used to locate the feed tray as it expresses the ratio of Sr and Ss as
"
#0:206
Sr Nr þ 1
xHK;F
xLK;B 2
B
¼
¼
(11.20)
D
Ss Ns þ 1
xLK;F
xHK;D
In fact the Kirkbride equation is more popular. There is also another way to locate the feed tray
using ErbareMaddox empirical correlation that is not included in this text.
312
Chapter 11 Distillation
Other shortcut methods
A conservative design of multicomponent distillation can be quickly arrived at by considering the
light key component and all lighter components as one group, and the heavy key component and all
heavier components as another group to get XF, XD, XB. The a of the keys themselves are used for
calculation.
The presence of components having a molar ratio (D/B) in distillate (D) to bottoms (B) greater than
100 or less than 0.01 can be neglected for quick calculations. The group a values are found by plotting
log(D/B) versus log(a) with a straight line drawn through the major points. The a value for each group
is read at the corresponding D/B value for the group. This procedure was introduced by Hengstebeck.
Rigorous methods
Rigorous methods involve tray-to-tray calculation. This considers mass balances and equilibrium
relationship equations, or in the fullest form includes both heat as well mass balances across each tray
along with equilibrium relationship equations.
There are several approaches, all of which are quite intricate and are more amenable to be programmed and solved using computers. These are primarily for simulating the operation of a column
where the total number of trays (N) and the feed tray location (NF) are known and the key operating
parameters (reflux ratio, column pressure, bottom tray temperature, etc.) are known. The basic approach
is to guess (i) the temperature and pressure profile in the column, (ii) the molar composition of top and
bottom product (or top and bottom tray compositions), (iii) stream flows, etc., and then follow an
iterative procedure to arrive at the steady-state stream flows, compositions and stage temperatures.
In case of a design problem, simulations are carried out with several options of N, NF, etc., to arrive
at the configurations delivering the functional requirements of the design objectives and meeting
constraints for the specific design problem, e.g., top and bottom compositions and limits on specific
components in product streams. The most suitable design option is chosen based on economic evaluation of these competing alternatives.
A distillation column is conceived to be represented by a set of equations known as the MESH
equation and these are
(M) e Material or flow balance equations
(E) e Equilibrium equations including bubble point and dew point equations
(S) e Summation or stoichiometric equations
(H) e Heat balance equations
These equations are framed around the stages of vapoureliquid contacting. The condenser and
the reboiler are also considered as stages. The simple contacting stages, feed stage(s), product draw
stage(s) along with the reboiler and condenser constitute the column model. Fig. 11.13A shows the
overall structure of a column with two feed, two product draws, partial condenser and reboiler. The
top products are vapour ‘Vtop’ and liquid ‘Ltop’ and the reflux is ‘L1’ and hence the reflux ratio is
R ¼ L1/(Vtop þ Ltop). Vi,j and Li,j stand for the ith component flow rates leaving stage j in vapour and
liquid phase. Vj, Lj are the total molar flow rates of vapour and liquid leaving stage j and their
corresponding molar enthalpies are HV,j and HL,j, respectively. The contacting stage, feed stage,
product draw stage are schematically shown in Fig. 11.13BeD, respectively. There Fi and F are the
flow rates of the i-th component and the total feed. Ki,F is the distribution coefficient of the i-th
component in feed after flashing at the conditions of the feed tray. HF is the molar enthalpy of the
feed. In Fig. 11.13D, molar flow rates of the i-th component in the vapour and liquid product streams
are Vi;NP and Li;NP , and the total product flow rates are V and L. Molar enthalpy of these streams are
HV;NP and HL;NP , respectively.
11.4 Fractionator
313
Vtop
(A)
Stage 1
Partial
Condenser
R = L1 /(Vtop + Ltop)
L1
Stage 2
Stage NP1
Ltop
(B)
P1
Stage j–1
Stage NF1
F1
ZF1
Stage NP2
P2
Vj,
Hv,j
Lj –1,
HL,j –1
Stage NF2
F2
ZF2
Stage j
Vj+1,
Hv,j+1
Stage N –1
VN
Stage N
Lj ,
HL,j
B
Reboiler
(C)
(D)
Stage NF –1
LN –1 ,
F
HL,N –1
F
FV
NF
FN
F
ZN
Stage NP –1
VN
LN –1,
P
HV,FNF
P
HV,N
P
HL,N –1
P
F
FL
NF
HL,FNF
Stage NP
WN
Vi,N –1,
VN
F
HV,NF
P
P
Stage NF
HV,N –1
P
LN
P
HL,NP
VN
,
HV,N –1
F
LN ,
F
HL,N
F
FIGURE 11.13
(A) A column with two feed, two product draws, partial condenser and the reboiler, (B) A typical stage j,
(C) A typical feed stage NF, (D) A typical draw off stage ‘P’.
314
Chapter 11 Distillation
Variables in the MESH equations are
• Stage temperatures (Tj)
• Internal vapour and liquid flow rates (Vj and Lj)
• Stage compositions (xi,j and yi,j or Vi,j and Li,j)
A) The summation/stoichiometric equations are
For the liquid phase
n
X
xi;j 1 ¼ 0 or
n X
Li;j = Lj 1 ¼ 0
i¼1
or
i¼1
n X
yi;j = Ki;j 1 ¼ 0
(11.21a)
i¼1
For the vapour phase
n
X
i¼1
yi;j 1 ¼ 0 or
n X
n X
Vi;j = Vj 1 ¼ 0 or
Ki;j xi;j 1 ¼ 0
i¼1
(11.21b)
i¼1
B) The equilibrium equations are
yi;j ¼ Ki;j xi;j
or Vi;j =Vj ¼ Ki;j Li;j =Lj
The expression of Ki;j in a real system will be a complex function of stage temperature, pressure
and compositions derived from thermodynamics:
Ki;j ¼ Ki;j Tj ; Pj ; xi;j ; yi;j
(11.22)
C) Component balance equations
For a single feed, single distillate and bottom product,
Fi Bi Di ¼ 0
(11.23)
Balance on a simple stage (no draw or feed on the stage) as shown in Fig. 11.13B,
Vi;jþ1 þ Li;j1 Vi;j Li;j ¼ 0
(11.24)
Balance on the feed stage NF contains only the liquid portion of the feed (FLi;NF ) as shown below
Vi;NF þ1 þ Li;NF 1 þ FLi;NF Vi;NF Li;NF ¼ 0
(11.24a)
The vapour fraction of feed appears in the balance of stage ðNF 1Þ.
Balance on the product draw off stage NP is
Vi;NP þ1 þ Li;NP 1 Vi;NP Li;NP wi;NP ¼ 0
(11.24b)
where wi;NP is the molar flow rate of the ith component in the side stream draw from tray NP.
The overall material balance equation for stage j is
Vjþ1 þ Lj1 Vj Lj ¼ 0
(11.25)
11.4 Fractionator
D) The bubble point and the dew point equations, respectively, are
8
9
9
8
>
>
>
>
>
>
>
>
n
n < 1 X
=
< 1 X
=
1
¼
0
and
1¼0
V
K
K
L
=
i;j i;j
i;j
i;j
n
n
P
P
>
>
>
>
>
>
>
>
: Vi;j i¼1
;
;
: Li;j i¼1
i¼1
315
(11.26)
i¼1
The bubble and the dew point equations are used in some methods to determine the stage
temperatures.
E) Energy balance equations
The overall energy balance equation for a column with one feed and only bottom and top product is
FHF DHD BHB WHW þ QReboiler QCondenser ¼ 0
(11.27)
Energy balance for the simple stage j (Fig. 11.13B) is
Vjþ1 HV;jþ1 þ Lj1 HL;j1 Vj HV;j Lj HL;j ¼ 0
The enthalpies are function of the stage temperature, pressure and composition
HV;j ¼ HV;j Tj ; Pj ; yi;j and HL;j ¼ HL;j Tj ; Pj ; xi;j
(11.28)
(11.29)
Energy balance for the feed stage and the product draw off stage are to include the stream flow rates
shown in Fig. 11.13C and D, respectively, multiplied by the corresponding enthalpy terms.
The energy balances for the reboiler is
LN1 HL;N1 VN HV;N BHL;N þ QReboiler ¼ 0
(11.30)
and the same for a partial condenser with a vapour and a liquid product is
V2 HL;2 L1 HL;1 Ltop HL;1 Vtop HV;1 QCondenser ¼ 0
(11.31)
The efficiency equations can also be written in terms of the tray flow and composition parameters
but are not presented here.
The foregoing set of equations would constitute the rigorous model of the distillation unit. Solution
of the system of equations with specified number of variables would provide the steady-state operating
conditions. The number of specified variables must be equal to the degrees of freedom of the system.
Intuitively one can say that the model would simulate the column operation when its configuration
(number of stages, feed stage and product draw stages) is specified along with the operating conditions
(say temperature and pressure on top and bottom stages, pressure on all other stages, temperature and
pressure of feed, feed composition, product flow rates) is known.
In order to use the model for design, the model is run with different input parameters selected as
design variables to generate solutions that respect the constraints on product compositions, limits on
top and bottom temperature, etc.
Several solution procedures for the rigorous model are available in literature and are implemented
in process simulators. However, these are not discussed here.
316
Chapter 11 Distillation
11.5 Design illustration e fractionator
Design Problem
Benzene is proposed to be recovered by fractionating a 20 m3/hr stream containing 35%, 25% and
40% mol benzene, toluene and ortho-xylene (O-x). At least 75% of the benzene in feed needs to be
recovered with 95% purity. Component property data are provided in Table 11.7.
Make a quick design of the fractionator.
Table 11.7 Component property data.
Benzene (B)
Toluene (T)
Ortho-xylene (O-x)
Molecular weight (MW)
78
92
106
N.B.P. (K)
353.05
383.6
417.4
Density, r (gm/cc)
0.8787
0.8636
0.8800
Constants in Antoine’s equation log10(p ) ¼ ab/(T þ c); p
sat
sat
(saturated vapor pressure) in kPa, T in C.
a
6.01905
6.08436
6.12699
b
1204.637
1347.620
1476.753
c
220.089
219.787
213.911
Cpl (kJ/kmol K),
average
134.8
155.96
187
Cpv (kJ/kmol K),
average
82.44
103.7
132.5
Heat of vaporisation at
NBP, l (kJ/kmol)
30.77
38.06
36.24
The l value at temperatures T1 and T2 are related by the equation
(l 1/l2) ¼ {(Tc T1) /(Tc T2)}0.38, where Tc is the critical temperature of the component.
Solution
Feed
MWF ¼ ð:35 78 þ :25 92 þ :4 106Þ ¼ 92:7
rF ¼ ð35 78 þ 92 25 þ 106 40Þ=
ð35 78 = :8787 þ 92 25 = :8636 þ 106 40 = :88Þ ¼ 0:8755 kg=L ¼ 875:5 kg=m3
Hence, F ¼ 875:5 20=92:7 ¼ 1888:9 kg mol/hr; (B ¼ 661.1, T ¼ 472.2, O-x ¼ 755.6 kg mol/hr)
zF ¼ 0:35=0:25=0:4; mole fraction
Deciding light and heavy key components: As per product specification, Benzene and Toluene are
set as light and heavy key components. This means that distillate D to have minimum 90 mol%
Benzene and the rest is Toluene.
Distillate Composition: Based on 75% benzene recovery and 95% mole purity of benzene,
11.5 Design illustration e fractionator
317
D ¼ (495.8 kg mol Benzene þ 26.1 kg mol Toluene) ¼ 521.9 kg mol distillate and
xD ¼ 0:95=0:05=0:00, mole fraction.
By balance, composition of B:
B ¼ (165.3 kg mol Benzene þ 446.1 kg mol Toluene þ 755.6 kg mol) ¼ 1367 kg mol
xB ¼ 0:1209=0:3263=0:5528; mole fraction
Deciding the column operating pressure
Reflux drum will have D at its bubble point. If cooling water (Supply @33 C, Return @47 C) is
used in condenser, the reflux drum temperature (condenser outlet temperature) is expected to be
around 60 C. The other option is to use air cooled condenser and have condenser outlet temperature
about 90 C. Estimated bubble pressure of D with possible options of drum temperature is
T( C)
60
90
Bubble pressure of D (kPa)
51.5
134.8
If cooling water is used and the reflux drum temperature is 60 C, the drum will be at subatmospheric pressure e a potentially hazardous condition for air-leakage into a hydrocarbon system. The
second option will operate the reflux drum at slightly above atmospheric pressure. So an air-cooled
condenser is selected to obtain the outlet temperature of 90 C.
Based on pressure drop across the condenser and the overhead vapour line pressure drop of 0.3 kg/
cm2, the column pressure is now estimated to be
Pcol ¼ 134:8 þ 101:325 0:3=1:0332 ¼ 164:2 kPa
Column top temperature is the dew point of D at column pressure 164.2 kPa, estimated to be
98.6 C. The condenser inlet and exit temperatures are therefore 98.6 and 90 C.
A small pressure drop is assumed across the column, which is guessed to have w10 trays.
Column bottom temperature is estimated to be 137.9 C, the bubble point of B at column bottom
pressure (164.2 þ 5.2 ¼ 169.4 kPa).
Estimation of relative volatility
Pure component vapour pressure, kPa
Temperature ( C)
B
T
O-x
Column top
98.6
173.17
70.97
25.17
Column bottom
137.9
450.77
207.33
84.98
aLK HK top ¼ 173:1=70:97 ¼ 2:439
aLK HK bottom ¼ 450:77=207:33 ¼ 2:174
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a ¼ 2:439 2:174 ¼ 2:303
318
Chapter 11 Distillation
Estimating minimum number of ideal stages for total condenser using Fenske equation (Eq. 11.13)
log xLK;D =xHK;D xHK;B =xLK;B
Sm ¼ ðNmin þ 1Þ ¼
log aavg
LKHK
¼
log½ð0:95=05Þ ð0:1209=3263Þ
¼ 2:34
logð2:303Þ
Estimating minimum reflux ratio considering saturated liquid feed (q ¼ 1) using Underwood
equation (Eq. 11.14a)
"
#
avg
1
xLK;D aLKHK 1 xLK;D
Rmin ¼ avg
1 xLK;F
aLKHK 1 xLK;F
1
:95 2:303 ð1 :95Þ
¼
¼ 1:947
ð2:303 1Þ
:35
ð1 :35Þ
Estimating number of ideal stages at a reflux ratio R (R > Rmin ) using Gilliland correlation (Eq. 11.
16)
N Nmin
R Rmin 0:5124
¼ 0:7591 0:7532 ; this can also be written as
Nþ1
Rþ1
R Rmin 0:5124
¼ 0:7591 0:7532 Rþ1
S Smin
S
Say, for R/Rmin ¼ 1.2, R ¼ 1:2 1:947 ¼ 2:336,
S Sm S 2:34
2:336 1:947 0:5124
¼ 0:7591 0:7532 ¼
¼ 0:5087
S
2:336 þ 1
S
i.e., S ¼ 2:34=ð1 0:5087Þ ¼ 4:76, the total number of ideal stages in the column.
Locating feed tray using Kirkbride correlation (Eq. 11.20)
Ratio of number of rectification trays to number of stripping trays is given by
"
#0:206 "
#0:206
Sr N r þ 1
xHK;F
xLK;B 2
B
0:25
0:3263 2
1367
¼
¼
¼
D
0:35
0:05
521:9
Ss N s þ 1
xLK;F
xHK;D
¼ 2:464
Actual number of trays to be provided assuming 70% tray efficiency,
Number of rectification trays in column ¼ 4:76 f2:464 =ð1 þ 2:464Þg=0:7 ¼ 4:84, say five
trays.
Number of stripping trays in column ¼ 4:76 f1 2:464 =ð1 þ 2:464Þg=0:7 ¼ 1:96, say two
trays.
One tray is additional for the feed entry section.
Condenser load, inlet to condenser is vapour at 98.6 C and exit is at 90 C.
11.5 Design illustration e fractionator
319
Based on heat of vaporisation and specific heat of components, estimated
Enthalpy of distillate vapour at 98 C ¼ 67,022 kJ/kg mol.
Enthalpy of distillate liquid at 90 C ¼ 12,227 kJ/kg mol.
Qc ¼ ðR þ 1Þ D Enthalpy difference
¼ ð2:336 þ 1Þ 521:9 ð67022 12227Þ ¼ 95401295 kJ=hr ¼ 26500 kW
Reboiler load,
Qreb ¼ Qc þ Enthalpy leaving with D þ Enthalpy leaving with B Enthalpy entering with F
¼ 26916 kW
Note: Individual enthalpies are calculated based on the problem data.
Table 11.8 is worked out for various values of R/Rm and it summarises the effect of R on the number
of trays. Corresponding condenser and reboiler loads can be arrived at from the base value at
R/Rm ¼ 1.2, i.e., R ¼ 2.3359. The basic relationship is
Qc ¼ ðQc Þbase case ðR þ 1Þ=ðR þ 1Þbase case ;
and
Qreb ¼ Qc þ ðQreb Qc Þbase case
Table 11.8 Effect of variation of reflux ratio.
Number of actual trays ðh [ 0:7Þ)
Total number of trays
considering one
additional tray for feed
section
R/Rm
R
1.05
2.0439
7
3
11
1.10
2.1413
6
3
10
1.15
2.2386
6
3
10
1.20
2.3359
5
2
8
1.25
2.4333
5
2
8
1.30
2.5306
5
2
8
1.35
2.6279
5
2
8
1.40
2.7253
5
2
8
1.45
2.8226
4
2
7
1.50
2.9199
4
2
7
1.55
3.0173
4
2
7
Rectification section
Stripping section
320
Chapter 11 Distillation
The number of trays is close to what was assumed and hence the column pressure drop is
reasonably assumed. Also the relative volatility estimation is ok.
Column diameter and internals are to be designed based on the content of Chapter 14.
11.6 Flash distillation
The process of flash distillation has been introduced right at the beginning of this chapter. This can also
be seen as a process of fractionation with a single stage. Since there is only one stage of contact, the
purpose of the fractionator column is served by a simple vessel called the flash drum. The feed can be
liquid or a mixture of vapour and liquid. Heat may be added, if necessary, to the system in a feed
preheat exchanger. In some cases a heating coil or jacket integral with the flash drum is used for adding
the heat. Fig. 11.14 shows a typical flash drum with a control valve in the vapour outlet line for
throttling the vapour flow to control the drum pressure. Level in the drum is controlled by regulating
the liquid outflow rate. We assume that the feed temperature and pressure is sufficient to flash the feed
in the drum and generate the vapour and liquid streams of desired composition. Hence, no heat addition
arrangements are included.
FIGURE 11.14
Typical Horizontal Flash Drum configuration with associated instrumentation.
Flash distillation problems are usually posed as a separation problem for a feed with known flow
rate (F mol/hr), composition (zFi mole fraction of i-th component), temperature (TF) and pressure (PF).
Feed has to be flashed to generate the vapour and liquid streams that meet specific composition
specification limit either on the vapour or the liquid stream.
11.6 Flash distillation
321
Deliverables from the process design phase forming the basis for mechanical design of a typical
flash distillation system are
•
•
•
•
•
General arrangement of the system, its instrumentation and control e P&ID.
Operating temperature (T) and pressure (P) of flash drum.
Flow rate and composition of vapour and liquid streams leaving the drum.
Feed preheat temperature and preheating load, if preheating is required. Heating coil/jacket
details in the drum and the heat load, if required.
Drum dimensions, internal fitting like demister pad, vortex breaker and nozzle connections and
their locations. Requirement of vacuum, if operation is envisaged under vacuum.
11.6.1 Design equations
Design equations related to the process streams
Assuming ideal system, the distribution coefficient of component i,
psat
i ðTÞ
P
psat
is
the
vapour
pressure
of
the
i-th
component
at
temperature
T and pressure P.
i
P
,
the
liquid-phase
activity
coefficient
gi can be calculated for
For nonideal systems: Ki ¼ gi psat
i
known temperature and composition. These calculations are straightforward and are dealt in details in
text books on thermodynamics.
In case of low pressure systems, where the pure component vapour pressure is below 2 atm, the
vapour pressures for component i can be estimated from Antoine’s equation:
Ki ¼ yi =xi ¼
log10 psat
¼ ai i
bi
ðT þ ci Þ
(11.32)
Antoine constants a, b and c for component i are in corresponding units based on the units of
T and psat
i .
When (V/F) is the fraction of moles of feed leaving the drum as vapour and zFi denotes the mole
fraction of the i-th component in feed for an n component system.
n X
zFi ðKi 1Þ
¼0
(11.33)
1 þ ðV=FÞ ðKi 1Þ
1
The above equation can be solved for ðV=FÞ using an iterative method.
Drum pressure P being between the bubble and dew point pressure Pbub and Pdew is the essential
condition for existence of both phases in the drum. Only one positive (V/F) value between 0 and 1 will
be obtained as a solution of the aforementioned equation. Once the (V/F) value is found from
Eqn. 11.33, the liquid and the vapour compositions can be found from the following equation
zFi
xi ¼
;
(11.34)
1 þ ðV=FÞð1 Ki Þ
where xi and yi ð ¼ xi Ki Þ are mole fractions of i-th component in the liquid and vapour phase.
322
Chapter 11 Distillation
11.6.2 Design considerations
The following considerations are helpful in proceeding with the design
•
•
•
Lower operating pressures require lower drum temperature and lower heating load.
Pressure versus vacuum operation e A slight positive pressure is usually preferred in case of
combustible systems in order to avoid/reduce the risk of air ingress into the drum. Air ingress may
lead to an explosive mixture and is particularly important while handling hydrocarbons. Vacuum
flashing is resorted to when there is a maximum limit of a lighter component concentration in the
liquid or when maximum recovery of a lighter component is warranted. Operating under vacuum
requires a lower operating temperature and heat load but increases vapour volume which in turn
results in larger drum size. Vacuum in most cases is created by a steam ejector. Ejector steam
consumption increases sharply with higher vacuum requirement and the steam cost may offset the
other advantages of vacuum operation. Unless there is some specific requirement, the operating
pressure lower limit is kept w0.1 atm (abs). This level of vacuum is easily achieved by a steam
ejector coupled with a barometric condenser.
Feed preheat versus heating arrangement integral with the drum
- A feed preheat exchanger for liquid feed followed by a properly sized restriction orifice allows
efficient exchanger design, avoiding vaporisation in the exchanger. The restriction orifice
provides the pressure drop and flashing starts immediately downstream. Therefore, the
restriction orifice is located close to the drum as shown in Fig. 11.15.
Restriction
Orifice close
to drum
Vapour
Demister
pad
Heating
steam
Feed
Condensate
Liquid
FIGURE 11.15
Typical vertical flash drum configuration.
Heating jacket or coil with condensing steam is usually used when the heat load is low. Since the
liquid side heat transfer coefficient in the drum is usually controlling, it is not a very efficient process.
•
Yield of desired stream e the split of vapour and liquid depends on the drum temperature and
pressure. Maximising the yield of the desired stream is a design objective. The operating
temperature and pressure maximising the yield of desired stream is found out by trial. It is easier
11.6 Flash distillation
•
•
•
323
to fix a temperature, compute the corresponding (V/F) splits by varying the drum pressure
between the bubble and dew pressure of feed and tabulating the splits that meet the specification
requirements. The design operating condition is chosen from the tabulated data, considering the
balance between the yield and the feasibility of adopting the corresponding design pressure and
temperature.
Choice between the horizontal and the vertical drum e Horizontal drums provide a longer travel
path and also a larger cross section for vapour travel that reduces vapour velocity. This helps
separation of the phases. Vertical drums on the other hand occupy less floor space. Length to
diameter ratio of vertical drums is usually between 3 and 5. While sizing a vertical drum, if the
length/diameter estimate exceeds 5, a horizontal drum is designed.
Demister pads e These are provided when the chance of liquid carryover is to be minimised.
Typical demister pads are 80e100 mm thick wire gauge pads and offer below 25 mm water
column pressure drop. These are bought out items. In horizontal drums the demister is provided
only for a section of the drum in the area below the vapour outlet nozzle. This is schematically
shown in Fig. 11.14 and 11.15.
One may refer to Chapter 17 for sizing the features of the flash drum.
11.6.3 Design steps
The design steps consist of
(i) Deciding the design operating conditions e the drum temperature and pressure required to meet
the composition specification assuming equilibrium conditions (TV ¼ TL & PV ¼ PL). This step
generates the flow rate and composition of the vapour and liquid streams leaving the drum,
preheat temperature requirement, heat load through preheat and/or through heating arrangement
integral to the drum.
(ii) Firming up the general arrangement of the process. This includes arrangement for preheating
the feed and/or heating arrangement for the drum, arrangements for controlling the feed rate,
drum temperature, pressure and liquid level. This generates the P&ID of the system.
(iii) Sizing of the drum is based on applicable design equations and industry practices to ensure safe
and trouble-free operation of the system. This includes decision on the drum configuration
(orientation) e vertical or horizontal; requirement of mist eliminator/demister pad to minimise
liquid entrainment in the vapour stream; sizing of feed inlet and vapour and liquid outlet
nozzles; location and sizing of nozzles for drain, vent, safety valve fixing, utility connections;
location and sizing of nozzles for instrumentation e temperature, pressure and level
measurements.
(iv) Detailed mechanical design of the drum and the associated system.
Sizing of the flash drum
Maximum allowable vapour velocity on the liquid surface is
uV;max ¼ SF fðrL rV Þ=rL g1=2
(11.35)
where rL and rV are the density of liquid and vapour (kg/m3) and mL ; mV are the corresponding flow
rates (kg/sec).
324
Chapter 11 Distillation
The system factor SF for horizontal and vertical vessels (with mist eliminator) is given in
Table 11.9 against values of the separation factor s.
s ¼ ðmL = mV ÞðrV =rL Þ1=2
(11.36)
Table 11.9 Separation factor at 85% flooding velocity (with mist eliminator).
System factor SF(m/sec)
s
For vertical drum, SFv
For horizontal drum, SFh
0.006
0.0762
0.0953
0.008
0.0914
0.1142
0.01
0.1006
0.1258
0.02
0.1219
0.1524
0.04
0.1341
0.1676
0.06
0.1341
0.1676
0.08
0.1310
0.1638
0.1
0.1280
0.1600
0.2
0.1128
0.1410
0.4
0.0884
0.1105
0.6
0.0671
0.0839
0.8
0.0549
0.0686
1.0
0.0488
0.0610
2
0.0228
0.0285
4
0.0101
0.0126
6
0.0055
0.0069
A higher value of the system factor SF allows a higher allowable maximum vapour velocity and
leads to lower cross section. Since higher disengagement height (hdisengaging) would reduce entrainment and allow higher SF to be used, a second approach to sizing is based on Table 11.10 that tabulates
(maximum) allowable SF against values of hdisengaging.
Table 11.10 SF values based on disengaging height (hdisengaging) with mist eliminator.
hdisengaging
(mm)
75
100
125
150
175
200
225
250
275
300
325
350
Allowable
SF value
0.12
0.15
0.19
0.22
0.25
0.29
0.32
0.35
0.38
0.40
0.42
0.43
11.6 Flash distillation
325
Vertical drum
The critical dimensions of a vertical drum are shown in Fig. 11.16.
Vapour outlet
h1
Feed
inlet
DØ
High
level of
liquid
h2
Normal level
Low level
hL
Liquid outlet
FIGURE 11.16
Vertical flash drum with its critical dimensions.
The minimum diameter (dmin ) in m is
1=2
2
dmin ¼ pffiffiffi mv = rv: uv;max
p
(11.37)
dmin is normally rounded off to the next higher multiple of 10 mm and incremented in steps of 150 mm,
if required to be revised. All variables in Eqn. 11.37 have to be in consistent units.
Feed inlet nozzle
Some amount of feed vaporises in the feed nozzle and hence the same cannot be sized based only
on volumetric flow of entering liquid. Inlet nozzle size is based on average (rmix ) density of the vapour
and liquid leaving.
rmix ¼ ðmL þ mv Þ=ðmL = rL þ mv = rv Þ; kg=m3
(11.38)
Maximum and minimum allowable inlet nozzle velocity are estimated from the following
empirical expressions
pffiffiffiffiffiffiffiffi
umax;nozzle ¼ 122= rmix ; m=sec
(11.39)
umin;nozzle ¼ 0:6 umax;nozzle ; m=sec
(11.40)
326
Chapter 11 Distillation
Minimum inner diameter of inlet nozzle, di;nozzle is
1=2
pffiffiffi di;nozzle ¼ 2 = p ðmL þ mV Þ= rmix umax;nozzle
; m
(11.41)
From the standard pipe size chart the nearest higher id pipe is chosen for use as nozzle and its
corresponding outer diameter value do;nozzle ðmmÞ is noted.
Nozzle locations, for a vertical drum
h1 ¼ 900 þ do;nozzle ðmmÞ=2; mm or 1200 mm; whichever is higher
h2 ¼ 300 þ do;nozzle ðmmÞ=2; mm or 450 mm; whichever is higher.
(11.42)
Time to fill the drum from minimum to the maximum liquid level is decided based on the emergency response of the operator and this is usually between 3 and 6 min. This is the surge time (ts , sec).
Surge volume Vs ¼ ts ðmL =rL Þ; m3
hL ¼ ð4=pÞ Vs =d2 ; m
hTotal ¼ h1 þ h2 þ hL
(11.43)
hTotal =d ¼ ðh1 þ h2 þ hL Þ=d
Desirable hTotal /d is between 3 and 5. In case hTotal /d exceeds 5, a horizontal drum is chosen.
Outlet nozzles for vapour and liquid
Sizing of liquid and vapour outlet nozzles are based on typical vapour line velocity around 15 m/s
and the liquid line velocity between 2 and 3 m/s.
Orientation and location of the remaining nozzles are done based on operability consideration, e.g.,
the drain and the vent are located at the highest and lowest points in the drum, utility connections (plant
air and water) are located at accessible positions, etc.
Finally, a general arrangement drawing of the drum is prepared that shows all nozzles, fixtures and
vessel support. This drawing becomes the basis for the fabrication drawing of the vessel.
11.7 Design illustration e flash distillation
Design problem: A 12 m3/hr stream of ortho-xylene is contaminated with 1%w/w benzene and 1.45%
w/w toluene. Design a flash distillation process to bring down benzene content in the stream to below
0.5%w/w.
Solution
The problem states the composition limit on the liquid stream from the drum. This needs to be met
while ensuring that the product yield should be as high as possible. This sets the benzene content in the
liquid stream to 0.5% w/w. Component properties are tabulated in Table 11.11.
11.7 Design illustration e flash distillation
327
Table 11.11 Properties of the B-T-(O-x) system.
Benzene (B)
Toluene (T)
Ortho-xylene (O-x)
Molecular Weight
78
92
106
N.B.P. (K)
353.05
383.6
417.4
Density, r (gm/cc)
0.8787
0.8636
0.8800
Constants in Antoine’s equation log10(p ) ¼ ab/(T þ c); p
sat
sat
in kPa, T in C
a
6.01905
6.08436
6.12699
b
1204.637
1347.620
1476.753
c
220.089
219.787
213.911
Cpl (kJ/kmol K),
average
134.8
155.96
187
Cpv (kJ/kmol K),
average
82.44
103.7
132.5
Heat of vaporisation at
NBP, l (kJ/kmol)
30.77
38.06
36.24
% w/w in feed
1.1
1.4
97.5
Mole% in feed (zF)
0.0149
0.0160
0.9691
l at temperatures T1 and T2 are related by the equation: (l 1/l2) ¼ {(TcT1)/(TcT2)}0.38, where Tc is the critical temperature of
the component.
Flash drum operating temperature and pressure
Since the temperature at which the feed may be available is not mentioned, it is assumed that the
feed is from a tank at ambient temperature, say w32 C. The N.B.P. of the limiting component benzene
is 78 C. This is not too high and easily attainable with heating using low pressure steam. Therefore, we
adopt drum temperature in the range 70e110 C so that it is achievable after preheating with steam or
any other hot stream. For a particular drum temperature (T), the bubble (PBub:F ) and the dew point
(PDew:F ) pressure of the feed are calculated from pure component vapour pressures and feed mole
fractions as
X
X
PBub:F ¼
zFi psat
zFi = psat
i .& PDew:F ¼ 1=
i
i¼1;3
i¼1;3
Flashing of feed at a pressure P between the bubble point pressure PBub:F and dew point pressure
PDew:F would give rise to vapour and liquid phases coexisting in the drum at temperature T. The V/F
value and the corresponding liquid mole fraction (xi ) are to be calculated from Eqs. 11.33 and 11.34.
Solution of Eq. 11.33 for V/F requires trial or use of a convergence routine, e.g., NewtoneRaphson.
The acceptable P with which the drum can be operated shall be the one with benzene concentration
0.5% w/w or lower in the liquid. It may be noted that selecting an even lower pressure would result in
benzene concentration below 0.5%w/w, which is acceptable but this will be at the cost of product
328
Chapter 11 Distillation
stream yield. Therefore, the optimum P corresponding to a T is the one with 0.5% w/w benzene in the
liquid phase.
It is simpler to compute xi values for different values of P and select the one that has 0.5% w/w
benzene in the liquid phase. Therefore, values of T and its corresponding optimum P along with the
V/F and phase compositions are estimated and tabulated in Table 11.12.
Table 11.12 Results of flashing at different temperature and corresponding optimum pressure.
Liquid-phase
mole fractionsa
Vapour-phase
mole fractionsa
Toluene
%w/w
Benzene
in bottom
product
%w/w
Yield of
bottom
product
0.0540
0.0357
0.49
82.94
0.0119
0.0522
0.0349
0.5
82.37
0.0067
0.0118
0.0497
0.0339
0.49
81.16
0.0067
0.0118
0.0482
0.0332
0.5
80.58
0.202
0.0068
0.0119
0.0468
0.0325
0.5
80.01
23.6
0.2146
0.0067
0.0118
0.0447
0.0317
0.5
78.75
100
28.06
0.2203
0.0068
0.0118
0.0435
0.0311
0.5
78.18
105
33.17
0.2334
0.0067
0.0117
0.0416
0.0303
0.5
76.88
110
39.04
0.239
0.0068
0.0117
0.0406
0.0298
0.5
76.31
T (o C)
Flash
drum
Pressure
(kPa)
V/F
Mole
ratio
Benzene
Toluene
Benzene
70
9.08
0.1728
0.0067
0.0119
75
11.14
0.1786
0.0067
80
13.56
0.1906
85
16.42
0.1964
90
19.75
95
a
Ortho-xylene mole fraction to be found by balance.
Finalising design T and P
High % yield (82.37e82.94) is observed when the flashing temperature is 70e75 C and flashing
pressure is 9e11.5 kPa. We choose design condition of 75 C and 10 kPa as the operating pressure
(vacuum) can be obtained by using steam ejector, followed by condenser and a separator for hydrocarbon and water/condensate. Steam consumption increases substantially at higher vacuum (pressure
below w10 kPa), thus increasing the ejector size/capacity, condenser size (area) and generates more
condensate contaminated with hydrocarbon. One may also consider a condenser cooled by cooling
water for the hydrocarbon vapour exiting the drum. Part of the vapour not condensing therein may be
sucked by the ejector condenser. This would reduce steam consumption at the cost of additional investment for the condenser and cost for its cooling water consumption.
Although a true cost optimisation can be done by considering the heat input requirement through a
feed preheater along with other considerations, we adopt T ¼ 75 C and P ¼ 10 kPa as design operating conditions. The process conditions are marked on the schematic diagram in Fig. 11.17.
11.7 Design illustration e flash distillation
329
V
75°C, 10 kPa
Steam
F
12 m3/hr
10 kPa
75°C
Condensate
L
75°C, 10 kPa
FIGURE 11.17
Schematic showing the design conditions of the flash drum.
Drum design
Feed (F, liquid)
Flow rate
Component
% w/w
MW
r (mt/m )
m /hr
mt/hr
Flow rate
mt mol/hr
B
1.1
78
0.8787
0.132
0.116
0.00149
3
3
T
1.4
92
0.8636
0.173
0.149
0.00162
O-x
97.5
106
0.88
11.695
10.293
0.09710
0.8798
12
10.558
0.10021
100
V/F ¼ 0.1786 mol/mol; V ¼ 0.10021 0.1786 ¼ 0.0179 mt mol/hr.
Product (L, liquid)
Component
% mol/mol
mt mol/hr
mt/hr
m3/hr
B
0.67
5.548 104
0.0433
0.0492
4
T
1.19
9.854 10
0.0907
0.1050
O-x
98.14
0.0812698
8.6145
9.7892
100
0.08281
8.7485
9.9434
rL ¼ 8:7485=9:9434 ¼ 0:8798 mt=m3 ¼ 879:8 kg=m3
mL ¼ 8.7485 mt=hr ¼ 8748.5 kg=hr
330
Chapter 11 Distillation
Vapour T ¼ 75 C; P ¼ 10 KPa
rVBenzene ¼
78 273 10
¼ 2:697 104 mt=m3 ¼ 0:2697 kg=m3
22:4 103 ð273 þ 75Þ 101:3
rVToluene ¼
92 273 10
¼ 3:18 104 mt=m3 ¼ 0:3181 kg=m3
22:4 103 ð273 þ 75Þ 101:3
rVoxylene ¼
106 273 10
¼ 3:665 104 mt=m3 ¼ 0:3665 kg=m3
22:4 103 ð273 þ 75Þ 101:3
Vapour stream (V) at T [ 75 C; P [ 10 kPa
Component
mt mol/hr
mt/hr
m3/hr
rV mt/m3
Benzene
9.352 104
0.0729
270.30
2.697 104
Toluene
6.346 104
0.0584
183.59
3.181 104
0-xylene
0.0158302
1.6782
4578.99
3.665 104
0.0174
1.8095
5032.88
3.595 104
rV ¼ 3.595 x 104 mt=m3 ¼ 0.3595 kg=m3
mV ¼ 1.8095 mt/hr ¼ 1809.5 kg/hr
Separator factor (s)
s ¼ ðmL =mV Þ ðrV =rL Þ1=2
¼ ð8748:5=1809:5Þ ð0:3595=879:8Þ1=2 ¼ 0:098
From Table 11.9 (system constant, SF, for vertical separator with demister pad @ 85% flooding),
SFV ¼ 0:1310 þ
uv;max ¼ SFv ð0:1280 0:1310Þ
ð0:098 0:08Þ ¼ 0:1283
0:02
rl rv 1=2
879:8 0:3595 1=2
¼ 0:1283 m=sec ¼ 6:346 m=sec
0:3595
rv
Inlet nozzle
rmix ¼
mL þ mV
ð8748:5 þ 1809:5Þ
¼ 2:0935 kg=m3
¼
8748:5 1809:5
ðmL =rL þ mV =rV Þ
þ
879:8 0:3595
11.7 Design illustration e flash distillation
For inlet nozzle (from Eqs. 11.39 and 11.40)
(
1=2
umax ¼ 122=rmix ¼
umin
¼
0:6 umax
122=ð2:0935Þ1=2
¼
331
¼ 84:32 m=sec
50:5 m=sec
From Eq. (11.41) ID of nozzle di;nozzle (m) is given by
2
pdi;nozzle
4
umax ¼
10:558
1
2:0935 103 3600
or
di;nozzle ¼
1=2
10:558 4
¼ 0:145 m
2:0935 103 3600 p 84:32
00
We choose 600 NB, schedule 40 steel pipe with inner diameter 6.065 ¼ 154 mm and outer diameter
6.62500 ¼ 168 mm as feed nozzle.
Drum internal diameter
From Eqn. 11.37, dmin , the minimum diameter (m) of the vessel is given by
p 2
1:8095
1
dmin uvap:max ¼
m3 =sec
4
3600
3:595 104
or
dmin ¼
1=2
1:8095 4
¼ 0:53 m ¼ 530 mm
4
3600 3:595 10 p 6:346
We choose an additional cushion of w150 mm for diameter and set d ¼ 700 mm ¼ 0.7 m.
Deciding vessel height and checking for hT =d limits (Refer Fig. 11.16)
hv ¼ h1 þ h2
Feed nozzle od ¼ 168 mm
h1 ¼ 900 mm þ od=2 ¼ 900 þ 168=2 ¼ 984 mm
Minimum acceptable h1 ¼ 1200 mm
Hence, h1 ¼ 1200 mm
h2 ¼ 300 mm þ od=2 ¼ 300 þ 168=2 ¼ 384 mm; say 390 mm
Minimum acceptable h2 is 450 mm. Hence, h2 ¼ 450 mm
Height of vapour space (excluding vessel head) is hv ¼ h1 þ h2 ¼ 1200 þ 450 ¼ 1650 mm.
Residence time of liquid is 3e5 min for vapoureliquid separator.
332
Chapter 11 Distillation
We consider 4 min (240 s)
9:9434 3
m ¼ 0:663 m3
3600
This shall correspond to the normal level at the average of high and low level of liquid. We consider
a level span of 300 mm, and further considering 300 mm above the high level, we locate the inlet
nozzle centre line (see Chapter 17 for additional details).
Depth of liquid filled space (excluding vessel bottom dished end) is
r Liquid holdup ¼ 240 hL ¼ p
0:663
ð0:7Þ2
¼ 1:72 m
4
rhT = d ¼ ðhL þ hV Þ=d ¼ ð1:72 þ 1:68Þ=0:7 ¼ 4:86 < 5
Hence, a vertical vessel is acceptable.
Vapour and liquid outlet nozzles
Typical nozzle velocities for vapour and liquid services are w15 m=sec and 2e3 m/s, respectively.
For vapour exit nozzle based on 15 m/s vapour velocity,
p 2
5032:88
dV;nozzle 15 ¼
4
3600
dV;nozzle ¼ 0:344 m ¼ 344 mm
Closest internal diameter standard nozzle (pipe) is 1400 NB, Schedule 40, with inner diameter ¼
13:37600 ¼ 340 mm f is used as vapour nozzle.
For liquid nozzle based on 2.5 m/s velocity,
p 2
8:7485
d
2:5 ¼
4 L;nozzle
3600
1=2
9:9434 4
dL;nozzle ¼
¼ 0:0375 m ¼ 37:5 mm
p 2:5 3600
We provide a minimum nozzle size of 200 NB, Schedule 40(di ¼ 2:06700 ¼ 52:5 mm f) as liquid
nozzle.
Vessel support and other nozzles for vent, drain, level measurement, temperature sensing and safety
valve mounting are also to be provided as per guidelines provided in Chapter 17. One may use the
information in Chapter 17 for details on instrumentation and other nozzles.
11.8 Batch distillation
Batch distillation, as the name suggests, is a process where the distillation is carried out on batches of
feed. In its simplest form, there is only one stage of vapoureliquid contacting and that involves a
‘charge still’ that may have heating coils or jacket integral to the vessel. The vessel is charged with a
fixed amount of liquid mixture that is to be separated by boiling and subsequent condensation. In some
cases, there can be an external heater through which the still charge is circulated and the heated charge
flashes on return to the still. The vapour leaving the still goes to a condenser from where the condensed
11.8 Batch distillation
333
liquid is collected in the accumulator vessel. Since the distillate gradually gets heavier, it can be
collected at different time intervals as batches of product with the desired composition. For example,
the equilibrium vapour composition corresponding to 50 mol % benzene in liquid (at w1 atm pressure) is about 70 mol %. Therefore, batch distilling a feed mixture of 50:50 mol ratio benzene and
toluene can produce distillate batches with 60% benzene, 55% benzene, etc., collected at different time
intervals for appropriate durations. Different quality of distillates may be collected in different
accumulator vessels. The quality of the distillate is judged from the samples of distillate collected and
also from the temperature of the vapour entering the condenser. This is usually a simple system with a
heated still and a condenser operating around atmospheric pressure. Such a configuration produces
poor separation with either high or low concentrations of light component and involves fairly large
energy expenditure. The performance can be improved by operating the still at a lower pressure but an
operating pressure (Pop) lower than 0.1 kg/cm2 (abs) significantly increases the ejector steam consumption for creating vacuum and the option becomes uneconomical. Redistillation of distillate in
subsequent batches can also be performed to obtain higher distillate purity.
On a different note, in small-scale batch distillation set ups with only the still and condenser,
equivalent number of vapoureliquid contacting stages is slightly more than one. This happens due to
the heat loss from the rising vapour through the equipment wall and its partial condensation providing
reflux that aids the separation. The ASTM D86
distillation test apparatus for light petroleum cuts
thus provides separation closely equivalent to 1.1
Batch distillation with multiple contacting stages
theoretical stages. The vapour condensing in the
neck of the standard ASTM D86 flask creates the
internal liquid reflux.
When the required purity of the product is higher than that attainable with a single stage of contacting or for systems with low relative volatility ða < 3Þ, batch distillation is carried out with multiple
vapoureliquid contacting stages. In this case (Fig. 11.18) the vapour rises through a packed or tray
tower where it meets a counter flowing liquid reflux. Batch distillation columns most commonly
employ sieve trays without downcomer or packed beds. As only a few trays are usually required, low
tray efficiency is not of much concern and sufficient extra trays are provided. Employing higher efficiency trays, e.g., cross flow sieve trays, bubble caps, etc., cost much more for such small scale
applications.
The tower is usually mounted directly on the charge still (Fig. 11.18A) in case of small units. In
other cases the tower is placed next to the still at an appropriate elevation to allow gravity flow of liquid
from the tower bottom back to the still (Fig. 11.18B).
The vapour leaving the tower top enters the condenser through the overhead vapour line. Part of the
condensed overhead stream is diverted back to the column as reflux and the rest is collected in the
accumulator vessel. The reflux usually is a metered flow, typically through a rotameter. In larger plants,
a pump may be used for sending the reflux from the accumulator to the tower top; else it is a gravity
flow, requiring the condenser and the accumulator vessel to be located at an appropriate elevation.
Pressure control in batch distillation is similar to a rectification column and is achieved by throttling
the noncondensable vapour venting from the accumulator top. In case the tower is to be operated under
334
Chapter 11 Distillation
(A)
Cooling
water in
Cooling
water out
Condenser
EQUALISER line
to condenser
shell
Reflex
line
(B)
Condenser
Cooling Water
3-way valve to
control reflux
Distillate
Tray
column
Distillate
Vapour
Packed
column
Steam
Change
still
Condensate
Liquid
Reboiler
Bottoms
Steam
Condensate
Bottoms
FIGURE 11.18
Multistage Batch Distillation (A) Tray column above still, (B) Packed column beside still.
vacuum, the vent is connected often through a surface condenser to the suction of an ‘ejectore
barometric condenser’ arrangement. The surface condenser upstream of the ejector condenses much of
the overhead vapour and reduces the vapour load to the ejector. The residual streams (bottoms) is
usually taken out of the still after the dilatation ends once the still is cooler and safer to drain.
Instrumentation scheme
Instrumentation of the process consists of temperature measurements of the liquid in the still,
vapour entering the condenser and the liquid collected in the accumulator vessel. Pressure is measured
at the top of the still. This needs to be a compound gauge measuring both vacuum and pressure as
condensation of vapour after shutdown may lead to vacuum in the system. The accumulator and the
charge still are provided with level gauge glasses. In small plants these instruments locally indicate the
readings, whereas in large plants there may be telemetry arrangement along with alarms associated
with the process parameters. The charge still heat input should be regulated as this decides the start-up
period and also production rate of distillate. In case of electrical heating the power to the heating
element is regulated. Opening of the control valve in the heating steam supply line is manipulated to
control heat input in case of steam heated still. Sudden increase of input heat may lead to large amount
of vaporisation in the still and carryover of liquid along with distillate vapour. This leads to poorer
11.8 Batch distillation
335
fractionation and needs to be avoided and a steady regulated heating rate in the still is achieved by the
flow control of the circulating heating oil or by pressure control of the heating steam supply.
Batch operation
Batch distillation is an unsteady state operation, i.e., the distillate and still compositions continuously vary with time. The process operates through time cycles of
i. loading of the feed charge in the batch still
ii. heating up/start-up phase e when the process absorbs energy without any distillate being
withdrawn. (Duration: t1)
iii. production run e this is the period during which the distillate is withdrawn. (Duration: t2)
iv. cooling down the still and preparing the equipment for the next batch. (Duration: t3)
Operation without fractionating stages and reflux e single-stage batch distillation
Following the initial inspection of the readiness of equipment the charge is loaded into the still. The
coolant flow in the condenser, which is cooling water in most cases, is started. If the process needs to
be connected to a vacuum system, the same is done and vacuum pulling is done right at the cold state.
If vacuum is pulled later when the still is already heated up, sudden vaporisation and foaming lead to
carryover of liquid with the vapour.
Production run starts as the first drop of liquid falls into the accumulator vessel. During production
run the distillate cut is collected. In case of more than one cut, separate accumulators are used. The still
pressure, if required to be kept at slightly above atmospheric pressure, is regulated by controlled
bleeding of noncondensable gases from the accumulator vessel top. In small set ups there may be a
water seal through which this gas may be bled, limiting the accumulator gauge pressure to the seal
liquid dip head. Such a seal system should also include arrangement to prevent seal-liquid suck-back in
case of vacuum creation in the equipment during cooling down or even otherwise. This is usually
ensured by a liquid trap installed in the line upstream of the seal. The cut specification control is done
by (i) periodic sampling of the liquid from the accumulator and its analysis, (ii) ascertaining the yield
of the cut against previous instructions based on assessment of feed composition. The vapour temperature leaving the still is the dew point corresponding to the instantaneous composition of the
vapour. This temperature is monitored to control the components going to a particular cut of distillate.
Operation of multistage column
The operational procedures of start-up, production and shutdown phases may differ slightly for
different column configurations but in general, the operation follows the following sequence.
Start-up phase
In practice, an empty conventional multistage batch column is started up in the following
sequential steps:
1. The still is charged with the feed to be processed and heat is applied to bring the material to its
boiling (bubble) point temperature.
2. Depending on the heat input, a part of the charge vaporises and the vapour travels upward through
the column internals. Part of the vapour condenses in contact with the cold column and its
internals that get heated in turn. The condensate travels down the column to the still as reflux. As
the tower and internals get hotter, the condensing amount reduces and after a while the vapour
reaches the condenser.
336
Chapter 11 Distillation
3. At this time, the coolant flow to the condenser is started and the liquid condensed starts
accumulating in the reflux drum. Some product may also be collected during this period. The
reflux valve is opened once the liquid level in the reflux drum reaches the normal operating level.
4. If no product is withdrawn in step 3, the column is run under total reflux operation, i.e., the entire
vapour reaching the condenser is condensed and refluxed back. This is continued till a steady
state, evidenced by steady temperatures in the column top and the still, is reached. Alternatively
the operation can be continued till the distillate composition reaches the desired product purity.
Duration of the first step is usually small compared to the overall batch time, whereas the duration
of steps 2e4 is important and in some cases it may take a long time to reach a steady state or the
desired initial distillate composition.
Production phase
Production period starts with withdrawal of distillate product from the reflux drum. Operation in
this period and its duration depends on the required specifications of the product or on the economics
of the process.
Operation in the production phase can be under the following conditions:
(i) Constant distillate composition operation (variable reflux operation): On reaching the required
distillate purity, the start-up period ends. Product take off is started and a constant composition
product is collected by steadily increasing the reflux ratio until a specified amount of distillate
has been collected. During this period the column top temperature is kept constant by
continuously increasing the reflux flow. The operation ends when the reflux ratio has attained
some high value considered to be uneconomic.
(ii) Constant reflux operation: The total reflux start-up period ends with the column reaching its
steady state, i.e., the still and the column top temperatures become steady. During this production
phase, the column operates with a suitably preset fixed reflux ratio so that the distillate purity
from the initial to the end reduces from a high value to a lower value and the collected distillate
with average purity matches the target.
In general, the constant reflux operation is preferred. The pros and cons of each operation is discussed in Section 11.8.1.
(iii) Optimal operation: A third mode of operation is a trade-off between the above two modes. An
optimal reflux policy is chosen so that some objective function is optimised (minimum batch
time, maximum product yield, maximum profit, etc.), subject to constraints (e.g., on product
amount and purity) at the end of the process.
Shutdown
At the end of the production phase, a batch distillation column is shut down in the following
sequence:
1. Heat supply to the column is cut off.
2. Holdup in the column is collected in the still.
3. Condenser holdup may be mixed with the top product or with the still material.
11.8 Batch distillation
337
11.8.1 Design
Choice of the mode of operation is the first step in designing a batch distillation process. Single-stage
distillation leads to maximum recovery of the light component but the concentration of the same in the
distillate is low. Due to the interaction of the rising vapour with the liquid reflux falling down the
column, the rate of change of distillate composition is much slower when the operation is with multiple
stages and reflux. Operation with refluxing requires more energy compared to ‘no reflux’, i.e., singlestage operation. Operation with varying reflux ratio needs highest energy requirement though the latter
permits highest purity of the overhead product. The reflux flow rate (and in turn the reflux ratio) is
manipulated to control the temperature of the vapour to the condenser (and in turn the distillate
composition). The highest fraction of more volatile is also left in the still for varying reflux ratio.
Constant reflux ratio operation is preferred due to its operational simplicity and the operation with
varying reflux ratio to obtain constant distillate composition is selected when the quality requirement
of distillate is very strict.
Batch distillation design problems are usually posed as the feed and product specifications being
specified, along with feed processing rate in terms of quantity per day. Operational constraints like
single/two/three shift operation of the plant may also be specified based on which the size and the
number of batches per day may be decided. The feed charge volume per batch decides the still size
(volume) and is considered while deciding in favour of batch distillation. The batch final volume left in
the still should not be too small so that its practical design considering submergence of the heating
surface is difficult. Also it should not be too large. The designer also decides whether a column with
contacting stages is needed in addition to the vapoureliquid contacting in the still. As already
mentioned, a column is required when the difference in purity of the distillate and the feed is large and
attainment of the desired product purity requires two or more stages. A McCabeeThiele diagram
drawn for the rectification section provides information to design the column. The minimum number
of stages is estimated under total reflux conditions with bottom product composition xB ¼ xF and top
product composition xD . In order to draw a finite quantity of top product, the reflux ratio needs to be
decreased. Alternatively the x-y plot can be altered by selecting a lower operating pressure. However,
this is rarely adopted from cost and safety considerations as discussed in Section 11.2.
The details of the design procedure for a simple batch with no reflux and a batch with column for
both constant reflux and constant top product composition are provided in the following section.
Design equations
Binary system with no reflux: The design for a binary system with no reflux is based on Rayleigh
equation relating the liquid amount (moles) and its composition (mole fraction) in the still at any
instant of time with the instantaneous composition of the vapour generated during differential
distillation.
B
ln ¼
F
ZxB
dx
y x
(11.44)
xF
where B and xB are the amount (in moles) and mole fraction of the more volatile component in the
still at the end of distillation and F and xF are the moles and corresponding composition of the feed
(initial charge). y is the vapour composition in equilibrium with x at any instant of time. For ideal
338
Chapter 11 Distillation
mixtures, y is related to x using relative volatility a, which is often temperature dependent. The
relationship already presented earlier in Eq. 11.11 is
ax
y ¼
1 þ ða 1Þx
Substituting the above expression in Eq. 11.44 gives
1=ða1Þ B
xB
1 xF a=ða1Þ
¼
F
xF
1 xB
(11.45)
Since the distillate becomes progressively less rich in the lighter component, one would be
interested in the mean distillate composition (xDavg ) given by
xF xB
(11.46)
xDavg ¼ xB þ
1 ðB=FÞ
Usually the design inputs are initial charge/Feed (F) and its composition (xF ) and either the
distillate (xDavg ) or the still composition (xB ) at the end. The corresponding outputs are either (xB ) and
B (bottom product composition and amount) or xDavg and D.
Multistage batch distillation of binary system with reflux: The calculation of multistage batch
distillation of binary mixtures is also based on Rayleigh equation with y replaced by the distillate
mole fraction xD
B
ln ¼
F
ZxB
xF
dxB
xD xB
(11.47)
The concentration (xD ) of the distillate depends on vapoureliquid equilibrium or a, separation
efficiency of the column (the number of equilibrium stages N or the number of transfer units NTOG) and
the reflux ratio R.
Mathematically,
xD ¼ f ðxB ; a; N; RÞ
(11.48)
The functional form of Eq. 11.48 depends on the operation, i.e., constant reflux ratio, constant
distillate composition or mixed mode. The reboil duty (Q) and the corresponding design rating would
also be different for each mode of operation. The option selected would dictate the number of theoretical stages (N or NTOG) required for separation. The corresponding vapour and liquid traffic also get
fixed. Calculation of height and diameter of the column additionally require details of the internals
(packing, trays, etc.).
(i) Constant reflux ratio operation: The top product purity in this mode decreases as distillation
proceeds (Fig. 11.19A) and xDavg is the targeted distillate product composition. Therefore, initial
xD has to be higher than the targeted xDavg and distillation would continue even after the
instantaneous xD drops below xDavg. Usually the inputs are N, R and xF and the outputs are D,
xDavg and energy requirement for distillation (Q).
In order to evaluate the aforementioned, a distillate composition (xD1 ) is set and an operating line is
drawn followed by the usual determination of the concentration (xB1 ) in the still by stepping off the
11.8 Batch distillation
339
number of stages (N). Subsequently, another distillate composition (xD2 ) and the corresponding
bottom concentration (xB2 ) is determined similarly.
R The operating lines are parallel (Fig. 11.19A)
. In this way, the relation between xD and xB is
as the reflux ratio R is constant and the slope is Rþ1
determined over the operating
range
and
the
integral
in Eq. 11.47 is solved by evaluating the area
1 under the curve plotted with xD x
on
the
ordinate
and
the actual bottoms composition (xB ) on the
B
abscissa. The area (A) between xF to xB represents the solution to the integral and gives the value of
B. The moles of distillate obtained is
D ¼ F ð1 B = FÞ ¼ F f1 expðAÞg
(11.49)
and the mean distillate concentration (xDavg ) is obtained from the material balance as
xDavg ¼
xF xB ðB=FÞ
1 ðB=FÞ
(11.50)
The amount of vapour (V) generated in the still is
V ¼ D ðR þ 1Þ
(11.51)
Usually the boil-up rate associated with a specific (distillation) system is known from past experience. In case of a new system, the boils up rate is found by dividing the total vapour load by the time
of distillation for only the production run (step iii in batch operation) and the charging time, heat up
time, cooling time and clean up time are not included.
The heat (Q) required for the separation is related to the other variables as
Q
¼ ð1 B = FÞ ðR þ 1Þ
F lF
(11.52)
where lF is the latent heat of vaporisation of the mixture.
(ii) Constant distillate composition operation: In this case the decrease in distillate concentration
(xD ) is avoided by continuously increasing the reflux ratio (R) with time. The relationship
between still concentration (xB ) and the corresponding reflux ratio (R) is determined graphically
on the x-y plot as shown in Fig. 11.19B. xD is located on the 45 degrees line and an initial reflux
ratio (R) and the position of the operating line is specified to satisfy N stages and the
corresponding still concentration (xB ) is noted. In this case, direct integration of Rayleigh’s
equation can be performed to give
xD xF
B ¼ F
(11.53)
xD xB
xF xB
D ¼ F
(11.54)
xD xB
Correspondingly, the energy requirement (Q) which depends on the variable R is
)
ZxB (
Q
ðR þ 1Þ
¼ ðxD xF Þ dxB
F lF
ðxD xB Þ2
xF
(11.55)
340
Chapter 11 Distillation
The term on the right-hand side of Eq. 11.55 is integrated graphically by plotting the still concentration xB on the abscissa and the term R þ 1 2 on the ordinate. The area (A) under the curve
ðxD xB Þ
between xF and xB gives the value of the integral. Thus, the heat requirement Q is found from
Q
¼ ðxD xF Þ A
(11.56)
F lF
It is evident from Eqs. 11.52 and 11.55 that the two operating modes require different quantities of
heat Q to obtain the same D and xD . The optimum energy requirement is expected to be a combination
of the two modes of operation, i.e., combination of distillate concentration decrease and increase in the
reflux ratio.
(B) 0.8
(A)
0.7
1.0
0.6
0.8
1
(0.8,
0.5)
0.5
3
y→
y→
3
4
0.4
1
3
4
0.0
0.3
xB = 0.067
xF = 0.25
0.2
0.4
0.6
x→
R = 0.70
0.4
(0.4,0.4)
2
0.2
(0.512,
0.572)
2
2
0.6
0.2
1,1'
2'
3'
R = 2.8
0.16
0.1
0.8
1.0
0.25
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x→
FIGURE 11.19
McCabeeThiele construction for (A) constant reflux ratio; (B) constant distillate composition.
Multistage batch distillation resembles a fractionator with only the rectification section and is
usually designed assuming negligible holdup in the column and condenser as compared to the receiver
and kettle. The liquid holdup always present in the column can greatly influence both the yield and
purity of the products. Column hold up affects the yield by hindering the sharp decrease of distillate
composition and the off specification intermediate fractions are large. The foregoing analysis ignores
the holdup in the column and the condenser compared to the holdup in the still.
Case of ternary mixtures
Rayleigh equation can also be applied to multicomponent batch distillation. For component i, yi ¼
Ki xi which gives
dLðKi xi Þ ¼ dðLxi Þ
(11.57)
Since the amount of liquid L in the still and its concentration (xi ) change during operation, it is
difficult to evaluate the term dðLxi Þ. In this case, it is advantageous to use component amount (li )
11.8 Batch distillation
341
instead of total liquid amount (L) where the component amount (li ) is defined as li ¼ Lxi , and the
liquid concentrations replaced by xi ¼ ðli =LÞ
This gives
dL 1 dli
1 dlk
¼
¼
L Ki li
Kk lk
(11.58)
For ideal systems with constant relative volatility (aLK ) with reference to the heaviest component k,
dli
dlk
¼ alk
li
lk
On integration
1=aik
li
¼
lfi
lj
lfj
!1=ajk
lk
¼
lfk
(11.59)
where the amount of liquid in the still is L ¼ Sðli Þ, and the concentration of each component in the
still is xi ¼ ðli =LÞ.
The same approach can be applied to multistage distillation of ternary/multicomponent mixtures
but distillate composition (xDi ) replaces equilibrium composition (yi) (similar to multistage distillation of binary system) to give
dB
dxBi
dxBk
¼
¼
B
xDi xBi xDk xBk
(11.60)
In general, determination of distillate composition (xDi ) requires rigorous column simulation and
the results are reliable only if the liquid holdup in the column is much lower than the liquid holdup in
the still. Batch distillation of ternary (or multicomponent) mixtures is preferentially performed with
constant reflux ratio although operation with periodically constant distillate concentration is also
possible.
11.8.2 Design deliverables
a) Configuration
e
e
e
e
e
e
e
Single stage or multistage e number of stages
Refluxing arrangement and reflux ratio e constant reflux/constant reflux ratio or constant
composition of top product
Operating pressure
Initial and final temperature of column top and still
Initial charge and final liquid holdup volume in still
Collection of top product in receivers in case of multiple grades of top product
Heat load for still heating e peak, average, variation with time
b) Equipment dimensions
Charge tank/still size
Volume: The still is chosen to be vertical or horizontal based on considerations same as in flash
distillation. This is already elaborated in Section 11.6.2.
342
Chapter 11 Distillation
Total volume of the still ¼ charge volume þ vapour space, typically 30% of total volume.
Foaming systems are provided with additional volume usually based on experience.
Dimensions: In case of stills with internal heating, the length and diameter of the still are selected
such that the heating element remains conveniently submerged at end of operation. This requires a
prior estimate of the heating surface and the heating element (coil or tubes) assembly size. For systems
with external heater, a circulating pump with adequate head needs to be located appropriately so that
the NPSH available is sufficient. In case of single-stage separation, the vessel must also accommodate
a demister pad typically of SS wire mesh around 100 mm thick to minimise entrainment. The nozzles
are sized based on the same considerations mentioned in Section 11.6.3.
Fractionation column
Internals e packing/trays: Selection is based on the considerations in Chapter 14, Sections 14.2 &
14.4.
Dimensions: Column height has to be sufficient to accommodate packed section, packing support
grid and packing restrainer grid (top) or the desired number of trays (usually sieve tray without
downcomer) as the case may be.
Column diameter is decided from flooding considerations which is a function of flow rates and
transport properties of vapour and liquid. The standard design procedure and correlations for packed
column flooding and the details of tray sizing are mentioned in Chapter 14.
The vapour and liquid flow rates corresponding to which sizing is done and checked depend on the
duration of distillation operation. The sizing is checked for
i) initial phase where vapour density is minimum
ii) end phase where the temperature is maximum
iii) maximum reflux ratio
Condenser and Heater (internal to the still or external) e These are designed as heat exchange
equipment. The external heater may be a shell and tube heat exchanger whose details are provided in
Chapter 4.
Estimation of heat duty for the condenser and the still heater
In either scheme of fixed reflux ratio or fixed top product composition, the total heat supply to the
still (Qstill) needs to be decided based on the batch time available. The duty should include an initial
load to bring the feed charge and the associated hardware to its bubble point (TbubF), (sensible heat)
that should also include the estimated heat loss from the still and the column (Q1) and heat required (Q)
during production run, i.e., boil up from (TbubF) to bubble point of bottoms product (TbubB).
If facility is kept to use a coolant after stopping of the heat input to the still and cool the final holdup
(B) of the still from TbubB to TB, the design of the heat transfer element should also consider this load
Q2 as well in its sizing.
Qstill ¼ Q1 þQ
(11.61)
Q1 ¼ FCpF ðTbubF TF Þ þ mCp ðTbubF TF Þ
(11.62)
where
In the above equation the second term is associated with hardware heating and heat losses are
considered negligible.
11.8 Batch distillation
Zt
Q¼
d
ðBSxBi li Þdt
dt
343
(11.63)
0
A rigorous evaluation of Q should make use of Eq. 11.63 and for quicker estimate Eq. 11.52
or Eq. 11.55 may be used depending upon the mode of operation selected.
Q2 ¼ BCpB ðTbubB TB Þ þ mCp ðTbubB TB Þ
(11.64)
where TB is the final temperature of the bottoms product.
The average cooling water requirement;
mCW ¼
Q2
m3 =hr
t3 CpCW DTcooling
(11.65)
In the above equation t3 ; CpCW and DTcooling are the still cooling time duration, specific heat of
cooling water and temperature range of cooling water, respectively.
Heat transfer coefficient in each stage of operation is different. Exchanger design must be capable
of handling each of these functions.
One may also like to operate by selecting a fixed Qstill based on the still heater heat load capacity/
rating. This is particularly true when electric reboilers with fixed wattage are being used. In such case
the reflux ratio needs to be suitably altered as distillation proceeds. The heating could be by steam
pipes or electrical heating elements which need to remain submerged till the end of the batch. In case
of electrical heating, extra heating elements are included. Say if a bench scale set up requires a total
power of 12 kW that can be served by using 2 kW elements, instead of using six elements, an additional two elements are usually provided. This requires selection of vessel dimensions such that the
liquid holdup at the end of the batch is sufficient to keep all the eight elements completely submerged
with a minimum of 80 mm liquid level above and below the heater section.
The condenser duty (QC) is estimated based on the vapour leaving the top of the column and is
given by
Zt dD
QC ¼
ðhV hL Þdt
dt
(11.66)
0
where hV and hL are the enthalpy values of D at its dew point and bubble point temperature,
respectively.
11.8.3 Design steps
The design steps and calculation procedure are outlined as follows:
1) Decide the operating pressure (Pop ) e Distillation pressure is decided with the same
considerations as design of rectification columns that are detailed in Section 11.4.1.
2) Generate the T-x-y data and x-y plot or find a from vapour pressure data obtained from Antoine
equation or available experimental data.
3) Note the bubble point at xF and dew point at xD . Find yF corresponding to xF .
344
Chapter 11 Distillation
If yF is reasonably more than xD , a single-stage distillation is sufficient. The calculation can follow
the Rayleigh’s equation (Eq. 11.44).
In case yF < xD , reduce Pop to increase yF and check if yF is reasonably more than xD . If Pop needs
to be reduced below 0.1 kg/cm2 (abs), then distillation under vacuum will possibly turn out to be
uneconomic in moderate to large scale operation and more than one stage of fractionation is
required. The stages need to be provided by a packed bed or a plate contactor as shown in
Fig. 11.18.
4) Initial operation: Starting from empty overhead receiver, filling under no reflux till the desired
level in receiver is achieved.
Time taken, ti ¼ Di =V , where V is the boil up rate decided considering the production capacity of
the plant.
Compute xBi bottoms composition at end of receiver filling from
FxF
Fð1 xF Þ
log
¼ a log
(11.67)
Bi ð1 xBi Þ
Bi xBi
and, from component material balance,
Di ¼
FðxF xBi Þ
Bi ðxDi xBi Þ
(11.68)
or
Bi
ln ¼
F
ZxB
xF
1
dxB
¼
a1
xDi xB
ln
ð1 xF ÞxBi
xF ð1 xBi Þ
þ ln
ð1 xF Þ
ð1 xBi Þ
(11.69)
Outputs: Bi , Di , xBi , xDi ;
axBi
xDi is in equilibrium with xBi , i.e., xDi ¼ 1þða1Þx
Bi
5) Selection of the mode of operation viz. (a) constant reflux ratio, (b) constant top product
composition (varying reflux ratio)
a) Operation with constant reflux
Inputs: Bi , Di , xBi , xDi
(i) Find Nmin from
log
Nmin þ 1 ¼
xDi
1 xBi
1 xDi
xBi
log a
(11.70)
and check N > Nmin , for N that has been decided a priori. N can also be computed from Smoker’s
equation, not included here.
11.9 Design illustration e batch distillation
345
(ii) To find Rmin , draw operating line from the point (xDi , xDi ) through the point (xBi ; yBi ) on
equilibrium curve to locate the point ðyint ; 0Þ on the ordinate. Calculate Rmin ¼ ðxD =yint Þ 1.
(iii) Select R in the range 1.5 Rmin < R < 10 Rmin . Larger the R, higher is the vapour boil-up rate and
more is the column diameter and an economic balance may be struck.
(iv) Estimate xDavg , V and Q from Eqs. 11.50e11.52 by replacing F with Bi . The expressions are
xDavg ¼
Bi
¼
ln
B
ZxB
xBi
xBi xB ðB=Bi Þ
; V ¼ DðR þ 1Þ
1 ðB=Bi Þ
dxB
Q
;
¼ ð1 Bi = FÞðR þ 1Þ
xDi xBi FlF
(b) Operation with constant distillate composition (by continuously increasing R)
(i) Initially R is minimum corresponding to liquid composition xBi in still. This is found by trial e
drawing operating lines through (xDi xDi ) intersecting the equilibrium curve and meeting the
ordinate at (yint , 0). On each operating line N stages are constructed starting from (xDi xDi ) and
ending in still composition of xB . The operating line corresponding to still composition of xBi is
chosen and the corresponding yint value is read off the ordinate scale. Calculate
R ¼ ðxD =yint Þ 1
(ii) Find B by integrating Eq. 11.47 after replacing F with Bi
B
ln
¼
Bi
ZxB
xF
dxB
xD xBi
(v) Use Eq. 11.53 through 11.55 to find B, D, Q, and V after replacing F with Bi.
The expressions are
xD xBi
xBi xB
; D ¼ Bi
xD xB
xD xB
Z xB
Q
Rþ1
¼ ðxD xBi Þ
dxB
2
FlF
ðx
xBi
D xBi Þ
B ¼ Bi
and
V ¼ Bi ðxD xBi Þ
Z xB
dxB
xBi
ðxD xBi Þ2 1 R
Rþ1
11.9 Design illustration e batch distillation
Few drums containing ortho-xylene contaminated with toluene (25% mol/mol toluene, 75% mol/mol Oxylene) are available. As much as possible amount of toluene is to be recovered from this material.
Decide on process to recover the toluene. Minimum acceptable purity of toluene-rich phase produced is
40% but this fetches a low selling value. The price improves substantially if the purity is above 55 mole%.
346
Chapter 11 Distillation
Solution 1A: Separation using a simple batch still
Since the charge is small, a batch distillation process is considered. The process involves
inflammable hydrocarbon and so the operating pressure is set to slightly above atmospheric
(¼ 1.1 101.325 ¼ 111.5 kPa) to avoid ingress of air.
P ¼ 111:5 kPa; xD;avg ¼ 0:4; xF ¼ 0:25
Checking the feasibility of using a simple batch still with no column and reflux
Bubble point of the feed calculated at P based on vapour pressure data of the components, gives
Tbub_feed ¼ 136.5 C.
Pure component vapour pressures for toluene and O-xylene at 136.5 C are 200.4 and 81.77 kPa,
respectively.
Relative volatility, a ¼ 200:4=81:77 ¼ 2:45
a xF
Initial composition of vapour leaving the still ¼
¼ 0:449 w ¼ 0:45.
1 þ ða 1Þ xF
Initial composition is higher than 0.4 and hence it is possible to continue the process and obtain
distillate with average composition xD;avg ¼0.4.
Based on Eqs. 11.45 & 11.46:
1=ða1Þ B
xB
1 xF a=ða1Þ
xF ðB=FÞ xB
¼
& xD;avg ¼
F
xF
1 xB
ð1 B=FÞ
Case 1
Case 2
Case 3 (Desired operation)
Case 4
Case 5
Case 6
xB
0.225
0.200
0.175
0.150
0.125
0.100
ðB=FÞ
0.88
0.79
0.67
0.57
0.48
0.39
xD;avg
0.433
0.416
0.400
0.382
0.364
0.346
0.4157
0.3799
0.3420
0.3019
0.2590
0.2140
xD ¼
a xB
1 þ xB ða 1Þ
The desired operation is for xD;avg ¼ 0.4.
At start of distillation, xD ¼ 0.45, equilibrium composition w.r.t. xB ¼ 0:25.
At end of distillation, xD ¼ 0.56, equilibrium composition w.r.t. xB ¼ 0:3420.
Checking for a value at end of operation: Bubble point of B calculated at P at end of operation,
gives Tbub_end ¼ 139.7 C and corresponding value of a ¼ 216:6=89:29 ¼ 2:43. This is not much
different from the value (2.45) used and no revised calculation is required.
Distillate collection starts at still temperature of 136.5 C and ends at 139.7 C.
Recovery of toluene ¼ 100 0:25 ðB=FÞ xB
0:25 0:67 0:175
¼ 53:1%
¼ 100 0:25
ð1 B=FÞ xD;avg
Design of the physical system
This requires information on the initial charge volume and temperature.
Still: A steam coil heated still is envisaged. Its design involves estimation of the charge volume.
The estimated diameter and height must ensure minimum 150 mm liquid depth above the heating coils
at end of operation. The vessel design may be guided by available information in Chapter 17. Heating
coil details are to be based on heat transfer rate with sufficient extra cushion for which Chapter 2 may
be referred to.
11.9 Design illustration e batch distillation
347
Condenser: The condenser is a small shell and tube condenser, cooled with water. Its design can be
carried out using the information in Chapter 4.
Comment: The recovery of 53.1% toluene is rather low, that too with 40% toluene purity. It is
therefore desirable to investigate the option of batch distillation with stages and reflux with around
50% toluene purity. This is illustrated in the following section.
Solution 1B: Batch distillation with constant reflux ratio
The problem is attempted considering batch distillation with stages and constant reflux ratio.
Small-scale distillation would usually employ packed tower for vapoureliquid contacting. Three
theoretical contacting stages in the tower (packed bed) and one stage for the reboiler still is considered.
The x-y diagram for McCabeeThiele construction is drawn for a ¼ 2.45. For xF ¼ 0.25, by trial
and error, the operating line is constructed with total four ideal stages and initial distillate xD ¼ 0.8.
This line passes through (0.8,0.8) and has y-intercept of 0.211[ ¼ 0.8/(R þ 1)]. Hence, R ¼ 2.8.
Since the reflux ratio R remains constant throughout the operation, the operating lines are parallel
to each other. xD reduces from 0.8 as distillation proceeds. Additional operating lines parallel to the
original are drawn arbitrarily that pass through (0.7,0.7), (0.6,0.6), (0.5,0.5), (0.4,0.4) and (0.35,0.35).
In fact it is easy to draw these lines passing through ðxD ; xD Þ and y-intercept values
xD
xD ¼
can be calculated.
¼
Rþ1
2:8 þ 1
For each operating line starting at (xD ; xD ), the xB that would result for four ideal contacting stages
are noted. The value noted corresponding to (0.4,0.4) is ¼ 0.08. The operating lines through (0.8,0.8)
and (0.4,0.4) are only shown in Fig. 11.20, else the figure would get clumsy. In fact it is desirable to
draw each operating line passing through (xD , xD ) on separate x-y diagram and note the corresponding
values of xD and xB . The xD and xB data from the graph is
xD
0.8
0.7
0.6
0.5
0.4
0.35
xB
0.25
0.184
0.140
0.107
0.080
0.067
1
ðxD xB Þ
1.8182
1.9380
2.1739
2.5445
3.1250
3.5336
1.0
0.8
1
0.6
(0.8,
0.8)
y→
2
3
4
0.4
1
0.2
3
4
(0.4,0.4)
2
xB = 0.067
xF = 0.25
0.0
0.2
0.4
0.6
0.8
1.0
x→
FIGURE 11.20
Construction of operating lines for constant reflux ratio operation.
348
Chapter 11 Distillation
A curve of 1/(xD xB ) versus xB is drawn in Fig. 11.21 to tentatively calculate the area under the
curve from xB to xF . As a first trial, xB ¼ 0.067 is considered.
3.6
3.4
3.2
1/ (xD – xB)
3
2.8
2.6
2.4
2.2
2
1.8
0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26
xB
FIGURE 11.21
Plot of 1/(xD xB ) versus xB
Z xF
dxB
¼
ðx
xB Þ
D
xB
Hence, (F/B) ¼ exp(0.4493), i.e., B/F ¼ 0.6381 and
The area under the curve from the graph
xD;avg ¼
Z 0:25
dxB
¼ 0:4493
ðx
xB Þ
D
0:067
xF ðB=FÞ xB
0:25 0:6381 0:067
¼ 0:572, highly acceptable as a product.
¼
1 0:6381
1 ðB=FÞ
Toluene recovery ¼ 100 ð0:25 0:6381 0:067Þ=0:25 ¼ 82:9%
For the distillate; lavg ¼ 0:572 38:06e3 þ ð1 0:572Þ 36.24e3 ¼ 37:28e3 kJ=kg mol
Total heat required for boil up ¼
ðR þ 1Þ ð1 ðB = FÞÞ lavg ¼ 3:8 ð1 0:6381Þ 37:28e3 ¼ 51268 kJ=kg mol charge
Therefore, it is feasible to have a batch distillation unit with three ideal stages in a column,
operating with constant reflux ratio 2.8, and recover about 82.9% toluene with 57.2% mol purity.
However, during operation the trays or packed tower will have a hold up that would drain into the still
increasing toluene content in the final hold up in the still. This may slightly reduce the recovery
percentage. In any case with this basic design scheme, 80% recovery of toluene with 55% purity can
safely be committed.
11.9 Design illustration e batch distillation
349
Solution 1C: Batch distillation with constant distillate composition
The problem is attempted considering batch distillation with stages and constant distillate
composition. Three theoretical contacting stages in the tower (packed bed) and one stage for the
reboiler still are considered.
The constant composition of distillate is considered to be same as in case of 1B, i.e., xD ¼ 0:572 .
This is not much away from the equilibrium vapour composition with feed (xF ¼ 0.25, y ¼ 0:45).
Four ideal stages were considered in 1B when the initial distillate concentration started from 0.8
and gradually fell; in this case only three stages are considered.
The x-y diagram for McCabeeThiele construction is drawn for a ¼ 2.45. The initial operating
line is constructed by trial and error with total three ideal stages starting from xB ¼ 0:25 and
going up to xD ¼ 0:572 by construction of three stages as shown in Fig. 11.19B. From the y-intercept
xD
( ¼ Rþ1
¼ 0.336) of the line the corresponding reflux ratio required is calculated as 0.7016. As
distillation proceeds, reflux ratio needs to be appropriately increased to keep xD ¼ 0:572, and xB
decreases from 0.25. Therefore, several operating lines passing through (0.572, 0.572) are drawn and
from the y-intercept their reflux ratio in each case is found out. xB is found in each case by constructing
three stages on the operating line from (xD ; xD ). Only the initial and another operating line is shown in
Fig. 11.19B that has y-intercept ¼ 0.151, and xB ¼ 0.16 read out from the graph. R ¼ 2.8 based on the
intercept value. This is also considered to be the ending operating condition as the constant reflux ratio
set for the previous case was also 2.8.
ZxF
Calculation of B=F : lnðB = FÞ ¼
xB
dxB
xD xF
0:572 0:25
¼ ln
¼ ln
0:572 0:16
ðxD xB Þ
xD xB
ðB=FÞ ¼ 0:78
% recovery of toluene ¼ 0:78 0:16=0:25 100 ¼ 50
The reboiler total heat load may be found from the expression
Z xB
Q
Rþ1
¼ ðxD xF Þ
dxB
2
Flavg
xF ðxD xF Þ
Observation on the results of this specific problem
(1) Single-stage batch distillation is most inefficient with about 53% toluene recovery of just
acceptable purity of 40% toluene in distillate. This would require minimum investment cost.
(2) Batch distillation with constant distillate composition (w57% purity) is next best as it can be
sold at a higher price. However, in this case the recovery is also low w50%. The distillation may
be continued to further recover toluene but the incremental effect on yield increase would be
lesser and lesser. The investment is more than single stage as two stages of contact in the column
need to be provided.
(3) Batch distillation with constant reflux ratio (w57% distillate purity) produces the same quality
of product that can be sold at a higher price. However, in this case the recovery is much higher
w83%.
350
Chapter 11 Distillation
For final decision a detailed economic analysis needs to be carried out that will include operating
cost and the price differential between 40% purity toluene and >55% purity toluene may become a
governing factor.
Further reading
Nag, A. (2015). Distillation & hydrocarbon processing practices. PennWell Books.
Kister, H. Z., Haas, J. R., Hart, D. R., & Gill, D. R. (1992). Distillation design (Vol. 1). New York: McGraw-Hill.
Smith, B. D. (1963). Design of equilibrium stage processes. McGraw-Hill Companies.
Treybal, R. E. (1980). Mass transfer operations. New York (p. 466).
Brennan, K. (1990). The process engineers pocket handbook (Vol. 2). Houston, Texas: Gulf Publishing Company.
CHAPTER
Adsorption
12
12.1 Introduction
Adsorption is one of the unique mass transfer processes in which component(s) from a fluid, either gas
or liquid adheres to the surface of solid without intimate admixture with the solid atoms. As mentioned
in Chapter 9, the solid on which adsorption occurs, often a porous material of a high specific surface
(m2/g), is referred to as adsorbent while the substance that is adsorbed on the solid surface is termed as
adsorbate or solute. All solids exhibit adsorption to some extent but certain substances exhibit preferential affinity towards specific solutes and can retain higher concentrations of those on their surface.
This results in selective mass transfer and enrichment/separation/fractionation of components from a
liquid solution or a gaseous mixture. Typical applications of liquid adsorption include adsorption of
coloured matter from sugar solutions, petroleum, and vegetable oil; removal of objectionable taste and
odour from potable water; removal of grease from dry cleaning liquids; removal of moisture dissolved
in gasoline and fractionation of mixtures of paraffinic and aromatic hydrocarbons. Gas adsorption is
widely used in industrial drying/dehumidifying air and other gases, removal of objectionable odours
and impurities from industrial gases, recovery of valuable solvent vapour from dilute gaseous mixtures
and fractionation of light hydrocarbons.
In all these operations, the mixture to be separated is brought in contact with an insoluble solid, and
the preferential distribution of the adsorbate on the (solid) adsorbent leads to the desired separation.
Like other mass transfer operations, the contacting arrangement can be stagewise or continuous and
the stagewise operation can be single-stage or multistage in crossflow or countercurrent mode. Since
countercurrent operations are more efficient from the viewpoint of mass transfer, an approach to the
same is achieved in some commercial adsorption processes that comprise an arrangement called
simulated moving bed. MOLEX and PAREX are two such patented processes. Semi continuous mode
of operation with the fluid flowing through a stationary bed of solid is also possible.
12.1.1 Modes of operation
The modes of contact are presented as a classification tree in Fig. 12.1. For the purpose of calculation,
the operation within each category except fixed-bed adsorption can be considered analogous to other
mass transfer operations discussed in this book. For example, single-component adsorption from a
gaseous mixture can be treated analogous to gas absorption where the added insoluble phase is
adsorbent in the present case and liquid solvent in absorption. Single-component adsorption from
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00012-9
Copyright © 2020 Elsevier Inc. All rights reserved.
351
352
Chapter 12 Adsorption
liquid solution performed in batch, semicontinuous, or continuous mode can be treated analogous to
mixer-settler operations of liquid extraction (contact filtration). Gas adsorption for solute removal or
fractionation is usually performed in fluidised beds. The aforementioned analogies are often used to
simplify the design procedure. Fixed-bed adsorption is an unsteady state rate controlled process, not
similar to other mass transfer operations. Therefore, in this Chapter, we first outline the principles and
governing equations for stagewise and continuous contact adsorption and then discuss in detail the
fixed-bed adsorption process and its design.
Adsorption
operation
Stagewise
contacting
Single stage
Continuous
contacting
Multistage
Cross-current
flow
Fixed bed
Moving bed
Fluidised bed
Rotary bed
Counter
current flow
FIGURE 12.1
Classification of adsorption operation based on the mode of contact.
Stagewise operation
Single-stage adsorption for liquids is used for extremely favourable distribution of solute towards
adsorbent. This is often employed to remove taste and odour from water
using powdered activated carbon. For greater economy of adsorbent, the
process is operated in multistage cross current or countercurrent mode
Contact filtration
accomplished by multiple tanks and filters connected in series. Countercurrent operation requires lower amount of adsorbent for the same separation, which is particularly important for expensive adsorbents like
activated carbon. Although the savings are greater for larger number of stages, it is seldom economical
to use more than two stages. A higher number of stages increase the expense of filtration and other
handling costs. If the process needs to be operated in continuous mode as in decolorising petroleum
lubricating oils, the filter press can be substituted by a centrifuge or a continuous rotary filter or the
solid can be allowed to settle when the mixture is passed through a large vessel. Even if counterflow
operation is more efficient and ensures greater adsorbent economy, cross current flow seems to be the
more practical option in small-scale processing of liquids. This is particularly true when the amount of
solution treated in every batch may vary considerably. Cross flow is also preferred when long intervals
between batches may require partially spent adsorbents to be stored. Adsorbents like activated carbon
12.1 Introduction
353
deteriorate on longer storage due to oxidation, polymerisation and other chemical changes. The
operation is usually performed at the highest convenient temperature to reduce viscosity and increase
rate of diffusion and ease the motion of adsorbent particles through the liquid. The faster approach to
equilibrium more than compensates the decrease in equilibrium concentration at the higher temperature. The highest permissible temperature can be close to the boiling point of the liquid provided the
solid can withstand that temperature. Nevertheless, where the adsorption isotherm is strongly affected
by temperature, the operation is best handled at room temperature.
Temperature rise due to adsorption can be ignored when (i) the quantity of solution treated is much
larger compared to the amount adsorbed, (ii) solute is adsorbed much more strongly compared to other
constituents of solution and (iii) adsorbent is insoluble in solution.
The component mass/mole balance can be expressed on solute free concentration basis, i.e., in
terms of Y moles (mass) adsorbed /moles (mass) solute free solvent, and X moles adsorbed/mole solute
free adsorbent.
For single-stage operation, this yields a linear operating curve of slope ðAs =Ls Þ on the X Y
plane, similar to the operating line for absorption.
Ls ðYi Yo Þ ¼ As ðXo Xi Þ
(12.1)
In the above equation, Ls and As are the mass (moles) of solute free solvent and solute free
adsorbent, respectively, and subscripts i and o represent the respective inlet and the outlet
concentration.
For an ideal stage, the adsorbate loading on the adsorbent is in equilibrium with the concentration
of adsorbate in solution at the process temperature. Quite often equilibrium is given by Freundlich
equation q ¼ KF ðpÞ1=Kc or q ¼ KF ðcÞ1=Kc , where p and c represent adsorbate partial pressure (in
case of gas adsorption) and adsorbate concentration (in liquid adsorption) at exit. In this case, the
amount of (fresh) adsorbent required to effect the change in feed concentration in a single ideal stage
(equilibrium contacting) is given by
As
ðY0 Y1 Þ
¼
Ls ðY1 =KF Þ1=Kc
For N stages in crosscurrent flow, the total amount of adsorbent required is
"
#
As
ðYN1 YN Þ
1=Kc ðY0 Y1 Þ ðY1 Y2 Þ
¼ KF
þ
þ :::: þ
Ls
ðY1 Þ1=Kc
ðY2 Þ1=Kc
ðYN Þ1=Kc
(12.2)
(12.3)
While for countercurrent operation with fresh adsorbent, the solute balance for N stages gives
Ls ðY0 YN Þ ¼ As ðX1 Þ
(12.4)
and the adsorbent requirement in the N th stage is
As ðYN1 YN Þ
¼
Ls ðYN =KF Þ1=Kc
(12.5)
354
Chapter 12 Adsorption
In Eqs. 12.2 e 12.5, the subscripts denote the exit concentration from the corresponding stage.
For isothermal operation with fresh adsorbent, the calculation for theoretical stages can be made
using Eq. 12.4. The same is also true for desorption/ regeneration. However, in practice the operation is
adiabatic and the equilibrium relationship changes with stage number due to considerable rise (fall) in
temperature during adsorption (desorption). Under this condition, the calculations are done stagewise
similar to nonisothermal gas absorption or any stage-wise operation.
For N stages of gasesolid contacting, solute balance in line with Eq. 12.4 is
Gs ðY0 YN Þ ¼ As ðX1 XNþ1 Þ
(12.6a)
where Gs and As are the respective flow rates of solute free gas and adsorbent. The enthalpy balance
gives
(12.6b)
Gs ðHG0 HGN Þ ¼ As HS1 HS;Nþ1
where HG is the enthalpy of gas mixture in energy/mass
HG ¼ Cp;g ðtG t0 Þ þ Y Cp;adsorbate ðtG t0 Þ þ lvap;0
(12.7)
and HS is the enthalpy of the solid plus adsorbate in energy/mass adsorbent
HS ¼ Cp;adsorbent ðts t0 Þ þ X Cp;adsorbent;liq ðtA t0 Þ þ DHads
(12.8)
In Eqs. 12.8 and 12.9, enthalpies are expressed with respect to adsorbent, nonadsorbed gas and
adsorbate as liquid, all at base temperature t0 , DHads is the integral heat of adsorption at X and t0 ; lvap;0
is the latent heat of vaporisation of adsorbate at t0 and Cp denotes specific heat of the component
denoted by subscript.
Continuous contact operation
Continuous contact devices can be operated in either continuous or semi continuous mode. In
continuous mode, fluid and solid move continuously at a constant rate (steady-state moving bed
adsorber) with either the solid moving relative to the walls of the container (moving beds) or the
particles remaining stationary relative to the walls (rotary beds). In semi continuous mode, fluid moves
through a stationary bed of solid and the composition changes with time (fixed bed adsorber). The
merits and demerits of fixed and moving bed processes are listed in Table 12.1.
In steady-state moving beds, the solid and the fluid phases move continuously through the
equipment at a constant rate. At any point in the equipment, the composition
of both the phases does not change with time. Use of moving bed is common
for collecting solutes and fractionation of gaseous and liquid mixtures through
Moving beds
adsorption and ion exchange. Since the purpose of these applications is to
achieve separation equivalent to many stages, only countercurrent operation is
considered. Parallel flow may be used when one theoretical stage of contacting
suffices. The major challenges of these equipment are (i) ensuring uniform flow of fluid and solid
particles, (ii) uniform distribution of solid particles in the fluid to minimise channelling and local
irregularities and (iii) continuous entry and removal of solids into the device. Attrition is unavoidable
in moving bed processes and high mechanical (attrition) strength of adsorbent particles in the bed is a
major requirement.
12.1 Introduction
355
Table 12.1 Merits and demerits of fixed and moving beds.
Fixed bed
Moving bed
Advantages
· Simple
inexpensive
· Relatively
· Minimal attrition of adsorbent particles
· Easier to design
adsorbent inventory (regeneration
· Low
immediately after adsorption possible)
· Better heat transfer
Disadvantages
· Difficult to design accurately due to the unsteady nature of · More complex and expensive equipment
process
· Attrition of adsorbent
inventory of expensive adsorbent and
· Large
proportionately large pressure drop for the slow progress
·
·
a
of MTZa
Safety concern for highly porous adsorbents as poor
thermal conductivity may lead to hot spots and fire
hazards, e.g., in case of activated carbon bed with air.
Also, the equilibrium may be adversely affected.
Multiple beds required for continuous operation.
Mass transfer zone (MTZ), elaborated later in the chapter.
For single component adsorption, the computations can be performed using Eq. 12.1
Gs ðYi Yo Þ ¼ As ðXo Xi Þ
which gives a linear operating line of slope As =Gs . The line lies below the equilibrium curve for
adsorption and above it for desorption. Minimum adsorbent requirement is given by the operating line
of maximum slope that touches the equilibrium curve at a point as discussed in Chapter 10 (Section
10.3). Although in practice, the operation is adiabatic and the temperature does not remain constant
except for solute collection from vey dilute liquid solutions, the calculations are usually done assuming
isothermal operation following the design procedure of packed bed discussed in Chapter 10. The
governing equations for gas adsorption are
As dX ¼ Gs dY ¼ KY aP ðY Y Þdz
(12.9)
Which on rearranging gives
ZY1
NtOG ¼
Y0
dY
KY aP
¼
Y Y
Gs
Zhbed
dz
0
(12.10a)
356
Chapter 12 Adsorption
where
HtOG ¼
Gs
KY aP
(12.10b)
Y is the equilibrium composition in the gas corresponding to the adsorbate composition X and
KY aP is the overall gas-phase mass transfer coefficient based on the specific surface area of the solid
particles ðaP Þ.
Rotary beds are employed to combine the advantages of both moving and fixed bed. Several beds
are on a rotating drum (or wheel) that makes each bed to go through cycles of
adsorption and desorption. At specific locations, each bed aligns with the
appropriate inlet and outlet piping connections for adsorption and desorption.
Rotary beds
Most often these beds are partitioned sectors. Recovery of volatile solvent
from air is one of the common applications of rotary bed adsorber.
Fluidised beds are extensively used for recovery of vapours, drying of air with silica gel,
fractionation of light hydrocarbon vapours with carbon, etc. Fluidised beds are
attractive because (i) interparticle heat and mass transfer is high and (ii) when
fully fluidised, its net weight is supported by drag forces due to fluid flow that
Fluidized beds
results in the pressure drop (DP) to be almost independent of flow rate
(Eq. 12.11).
DP
¼ ð1 aÞðrs rf Þg
Lbed
(12.11)
where rs and rf are the density of the solid and fluid, respectively, and a is the bed voidage at the onset
of fluidisation.
12.1.2 Adsorption mechanisms
Bonding of a solute on a solid surface can be physical bonding (Physisorption) or chemical bonding
(Chemisorption). Table 12.2 lists the major differences between the two processes. There may be
situations when bonds of both types may be present. A third mechanism e capillary condensation,
happens in the case of gas adsorption in porous media. This involves localised condensation inside
pores at temperatures above the dew point of the bulk fluid allowing the formation of multiple solute
layers on the surface.
Porous adsorbents with capillaries not too narrow on the molecular scale adsorb by the same
mechanism as nonporous adsorbents for a low relative partial
pressure (partial pressure/vapour pressure). With increasing pressure, multilayer adsorption takes place with adsorbate condensing
Adsorption in Porous media
inside pores and the heat of adsorption similar to the heat of
condensation. This phenomenon termed “capillary condensation”
can be explained by considering the vapour pressure over a curved
surface. At the same temperature, the vapour pressure is lower over a concave surface as compared to a
flat or convex surface. In the narrow capillaries, the adsorbed liquid meniscus is concave. This results
in the vapour condensing at a lower pressure than the vapour pressure over a flat surface. Capillary
condensation causes hysteresis of adsorption equilibrium (Fig. 12.2) in porous adsorbents.
12.1 Introduction
357
Table 12.2 Physisorption versus Chemisorption.
Physisorption
Chemisorption
High enthalpy of adsorption (200e400 kJ/mol)
Reversible
Irreversible
Weak forces of attraction like van der Waals
forces, hydrogen bonding, etc.
Chemical bonding involving orbital overlap and
charge transfer
Multilayer adsorption.
BET isotherm used to model equilibrium.
Generally, monolayer adsorption
Langmuir isotherm used to model equilibrium
Observed at low temperature (higher temperature
reduces surface coverage)
Observed at higher temperature
Not specific
No surface reactions
Highly specific adsorbate-adsorbent pairs
Surface reactions e dissociation, reconstruction,
catalysis possible
p*, Equilibrium partial pressure
Low enthalpy of adsorption (5e50 kJ/mol)
Adsorption
Desorption
q, kg adsorbate/kg adsorbent
FIGURE 12.2
Adsorption isotherm exhibiting hysteresis.
12.1.3 Adsorption equilibrium
Isotherms relating adsorbate loading capacity to adsorbate concentration in the process stream at a
given temperature are the most common form of expressing the equilibrium data. Equilibrium data
governs capital cost to a large extent since adsorption capacity decides the amount of adsorbent
required.
358
Chapter 12 Adsorption
Adsorption isotherms are influenced by:
•
•
•
•
Nature of adsorbent
Cycles of adsorption and desorption which alter adsorbent characteristics possibly due to
progressive changes in the pore structure
Origin and method of preparation of adsorbent
Temperature and relative humidity of the vapour/gas stream
Diffusive characteristics in liquids significantly affect the adsorbent performance, and vapourphase isotherms are more readily available than liquid-phase applications. The designer, however,
needs to judiciously consider the equilibrium relationship in the gas phase since it is affected by
hysteresis as well as loss in adsorption capacity with cycles of regeneration of the adsorbent. It is,
therefore, a common practice to use adsorption isotherms developed from experiments on a pilot scale
before designing industrial adsorbers.
The phenomena of hysteresis observed in gas adsorption is illustrated in Fig. 12.2 which shows that
the equilibrium path followed during adsorption and desorption (from the final
state of adsorption) are different. The desorption (equilibrium) pressure is always
lower than the corresponding adsorption pressure. The phenomenon arises when
Hysteresis
adsorption occurs primarily following the capillary condensation mechanism and
can be attributed to the difference in liquid meniscus shape (curvature) during
adsorption and desorption. Spherical and cylindrical menisci are formed during
adsorption whereas during desorption the menisci are spherical. Hence, desorption isotherm is used to
determine effective pore size. Due to the absence of capillary condensation during liquid-solid
adsorption, liquid adsorption is usually reversible and does not exhibit hysteresis. However, there
may be a loss in capacity with cycles of regeneration that the designer has to consider.
12.2 Packed bed adsorption
Packed beds are widely used with both gas and liquid feeds. Separation in a fixed bed is an unsteady
state rate-controlled process and at a particular axial location within the bed, the conditions vary with
time. At the start of the process, as feed enters the bed, mass transfer occurs near the inlet and concentration of the adsorbent in the fluid phase decreases from inlet value to near-equilibrium concentration over a narrow zone. This portion of the bed is termed the mass transfer zone. With progress
of time, the initial part of the mass transfer zone (MTZ) becomes almost saturated and is unable to
adsorb further solute (equilibrium zone). The “unadsorbed” adsorbate then gets carried further
downstream, and thus, the mass transfer front proceeds in the direction of feed flow while the rear end
of the mass transfer zone gets saturated. The net effect is a forward movement of MTZ, leaving behind
an equilibrium zone saturated with solute. The portion of the bed beyond MTZ is not yet in contact
with the solute and is, therefore, unutilised. It is capable of mass transfer and is termed the active zone.
Thus, at any instant of time, the entire bed can be divided into three zones based on mass
transferdequilibrium zone, mass transfer zone, and active zone, as illustrated in Fig. 12.3A. At any
instant, adsorption is confined to MTZ, and the adsorbent upstream or downstream of MTZ do not
participate in the adsorption process. As the fluid continues to flow, the mass transfer zone (MTZ)
moves downward as a wave (Fig. 12.3B) at a rate usually much slower than the fluid velocity and the
effluent concentration is substantially zero, till MTZ reaches the effluent end of the bed.
12.2 Packed bed adsorption
(A)
Mass
Equilibrium
transfer
zone
zone
Feed
Ci
(B)
Active zone
359
Effluent
1
t1
C/Ci
0
t2
C*
Ci
t3
t4
Distance along bed (z)
Concentration in fluid phase are shown
at time instants t1, t2, t3, t4
FIGURE 12.3
(A) Zones in packed bed during adsorption (at time instant t2); (B) Solute concentration profiles in the fluid
phase with progress of time (c is equilibrium concentration).
12.2.1 Breakthrough curve, breakthrough point, and bed exhaustion
As adsorption in a packed bed continues, adsorbate concentration in bed effluent remains “zero” as
long as the MTZ remains within the bed and has at least an infinitesimally
small active bed in front of it. Beyond this point of time, as the MTZ
moves further downstream and exits the bed, adsorbate starts slipping out
Breakthrough curve
of the bed along with the effluent. This is observed as an increase in the
concentration of adsorbate in the effluent stream with time from “nil” or a
“negligible value.” The, typically “S-shaped,” concentration versus time curve shown in Fig. 12.4 is
called the concentration breakthrough curve.
The heat released during vapour adsorption from a gas mixture is not quickly dissipated due to the
lower thermal conductivity of the gas phase and also the porosity of the adsorbent. This increases the
temperature locally, and a temperature wave similar to the adsorption wave is generated. The rise in
C/Ci
1.0
C/Cex
C/Cb
0
Bed exhaustion
Bed
saturation
Breakthrough
point
Time, t
FIGURE 12.4
Concentration breakthrough curve.
360
Chapter 12 Adsorption
temperature at the fluid outlet can thus be used as a rough indication of breakthrough point.
The temperature rise is relatively small for liquid adsorption as the heat gets more easily dissipated.
The onset of presence of adsorbate in the effluent is the ideal “breakthrough point.” However, in
practice, the effluent stream is inevitably used in a downstream process
and the maximum allowable solute concentration in the stream acceptable
by the said process is the “breakthrough concentration” considered in bed
Breakthrough point
design. Operation beyond the breakthrough concentration renders the
effluent stream unacceptable for the downstream process.
Operation beyond the breakthrough point continuously increases the concentration in the effluent
stream, and finally, the entire bed gets fully “exhausted.” No further adsorption takes place in this condition, and the effluent stream concentration is
close to the feed stream concentration. In practice, the bed is considered
Bed exhaustion
exhausted when the effluent concentration is around 95% of the feed
concentration. One may also note that when some very strongly adsorbed
components are present in feed stream along with a mixture of less strongly
adsorbed components, the effluent concentration may not attain the feed concentration as only the
components that move fast through the bed, are in the breakthrough curve.
Shape of the breakthrough curve strongly depends on
(i) Rate and mechanism of the adsorption process
(ii) Nature of adsorption equilibrium (a flat isotherm indicates a narrow MTZ and a steep
breakthrough curve)
(iii) Fluid velocity; Concentration of adsorbate in feed
(iv) Mass transfer kinetics: fast kinetics implies a steep breakthrough curve while slow kinetics
results in a distended shape.
Slow kinetics may be tackled by increasing cycle time and also by using smaller adsorbent particles, but the designer needs to consider that increased cycle time requires a higher inventory of
adsorbent and smaller particles entail higher pressure drop.
Breakthrough capacity (BC) of a bed is the mass of adsorbate held per unit mass of adsorbent at the
point of breakthrough, and this clearly depends
on the breakthrough concentration (cb,) at
breakthrough time (tb) (Fig. 12.4) considered by
Breakthrough capacity and Saturation capacity
the designer. Similarly, the saturation capacity of
the bed (SC) is the maximum loading of adsorbate when the entire bed is fully saturated and is
known from the equilibrium data/exhaustion point (cex). The monotonically increasing concentration
profile in the mass transfer zone is considered as symmetric around its midpoint, and hence, the
average bed loading in the mass transfer zone of length MTZ is 50% of SC. This leads to the following
relationship for a bed of length L
½L MTZ
MTZ
þ 0:5
BC ¼ SC
(12.12)
L
L
Industrial beds go through cycles of adsorption and regeneration, and some residual solute loading
(RC) remains in the bed after regeneration. Designers incorporate the effect of RC and use working
12.2 Packed bed adsorption
361
capacity WC as a measure of the actual adsorption capacity of the bed. If experimental data is
available, WC may be estimated as
½L MTZ
MTZ
þ 0:5
WC ¼ SC
RC
(12.13)
L
L
In the absence of data WC is taken as a fraction of SC as
WC ¼ SC f
(12.14)
Typical value of f may be 0.85e0.9.
During operation, the adsorption step is terminated slightly before the breakthrough point. This
ensures that the effluent always remains “on-spec.”
In planning new processes, it is best to determine the breakthrough point and breakthrough curve
for a particular system experimentally under conditions as close as possible to the process conditions.
12.2.2 Desorption/regeneration
The saturated adsorbent is either regenerated or disposed off. Disposal may be considered as an option
when (1) adsorbent cost is low, (2) regeneration is very difficult/expensive, (3) nonadsorbed component is a very high value desired product, (4) chemisorption occurs and reversibility is impractical. In
most applications, disposal is uneconomic, and adsorbent is regenerated for reuse either in-situ or in a
separate process. The environmental effect of the disposed adsorbent is also a concern for the designer.
Gas-phase adsorption
q1
Adsorbent loading
Adsorbent loading
Regeneration of gas adsorbers, i.e., the desorption step, involves changes in temperature, adsorbate
partial pressure, or passing a competitively adsorbing component through the bed. The effect of temperature and pressure on equilibrium loading can be understood from Fig. 12.5. Reducing partial
pressure of solute from p1 to p2 reduces equilibrium loading from q1 to q2 (Fig. 12.5A). At constant
partial pressure/concentration of the adsorbate in the gas phase (or concentration in the liquid phase), an
increase in temperature from T1 to T2 decreases the equilibrium loading from q1 to q2 in Fig. 12.6B.
q2
p2
p1
Partial pressure
q1
T1
q2
T2
q3
T2>T1
p2
p1
Partial pressure
FIGURE 12.5
Effect of process variables on adsorption equilibrium for a Type I isotherm: (A) Adsorbate partial pressure
(PSA pathway) (B) Temperature (TSA pathway).
362
Chapter 12 Adsorption
Further reduction of partial pressure from p1 to p2 at temperature T2 reduces the concentration to an even
lower value of q3. In practice such combinations of depressurising and heating is employed for
desorption.
The final choice of the regeneration method is based on technical and economic considerations
(capital and operating cost). A brief description of the processes is provided below, and the general
comparison of the methods along with specific applications is listed in Table 12.3.
In PSA, the partial pressure of adsorbate may be reduced by reducing the total pressure (evacuating
the bed), and also by introducing an inert component
(diluent) through the bed while keeping the total pressure
same. In many practical processes, both are used in
Pressure Swing Adsorption (PSA)
sequence. If the reduction in pressure involves a vacuum, the
process is often called Vacuum Swing Adsorption (VSA).
The use of only a diluent stream for regeneration is not very popular. Since pressure change is a quick
process, the cycle time of PSA systems is low, usually in minutes.
One may also note that PSA (and VSA) can be controlled either by equilibrium or by kinetics
depending on the adsorbent. Both types are important commercially, and a typical example is air
separation. With zeolite as adsorbent, nitrogen is adsorbed more strongly than oxygen, and the
equilibrium controlled separation produces oxygen of almost 96% purity as product. On the other
hand, when using carbon molecular sieves, the equilibrium loading of both nitrogen and oxygen are
close but very high purity (99%) nitrogen is obtained in the effluent, as oxygen, due to its high
diffusivity, gets rapidly adsorbed.
Regeneration in the TSA process is achieved by
increasing the temperature at a constant partial pressure in
the gas phase or concentration in the liquid phase. Since
Temperature Swing Adsorption (TSA)
the strongly adsorbed components have a high heat of
adsorption, an increase in temperature causes a substantial
decrease in their loading. Hot purge gas or steam is almost
always used along with bed heating. The use of purge gas flushes the desorbed component(s) from the
bed and also reduces its partial pressure that aids further desorption. Thermal processes are always
slower, and so TSA processes operate with longer cycle time. This is a major reason for using TSA
virtually exclusively for treating feeds with a low concentration of adsorbate.
Temperature cycling of TSA beds lead to cycles of expansion and contraction that creates stress on
the adsorbent particles and generation of fines that may increase bed pressure drop. Also, accidental
running with high temperature may cause deactivation of bed. Therefore, degradation of adsorbent is a
cause of concern in TSA.
Some adsorbates are difficult to separate by PSA or
TSA. These can be desorbed by displacement with a
more preferentially adsorbed species that can be a gas,
Displacement Purge Adsorption (DPA)
vapour or liquid. The choice of the displacement fluid is
important as a displacement fluid adsorbed too strongly
may be difficult to remove from the adsorbent in the next step. Desorption occurs due to a reduction in
partial pressure (or concentration) of original adsorbate in the fluid phase, as well as competitive
adsorption of the displacing component. Since adsorption and desorption go on simultaneously, the net
heat effect in the bed is small, and this keeps a more or less constant bed temperature throughout the
12.2 Packed bed adsorption
363
Table 12.3 Comparison of the typical regeneration processes.
Method
Salient
characteristics
Typical
processes
Typical
adsorbent
& process
Advantages
Disadvantages
TSA
Suitable for both
gases and
liquids.
Good for
strongly
adsorbed
species.
Desorbate
recovered at
high
concentrations.
Thermal aging
of adsorbent.
Adsorbent
degradation at
very high
temperatures.
Long cycle times
(several hours).
High initial cost
due to heating
arrangement.
Consumes large
energy per unit
adsorbent
quantity.
More complex
control need
skilled personnel
for maintenance.
Always used in
conjunction with
hot gas/steam
purge.
Used virtually
exclusively for
feeds with low
adsorbate
concentration.
Drying of
gases/
organic
vapour.
Drying of
solvents.
Molecular
sieve;
activated
carbon
PSA
Good for weakly
adsorbed species
required in high
purity.
Lower adsorbent
inventory and
smaller size of
adsorbent bed
lower cycle time
Cannot be used
for liquids.
Very low
pressure may be
required.
Mechanical
energy more
expensive than
heat
Operates close to
ambient
temperature.a
Low adsorbent
loading.b
Drying of
gases;
Hydrogen
recovery;
Bulk gas
separation
(air
separation).
Molecular
sieve;
carbon
molecular
sieve;
zeolite.
VSA
Rapid cycling
gives efficient
use of adsorbent.
Desorbate
recovery at low
purity.
Separation
of linear
paraffins.
Molecular
sieve.
Displacement
Isothermal
operation.
Good for
strongly held
species.
Avoids risk of
cracking
reactions during
regeneration
Avoids thermal
aging of
adsorbent.
Product
contamination
by displacement
fluid.
Product
separation and
recovery
necessary.
Separation
of linear
from cyclic
and
branched
paraffins.
Molecular
sieve
Adsorption of
displacement
fluid almost as
strong as
desorption of
adsorbate.
Continued
364
Chapter 12 Adsorption
Table 12.3 Comparison of the typical regeneration processes.dcont’d
Method
Advantages
Disadvantages
Purge gas
stripping
Essentially at
constant T and P.
Simple process.
Little
maintenance.
Cheap (low
capital cost)
Safe.
Only for weakly
adsorbed
species.
High purge flow.
Usually not used
when desorbate
needs to be
recovered.
High operating
cost in large
systems.
Steam
stripping
(combination
of TSA and
displacement)
Same as TSA
and
displacement
Same as TSA
and
displacement
Typical
adsorbent
& process
Salient
characteristics
Typical
processes
For small
capacity systems
(smaller than
3500 m3/hr
approx.).
Relatively uncommon without
thermal swing.
Purging alone suitable for
only weakly adsorbed species.
Waste water
purification;
Solvent
recovery.
Activated
carbon.
a
Typically PSA processes are operated close to ambient temperature since the loading increases as temperature is decreased at a
constant partial pressure.
b
PSA processes are often operated at low adsorbent loading since selectivity among gaseous components is often greatest in
Henry’s law region.
cycle. The displacement purge also flushes the desorbed components out of the bed. The contamination of the products by the displacement fluid is a disadvantage of the process. The cost of further
separation of the contaminated product, if involved, needs to be considered in assessing the overall
economics of the process.
Liquid-phase adsorption
PSA is inapplicable in this case, as the effect of pressure on equilibrium is minimal. Since the equilibrium in the case of liquid-phase adsorption is sensitive to temperature, TSA is used for desorption in
some cases. Hot gas is often used for heating. In these cases, arrangements for bed draining after the
adsorption step and refilling it with liquid are provided.
Table 12.4 lists process features and the feasible regeneration techniques for each. For an assigned
adsorption operation, one needs to identify the relevant features pertaining to the operation and then
note the techniques denoted by Y/N for each. The techniques with N are eliminated, and a process with
Y for all conditions is the best choice. Entries other than Y/N are used to rank processes if more than
one option seems to be feasible for the said operation.
12.2.3 Adsorbent aging
Adsorbent capacity gradually reduces during the working life of adsorbent. It occurs due to multiple
regeneration and results from loss of active surface area. In commercial units, hydrothermal
Table 12.4 Cyclic adsorption process options for various conditions.
Sl.
No.
TSA
b
c
Inert
purge
SMBa
Chromatography
Displacement
PSA
Process conditions
G
1
Liquid feed that can be
completely vaporised
below 200 C
Not
likely
Y
Y
Y
Y
Y
Y
Y
2
Liquid feed that cannot
be fully vaporised below
200 C
N
Y
N
Y
Y
N
N
N
3
Adsorbate concentration
in feed
<3 wt%
Y
Y
Not
likely
May be
Not likely
Y
Not likely
Not likely
4
Adsorbate concentration
in feed
3e10 wt%
Y
N
Y
Y
Y
Y
Y
Y
5
Adsorbate concentration
in feed
>10 wt%
N
N
Y
Y
Y
Y
Y
Y
6
Adsorbate recovery at
high purity->90%e99%
rejection of carrier
Y
Y
Y
Y
Y
Y
Y
Maybed
7
Adsorbate only desorbed
by TSA
Y
Y
N
N
N
N
N
N
8
Practical (cheap,
noncorrosive nontoxic
adsorbate)
Y
Y
N
N
N
Y
Y
Y
9
Displacement or purge
agents not easily
separated from adsorbate
May be
May
be
Not
likely
Not
likely
Not likely
Not likely
Not likely
N
10
Vaporised liquid/Gaseous
feed
Y
N
Y
N
N
Y
Y
Y
a
L
G
SMB e Simulated Moving Bed.
G e Gas-Phase Applications.
c
L eLiquid-Phase Applications.
d
Greater than 10:1 ratio of feed to desorption pressure/vacuum desorption required.
b
L
Only for L
Only for G
366
Chapter 12 Adsorption
deterioration and chemical contamination/fouling are the main causes. The hydrothermal effect due to
water exposure at regeneration temperature results in “collapsed pore structure” and is irreversible.
Contamination occurs when the adsorbent active surface is blocked by direct deposit or by degradation, polymerization, or oxidation of unstable compounds present in the fluid. Although this form of
aging is considered theoretically reversible, in practice, the immobile adsorbent deposits increase at
each regeneration and decrease adsorption capacity. Formation of fines with time, particularly after
each regeneration, also increases bed pressure drop with time.
Longer intervals between regenerations, therefore, allow greater utilization of the available
capacity. This may be done by operating columns in series such that the first column is operated until it
is fully saturated and the second column ensures that the specification is met.
12.2.4 Bed design
Fixed-bed adsorbers can be designed either by the rigorous solution of conservation, transport, and
thermodynamic equations or by experimental breakthrough curve data generated in the laboratory
scale, pilot scale, or industrial scale, and scaling up for the design of the actual column. Data required
for design by rigorous methods is often unavailable, and predictive modeling of heat, mass, and
momentum transfer are resorted to. Accuracy of prediction depends on the availability and reliability
of fundamental data and the validity of the assumptions and approximations to obtain the solution.
These solutions are usually obtained by numerical analysis.
Rigorous methods
Due to the unsteady nature of the adsorption process, the mathematical model is in the form of partial
differential equations. Both energy balance and mass balance equations are to be considered for an
accurate design. However, many fixed-bed designs consider an isothermal operation that is valid for
low concentration of adsorbate and low heat of adsorption. This allows the design to be based on mass
balance only. The fluid phase unsteady-state mass balance for a single adsorbate (from liquid
feedstock) is
v2 c vðucÞ vc
1 a vq
DL 2 þ
þ þ rp
¼0
(12.15)
vz
vz
vt
a
vt
where the first, second, third, and fourth terms represent axial dispersion (DL is axial dispersion
coefficient), convective flow within the bed (u is the interstitial velocity, i.e., the superficial velocity/
void fraction a), accumulation of adsorbate in the fluid phase and rate of adsorption, which is a
function of fluid phase concentration and adsorbent loading.
vq
¼ f ðq; cÞ
(12.16)
vt
The equation is used for gas-phase adsorption by replacing the concentration terms with adsorbate
partial pressure. In that case, a pressure drop equation to estimate total pressure along the bed may be
necessary as it will affect the adsorbate partial pressure. If the bed pressure drop is small compared to
the total pressure, the average bed pressure is considered.
Simultaneous solution of Eqs. (12.15) and (12.16) along with the initial and boundary conditions
generate the transient response of the bed. The shape of the MTZ depends on the shape of the
12.2 Packed bed adsorption
367
equilibrium isotherm, concentration of an absorbable component, hydrodynamics, and choice of a
kinetic model.
The simplest design case considers a single dilute adsorbate in an isothermal process for axially
convected plug flow and no mass transfer resistance. This simplifies Eq. (12.15) to
vc vc
1 a vq
¼0
(12.17)
u þ þ rp
vz vt
a
vt
And the equilibrium isotherm is given by
q ¼ f ðcÞ
(12.18)
An a priori design of cyclic TSA and PSA processes is not very reliable as the mathematical models
of all the steps are not sufficiently detailed to capture the process fully. Much of the input data
necessary are also estimates and mostly tested on small-scale laboratory set up. Hence, industrial
adsorbers are often designed by scale up of pilot plant data using empirical methods.
Empirical or short-cut methods
The usual practice is to design adsorbers based on bench scale isotherm data and pilot plant data on
breakthrough characteristics where the pilot operating characteristics (adsorbate loading rate, detention time, superficial velocity through the bed) are as close as possible to those expected in the scaled
up system. The data on breakthrough characteristics (breakthrough curve and time of breakthrough, %
approach to saturation at breakthrough) corresponding to selected process parameters like surface
loading rate and empty bed contact time generate scale up factors for full-scale design. These are
utilized along with the following assumptions:
(i) isothermal adsorption from dilute feed mixtures
(ii) adsorption isotherm is concave to solution concentration axis
(iii) constant length of MTZ as it travels through the adsorber bed
(iv) height of adsorber bed is large compared to the depth of MTZ
(v) axially dispersed plug flow
(vi) negligible mass transfer resistance
Many industrial adsorbers conform to these assumptions.
Pilot plant design
Many of the practices valid for the scaled up version are valid for the pilot plant as the scale up is based
on similarities in mass transfer. Pilot plant studies are almost always desirable for liquid-phase applications due to the high sensitivity of site-specific parameters like change in pH, etc.
An accurate scale up requires the following considerations:
- Same fluid and adsorbent pair and adsorbent particle size, shape porosity, and other
characteristics.
Similar hydrodynamics and dispersion characteristics as actual bed. Mal-distribution/channelling,
usually more pronounced at lower flow rates should not occur. Designers attempt to minimise
channelling by keeping the ratio of bed diameter (D) to particle diameter (dp) above a minimum
limit. This limit varies from 20 to 30. Also, the minimum ratio of adsorbent bed length (L) to the
368
-
-
Chapter 12 Adsorption
adsorbent particle diameter (dp) is kept at least 100. This is done to allow the mixing of liquid at the
wall and the rest of the bed.
To summarise, the designer respects (D/dp) > 20 to 30, and (L/dp) > 100.
More than one MTZ will occur for all isotherms e favourable, unfavourable or mixed for
multicomponent and/or nonadiabatic systems and it is a conservative approach to consider the
same bed length for small-scale and scaled up process.
Length of the pilot-scale bed needs to cover several mass transfer zone lengths.
It may be noted that breakthrough curves are different for adsorption and desorption (Fig. 12.6).
The designer usually considers the breakthrough curve pertaining to adsorption and verifies the adequacy of design for the desorption step. Identical filtration rate (FR) and empty bed contact time
(EBCT) for full scale and pilot plant ensure similar mass transfer characteristics and superficial velocity (US) defined as volumetric flow rate/cross-sectional area of the empty bed. For scale up with the
same superficial velocity, the cross-sectional area of the actual plant needs to be increased. This can be
either by increasing the number of beds operating in parallel and/or using a single bed with a large
diameter. The first option requires higher capital cost but ensures identical operation of the full-scale
and small-scale unit. On the other hand, the second is a cheaper option but requires proper flow
distribution and redistribution arrangements.
Adsorption
1
2
3
C/Ci
1: Minimal diffusion
2: Moderate diffusion
3: Moderate dispersion and diffusion
3
2
1
Time
2
Desorption (Regeneration)
1
C/Cinit
3
1: Minimal diffusion
2: Moderate diffusion
3: Moderate dispersion and diffusion
3
1
2
Time
FIGURE 12.6
Typical breakthrough curves during adsorption and desorption (ci is the concentration of adsorbate in feed
and cinit is the concentration at the start of the desorption cycle).
12.2 Packed bed adsorption
369
Data/information required for design
- Choice of adsorbent; Equilibrium data, appropriate interaction data for multicomponent systems/
effect of other adsorbates on equilibrium; Selection of desorption method
- Adsorbent-adsorbate kinetics/suitable interaction data for multicomponent systems
- Heat of adsorption at the operating conditions. This may be used to check if the isothermal
operation can be assumed for design
- Hydrodynamic data to estimate pressure gradient
- Property data over the operating range
Typical commercial adsorbents and their applications are listed in Table 12.5. Properties of some
common adsorbents are listed in Table 12.6. Usually, aqueous solutions are treated with freshly prepared activated carbon and organic
liquids (oils) are adsorbed by clays (inorganic adsorbent). OccaCommercial adsorbents
sionally mixed adsorbents are used.
Table 12.5 Commercial adsorbents and their typical applications.
Adsorbent
Application
Zeolite
Separation of normal paraffin (adsorbate)/isoparaffin/aromatics; N2
(adsorbate)/O2; H2O (adsorbate)/ethanol
Adsorption of CO2 from C2H4 natural gas, etc; SO2 from vent streams; sulphur
compounds from organics, natural gas, H2, LPG, etc.; NOx from N2; water from
olefin containing cracked gas, natural gas, air, syn gas, etc.
Liquid bulk separation of n-paraffin/isoparaffin/aromatics/p-xylene (adsorbate)
from o-xylene, m-xylene; detergent-range olefins (adsorbate) from paraffins;
(adsorbate); fructose (adsorbate) from glucose; sulphur compounds (adsorbate)
from organics
Activated carbon
Gas-phase separations of ethylene and organics (adsorbate) from vent streams;
solvent/odours (adsorbate) from air stream;
Removal of organics, oxygenated organics, chlorinated organics, etc. from
water; odour, taste bodies from drinking water; fermentation products from
fermenter effluent; decolorising petroleum fractions, sugar syrup, vegetable oil,
etc.
Alumina
Water removal from organics, oxygenated organics, chlorinated organics, olefin
containing cracked gas, natural gas, air syn gas, etc.
Silica
Water removal from organics, oxygenated organics, chlorinated organics, olefin
containing cracked gas, natural gas, air, syn gas, etc.
Carbon Molecular sieve
Separation of O2 (adsorbate) from N2
370
Chapter 12 Adsorption
Table 12.6 Physical properties of typical commercial adsorbents.
(a) Adsorbent grade activated alumina
Bulk density of 800 kg/m3, pore size 1e7.5 nm, pore volume 0.40 cc/g
Adsorption properties
% w/w
H2O capacity at 4.6 mm Hg, 25 C
7
H2O capacity at 17.5 mm Hg, 25 C
16
capacity at 250 mm Hg, 25 C
2
CO2
(b) Adsorbent grade silica gel
Bulk density of 250 kg/m3, pore size 1e7.5 nm. Pore volume 0.40 cc/g
Adsorption properties
% w/w
H O capacity at 4.6 mm Hg, 25 C
11
H2O capacity at 17.5 mm Hg, 25 C
35
capacity at 250 mm Hg, 25 C
3
capacity at 100 mm Hg, (183 C)
22
capacity at 250 mm Hg, 25 C
17
2
CO2
O2
n-C4
(c) Activated carbon
Physical properties
Liquid-phase application
Vapour-phase application
Wood based
Coal based
Wood based
Coal based
Bulk density (kg/m )
250
500
500
530
Mesh size (Tyler)
100
8þ30
4þ10
6þ14
Ash (%)
7
8
8
4
3
Adsorption properties
% w/w
H O capacity at 4.6 mm Hg, 25 C
11
H2O capacity at 250 mm Hg, 25 C
5e7
2
n-C4
capacity at 250 mm Hg, 25 C
25
(d) Molecular sieve
Zeolite type
Designation
Pore size (nm)
3
Bulk density (kg/m )
A
LiA/KA
NaA
CaA
X
NaX
3A
4A
5A
13X
0.3
0.4
0.5
0.8
670e740
660e720
670e720
610e710
12.2 Packed bed adsorption
371
Table 12.6 Physical properties of typical commercial adsorbents.dcont’d
O2 capacity at 100 mm
Hg, (183 C)
Not adsorbed
22 %w/w
22 %w/w
24 %w/w
H2O capacitya at
4.6 mm Hg, 25 C
20 %w/w
23 %w/w
21 %w/w
25 %w/w
CO2 capacitya at
250 mm Hg, 25 C
Not adsorbed
13 %w/w
15 %w/w
16 %w/w
n-C4 capacitya at
250 mm Hg, 25 C
Not adsorbed
Not adsorbed
10
12
a
% wt on activated pellet.
Particle sizes for adsorbents typically range from 100 or 200 mesh, going up to 6.5 mm nominal
size. The typical size and shape factors of adsorbents are
given in Table 12.7. Bead size is also denoted by screen
analysis as it is difficult to manufacture beads of a uniform
Choice of Particle Shape and Size
size. Higher mass transfer rates are obtained for high specific surface area and lower pressure drop results for larger
shape factor.
Table 12.7 Adsorbent size and shape factors.
Particle shape
Granules
Beads
Pellets
Typical size
100/200 to 4/8 mesh screen analysis
50 mm to 12 mm diameter
16/40e4/8
0. 4e0. 8 mm
Shape factor (j)
0.45e0.65
1
0.63
(DP/L)N jn3; n ¼ 1 for laminar and 2 for turbulent flow
For any application, particle size is selected from the range of commercial adsorbent sizes available
and its effect on (1) mass transfer, (2) pressure drop, (3) axial dispersion. While larger particle size is
favoured from pressure drop and axial
considerations,
they result in a lower rate of mass
h dispersion
i
transfer leading to larger bed size ðkc aÞN dp1.5 to 2.0
. Thus, the optimum size is an economic
balance between operating costs due to pressure drop and capital investment. Typically, 4/6 or 4/10
mesh carbon is selected for gas purification/adsorption, and pressure drop is not a problem. Smaller
particles are chosen for liquid adsorption, e.g., 20/50 mesh carbon (0.3 mm dp .85 mm) is chosen
for water treatment.
In some applications, two sizes of adsorbents are used to trade-off between pressure drop and mass
transfer rate. Larger sized particles are placed at bed inlet since mass transfer effects are more
important towards the effluent end after MTZ terminates.
372
Chapter 12 Adsorption
Spherical particles are preferred over pellets and extrudates as they enable higher flow rates and
taller towers due to
(i) Lower pressure drop per unit volume
(ii) Comparatively uniform and compact loading with little subsequent settling
(iii) Lower attrition and crushing
Few specific gas adsorption applications use the adsorbent slurried in liquid for ease of handling
and sparged vessels used for contacting may operate in semibatch mode (continuous gas flow), concurrent flow, or both. A typical application is adsorption of SO2 from the air-SO2 mixture using
activated carbon slurry in water. It has been shown that the capacity of adsorbent remains unchanged in
dry or in slurry and is much larger than that of liquid solvent alone.
Operating parameters from pilot tests
(a) Loading rate/filtration rate (LR) for liquid-phase applications
Loading rates are usually 80e240 lpm/m2 of bed cross-section. Occasionally high rate up to 400
lpm/m2 may be used.
Bed diameter D is
sffiffiffiffiffiffiffiffiffiffiffiffiffi
4Q
D¼
(12.19)
pðLRÞ
Where Q is the fluid volumetric flow rate through the bed and
LR ¼ LRpilot ¼ ðQ=AÞpilot
(12.20a)
One needs to note that the variables have to be in consistent units and subscript pilot refers to pilot
plant data.
(b) Superficial velocity (Us) for gas-phase applications
The diameter of the adsorber vessel decides the superficial velocity, i.e., the volumetric inflow rate/
cross-sectional area of the empty bed. This influences the MTZ by affecting the kinetics of solute
transfer from the fluid to the adsorbent surface.
ðUs Þ ¼ ðUs Þpilot ¼ ðQ=AÞpilot
(12.20b)
Beds are typically designed with Us between 0.25 and 0.6 m/s. Using a higher velocity results in a
lower diameter. This is often not desirable, the reason is not entailing higher pumping cost but lower
residence time. In case of pressure drop limitation, Us can be lowered up to 0.12 m/s.
(c) Empty bed contact time
Empty bed contact time (EBCT) is related to the contactor dimension as
V
LA
LA
EBCT ¼
¼
¼
Q
Q
Q pilot
(12.21)
and provides an estimate of actual bed depth from pilot plant data where V, L, and A are the volume,
length, and cross-sectional area of the adsorbent bed while the corresponding nomenclatures
12.2 Packed bed adsorption
373
subscripted as “pilot” refer to the pilot plant data. Contact time specified for drying liquids are much
higher than those for drying gases.
In practice, EBCT for liquids depends on the contaminant and is usually 2e20 min. A minimum of
6 min per column is typically used for the treatment of contaminated groundwater using granular
activated carbon. For drying of some liquids, an empty bed contact time of 1 min or less may be
sufficient. EBCT for air dryers vary from 5 to 30 s.
(d) Breakthrough time (tb)
The breakthrough time (tb) is the time required to attain the breakthrough concentration cb, the
maximum limit that can be discarded/tolerated by the downstream process. This often lies between 1%
and 5% of ci, where ci is concentration of adsorbate in the inlet fluid phase.
tb is read from the breakthrough curve generated from pilot test data and usually plotted as c/ci
against t, the elapsed time, starting from c/ci ¼ 0. Also,
Vb
(12.22)
tb ¼
Q pilot
Where Vb is the cumulative fluid volume at breakthrough and Qpilot is the fluid inflow rate in the pilot plant.
The breakthrough time may be considered same for the pilot plant and the scaled up plant when LR
(or Us) and adsorbent bed length are the same.
(e) Fraction of bed utilised (f)
Considering similar bed characteristics in pilot scale and actual plant, fraction of bed utilized (f) for
adsorption is the same for the two cases. This can be estimated as
f ð%Þ ¼
ðAdsÞb
100
ðAdsÞex
(12.23a)
Where (Ads)ex is the mass of adsorbate removed at exhaustion and (Ads)b is the mass of adsorbate
removed at breakthrough.
Typical design value of f as stated above is 85%e90%.
f can also be obtained from the breakthrough curve as the ratio of the area (ABDE) between the
curve and the concentration axis between t ¼ 0 to tb to the area (ABCDE) between the curve and
the concentration axis from t ¼ 0 to t ¼ tex. This is illustrated in Problem 1 (Figure P12.1). Under the
assumption that the breakthrough curve is steep, tex is far from tb, and ci >> cb.
Also, (Ads)ex ¼ Vexci and (Ads)b ¼ Vbci where Vb and Vex are the respective cumulative fluid
volume passed till breakthrough point and exhaustion point (corresponding to cex which is approximately equal to ci) and ci >> cb. This gives,
f ð%Þ ¼
Vb
100
Vex
(12.23b)
(f) Adsorbate loading (qs)
Mass adsorbate removed per unit weight of adsorbent utilised can be approximated as
qs ¼
Q tex ci
Mads
(12.24a)
374
Chapter 12 Adsorption
It may be approximated from pilot plant data using breakthrough information as:
qs ¼
Vex ci
Vpilot f rB
(12.24b)
Where Vpilot, is the volume of adsorbent in pilot column and rB is the adsorbent bulk density.
qs obtained from Eq. (12.24) may be used to cross check tb obtained from pilot plant data. Using the
following expression involving adsorbent usage rate AdUR and the total amount of adsorbent
consumed
tb ¼
Mbed f
AdUR
(12.25)
Where
AdUR ¼ ðQ ci Þ=qs
(12.26)
(Qci) is the adsorbate loading, ci is inlet adsorbate concentration in actual column and qs is
adsorbate loading as obtained from breakthrough curve.
Problem 2 illustrates a more accurate estimation of the aforementioned parameters.
Bed design
Contactor Dimensions: For gas adsorption, typical L is between 0.3 and 1.2 m, depending on the
solute concentration in the gas stream. At times L is selected based on the amount of adsorbent to be
provided by the manufacturer, and EBCT is recalculated to check if it is within permissible limits. The
final selection of contactor dimensions is made from standard vessel dimensions discussed in Chapter
17. Accordingly, the loading rate (LR) or superficial velocity (Us) is modified and checked to lie within
permissible limits.
Cycle time: The cycle time comprises of time required for adsorption (tads) which is equal to the
breakthrough time (tb) obtained from pilot test, desorption time (tdes), and time required for changeovers. Efforts are made to ensure minimum desorption and change over time as this builds in some
cushion in plant capacity and becomes helpful as the adsorbent deteriorates with time. Initially, one
can assume tads ¼ tdes, which gives tcycle ¼ 2tads, but this needs to be checked with the actual time for
desorption required, in case (EBCT) is different for pilot and actual plant due to adoption of standard
contactor dimensions
ðtcycle Þ ¼
ðEBCTÞ
ðtcycle Þpilot
ðEBCTÞpilot
(12.27)
In practice, cycle time for the dryer is specified between 8 and 24 hr.
Mass of adsorbent required (Mads): This may be estimated as follows
Mads ¼ VrB
It may also be obtained from adsorbate loading using Eq. (12.24)
Mads ¼
Q ci tads
qe
(12.28)
12.2 Packed bed adsorption
375
Considering that only a fraction f of the bed is utilised for adsorption, the adsorbent required is
Mbed ¼ Mads =f
In order to provide extra nonadsorbent volume as margin for design and operational uncertainty,
Mbed is further multiplied by a safety factor SF to give
Mbed ¼
Mads
ðSFÞ
f
(12.29)
Typically SF is taken as 1.2e2.5. It depends on the designer’s experience with similar systems as
well as the reliability of the data used in the specific design.
Volume of fluid treated/change out period
Vf ¼ Vb ¼ Qtb
(12.30)
Pressure drop
Pressure drop is of extreme importance in fixed-bed adsorber design. The processing rate can be
limited by pressure drop as excessive pressure drop results in bed compaction or lifting and very lowpressure drop results in uneven distribution and channeling. Nevertheless, most adsorption plants
operate with a small pressure drop across the adsorbent bed to keep power costs low because large
particles are used whenever possible and velocity is also typically low to approach equilibrium between fluid and adsorbent. Typical pressure drop through a vapour-phase carbon bed is 8e35 cm of
water column per m of bed.
Table 12.8 provides the pressure drop guidelines for spherical, granular or extruded adsorbent with
1.5 dp 6 where dp is the nominal particle size (mm).
Table 12.8 Pressure Drop Guidelines for gaseous and liquid services for spherical,
granular, or extruded adsorbent with 1.5 £ dp (mm) £ 6.
Pressure drop range (cm WC/m bed depth)
Bed characteristics
Gas flowing
Liquid flowing
Uneven distribution and channelling
<2.5
<0.2
Upflow or downflow operation
2.5e45
2e45
Downflow operation only (upflow will
result in bed lifting)
45e22500
45e2250
Bed compaction
>22500
>2250
376
Chapter 12 Adsorption
Bed pressure drop is a function of process fluid properties, adsorbent characteristics, and vessel
dimension. It is usually estimated by Ergun Equation for both gases and liquids.
Dp a3 dp;eff rf 150ð1 aÞ
¼
þ 1:75
L ð1 aÞG2f
Rep
(12.31)
Where ðDp=LÞ is the pressure gradient in Pa/m of adsorbent bed, Gf is superficial mass flux in kg/
(s$m2), rf is process fluid density (kg/m3) and a is bed void fraction. Rep, the particle Reynolds number
d Gf
is defined as Rep ¼ p;eff
m , dp,eff is the effective diameter of the particles (m), i.e., the diameter of a
f
sphere of same surface to volume ratio as the adsorbent particles which is not usually equal to the
nominal particle size and is given by dp;eff ¼ 6 ð1aÞ
ap j , where ap$is the specific surface area (particle
external area/volume, m2/m3) of the particle and j is the particle shape factor (1.0 for beads, 0.91 for
pellets and 0.86 for flakes).
It is important to note that
(1) The constants in Ergun Equation are obtained for specific packings and the equation may not be
strictly valid for adsorption columns packed with granular or pellet form of particles.
(2) The correlation has been obtained for steady-state flow conditions and one needs to be careful
while applying them to situations when velocity rapidly changes with time, e.g., in pressurisation
and depressurisation steps of PSA process
(3) The highest pressure drop is likely to occur during the regeneration step since the fluid is at its
highest temperature and/or lowest pressure in this step. It is therefore important to perform
pressure drop analysis for each step in the cyclic operation of a fixed-bed adsorber.
(4) The pressure drop is often high in low-pressure gas-phase applications like vent gas cleaning and
solvent recovery due to low density and high velocity of the fluid. Under this condition, shallow
adsorption beds (low L/D ratio) may lead to lower pressure drop. However, adsorption beds with
low aspect ratio often result in flow mal-distribution and may require flow distribution systems
like manifolds, baffles, and screens, which may add to the pressure drop and offset the advantage
gained. Due to this, granular rather than powder adsorbents are used. Use of specially designed
adsorbent, such as trilobe and monolith, also assists in keeping pressure drop low in low-pressure
gas-phase applications.
(5) For situations where superficial velocity rapidly changes with length as in bulk separation
processes (air separation), a summation of pressure gradient along the incremental length is
necessary to obtain an accurate estimate of pressure drop.
Bed configuration and mode of operation
Total feed flow rate, allowable pressure drop, length of MTZ, method of adsorbent regeneration, and
capital investment are the factors that determine the number and arrangement of fixed beds. In order to
achieve a steady flow of product, the simplest arrangement requires two columns operated simultaneously e one in adsorption and the other in regeneration mode. Regeneration is done when the MTZ
approaches the bed outlet, i.e., most of the bed is saturated. However, this is possible only when the
breakthrough curve is steep, and the first column can be operated safely until the breakthrough point to
discharge effluent substantially free of solute. In this case, the influent stream is diverted to the second
column, and the first is set for regeneration.
12.2 Packed bed adsorption
377
When the breakthrough curve is relatively flat so that a substantial amount of adsorbent remains
unsaturated at the breakpoint, the gas flows through the second adsorber in series with the first until the
adsorbent in the first column is almost entirely saturated, but a breakthrough is not allowed in the lag
adsorber. The first bed is then sent for regeneration, and the influent stream is passed through the
second bed which now becomes the lead vessel and a freshly regenerated third adsorber in series is
now the lag bed. Thus, in practice, more than two beds are often used, which introduces the need for
complex piping and valve arrangements together with a control system. While multiple beds in series
are preferred for a long MTZ, a series-parallel combination of multiple beds is a likely choice for high
flow rates and large MTZ lengths.
Multiple beds in parallel is used for a relatively high flow rate and a short MTZ length to substitute
a single large vessel difficult to ship and operate. Usually, the beds are identical, and the feed is split
equally among them, and the product streams are subsequently rejoined. It is desirable to have a
separate regeneration system for each bed to enable independent flow.
Usually, flow through a packed bed is in the vertical direction, and a proper flow distribution is
ensured by providing adequate plenum space above and below the packed bed. The same effect can be
achieved by employing perforated baffle plates, and placing the inlet and outlet nozzles symmetrically.
Details on the flow distributor can be found in Chapter 14.
Fixed-bed adsorbers are commonly vertical cylindrical vessels. Such an orientation ensures
symmetric fluid distribution and is opted for Q < 1.2 m3/s. A typical bed for water treatment may use
filter blocks at the bottom covered by smaller sized particles (commonly ceramic and gravels) and have
sand as the uppermost layer.
When large volumes need to be treated by small amounts of adsorbent, the pressure drop becomes
excessive except for shallow beds. Under such conditions, a horizontal bed with vertical flow is
preferred. A shallow bed in a horizontal vessel is also selected for low-pressure gas systems like vent
stream clean up and recovery of solvent vapour where low density and large velocity of the gas stream
causes a high-pressure drop. However, in the horizontal configuration, since settling/bed movement is
inevitable, there is always a tendency for fluid to bypass the adsorbent. At times, the challenges
involved in uniform flow distribution often offset the savings in pressure drop.
In vapour-phase adsorption, the flow direction is usually upward during adsorption to accommodate some bed expansion. During desorption, (usually the limiting step), the flow is in the downward
direction as allowable velocities are greater for crushing than lifting. In temperature swing, keeping the
desorption flow countercurrent to adsorption leads to the lowest residual loading.
The critical parameter for upflow at high flow rates is bed lifting. This occurs at the onset of
fluidisation where the pressure drop is expressed as
Dp
¼ ð1 aÞðrs rf Þg
(12.32)
L
The critical consideration for downflow is bed crushing which occurs when the summation of
pressure drop and bed weight exceeds the compressive pressure for crushing.
While gas adsorption operates in upflow mode, downflow operation is generally preferred for liquid
streams. If all the adsorption stages involve liquid, the design considerations are similar to gas phase
adsorption. However, when the regeneration step of a liquid-phase adsorbent involves a vapour, a fill
378
Chapter 12 Adsorption
(upflow) and a drain step (downflow) is necessary. It is preferable to refill the adsorbent bed in upflow
for an easier displacement of gases and vapours and prevention of maldistribution in the subsequent
adsorption step. Refilling should be done for sufficient length of time to ensure complete removal of
the gas pockets; otherwise, products in the adsorption step may be contaminated, causing excessive
bed lift. The design of the drain is critical to ensure uniform exit of the mass transfer zone from the
column. A minimum of 30 min should be provided for thorough draining, and even after careful
drainage, the liquid holdup can be 40 cc/100 g adsorbent. The drain may also be used to introduce
backwash liquid, and in that case, it should ensure uniform distribution of liquid across the entire bed
cross-section. Backwashing is the process of reversing flow through a bed to dislodge material trapped
in pores or attached to media. It is essential for liquid streams containing suspended solids. In this case,
downflow with backwashing capabilities is the best option, and the column is provided with a
20%e50% bed expansion allowance for adsorbent backwashing before the contactor is put in service.
It not only removes solid accumulation but also reduces microbial growth and pressure drop due to
fouling of the bed. Sand filters in water service are typical with backwashing facility. Upflow
adsorption is preferred for liquids containing suspended solids as the bed, in this case, does not act as a
filter and gets plugged by deposited solid. Downflow mode is also not preferred if the equipment is
susceptible to biological fouling. The design of an adsorption system for the liquid phase should thus
include the contactor as well as accessories, such as distributor, bed support, drain, and backwash
equipment.
Generally, adsorption is performed at the temperature and pressure of the inlet fluid. In case options
are available, the lowest temperature and the highest pressure (for gases) is selected to maximise the
adsorptive load. If a gaseous feed contains a condensable vapour component, the temperature (pressure) needs to be high (low) enough to prevent condensation inside the bed. However, for PSA, the
adsorption pressure is decided from economics e larger swings lead to better adsorption but consume
more compressive power.
12.3 Design illustration
These illustrate only the steps of bed design that includes adsorbent quantity, breakthrough time, bed
orientation, bed dimensions, and operating conditions. The reader should follow Chapters 14 and 17 to
arrive at the details of the adsorber vessel.
3
Problem 1. An adsorber is to be designed for air decontamination. This air stream (w200 m /hr, 1 atm,
20 C) contains acetone (MW ¼ 58) vapour (0.13 mol/m3) from a pharmaceutical process. Maximum
limit of acetone concentration in the treated air is 0.004 mol/m3.
Solution
Step 1: Literature survey and selection of adsorbent.
Brosillon, Manero, and Foussard (Enviro. Sci. Technol., 2001, 35, 3571e3575) reported column
adsorption experiments for acetone removal from air using Zeolite adsorbent. The same adsorbent is
considered for design and the experimental data is treated as pilot plant data. Reported experimental
details for the plant are e
12.3 Design illustration
379
Adsorbent: Silicalite, a commercial zeolite having MFI structure as trilobe particles.
1 mm
External area
1180 m2/m3
Lobe height
5 mm
Pellet porosity
0.5
Particle density
1143 kg/m3
Tortuosity
4
Si to Al ratio
47 to 70
Lobe diameter
10
10 10
Pore diameter
m
3
Particle diameter for pressure drop estimation, dp,effective ¼ 4 10
m
Adsorption column
Bed volume
1L
Bed height
0.2 m
Temperature
298 K
Superficial velocity
0.29 m/s
Bed porosity
0.4
Bed density
4
Inlet air humidity
0
Si to Al ratio
700 kg/m3
Feed:
0.13 mol/m3 acetone mixed in air at 1 atm, 20 C.
mfeed ¼ 1.825 105 kg/(m.s) is taken for air as acetone concentration is small.
rfeed ¼ 1.20175 kg/m3, calculated from feed composition, temperature and pressure.
MWacetone ¼ 58, MWair ¼ 28.8
Humidity of air nearly “zero.”
Breakthrough curve obtained experimentally is as shown below e
1.0
E
D
0.97
C
0.8
Area ABCEA = 40.18
0.6
C/Ci
Area ABDEA = 26.98
f = 26.98/40.18 = 0.67
0.4
0.2
0.031
A
0
0
B
20
81.5
28.3
40
60
80
100
120
time (min)
FIGURE P12.1
Concentration breakthrough curve and estimation of bed fraction (f) utilized.
380
Chapter 12 Adsorption
Step 2: Experimental conditions, breakthrough, and bed exhaustion.
Superficial velocity in bed, Us,pilot ¼ 0.29 m/s
In this problem, with notations used in the chapter text,
ci ¼ 0.013, cb ¼ 0.004, cb/ci ¼ 0.0308.
We assume bed exhaustion at cex/ci ¼ 0.97, i.e., cex ¼ 0.1261.
From the breakthrough curve, the breakthrough time and the bed exhaustion time are read as
tb ¼ 28.3 and tex ¼ 81.5 min. In fact, the numerical data available in the paper has been used for more
accurate interpolation.
Summary of the data pertaining to the pilot plant experiments:
Lpilot ¼ 0.2 m, Vpilot ¼ 1000 cm3 ¼ 1 L ¼ 1 103 m3, Qpilot ¼ 2 m3/hr ¼ 5.556 104 m3/s
EBCTpilot ¼ Vpilot/Qpilot ¼ 1.8 s
Step 3: Design calculations
Qplant ¼ 200 m3/hr ¼ 5.556 102 m3/s
Fraction of bed utilised up to breakthrough e
f¼
ðShaded area in the breakthrough plot from t ¼ 0 to tb ¼ 28:3 minÞ
¼ 26:98=40:18 ¼ 0:67
ðShaded area in the breakthrough plot from t ¼ 0 to tex ¼ 81:5 minÞ
Adsorbate transfer rate in pilot plant per unit total bed volume.
¼ Qpilot (cicb)/Vpilot ¼ 2 (0.13 0.004)/1 ¼ 0.252 mol/(hr. liter bed)
Since 67% of the bed gets utilised, adsorbate transfer rate in pilot plant per unit bed volume
utilized,
¼ Qpilot (cicb)/f ¼ 0.252/0.67 ¼ 0.376 mol/(hr. litre bed)
Adsorbate transfer rate in plant.
¼ Qplant (cicb) ¼ 200 (0.130.004) ¼ 25.2 mol/hr
Adsorbent loading per litre of bed volume utilized.
¼ 0.376 tb ¼ 0.376 28.3/60 ¼ 0.1773 mol per litre bed.
Considering tcycle ¼ 8 hr, tads ¼ 4 hr,
Adsorbate transfer in plant during tads ¼ 4 25.2 ¼ 100.8 mol.
Therefore, bed volume that gets utilised in the plant ¼ 100.8/0.1773 ¼ 568.5 L.
A safety factor SF ¼ 1.3 is considered as the pilot plant data used is for fresh adsorbent and the
scaled up plant will use regenerated adsorbent in cycles. This takes care of inefficient regeneration as
well as adsorbent ageing.
Adsorbent volume in plant for utilisation up to breakthrough ¼ 1.3568.5 ¼ 738.8 L.
Total adsorbent volume to be provided in plant ¼ 1.3 568.5/f ¼ 738.8/0.67 ¼ 1103 L.
Mass of adsorbent to be provided in the plant ¼ 1103 700/1000 ¼ 772 kg.
Finding Dplant and Lplant
L/D to lie between 3 and 4, and hence, assumed Lplant/Dplant ¼ 3.
rðp = 4Þ ðDplant Þ2 ð3 Dplant Þ ¼ 1:103 m3
12.3 Design illustration
381
Dplant ¼ 0.78 m and Lplant ¼ 2.34 m. The diameter lies in the typical range of 0.3e1.2 m for gas
service.
1
Superficial velocity in plant Us;plant ¼ ð200 =3600Þ ¼ 0:12 m/s.
ðp=4Þ ð0:78Þ2
The above is less than 0. 29 m/s (Us,pilot), and hence, OK.
Checking for (L /dp,effective) > 100: this is obviously met. The other limit of Dplant / dp,effective is met
too.
Checking for adequate EBCT: This is required to ensure sufficient time of contact for the desired
rate of solute transfer.
EBCTplant ¼ Vplant =Qplant ¼
1103 103
¼ 19:9 s
ð200=3600Þ
EBCTplant is more than EBCTpilot (¼1.8 s). It is also comparable with 30 s, which is a typical limit
for a well-designed air drier.
Other performance parameters
Feed processed per cycle ¼ Qplant tads ¼ 2004 ¼ 800 m3 at 1 atm, 20 C
Adsorbate in bed before regeneration ¼ 800 (0.13 0.004)58 ¼ 5865 g
Rep ¼ (dp,effective Us,plant rfeed)/mfeed ¼ (4 103 0.12 1.20175)/1.825 105 ¼ 31.61,
this satisfies the 20e40 limit.
Orientation: Vertical, since the feed flow rate is below 1.2 m3/s.
The adsorbent bed shall be sandwiched between two beds of 6 mm f ceramic balls, each 150 mm
deep, to ensure uniform flow distribution and bed stability. This would make the total bed length
2 0.15 þ 1.34 ¼ 1.64 m.
Bed pressure drop is given by Eq. (12.31).
Rep ¼ 31.61; a ¼ 0.4; dp,eff ¼ 4103m; rf ¼ 1.20175 kg/m3, and
Gf ¼ rf Us,plant ¼ 1.20175 0.12 ¼ 0.14421 kg/(m2$s).
L ¼ 1.34 þ 0.3 ¼ 1.64 m, the pressure drop (Dp/L) in the larger size ceramic balls of 0.3 m total
depth will be lower than that in the adsorbent bed. Hence, using L ¼ 1.64 m for pressure is a conservative (lower) estimate.
Dp/L ¼ 496.1 Pa/m and Dp ¼ 1.64 496.1 ¼ 813.6 Pa.
Bed pressure drop Dp (813.6 Pa) is small compared to the total pressure (1 atm ¼ 101.3 103 Pa),
and hence, the consideration of the design pressure of 1 atm is OK. The pressure drop at inlet nozzle,
outlet nozzle, and distributor (if provided) is also added to the bed drop. The said components are to be
sized/designed so that the total pressure drop, including all components, remains low compared to
1 atm.
Design output summary
Adsorbent bed
Adsorbent: Zeolite adsorbent, trilobe particle shape, 4 mm effective particle diameter.
Amount of adsorbent in bed: 1103 L (772 kg)
Length: 1640 mm of adsorbent packing including 2 150 mm of 6 mm diameter ceramic balls
upstream and downstream.
382
Chapter 12 Adsorption
Diameter: 780 mm f.
Bed orientation: vertical.
Operation
Feed rate: 200 m3/hr, at 1 atm, 20 C
Cycle time: 8 hr, Adsorption time per cycle: 4 hr.
EBCT for the adsorbent bed 19.9 s.
Cumulative volume of feed processed per cycle 800 m3, at 1 atm, 20 C.
Bed pressure drop: 813.6 Pa, including ceramic ball packed depth but excluding pressure drop in
inlet and outlet nozzles, and distributor, if provided.
3
Problem 2. A 200 m /day stream of wastewater containing 200 mg/L of total organic carbon (TOC)
needs to be treated to less than 10 mg/L TOC content. Design the adsorption column based on a
column (9.5 cm diameter. 175 cm long, 60 L /hr inlet flow rate) study with a cheap 8þ20 mesh
(0.841e2.38 mm) coal-based adsorbent (Ref. Table 12.6) having bulk density 500 kg/m3. Cumulative
volume processed up to breakthrough and bed exhaustion are: Vb,pilot ¼ 8500 L; Vex,pilot ¼ 9600 L.
Solution
Data
ci ¼ 200 mg/L; cb ¼ 10 mg/L;
Dpilot ¼ 9.5 cm, Lpilot ¼ 175 cm.
2 Vpilot ¼ ðp =4Þ 9:5 102 175 102 ¼ 0:012404 m3 ¼ 12.404 L.
Vb,pilot ¼ 8500 L; Vex,pilot ¼ 9600 L; Qpilot ¼ 60 L/hr ¼ 1 L/min;
tb,pilot ¼ Vb/Qpilot ¼ 8500/1 ¼ 8500 min; tex,pilot ¼ Vex/Qpilot ¼ 9600/1 ¼ 9600 min
Qplant ¼ 200 m3/day ¼ 200 103/(24 60) ¼ 138.9 lpm ¼ 0.1389 m3/min
Particles: 20/8 mesh, i.e., 0.841e2.38 mm, j ¼ 1, assumed as the particles are small.
Average particle size, dp ¼ (0.841 þ 2.38)/2 ¼ 1.60 mm;
Since the feed is dilute, we take density and viscosity same as water at 27 C, i.e.,
rf ¼ 0.9965 g/cc ¼ 996.5 kg/m3; mf ¼ 0.8591103 Pa s.
Qpilot
1
¼
¼ 141:08 lpm/m2, this is within the typical
LRpilot ¼
2
2
ðp=4Þ ðDpilot Þ
ðp=4Þ ð9:5 102 Þ
limits of 80 and 240.
Keeping the same LR, scaled up plant cross-section,
Aplant ¼ Qplant =LR ¼ 138:89=141:08 ¼ 0:9845 m2
rDplant ¼ ðAplant 4=pÞ1=2 ¼ ð0:9845 4=pÞ1=2 ¼ 1:12 m
EBCTpilot ¼ Vpilot =Qpilot ¼ 12:404=1 ¼ 12:404 min
EBCTplant is kept the same as pilot scale to ensure that the scaled up plant adsorbate transfer rate is
close to that in the pilot scale. This is between 6 and 20 min, the range for liquid-phase adsorption in an
industrial scale.
Based on EBCTplant ¼ 12.404 min.
Lplant ¼
EBCTplant Qplant
ðp=4Þ ðDplant Þ
2
¼
12:404 138:9 103
ðp=4Þ ð1:12Þ2
¼ 1:75 m
12.3 Design illustration
383
Vplant ¼ EBCTplant Qplant ¼ 12:404 138:9 103 ¼ 1:723 m3
Assuming symmetric breakthrough curve in its rising zone in pilot plant, the adsorbate transfer rate
may be estimated as: Adsorbate transfer from tb to tex ¼ (Vex Vb) (cb þ ci)/2.
A conservative estimate of adsorbate transfer rate in pilot plant is based on effluent concentration
always close to cb.
rAdsorbate transfer (from t ¼ 0 to tb) ¼ Vb(ci cb)
f ¼
¼
Adsorbate transfer from t ¼ 0 to tb
Adsorbate transfer from t ¼ 0 to tex
Vb ðci cb Þ
8500 ð200 10Þ
¼ 0:93
¼
Vb ðci cb Þ þ ðVex Vb Þ ðci þ cb Þ=2 8500 ð200 10Þ þ ð9600 8500Þ ð200 þ 10Þ=2
In a real plant, there are fluid distribution problems and f is usually between 0.85 and 0.9. Hence,
we assume, f ¼ 0.87 for the scaled up plant as a conservative estimate for design.
Adsorbent loading in the utilised portion of pilot plant bed at breakthrough, based on f ¼ 0.93,
Vb;pilot ðci cb Þ 8500 ð200 10Þ
¼ 139887 mg=L
¼
12:414 0:93
Vpilot f
Same loading is assumed in the plant, i.e., qs,plant ¼ 139887 mg/L of the utilised portion of bed at
breakthrough.
Such a bed is expected to be run continuously for 5 days or more, and hence, assumed e
tads,plant ¼ 4 days.
Adsorbate transfer during this period
qs;pilot ¼
¼ tads;plant Qplant ðci cb Þ ¼ 4 200 103 ð200 10Þ ¼ 152 106 mg
r Utilized bed volume in the plant bed at breakthrough ¼ (152 106)/139887 ¼ 1086.6 L.
Considering f ¼ 0.87, total bed volume ¼ 1086.6/0.87 ¼ 1249 L.
Considering a safety factor, SF ¼ 1.5, total bed volume, ¼ 1.5 1249 ¼ 1873.5 L.
This bed volume is little above the bed volume estimated earlier considering EBCT, and is,
therefore, OK.
Reestimation of Dplant and Lplant based on L/D ¼ 3 for the adsorbent packed bed
Vplant;revised ¼ ðp = 4Þ ðDplant Þ2 ð3 Dplant Þ ¼ 1:8735 m3 ;
Dplant, revised ¼ 0.93 m, Lplant, revised ¼ 30.93 ¼ 2.79 m, say 2.8 m.
rFinal dimensions
Dplant, revised ¼ 0.93 m, Lplant, revised ¼ 2.8 m, Vplant;revised ¼ ðp =4Þ ðDplant Þ2 Lplant ¼ 1:9 m3
Qplant
138:9
LR ¼
¼
¼ 204:5 lpm/m2, well within limit of 240.
2
ðp=4Þ ðDplant Þ
ðp=4Þ ð0:93Þ2
Mass of adsorbent in bed, Mads ¼ Vplant, revised rbulk ¼ 1.9 500 ¼ 950 kg.
0:87 1:9 103 139887
¼ 6:1, say 6 days. This is higher than
Breakthrough time of plant ¼
200 103 ð200 10Þ
the original assumed value but is reasonable.
384
Chapter 12 Adsorption
Us;plant ¼
Rep ¼
Qplant
200=ð24 60 60Þ
¼ 3:41 103 m=s
2 ¼
ðp=4Þ ð0:93Þ2
ðp=4Þ Dplant;revised
dp;effective Us;plant rfeed 1:6 103 3:41 103 996:5
¼
¼ 6:32
0:8591 103
mfeed
Bed orientation, support, pressure drop, etc.
Orientation: Vertical.
The 930 mm f adsorbent bed shall be sandwiched between two beds of 4 mm f gravel, each
150 mm deep, to ensure even flow distribution and bed stability. This would make the total packed bed
length 2.8 þ 0.3 ¼ 3.1 m.
Bed pressure drop is given by 2
Dp ð1 aÞGf
150ð1 aÞ
¼ 3
þ 1:75
L
Rep
a dp;eff rf
Rep ¼ 6.32;
a ¼ 0.4 e although this data is not provided, the voidage is expected to be close to 0.4 as the ratio
of bed diameter to particle diameter increase beyond 15, which is true in this case.
dp,eff ¼ 1.6103m; rf ¼ 996.5 kg/m3, and
Gf ¼ rf Us;plant ¼ 996:5 3:41 103 ¼ 3:4 kg= m2 $ s ;
L ¼ 3.1 m, the pressure drop (Dp/L) in the larger size gravel of 0.3 m total depth will be lower than
that in the adsorbent bed. Hence, using L ¼ 3.1m for pressure is a conservative (lower) estimate.
rDp
L ¼ 1087 Pa/m and Dp ¼ 3.11087 ¼ 3370 Pa.
Bed pressure drop Dp (3370 Pa) is small enough. The inlet nozzle, outlet nozzle, and the distributor
(if provided) pressure drop is also added to the bed pressure drop to obtain the total pressure drop
across the adsorber vessel. The said components are to be sized/designed so that the total pressure drop
is within the allowable limit. Typical maximum limit for similar applications is w0.5e0.7 atm, and
there is sufficient margin for adequate sizing of the nozzles.
Design output summary
Adsorbent: Coal-based adsorbent particles, 8 þ20 mesh.
Amount of adsorbent in bed: 1900 L (950 kg)
Length: 2800 mm of adsorbent packing between 2 150 mm of 4 mm diameter gravel.
Diameter: 930 mm.
Bed orientation: vertical, downflow during adsorption.
Pressure drop: 3370 Pa.
Further reading
Crittenden, B., & John Thomas, W. (1998). Adsorption technology and design (1st ed.). Elsevier.
Treybal, R. E. (1980). Mass-transfer operations (3rd ed.). New York: McGraw-Hill.
CHAPTER
Extraction
13
13.1 Introduction
Liquideliquid extraction (LLE), also termed as solvent extraction, is a separation process where
component(s) from a solution is recovered by the addition of a second immiscible liquid (solvent)
which has a greater affinity for the component(s) to be recovered. As mentioned in Chapter 9, the
solution left after extraction is termed raffinate and the solvent-rich phase containing the solute is
termed extract. Similar to other mass transfer operations, the process is carried out by bringing the feed
solution and solvent into intimate contact for a sufficient length of time to ensure maximum solute
transfer and subsequently, allowing the phases to separate, generally by gravity. Compared to absorption and distillation, liquid-liquid phase separation is more difficult and slow since the density
difference between the phases is not large. Centrifugal force is used for phase separation in case of
closer density of the liquid phases. The solute (desired product) is then recovered from the solvent
usually by distillation and the solvent is recycled along with fresh makeup solvent to compensate for
the losses.
Extraction processes therefore always require additional steps to recover and recycle the solvent
and the operating and capital cost of solvent recovery is usually higher as compared to the extraction
step. Therefore, extraction is opted as a separation process usually when other mass transfer operations
namely distillation is (a) infeasible or (b) expensive or (c) requires complex sequencing and when
opted, it is important to consider the solvent recovery aspect at the design stage itself.
The conditions under which extraction is preferred include the following:
(i) Solution of components with close relative volatility, e.g., separation of acetic acid from
aqueous solution using methyl tertiary-butyl ether (MTBE) as solvent which can be evaporated
easily to recover the acid. Extraction of aromatic compounds from lube oil vacuum distillation
cuts using solvents like phenol, furfural, n-methyl pyrrolidone (NMP) is a standard practice.
(ii) Azeotropic mixtures particularly when the azeotrope cannot be split by adding a third
component or a change in the operating pressure does not influence the volatility of one
component more than the other. Typical examples include separation of tetrahydrofuran,
pyridine and formic acid from water or separation of dichloromethane or ethyl acetate from
ethanol.
(iii) Heat-sensitive products encountered in food, pharmaceutical and green chemistry biomolecules
namely vitamins, penicillin, flavours and fragrances as well as certain aldehydes and organic
acids in chemical industries.
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00013-0
Copyright © 2020 Elsevier Inc. All rights reserved.
385
386
Chapter 13 Extraction
(iv) Nonvolatile metal ions (precious or rare earth metals) in an aqueous solution by addition of an
organic solvent, e.g., separation of copper/iron, nickel/cobalt or chromium/vanadium. In most
cases, one of the ions forms a chelate complex in the organic phase, while the other remains in
the aqueous solution.
(v) Nonvolatile organic compounds (higher boiling point than water) from aqueous effluents, e.g.,
removal of phenols, cresols, aniline or other aromatic derivatives from industrial waste water,
removal of organic compounds during oxidation of organic products, production of
caprolactam, etc. In such cases, a low boiling point solvent with a higher concentration of solute
makes extraction economically more feasible than distillation. For separation of high molecular
weight fatty acids from vegetable oils, vacuum distillation is more expensive and the preferred
option is extraction using liquid propane as solvent.
13.2 Extractor types and selection
The classification of extractors based on different criteria is presented in Fig. 13.1. These are classified
based on (a) the mode of contacting of the two liquid phases and (b) the nature of solvent. Extractors
may use a single solvent, thus forming ternary systems or systems equivalent to ternary systems where
two components are to be separated by addition of the third component. A mixed solvent system
employs a solvent solution of at least two components where the solubility relationship cannot be
reduced to an equivalent ternary system. Double solvents are used for fractional extraction where the
solution to be separated is distributed between two immiscible solvents, thus comprising a fourcomponent system. In this chapter, we limit our treatment only to extraction with single solvents.
13.2.1 Extractor types
Similar to other fluidefluid operations, the two phases can be either in continuous contact, separated only at
the end of the operation, or be contacted in stages, i.e., contacted and separated sequentially where the
number of contacts constitutes the number of stages (Fig. 13.2). In an ideal stage, the two liquids are
assumed to attain equilibrium during each contact. In continuous contact, equilibrium is not normally
achieved. Both types of equipment with continuous or stagewise contacting can be operated continuously.
Stagewise contact
Flow arrangements of the different contacting schemes along with the associated solvent recovery
sections are shown in Fig. 13.2. Simple case of a single stage of contacting with sections for solvent
recovery (SR) from extract and raffinate streams is shown Fig. 13.2A. In multistage cases, the fluids
can be in cross or countercurrent flow. In cross flow, raffinate is contacted repeatedly with fresh solvent
(Fig. 13.2B). This is generally uneconomical for large commercial processes and is used in laboratories to generate equilibrium data and to demonstrate feasibility of solute removal to low residual
concentration. Countercurrent operation (Fig. 13.2C) requires less solvent for same feed rate, solvent
Extractor
Continuous
(Countercurrent
flow)
Mode of
contact
Discrete
(Stagewise)
Mixersettler
Cross flow
Multistage
Spray
column
Countercurr
ent flow
Countercurr
ent flow
with reflux
Packed
column
Centrifugal
extractor
Sieve tray
Wetted wall
column
Agitated
tower
Karr column
FIGURE 13.1
Classification of extractor types.
Scheibel
column
Single
solvent
RDC
Double
solvent
Pulsed
column
Mixed
solvent
13.2 Extractor types and selection
Single stage
Static tower
Nature of
solvent
system
387
388
Chapter 13 Extraction
and raffinate composition, forms less amount of extract solution and achieves higher solute concentration in extract. Thus, similar to other mass transfer operations, countercurrent operation is the
preferred option. The improvement is less significant for five or more number of stages. Typical stage
efficiency is 75%e100% and in most industrial plants, the reduced efficiency is due to incomplete
separation (settling) of phases rather than due to inadequate mixing. Continuous countercurrent
operation with multiple contacting can be supplemented with a reflux arrangement to enhance recovery. In this case, the extract and raffinate are in countercurrent flow through the cascade of stages
with feed solution entering at an intermediate stage and solvent introduced at one end. Reflux may be
provided at both ends of the cascade as shown in Fig. 13.2D or only at one end corresponding to the
enriching or stripping end of distillation. In some columns, the two end temperatures are sometimes
maintained at different values to alter the equilibrium in favour of a purer stream. Temperature control
is achieved by a pump back reflux/circulating reflux appropriately located close to one end of the
tower. Extraction towers for aromatics from lubricating oil stocks often employ this.
While single-stage contact (Fig. 13.2A) can be treated analogous to flash distillation, countercurrent multiple contact is akin to gas absorption and its operation with reflux is analogous to rectification. The fundamental balance equations of the analogous mass transfer operation are similar to the
different stagewise operations and the design equations formulated therein can be used, rewritten in
terms of flow rates and composition of raffinate (R) and extract (E). However, the equilibrium relationships are more complex due to the mutual solubility of the two liquid phases. As a result,
simplifying assumptions like constant molar flow rate and linear equilibrium and operating curves are
not directly applicable. Stagewise contacts generally take place in mixer settlers, the details and design
of which is discussed in Section 13.5.
Continuous contact
Continuous contacting devices have gained importance with the increased application of extraction in
petrochemical and chemical industries processing high volumetric flow rates. These towers contain an
equivalent of several stages where the two fluids flow countercurrent to each other. In centrifugal
extractors, centrifugal force is used for phase separation and is opted for closer density of the extract
and raffinate phase. The lighter liquid is introduced from the tower bottom and the heavier phase from
the top. Either of the phases can be the dispersed phase, depending upon the proportion of the two
phases, interfacial tension and relative viscosity. Usually one liquid is pumped through the equipment
and that fixes the maximum velocity of the second liquid (flooding condition). In all commercially
important towers, the interfacial area is in the form of droplets where one or both liquids are dispersed
by flow through nozzles, orifices, screens, packings, etc., or by agitation. One liquid flowing as a film
over a surface while in contact with the second liquid may occur over part of the equipment when the
tower internals are preferentially wetted by the dispersed phase.
Continuous contact is effected in vertical static or agitated towers. Static towers are opted for low to
medium interfacial tension (10e15 dyne/cm) when only a few theoretical stages are required. Packed
13.2 Extractor types and selection
(A)
R
F
S
SR
389
R'
E'
E
SR
SE
SR
Recycled S
Smakeup
∑E
(B)
E2
E1
F
R1
1
2
S1
SE
R'
EN
RN-1
R2
E'
SR
N
RN
SR
SN ∑S
S2
SR
Smakeup
(C)
F(R0)
R1
E'
SR
1
R2
RN-1
E3
EN
E2
SR
N
2
E1
RN
S(EN+1)
R'
SR
Smakeup
SE
(D)
SE
E1
SR
E' R0
PE'
E2 Ee
1
R1 R
Ee+f
e
e-1
Re
Ef
Ef+t
f
Rf-1
F
Rf
Et
Rt-1
Et+f
t
EN
EN+1
N
Rt
RN-1
SM
R N RN
PR
SR
Smakeup
SR
N'
PR'
FIGURE 13.2
Stagewise contacting configurations with solvent recovery. (A) Single stage, (B) crosscurrent multiple stage,
(C) countercurrent multiple stage and (D) countercurrent multiple stage with extract and raffinate reflux.
Nomenclature used in Fig. 13.2: SR, solvent recovery unit; SM, solvent mixer unit; F, feed solution; S, solvent;
R, raffinate; E, extract; subscripts on individual streams denote stage numbers from which the stream exits;
R 0 , solvent-free raffinate after solvent recovery unit; E 0 , solvent-free extract; SR , recovered solvent from
raffinate; SE , recovered solvent from extract; Smakeup , makeup solvent; PR , saturated raffinate product; PE ,
saturated extract product; f,e,t, feed stage, typical enriching and a typical stripping stage. SR denotes section
of plant for solvent recovery.
390
Chapter 13 Extraction
towers with random or structured packings and sieve plate towers with or without downcomers are
commonly used. Spray columns are not very common in industries and are used for rapid irreversible
chemical reactions like neutralisation of waste acids. Wetted wall columns are rarely used. Their only
advantage is that they do not have any internals. Bubble caps generally display low capacity and low
tray efficiency and so are not used for extraction process.
Agitated towers are more economical when more than two to three theoretical stages are required
and interfacial tension is moderate to high. The different types of agitated towers are Karr tower,
Scheibel tower, pulsed tower and Rotating Disc Contactor. In each of these, some form of motion is
imparted to the liquid contents for enhancing capacity and mass transfer rate. The motion also provides
an additional parameter for operational optimisation, albeit at an increased capital cost. Pulsing during
flow can be achieved in both packed and sieve plate towers by connecting the fluid space to a
reciprocating plunger pump, bellows pump or high pressure air pulse. Pulsing in plate towers is shown
in Fig. 13.3A. The rapid oscillatory motion of short amplitude imparted to the fluid increases mass
transfer efficiency and improves radial distribution but there is a small reduction in throughput. In Karr
reciprocating plate tower, the sieve trays are imparted an up and down motion. Scheibel tower operates
as a series of mixer-settler units where each unit has a rotating turbine agitator to disperse droplets. The
droplets coalesce while passing into the outer settling zone as shown in Fig. 13.3B. Rotary disc
contactors (Fig. 13.3C) are divided into compartments by horizontal doughnut-shaped or annular
baffles and within each compartment, agitation is provided by the rotating motion of a centrally located
horizontal disk. Generally the disk is smooth and flat with diameter less than the opening in the
stationary baffle.
13.2.2 Contactor selection
A suitable contactor for a given extraction process is selected based on (A) liquid physical properties
namely density difference and interfacial tension and (B) difficulty of separation denoted by the
number of theoretical stages (NTS) to achieve the desired raffinate and extract composition. A preliminary guideline suggests the following:
(i) Mixer-settler batteries for high NTS (2.5 NTS 9) and easy phase separation.
(ii) Static columns for easy separation with low NTS.
(iii) Centrifugal contactor for difficult phase separation and relatively low NTS.
(iv) Agitated columns (with reciprocating, rotating, pulsing devices) for moderate ease of phase
separation and high NTS (1.5e9).
Other considerations guiding contactor selection can be obtained from Table 13.1 that summarises
the limitations and advantages of the commonly used extractors.
13.2 Extractor types and selection
(A)
391
Lighter
phase
Heavier
phase
Compressed air
Timer
controlled
valves
Air
Liquid
Lighter
phase
Air Bleed
Interface
control
Interface
Heavier
phase
(B)
(C)
Roter
Lighter
phase
Heavier
phase
Mixing region
Settling region
Baffle
Turbine
impellor
Shaft
Lighter
phase
Heavier
phase
Fixed/stator
baffles
Rotating
disc(s)
h
Lighter
phase
Interface
Interface
control
Heavier
phase
Lighter
phase
DS
Dr
D
Interface
Interface
control
Heavier
phase
FIGURE 13.3
Agitated extractors with the heavier phase dispersed. (A) Pulsed extractor; (B) Scheibel tower and (C) Rotary
disc contactor.
392
Chapter 13 Extraction
Table 13.1 Advantages and limitations of common extractors.
Equipment
Advantages
Limitations
General applications
a
Mixer settler
Large flow
Intense mixing promotes
mass transfer
Less headroom
Rapid restart but does
not reach steady state
quickly
Low capital cost
Long residence time ,
large floor space, not
very easy to scale-up,
cannot tolerate solids,
higher holdup volume,
low throughput, large
solvent inventory and
losses
Metal industries
Spray extraction tower
Cheap
Simple to construct
Easy to clean
Trouble-free operation
High throughput
High HETP (3e6 m)
Rarely used
Adopted for rapid
irreversible chemical
reactions like
neutralisation of waste
acids
Packed extraction tower
High throughput
Easy operation and
maintenance (no moving
parts)
Simple operation even at
high temperature and
pressure conditions
Can handle corrosive
liquids by proper choice
of packing materials
Not suitable for fouling
service. Although more
efficient than spray
tower, backmixing
results in a higher HETP
compared to pulsed and
mechanically agitated
towers
Extensively used in
solvent refining of
lubricating oils, removal
of hydrogen sulphide
from petroleum fraction,
sweetening of naphtha,
removal of phenols from
ammoniacal liquor,
solvent refining of
vegetable oils and
chemical recovery in
synthetic organic
chemical industries
(operation generally
limited to
Dr > 30 50 kg/m3,
0:5 a 5,
s < 10 dyne/cm and
NTS 10)
Sieve tray tower
High capacity
Good efficiency
(minimum backmixing)
Affected by changes in
wetting characteristics
Refining,
petrochemicals
Centrifugal extractor
Short residence time
Low headspace
Moderate floor space
Easy to scale-up
Low holdup volume
Corrosive fluids
Moderate capital cost
High throughput
Rapid restart and
reaches steady state
quickly
Cannot tolerate solids
High-speed device
require maintenance
Susceptible to fouling
and plugging due to
small clearance
Pharmaceutical industry
especially for low
density difference
between phases
13.2 Extractor types and selection
393
Table 13.1 Advantages and limitations of common extractors.dcont’d
Equipment
Advantages
Limitations
General applications
Pulsed towers
Reliable
High throughput
Provides an additional
parameter for
operational optimisation
Can tolerate solids
Low floor space but
useful for liquids of high
interfacial tension
(30e40 dyne/cm).
Not easy to scale-up
High capital cost
Large building
headroom
Limited stages due to
backmixing
Limited diameter/height
due to pulse energy
required
Best suited for nuclear
applications due to lack
of seal
Suited for corrosive
applications
Karr reciprocating plate
towers
Highest capacity
Good efficiency
Good turndown capacity
(4:1)
More uniform droplet
size
High capital cost
Chemicals,
petrochemicals, refining
Pharmaceutical (for
difficult systems which
emulsify and/or flood
early, fouling
applications, solids
precipitation)
Scheibel tower
High efficiency
More uniform droplet
size coupled with better
phase separation
Good turndown capacity
(4:1)
High flexibility
High capital cost
Not recommended for
highly fouling/high
emulsifying systems
Chemicals,
petrochemicals,
refining,
Pharmaceutical (best
suited when many stages
required or for low mass
transfer rates)
Rotating disc contactor
Suitable for viscous
materials (>100 cp)
Suitable for fouling
materials
High capital cost
Limited efficiency (axial
backmixing)
Furfural extraction of
lubricating oil
Desulphurisation of
gasoline
Phenol recovery of
wastewater (suitable for
mass transfer controlled
systems with few
theoretical stages)
Advantageous for processes with relatively slow reactions; a is the volume phase ratio of dispersed to continuous phase; s is the
interfacial tension.
a
394
Chapter 13 Extraction
13.3 Choice of solvent
Solvent selection is based on equilibrium, economic and environmental considerations. To understand
equilibrium considerations, the ternary plot (Fig. 13.4A) that has been discussed in Chapter 9 is
considered for extraction of solute B from a feed solution of A and B using pure solvent S. The feed
solution has xB;F % B corresponding to point F on the AB arm of the diagram. Addition of adequate
amount of pure solvent S shall result in mixture composition corresponding to point M. M shifts towards S with addition of more and more amount of solvent and its locus is the line joining the feed and
the solvent composition, i.e., line SF. M inside the two-phase envelope splits into the extract (E) and
raffinate (R) phases with composition of B as yB and xB in E and R respectively. yB ; xB correspond to
the two ends of the tie line passing through M. Now on considering complete recovery of solvent from
the phases E and R, the solvent-free extract and raffinate compositions would be the points E0 and R0 on
line AB. A larger distance between points E0 and R0 denotes a greater extent of separation by extraction.
One may note that this also depends on the proportion of feed and solvent mixed as the composition of
E0 and R0 denotes the composition of the extract and raffinate streams obtainable by using the solvent
amount that leads to the feed plus solvent composition at M. The above information is used in selection
of solvent. The same construction is done for solvents being compared, keeping the composition same
for point M, i.e., the ratio of feed and solvent is kept same. The composition of E0 and R0 is compared
and the solvent with a larger distance between E0 and R0 is a better solvent with higher selectivity.
Fig. 13.4B shows the equilibrium curves xPz and x0 P0 z0 for two solvents where the former has a
larger envelope of immiscibility. The line joining the feed composition xB;F with the pure solvent
vertex denotes the locus of the mixture composition that would result if pure solvent is used for
extraction. This must lie within the two-phase envelope to create the extract and raffinate phases.
Minimum amount of solvent required for the mixture to touch the equilibrium line corresponds to the
point Q and Q0 for the two solvents. Relative to Q, the location of Q0 is closer to the solvent vertex S,
denoting a higher proportion of S in the mixture for the same feed composition. This illustrates that
smaller envelope of miscibility requires a higher amount of solvent for the same separation. Such
ternary plots denoting different immiscibility ranges are obtained not only for different solvents but
also for the same solvent at two different extraction temperatures since greater miscibility (smaller
envelope) results at higher temperatures. However, the advantages of operating at a higher temperature
with lower viscosity and mass transfer rate needs to be weighed against higher amount of solvent
requirement.
Additional factors influencing solvent selection include
-
-
Low interfacial tension which is desirable for easy dispersion of the two liquid phases. However,
too low a value may lead to stable dispersion and make separation difficult. Since data on
interfacial tension are not always available, a rough estimate can be obtained from a difference in
surface tension of the two liquids and this is further lowered by presence of emulsifying agents.
The presence of minute dust particles also prevents droplet coalescence as they usually
accumulate at the interface of an immiscible liquid system.
Significant density difference with feed and raffinate throughout the entire range of operation
ensures easy separation of extract from raffinate and increases the capacity of the contacting
equipment.
13.3 Choice of solvent
(A)
395
B
100
20
80
E'
60
40
F
xB,F
60
40
P
E,yB
M
80
R'
20
R,xB
100
A
20
40
60
S
100
80
B
(B)
80
20
60
40
P
40
60
P'
20
80
xB,F Q Q'
S
A
x x'
20
40
60
z'
z
FIGURE 13.4
Ternary plots depicting (A) extraction process and (B) effect of solvent miscibility on extraction.
- Low viscosity requires lower pumping power, leading to higher extraction rate, higher heat
transfer and greater ease of handling. Since separation of solvent from feed solution occurs both
by gravity and coalescence of dispersed phase droplets, settling is slower for higher viscosity of
the continuous phase and smaller drop size.
- No azeotrope formation and high relative volatility with respect to the extracted phase
within the range of operation is desirable if the solvent is recovered from extract by distillation.
Usually in extraction, since the quantity of solvent is larger, choice of a more volatile solute would
396
-
-
Chapter 13 Extraction
require lower heat of vaporisation and lower the operating cost. In case of a highly selective
solvent, the amount of solvent may be less and vaporising the solvent is a cheaper option.
Low vapour pressure and freezing point enables easy storage and handling of the solvent at
atmospheric or moderately high pressure. However, low vapour pressure should not conflict with
the requirement of high relative volatility with feed solution that helps separation by distillation.
Chemically inert to feed solution and stable under operating conditions.
Nontoxic, nonflammable and noncorrosive nature of solvent as well as low cost and easy
availability.
In mixer-settler arrangement, liquid with higher volume fraction tends to be the continuous phase.
Partial or arrested inversion may result in dual emulsions where the
continuous phase is dispersed as droplets in the drops of the dispersed
phase. In continuous contact devices, the phase with higher flow rate
Selection of dispersed phase
is dispersed in sieve tray and packed towers while in all other towers,
the liquid with lower flow rate forms the dispersed phase. Presence of
interphase at top signifies lighter liquid dispersed and with heavier
liquid dispersed, the interphase is at the bottom of the column.
Other factors affecting choice of dispersed phase are
e
e
e
e
More viscous phase dispersed for higher capacity (droplet settling/rise slower in viscous liquid)
and less viscous liquid dispersed for efficient operation (slow diffusion inside viscous droplets).
Emulsifying agents may be used to increase diffusion in viscous droplets.
Preferable direction of mass transfer is from continuous to dispersed phase.
Phase that preferentially wets the packing material/tower internals is the continuous phase.
Dispersion of inflammable liquid is a safer option.
13.4 Design of continuous countercurrent contactors
Extraction involves the complex phenomena of droplet breakage and coalescence as well as axial and
radial mixing. Presence of impurities significantly affects the interfacial phenomena and equipment
performance. As a result, there is lack of reliable data on mass transfer coefficient and interfacial area
which makes estimation of process parameters from fundamental theory difficult. The best option is
pilot plant testing with the same equipment type selected based on process considerations of the actual
production. This is followed by certain empirical scale-up procedures based on experience. The
success of design depends on proper solvent selection as well as pilot plant tests with actual liquids for
the entire process including solvent recovery over a wide range of operating conditions. Tests with
synthetic mixtures resembling plant fluids often lead to unsatisfactory performance. Typical dimensions of pilot columns (based on experience) for different continuous contact extractor types are
listed in Table 13.2. The design parameters to be estimated in each case are also mentioned in the table.
Scaling-up needs to be based on proven techniques with use of proper safety factors. The generalised
scale-up relationships relate column diameter D, volumetric throughput Q, and height per unit stage
efficiency HETP as
13.4 Design of continuous countercurrent contactors
Dplant
Qplant
¼ k1
Dpilot
Qpilot
397
!m1
(13.1a)
and
HETPplant
Dplant
¼ k2
HETPpilot
Dpilot
!m2
(13.1b)
In case of agitated columns, there is an additional parameter f , the frequency of agitation at same
specific power input that is related to column diameter.
!m3
fplant
Dplant
¼ k3
(13.1c)
fpilot
Dpilot
In Eq. 13.1, k1,m1 are capacity scale-up factors, k2,m2 efficiency scale-up factors, and k3,m3 power
scale-up factors. Continuous contact equipment is further sized with the active zone height, together
with the top and bottom settling zones and instrumentation for control of the column interface.
Table 13.2 Typical pilot column dimensions.
Column type
Dimension
Packed
Sieve tray
Karr
Scheibel
D
50e150 mm
100e150 mm
25 mm
75 mm
Height per
theoretical stage
Packing height
2e5 m
1200e1500 mm tray
spacing
30e900 mm
3e6 actual stages
(75e150 mm)
Process factor
NTS, S/F
NTS, S/F
NTS, S/F
NTS, S/F
Column variable
D, H
D, H
D, H
D, H
Process variable
FþS
FþS
F þ S, f
F þ S, f
Design parameters
F e feed flow rate, S e solvent flow rate, f e frequency of agitation or vibration, H e column height, D e column
diameter
Unlike absorption and distillation, processing capacity of extraction equipment (column) refers to
the sum of the flow rates of the dispersed and the continuous phase (denoted by subscripts d and c,
respectively) and tower cross section is determined from total flooding velocity ðUd þ Uc Þflooding.
Prediction of total flooding velocity involves uncertainties and hence extraction columns are designed
to operate at 50% flooding velocity or even lower in many cases.
The steps of design are as follows:
e
e
e
Choice of solvent, compilation of property data over the operating range
Feasibility test and equilibrium data from laboratory tests
Contactor selection
398
e
e
e
e
e
e
Chapter 13 Extraction
Deciding on the dispersed and continuous phase
Pilot plant tower design and tests to obtain mass transfer data
Calculation of NTS or transfer units and column height
Estimation of tower diameter from flooding considerations
Design of actual column using scale-up relationships
Hydrodynamic calculations to estimate pressure gradient
Flooding
Flooding in extractors occurs by three mechanisms e phase inversion due to high flow rate of
dispersed phase, entrainment of dispersed phase droplets at high flow rate of continuous phase and
presence of contaminants at the interface that causes phase inversion by interface instability. Thus
flooding in extractors occur with increase in flow rate of either dispersed or continuous phase and both
phases leave from the outlet of the continuous phase. It can be visualised by the appearance of a second
interface inside the column. Increase in agitation speed and decrease in interfacial tension promotes
flooding.
13.4.1 Calculation of the number of stages
In a multistage extraction process, the number of theoretical stages N decides the length of liquid travel
and governs the compromise between equipment size or the number of mixer-settler contactors
(capital cost) and the ratio of solvent to feed flow rate required for the desired extent of extraction
(operating cost). Optimum combination of flow rates, number of stages and degree of solute transfer is
decided based on economics including cost of solvent recovery.
The theoretical number of stages, N, required for separation is estimated by graphical construction
on triangular diagram or rectangular ternary plot as per convenience. As discussed in Chapter 9, the
ternary rectangular plot is commonly used with the vertical and horizontal axes denoting the respective
equilibrium concentration of solute B and extraction solvent S. The composition in the raffinate and
extract phase is denoted in Fig. 13.5 by x and y, respectively, and the subscripts denote the components.
The computation is based on locating the mixture point M and the difference point D.
In the most general case, all three components (A, B and S) may be present in the feed as well as the
solvent used for extraction. Presence of A and B in the solvent stream is particularly common as the
recovered solvent, often reused, may still contain small amount of A and B.
Design input
Flow rate (kg/hr or kg mol/hr)
%
A
%
B
%
S
Feed
F
zA;F
zB;F
zS;F
Extraction
solvent
S or ENþ1
yA;S
yB;S
yS;S
Raffinate
R
xA;R
xB;R
xS;R
Stream
Steps to find the number of stages N
1. Desired composition of raffinate is usually specified in terms of concentration of B in solventfree basis and so this composition lies on the y-axis and is located at R0 .
2. The feed and the solvent point (F and ENþ1 ) are located on the diagram (Fig. 13.5A).
13.4 Design of continuous countercurrent contactors
399
3. The mixture point M is located from the flow rates ðF and SÞ and composition of feed and
solvent as shown below.
Ordinate:
zB;M ¼
F xB;F þ S yB;S
FþS
(13.2a)
zS;M ¼
F xS;F þ S yS;S
FþS
(13.2b)
Abscissa:
In case pure solvent is used and the feed stream is free of solvent, yS;S ¼ 1 and xS;F ¼ 0
4. The line joining ENþ1 and R0 intersects the raffinate curve at RN .
5. The tie line that passes through point F (extended beyond the envelope) is drawn and its extract
end is E1min . Coordinates of E1min denote extract composition when minimum amount of
solvent stream is used to produce raffinate of desired composition ðR0 Þ.
6. The line joining ENþ1 and F intersects the line RN E1min at Mmin which corresponds to the
mixture composition using minimum amount of solvent stream.
ðFM
Þ length
min
7. Minimum solvent to feed ratio is calculated as rmin ¼ ðENþ1 M
, based on the ‘lever arm
min Þ length
rule’.
8. Operating solvent to feed ratio is calculated as r ¼ rmin k, where typically 1.1 < k < 2. The
value of r should be less than rmax which corresponds to maximum solvent required. This is
obtained when M lies on the extract curve. Exceeding this upper limit on solvent shall lead to a
mixture that shall not separate as extract an raffinate phases.
9. Based on r, composition of mixture M is located as ðFMÞlength ¼ r ðENþ1 FÞ length. One
may note that coordinates of M can also be obtained from expressions based on balance of
component B and S.
10. The line RNM is drawn and extended to meet the extract curve at E1 that corresponds to the
operating extract composition from the process. [The construction may be continued on the
same graph for estimating the number of stages (N), but to avoid clumsiness a separate graph as
in Fig. 13.5B is often used to locate the difference point ðDÞ and continue with the construction.]
11. On the new graph, all except RN E1min line and the tie line through E1min is drawn.
12. Lines E1 F and ENþ1 RN are extended to meet at the operating difference point ðDÞ as shown in
Fig. 13.5B.
13. The tie line ðE1 R1 Þ through point E1 is drawn to obtain raffinate composition leaving stage 1
denoted as R1 .
14. In order to locate details of the next stage, a line through the point D and R1 is extended to meet
extract curve at E2 .
15. The tie line ðE2 R2 Þ through point E2 is drawn to obtain raffinate composition leaving stage 2
denoted by R2. Tie lines are conveniently drawn with the help of an xey plot (denoting
equilibrium composition of solute B in the raffinate and extract phase) drawn beside the ternary
rectangular plot. The procedure is illustrated in Figs. P13.2 and P13.3 and outlined below.
A horizontal line is drawn from any point, say E on the extract curve to intersect the diagonal of
the xey plot. This locates yE ¼ xE . A vertical line downward from yE ¼ xE point intersecting
the equilibrium curve locates xE in equilibrium with yE . A horizontal line from point xE to the
400
Chapter 13 Extraction
B
(A)
100%
m
Min. .. solvent = F ×
FMmin length
EN+1 Mmin length
m
Actual solvent = k × Min. .. solvent
xB, yB →
FM length
Extract
=F×
EN+1 M length
curve
Raffinate
E1min
curve
P
Tie line
F
E1
Mmin
R'
RN
M
EN+1
S
100%
0% A
0%
xS, yS →
B
(B)
100%
feed
=
xB, yB →
FM length
solvent
Extract
curve
Raffinate
curve
P
EN+1 M length
Δ
xS,Δ =
xB,Δ =
(F.xS,F – E1.yS,E1)
(F – E1)
(F.xB,F – E1.yB,E1)
(F – E1)
R'
,abscissa
,ordinate
Tie line
F
0%
A 0%
R1
RN
R2
E1
E2
M
Tie line
EN+1
S
100%
x S, y S →
FIGURE 13.5
Countercurrent multistage extraction (A) locating Mmin (B) estimating N.
raffinate curve locates xE in the ternary rectangular plot. Line yE xE drawn from the extract to the
raffinate curve is then the required tie line through point E.
16. Steps 14 and 15 are repeated till stage N, where the composition of raffinate falls below RN . In
the case shown in Fig. 13.5B, the condition is satisfied for N ¼ 2.
13.4 Design of continuous countercurrent contactors
401
17. The composition of extract and raffinate streams can then be read off the graph.
Often the number of stages is estimated by available shortcut methods. One such method is the
McCabeeThiele construction of stages discussed in Chapter 11 for straight operating and curved equilibrium line. The technique can be used here for constant flow rate of feed solvent F 0 and extract solvent S0
where the solute concentrations are given as weight ratio (X) of solute to feed solvent in raffinate and ratio
(Y) of solute to extraction solvent in extract. For perfectly immiscible solvents, both flow rates F 0 and S0
remain constant in all the stages and a linear operating curve of slope ðF 0 =S0 Þ ¼ ðE0 =R0 Þ is obtained.
Material balance from the feed end to stage n gives
Ynþ1 ¼
F0
E0 YE F 0 XF
X
þ
n
S0
S0
(13.3a)
and from raffinate end to stage n gives
F0
E 0 Y E R0 XR
X
þ
(13.3b)
n1
S0
S0
Thus, from overall material balance, the end points of the operating lines XR YS and XF ; YE are
related as
Yn ¼
F 0 XF þ S0 YS R0 XR
(13.3c)
E0
The equilibrium curve is plotted in the XeY coordinates and the number of stages is obtained by
McCabeeThiele stepwise construction discussed in Chapter 10. An example plot is shown in Fig. 13.6.
YE ¼
1.0
(XB,F,YB,E)
Y
1
2
(XB,RN,YB,RN+1)
0
1.0
0
X
FIGURE 13.6
McCabeeThiele construction for finding number of stages.
402
Chapter 13 Extraction
For a linear operating and a linear equilibrium curve of slope m passing through the origin, the
number of theoretical stages can be estimated from Kremser equation as function of the extraction
factor ε which is the ratio of the slope of the equilibrium line and the operating line, i.e. ε ¼ mS 0 =F 0 .
For ε s 1,
XF YS =m
1
1
ln
þ
1
XR YS =m
ε
ε
(13.4a)
N¼
ln ε
For ε ¼ 1,
N¼
XF YS =m
1
XR YS =m
(13.4b)
For non-zero intercept of equilibrium line; m0 the partition ratio in coordinates XeY should be used
instead of m. For nonlinear equilibrium curve, the geometric mean of m at the concentration leaving
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
stage 1 and stage N is used, i.e., m ¼ m1 mN .
Calculation of differential countercurrent extraction (packed column) is done by NTU method
discussed in Chapter 10. This is adopted if data on mass transfer coefficient is available. The number of
transfer units can be defined based on extract ðNtoE Þ or raffinate phase ðNtoR Þ as
Z x0
dx
NtoR ¼
(13.5a)
x
x
xN
Z y0
dy
(13.5b)
NtoE ¼
y
y
yN
where x is fraction (weight/mole) solute in raffinate phase and x is fraction solute in raffinate phase in
equilibrium with extract phase of composition y. For a linear operating and equilibrium curve with zero
intercept, NtoR can be obtained from Kremser equations (Eq. 13.4). The denominator of Eq. (13.4a) is
only different for εs1:0.
XF YS =m
1
1
ln
þ
1
XR YS =m
ε
ε
NtoR ¼
(13.6)
ð1 1=εÞ
The difference is more pronounced for high ε where
ε NtoR ¼ N ln
1ε
This gives the column height as
(13.7)
L ¼ HtoR NtoR ¼ HtoE NtoE
(13.8a)
L ¼ NTS HETP
(13.8b)
and in terms of NTS as
Presence of significant axial dispersion in large diameter towers of actual plant decreases the
effective concentration driving force and so the tower height to be provided is larger than that predicted
by plug flow NTU. This is incorporated by adding height of dispersion units HDU to transfer units, viz
13.4 Design of continuous countercurrent contactors
403
ðHTUÞov ¼ HTU þ ðHDUÞc þ ðHDUÞd
(13.9)
where subscripts c, d and ov denote continuous phase, dispersed phase and overall, respectively.
Staged equipment are also best modelled by NTU method for low-stage efficiency when extraction
factor ε >> 1:5. The overall stage efficiency is defined similar to staged distillation and absorption
towers, as the NTS to the number of actual stages and expressed as %. Commonly used extraction
equipment is designed to achieve the equivalent of 1e8 theoretical countercurrent stages. The overall
efficiency of mixer settler is more than 80% (usually around 90%e95%) and that of sieve tray is
typically 8%e30%.
13.4.2 Design parameters for extraction towers
Typical design parameters of extraction towers are discussed in the subsections below.
Packed tower
Unlike gaseliquid and vapoureliquid contactors, the interfacial area for mass transfer in packed
extraction tower is not the packing-specific surface area. Rather, the mass transfer area is almost independent of packing surface area and is a function of dispersed phase holdup. Packing in this case
merely increases the turbulence and also serves to redisperse the coalesced droplets.
Both random and structured packings can be used to cause droplet coalescence and breakup.
Structured packings provide higher values of turndown (operational
flexibility), allowable bed height and throughput. The throughput is
40e80 m3/m2 hr while that of random packed towers is 20e30 m3/m2
Packing characteristics
hr. Nevertheless, random packing is still a choice in industries. This is
mainly because it is cheaper and easy to clean. The HETP is typically
0.4e1.5 m for random packings (overall height of transfer unit HOL:
0.9e1.7 m) and 0.5e1.6 m for structured packing. Raschig rings were
the most common random packing but now Berl saddles are popular.
In LLE. corrosion and wetting are two major considerations for selection of packing material. The
packing needs to resist corrosion and be well wetted by the continuous phase. Strength is also a
consideration and ceramics is usually avoided. This is because ceramics is brittle and often breaks and
clogs the flow and pump suction strainers and valves. Nevertheless, they are used for corrosive liquids
when aqueous phase is continuous. Stoneware packings and metal packings are used when water is the
continuous phase and carbon rings or saddles are adopted for continuous organic phase (say toluene).
Similar to absorption towers, the ratio of tower diameter to packing size should be greater than 8:1
to minimise wall effect. Pilot columns usually use smaller packings, or else an unnecessarily large
diameter pilot column is required. In case structured packing is selected, the test columns can be
equipped with industrial packing. This minimises scale-up risk on throughput but limits the minimum
pilot column diameter to 50 mm and also requires efforts to minimise wall bypassing.
Liquideliquid flooding velocity in packed bed can be predicted from the flooding velocity correlation plot in packed extraction towers correlation (McCabe and
Smith, Unit operations of Chemical Engineering, McGraw Hill Int’l
Student’s Edn., 4th edition, pg 542, 1985), an analytical form of
L-L flooding in packed bed
which is
404
Chapter 13 Extraction
C ¼ exp 8.8082 0.0563 flnðDÞg2 0.4981 lnðDÞ
0.2 s
mc
a 1.5
where D ¼
rc
ε
Dr
(13.10)
(13.11a)
and
C¼
pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi 2
Us;d þ Us;c rc
amc
(13.11b)
The above is valid for 1 < C < 1000.
It is important to note that the group D is not dimensionless and the following units are to be used.
Us;d ; Us;c the superficial velocity (volumetric flow rate per unit tower cross section) of dispersed
and continuous phase in ft/hr, rc is density in lb/ft3 and mc is viscosity of the continuous phase in lbm/ft
hr. a the specific surface area of packing is in ft2/ft3 and ε is the packing void fraction. The values of a
and ε provided in Chapter 14 for gaseliquid packed towers can be used for extractors as well. Dr ¼
rc wrd and s is interfacial tension in dyne/cm.
While working with SI units, the following conversion factors may be used:
1 m/sec ¼ 11,811 ft/h
1 kg/m3 ¼ 0.062428 lb/ft3
1 kg/(m sec) ¼ 2419.08833 lb/(ft hr) and 1 cP ¼ 2.419 lbm/(ft hr)
1 m2/m3 ¼ 0.3048 ft2/ft3
Most critical data for an accurate estimation of flooding capacity is the value of interfacial tension
that governs the droplet size. In absence of experimental data, s in dyne/cm can be estimated for a
ternary system of solvent A, solvent S and solute B as
ðxBA þ xBS Þ
s ¼ 7.34 ln xAS þ xSA þ
4.90
(13.12)
2
where xAS is the mole fraction of solvent A in saturated solvent-rich S, xSA is the mole fraction of
solvent S in saturated solvent-rich A and xBA and xBS are the mole fractions of solute B in A and S,
respectively. Eq. 13.12 is applicable for 4 s 52:5 dyne/cm and predicts s within an uncertainty
around 15% for ternary systems with partially miscible solvents and solute completely miscible in
both solvents. The design flow rate is recommended at 50% flooding or lower, even up to 20% in
unknown systems.
Packed columns with D < 800 mm are usually flanged from cost considerations, while in higher
diameter columns, the sections are welded. Manholes are provided for
inserting the internals in pieces inside the welded columns. Nozzles for feed,
draw off, level measurement and temperature control are required. Often
inspection glasses are provided but these require cleaning due to accumuColumn accessories
lation of dirt settling from the liquids. Tapping nozzles at various elevations
are provided for sample withdrawal from the column. These are called tryline. Samples from the try-lines are visually compared to identify the
interphase location between two consecutive try-lines. This is important for systems that are dark, dirty
or when inspection glasses cannot be provided usually for safety reasons.
13.4 Design of continuous countercurrent contactors
405
Performance of a column strongly depends on the quality of flow distribution. Large diameter
columns should have sufficient pressure drop to ensure good radial distribution
at turndown conditions while avoiding formation of spray caused by high
velocity through nozzles at design rates. Sufficient open area is also necessary.
Flow distributor
Similar to vapoureliquid and gaseliquid distribution, redistributors are
required after 1.5e3 m to ensure proper drop size distribution. Long bed
heights (>10e12 m) with structured packing are not advisable.
Sieve tray tower
These are similar to the trays used for distillation and absorption. The lighter liquid is dispersed as
droplets while passing through the sieve trays. They coalesce and jet above each tray and get redispersed as they rise through the sieves of the upper tray. The heavy liquid flows as the continuous phase
across the tray. The tray spacing (TS) is 10e25 cm and the perforations on the tray (do) are 3e7 mm in
diameter. Tray active area (Aa) is 15%e25% of column cross-sectional area. Typically, downcomer
area (Ad) is 5%e10% of column cross-sectional area. Overflow weirs are not used on downcomers in
liquideliquid service.
Fractional tray efficiency h can be estimated from
pffiffiffiffiffiffi
0.2945 TS
h¼
ðUd =Uc Þ0.42
(13.13)
sd00.35
where s is in dyne/cm, TS and do are both in m and Ud and Uc are in m/sec. Typical tray efficiency is
8%e30% and HETP is 0.8e1.2 m. Systems with high interfacial tension require larger HTU and the
stage efficiency is low. Sieve plate towers have capacities ðUd þ Uc Þ of 27e60 m3/(m2 hr) and are
scaled-up keeping the mixture superficial velocity ðUd þ Uc Þ same.
Flooding occurs when either the liquideliquid interface does not remain at the tower bottom or a
large portion of dispersed layer accumulates on the trays and restricts the flow of the continuous phase.
Proper tray design solves the dispersed-phase accumulation problem. To keep the interphase close to the
tower bottom, the dispersed-phase flow rate should be high enough to overcome the head losses due to
(a) Flow of dispersed phase through perforations on each plate, ho (obtained from standard orifice
equation).
r U 2 ð1 A0 =AÞ2
ho ¼ d o
2gDrCo2
(13.14)
Typically Uo is in the range 15e30 cm/s and Co w0:67.
(b) Interfacial tension hs , important when continuous phase preferentially wets the tray.
hs ¼
4s
Drdo
(13.15)
406
Chapter 13 Extraction
(c) Flow of continuous phase hc which includes friction on plate, in downcomer (negligible),
contraction and expansion at downcomer entry and exit and abrupt changes in direction. This is
considered to be 4.5 velocity heads.
hc ¼
4.5 Ud2 rc
2g Dr
(13.16)
In Eq. 13.14e13.16, the terms with subscript ‘o’ refer to parameters at the perforations and Co is
the discharge coefficient. The depth of liquid layer for preferential wetting of tray by continuous
phase is the higher of hs and ðho þ hc Þ.
It is important check that TS > ðhc þ hd Þ, where hd ¼ ho þ hs . This avoids excessive
entrainment and break up of dispersed-phase stream into droplets before entering the next plate.
Spray extraction tower
The following are the typical features:
-
One or two stages
Large axial dispersion in continuous phase
Range of ðUd þ Uc Þ is 15e75 m3/(m2$hr)
HOL and HETP: 3e6 m
Agitated tower
Typical design specifications of pulsed towers are listed in Table 13.3 and that for Scheibel tower,
Karr reciprocating plate tower and rotary disc contactor are mentioned in Table 13.4. Schematic
diagrams of pulsed tower, Scheibel tower and rotary disc contactor with typical internals and key
dimensions marked are shown in Fig. 13.3AeC, respectively.
Table 13.3 Typical design specifications of pulsed sieve tray and packed towers.
ðUd DUc Þ
m3/(m2 hr)
Flooding
velocity
ðUd DUc ÞF
m3/(m2 hr)
HETP (m)
Pulsation
Specification
Tower details
Pulsed sieve tray
tower
6e25 mm
amplitude
100e250 cycles
per minute
TS 50 mm,
Aa 0.2e0.25 A do
3 mm
No downcomer
25 to 35
60
0.15e0.3 m
Pulsed packed
tower
6e8 mm
amplitude
Frequency <150/
min
Scale-up at same
ðUd þ Uc Þ and
frequency
17 to 23
40
0.15e0.3 m
Equipment
13.5 Design of mixer-settler
407
Table 13.4 Design parameters and scale-up equations for mechanically agitated towers.
Scheibel tower
(Fig. 13.3B)
Karr reciprocating
plate tower
Rotary disc contactor
(Fig. 13.3C)
General characteristics
Four bladed flat turbine
operated at 600 rpm
depending on material to
be extracted
TS (tray spacing)
w25e200 mm
Sieve trays impart
vertical motion
w25 mm amplitude and
100 to 150 strokes/min
(SPM).
TS e 50 to 150 mm do
15 mm
Open space 50%e60%
Petroleum services e
2400 mm 4 max and
12 m height
Proportions of internals
shown in Fig. 13.3c and
listed in Table 13.5
Throughput
10e14 m3/(m2 hr) for a
7.6 cm diameter tower
30e40 m3/(m2 hr)
20e30 m3/(m2 hr)
Flooding throughput
40 m3/(m2 hr)
80e100 m3/(m2 hr)
HETP
0.1e0.3 m
0.2e0.6 m
Scale-up equations
Dplant
Q
¼ Qplant
pilot
Dpilot
Equipment
HETPplant
D
¼ Dplant
pilot
HETPpilot
0.4
HETPplant
D
¼ Dplant
pilot
HETPpilot
0.15e0.3 m
0.38
0.5
SPMplant
Dpilot
¼ Dplant
SPMpilot
Based on equal specific
power input
0.14
Table 13.5 Proportions of internals of rotary disc contactor.
h ¼ f ðDÞ
pffiffiffiffi
h¼ D
D < 0:1m
h ¼ 0.15D
0:1 D < 1m
h ¼ 0:12D
1 D < 1:5m
h ¼ 0:1D
1:5 D < 2:5m
h ¼ 0:08D
D 2:5m
Valid in the range
Ds =D ¼ 0:7, Dr =D ¼ 0:6
D; Ds and Dr are the tower diameter, stator diameter and rotor diameter, respectively, and h is stage height
13.5 Design of mixer-settler
The different components of a mixer settler are described in the subsections below.
Mixing section
The dispersion/mixing section is a cylindrical tank preferably with a dished bottom and liquid
depth Lliq > Dtank . Settling and coalescence may occur in the dispersion tank after agitation has
stopped or the two-phase mixture can be directed to a gravity settler after the dispersion section. Both
408
Chapter 13 Extraction
types can be used in series for countercurrent operation. Such a countercurrent arrangement is used in
extraction of uranium or copper salts from aqueous solution.
Gravity settlers are vertical/horizontal tanks where the liquideliquid dispersion is continuously
settled and coalesced and the settled liquids are continuously withdrawn. The inlet velocity must be
kept low for minimum interfacial disturbances. (See Chapter 17 for sizing etc.)
Impeller: Mixing in the tank is by agitator/impeller which may be closed or open type. It is
mounted on a shaft and driven by an electric motor. A properly designed impeller should impart
circulatory motion in both radial and axial direction to prevent gravity settling and separation due to
centrifugal force (as heavier liquid has a tendency to form a layer close to the tank wall). While
adequate dispersion is necessary for rapid extraction, it is important to prevent formation of stable
emulsions.
Impellers are usually classified based on the type of flow they induce e tangential (paddle), axial
(propeller) and radial (turbine). The typical characteristics of propeller and turbine are listed in
Table 13.6 and their schematics are presented in Figs. 13.7 and 13.8.
Table 13.6 Typical characteristics of propeller and turbine type impeller.
Propeller
Turbine
· Most economical
for low viscous liquids in small tanks
· Suitable
(<3000 cP)
mixing
· Poor
· Ineffective for suspending solids
mounted along tank axis enters from top.
· Shaft
Off-centred entrance at an angle at times used
· Most common
range of liquid viscosity (<100000 cP)
· Wide
blade types are used
· Several
Pitched blade turbine with blades at 45
to avoid vortex formation in absence of baffles
· Three blades most common; marine type with
two, three or four blades are also used
100e1000 rpm depending on diameter
· Nand¼ propeller
pitch and nature of liquid
· Baffles required at high speed
·
·
provides axial as well as radial flow
Flat/radial type has fouresix blades, attached
directly to shaft or to a horizontal disk
Back sloped/centrifugal turbine suitable for
most difficult mixing and large quantity of
liquid
Axial flow impeller is opted for suspending
solids
For liquid depth >> tank diameter D,
twoethree impellers on same shaft with
bottommost impeller located DeD/3 above the
tank floor
High speed
Turbine: The geometric parameters defining the turbine agitator are shown in Fig. 13.7 and their
typical standard dimensions are as follows with 4 baffles.
DI
WI 1
1 Ddisc 2 L1
¼ 0:3 0:5;
¼ to ;
¼ ;
¼ 0:25
5
3 DI
D
DI 8
DI
H
H 1 1 Wb 1
1
¼ 1;
; tgap ¼ 0:1 0:15Wb ; Nb ¼ 4
¼ ;
¼ to
D
3 D
8
12
D
13.5 Design of mixer-settler
409
tgap
Wb
Baffle
LI
H
WI
Ddisc
HI
DI
D
FIGURE 13.7
Standard six flat blade turbine agitator with disc.
Baffle
H≈D
HI
DI
D
FIGURE 13.8
Schematic of three-blade propeller agitator.
Propeller: Marine type propellers are more common. These have square pitch, i.e., in one revolution, the propeller pushes the liquid forward by a distance P (Pitch) equal to its diameter DI . Usually
DI
DI
1
1
D 5 is adopted for single-phase mixing but for two phases D ¼ 3 is used. The preferred propeller
elevation ðHI Þ above the vessel floor is DI , though the propeller may also be submerged by a depth DI
from the top liquid surface.
Paddle type is generally not recommended for extraction as they have low speed (20e200 rpm) and
produce poor circulation. These are used for viscous liquids like starch, paste, paints, adhesives,
410
Chapter 13 Extraction
cosmetics, etc. Modified paddles, e.g., anchor agitator, can mix viscous liquids (50,000 to 500,000 cP).
For still higher viscosities (usually 500,000 to 1,000,000 cP and up to 25,000,000 cP), helical ribbon
agitators (ribbon formed in a helical path and attached to a central shaft), which have low rotation
speed, are used.
Baffles
Vortices are inevitable with any impeller type except for highly viscous liquids or marine propellers
in an off-centre arrangement. These are eliminated by installation of baffles that are narrow, flat strips
welded or fastened vertically along the tank wall. Typically, four equally spaced vertical baffles of
length equal to liquid depth and width equal to D=10 to D=12 are arranged radially around the vessel
diameter. This arrangement has been observed to produce negligible swirl and no further advantage is
obtained with additional number of baffles.
13.5.1 Holding time
The mixer settler can be sized from an estimate of holding time obtained from mass balance equation
for mixing and from terminal velocity of droplets for settling as outlined in Chapter 17.
For N moles of solute transfer from raffinate to extract (denoted by subscripts R and E, respectively)
during time t, if phases attain equilibrium, the concentration of solute changes from coE to cE in extract
and coR to cR in raffinate.
Considering a linear equilibrium relationship within the range of concentration change,
cE ¼ mcR
(13.17)
Assuming immiscible extract and raffinate phases with flow rates E and R, respectively,
c
E cE c0E ¼ R c0R E
(13.18)
m
dN
dcE
¼E
¼ KE a cE cE
dt
dt
(13.19)
where KE a is the overall volumetric mass transfer coefficient based on overall concentration gradient
cE cE in the extract phase as discussed in Chapter 10.
This gives
E
t¼
lnð1 hÞ
mE
ðKE aÞ
1þ
R
(13.20)
where N is the moles solute transferred in the stage in time t and N is the moles solute transferred till
cE c0E
equilibrium is reached. This gives stage efficiency as, h ¼ NN ¼ .
cE c0E
Eq. 13.20 can also be obtained in terms of a raffinate rate coefficient as
R
1þ
R
mE
t¼
lnð1 hÞ
(13.21)
ðKR aÞ
13.5 Design of mixer-settler
411
The holding time in mixer is usually 1e3 min except in cases like metal extraction where due to
reactive extraction, a holding time of 10e15 min is usual. It is important to consider settling along with
mixing time. Often a higher intensity of mixing reduces residence time for mass transfer while creating
fine droplets difficult to separate. Droplet size is a design parameter to estimate settling time. Small
droplets achieve large interfacial area and faster extraction while requiring a longer settling time. Most
stable emulsions are characterised by maximum droplet diameter of the order of 1e1.5 microns while
diameters around 1 mm produce relatively coarse dispersions that separate readily. Coarse dispersions
are preferred in extraction and reacting systems involving two liquid phases that need to be separated.
13.5.2 Power and mixing time
Agitator design needs to consider power requirement as well as adequacy of mixing since higher power
consumption is not necessarily associated with adequate mixing. Several empirical correlations are
available to predict the power required. A typical correlation for commonly used turbines and propellers (Fig. 13.9) with Newtonian liquids in baffled, cylindrical vessels correlates the dimensionless
D2 N r
Power number, NP ¼ D5 NP3 r with impeller Reynolds number, ReI ¼ I m I m for axial impeller
I
I
m
m
shaft and liquid depth equal to tank diameter. The parameters defining the numbers are P (power in W),
DI (impeller diameter in m), NI (impeller rotational speed in revolutions per second), rm (mixture
density in kg/m3), and mm (mixture viscosity in kg/m sec). The flow is laminar for ReI < 10 and
turbulent for ReI > 104. In the range 10 < ReI < 104 , the flow is transitional, i.e., turbulent at the
impeller and laminar further away. For immiscible liquid mixtures, rm and mm can be expressed in
terms of individual liquid properties and mixture composition expressed as volume fraction vE and vR
of the extract and raffinate phases. Note that vE þ vR ¼ 1.
For baffled vessels
mm ¼
rm ¼ vE rE þ vR rR
(13.22)
mm ¼ mvEE mvRR
(13.23)
mc
1.5md a
1þ
mc þ md
ð1 aÞ
(13.24)
where a is the dispersed-phase fractional holdup in the vessel.
Viscosity of individual phases with n components with xi mole fraction of each component, may be
n
P
found from the mixing rule: lnðmÞ ¼ ðxi lnðmi ÞÞ.
1
For high agitation speed, emulsion formation may increase mixture viscosity and Eq. 13.24 does
not give accurate results.
Typically, P ¼ 0:8 to 2 kW/m3 of fluid for intense agitation required in extraction where P is the
power imparted to liquid by impeller and does not include losses in the motor, speed reducing gears,
bearings, stuffing box, etc., which is around 0.3 to 0.4 times P. The power required for liquids of low to
moderate viscosity is 0.1e0.2 kW/m3 for mild agitation and blending and 0.4e0.6 kW/m3 for vigorous
agitation.
For flat six-blade open turbine, deviations from the standard design influences Power number as
follows:
(a) NP fWI =DI
412
Chapter 13 Extraction
(b) NP almost same for DI =D in the range 0.25e0.5
(c) For two turbines installed on same shaft with spacing w DI, the total power is 1.9 times the
power required for single impeller where spacing refers to the vertical distance between the
bottom edges of the two turbines. This also applies to six-blade pitched blade (45 ) turbine.
P
Np =
5
3
DI .NI . ρm
102
101
1
2
3
4
100
5
10–1
100
101
102
103
104
105
106
ReI = (DI2.NI. ρm/μm)
FIGURE 13.9
Correlation of NP versus ReI for different impeller types in baffled agitators. (1) Flat six-blade turbine with disc
DI =WI ¼ 5; 4 baffles with ðD=Wb Þ ¼ 12, (2) flat six-blade open turbine with disc DI =WI ¼ 8; 4 baffles with
ðD=Wb Þ ¼ 12, (3) six-blade turbine (45 blade), DI =WI ¼ 8; 4 baffles with ðD=Wb Þ ¼ 12, (4) propeller
turbine with Pitch ¼ 2 DI ; 4 baffles with Pitch ðD=Wb Þ ¼ 10, also valid for off centre in angular off-centre
position without baffles, (5) propeller turbine Pitch ¼ DI ; 4 baffles with ðD=Wb Þ ¼ 10, also valid for off centre
in angular off-centre position without baffles.
From sources - Curves 1,2 & 3 are from Bates, R.L., Fondy, P.L. & Corpstein R.R. (1963). Examination of some geometric
parameters of impeller power. Industrial & Engineering Chemistry Process Design and Development. 2(4), 310e314. Curves 4
and 5 from Rushton, J.H., Costich, E.W. & Everett, H.J. Power characteristics of mixing impellers. Chemical Engineering Progress.
46, 395e404, 1950; 46:467e79, 1950. [Mixing Equipment Co., Rochester, NY, and Illinois Inst. Technology, Chicago, IL].
Same NP read from Fig. 13.9 can be used for Re < 300 in case of unbaffled vertical and horizontal
cylindrical vessels and for baffled square section tanks. The power consumption in unbaffled vessels is
less as compared to baffled vessels when Re > 300.
For helical ribbon agitator, the NP ReI correlation is as follows for ReI < 20(viscous liquids)
NP ¼
186
; for agitator pitch ¼ D
ReI
(13.25)
NP ¼
290
D
; for agitator pitch ¼
ReI
2
(13.26)
I
and the typical dimensions are DDI ¼ 0:95 with minimum 0.75 and W
DI ¼ 0:095.
13.5 Design of mixer-settler
413
The efficacy of mixing expressed as dimensionless mixing factor fmix can also be correlated with
ReI for a turbine agitator in a baffled tank where
2
fmix ¼ tmix
1
1
NI D2I 3 g6 D2I
1
(13.27)
3
H 2 D2
and tmix is the mixing time in seconds. The graphical correlation presented in Fig. 13.10 shows that fmix
2
and tmix NI3 is constant for ReI > 1000.
3/2
.D
102
H
1/2
fmix = tmix ×
(NI.DI2)
2/3
.g
1/6
.DI
1/2
103
101
100
100
101
102
103
104
105
106
ReI = DI2.NI. ρm/μm
FIGURE 13.10
Mixing time as function of Reynolds number for miscible liquids in a baffled vessel agitated by turbine
impeller.
From Norwood, K.W., & Metzner, A.B. (1960). Flow patterns and mixing rates in agitated vessels. AIChE Journal, 6, 432.
13.5.3 Scale-up
For most LLE applications, the mixing section is scaled based on geometric similarity, i.e., in pro1
portion to increase of vessel diameter for D ¼ H1 or as (vessel volume) 3 with the same power per unit
volume and equal holding time. It is difficult to achieve dynamic (ratio of viscous, inertial or gravitational forces) and kinematic (velocity ratio) similarity at the same time.
2
Using the same scaling for all dimensions shown in Fig. 13.7, DI scales as D while NI fð1=DÞ3 for
equal mass transfer rate or equal power per unit volume. For fully developed turbulence, PfNI3 and
11
tmix can be scaled for similar geometry and same power per unit volume in turbulent flow as tmix f DI8 ,
11
while for same tmix ; VPfDI4 . Usually agitators are scaled at constant power per unit volume which
gives a larger mixing time for larger vessels.
Scale-up to continuous process can also be performed from approach to equilibrium in batch
ktb , and approach to equilibrium in continuous process E
o
process Eb where Eb ¼ ccii c
cont is
c ¼ 1 e
ktcont
Econt ¼ 1þktcont .
414
Chapter 13 Extraction
The value of k as obtained from batch data (mixing time tb in batch process) is used to compute
residence time tcont for continuous process. From residence time and power input, scale-up is done
based on geometric similarity and equal power input per unit volume.
13.5.4 Flow mixers
These are widely used for refining light petroleum distillates with small quantities of solvent.
Dispersion is achieved by ‘in-line’ or flow mixers where agitation occurs by fluid flow. Their use is
limited to low viscosity liquids (<100 cp) where dispersion is not difficult and small holding volumes
which provide very little holding time for diffusion to occur. There are four basic types of ‘in-line
mixers’.
(a) Jet formed by impingement of one liquid into another
(b) Injector where mixing occurs by flow of one liquid inducing flow in other
(c) Orifice and nozzle or even mixing valves that induce mixing by high degree of turbulence in the
flowing liquid streams
(d) Mechanical agitator, e.g., centrifugal pump, baffle mixer, etc.
In-line mixers are relatively inexpensive and serve as an economical option to produce a fairly
coarse dispersion. However, the high pressure drop encountered during intense mixing results in high
operating cost and since mixing and separation occurs in separate vessels, separate mixers and settlers
need to be designed. Usually, settler is a vessel of larger cross section which provides minimum
turbulence and sufficient settling time. An example of this is the ‘mixing valve’ for mixing demineralised water and crude oil for the purpose of ‘desalting’ and subsequent separation of the aqueous
and the oil phases due to long residence time in the electric desalter vessel where separation is aided by
an electric field that helps coalesce the water droplets and settles the same. Holding time used to design
settlers (see Chapter 17) cannot be specified since emulsion breakage depends on mixture properties,
droplet size and nature of agitation. In petroleum industry, most settlers are designed for holding time
of 30 min to 1 hr and this may be reduced by baffling to ensure laminar flow and shorter settling
distances for the dispersed drops.
13.6 Design illustrations
This section provides examples of design for (A) continuous countercurrent extractor and (B) mixer
settler and concludes with an outline of the steps for scaling-up RDC from pilot plant data.
Acetone is to be recovered from a 1200 kg/hr aqueous stream that contains 40%w/w
acetone at around 26 C such that the spent solution (raffinate) contains no more than 5% acetone after
solvent recovery.
Solution
Problem 13.1.
Solvent selection
As mentioned in text, MIBK is commonly used as solvent to recover acetone from aqueous solution. The equilibrium data for watereacetoneeMIBK system is shown as a rectangular plot in
Fig. P13.1. This is based on equilibrium data points presented in Table P13.1. From the figure, we note
that the ternary mixture approaches plait point close to feed composition xF ¼ 0:4
13.6 Design illustrations
415
Table P13.1 Equilibrium Data for watereacetoneeMIBK system.
Acetone distribution %w/w
Mixture composition %w/w
Raffinate phase
Extract phase
xB
yB
zAM
zBM
zSM
2.00
0
98.0
2.5
4.5
2.33
4.6
93.2
5.5
10.0
3.86
18.95
77.3
7.5
13.5
4.66
24.4
71.0
10.0
17.5
5.53
28.9
65.5
12.5
21.3
7.82
37.6
54.7
15.5
25.5
10.7
43.2
46.2
17.5
28.2
45.0
42.7
12.4
20.0
31.2
64.2
30.9
5.01
22.5
34.0
75.8
20.9
3.23
25.0
36.5
94.2
3.73
2.12
26.0
37.5
97.8
0
2.20
Ref.: D F Othmer, R E White and E Trueger, Ind. Eng. Chem. 33,1240 (1941).
B
1.0
0.8
xB, yB
0.6
0.4
0.2
0.0
A
S
0.0
0.2
0.4
0.6
0.8
xs, ys
FIGURE P13.1
Ternary rectangular plot for watereacetoneeMIBK system.
1.0
416
Chapter 13 Extraction
So we try chloroform as the extraction solvent. Equilibrium data for watereacetoneechloroform
system shown in Fig. P13.2 is based on the following equilibrium data (Table P13.2) at ambient
temperature.
Table P13.2 Equilibrium Data for watereacetoneechloroform system.
Aqueous phase (Raffinate)
xA
xS
0.992
0.830
Chloroform phase (Extract)
xB
yA
0.008
0
0.005
0.995
0
0.012
0.158
0.013
0.700
0.287
0.731
0.013
0.256
0.022
0.557
0.421
0.623
0.017
0.360
0.044
0.429
0.527
0.456
0.051
0.493
0.103
0.284
0.613
0.345
0.098
0.557
0.186
0.204
0.610
yB
B
1.0
y
B
1.0
yS
0.8
x
B =
0.8
xB, yB
yB
0.6
E1min
E1
E2
0.6
E3
E4
E5
F
0.4
Mmin
0.2
0.2
Δ
E6
E7
M
R'
E8
RN
E9
0.0
0.0
0.0
0.2
0.4
xB
0.6
0.8
1.0
0.0
A
0.2
0.4
0.6
0.8
1.0 S
xs , ys
FIGURE P13.2
Ternary rectangular plot for watereacetoneechloroform system and estimation of NTS with
ðS=F Þ ¼ 1:3 ðS=F Þmin
We observe that (1) plait point is at (0.575, 0.575), which suggests that the feed composition lies
close to immiscibility envelope, (2) there exists only a small range of miscibility of chloroform
(extraction solvent) and water (feed solvent), (3) acetone is completely miscible with both solvents
(water and chloroform).
13.6 Design illustrations
417
So we proceed with chloroform as the extraction solvent and the component properties are as
follows:
Component
Density
(kg/m3)
Viscosity m
(cP)
Surface tension
s(dyne/cm)
MW
Acetone
790
0.316
24.1
58
Water
996
0.89
72
18
Chloroform
1490
0.51
26.2
119.4
Continuous multistage countercurrent extraction process configuration (Fig. 13.2C) is considered
where the recovered solvent will be recycled and supplemented with fresh solvent to make up for any
loss.
Estimating the number of stages
The steps to estimate the number of stages following the nomenclature of Fig. 13.2C are as follows:
•
•
•
•
The distribution xey plot is drawn beside the extract and raffinate curves in rectangular
coordinates in Fig. P13.2 for solute (Component B: acetone) and solvent (Component S:
chloroform).
Considering the low solubility of (feed solvent) water and extraction solvent (chloroform),
solvent is assumed to be nearly pure chloroform even if recycled solvent is used and yS z 1 is
considered. Solvent composition ENþ1 to the last stage (N) therefore coincides with pure solvent
vertex S in Fig. P13.2.
For the raffinate stream free of solvent (S) having 5% acetone (B), during operation even if a small
amount of solvent remains in the final raffinate, the composition of final raffinate would still meet
the requirement of maximum 5%w/w of acetone. So as a conservative measure, the composition
of 5% acetone is located on the acetone (component B) axis (vertical axis) at point R0 (5% B,
95% A). Line R0 S is drawn and it intersects the raffinate curve at RN (ordinate ¼ 0.049), in the
figure.
To estimate the minimum solvent requirement Smin, feed composition point F (40% B, 60% A) is
located on y-axis. The tie line that on extension passes through F is drawn. The tie line has its
extract end at E1;min yS;min ¼ 0:34; yB;min ¼ 0:575 . Lines RN E1;min and FS intersect at Mmin ,
the mixture point requiring minimum amount of solvent. Minimum solvent to feed ratio is located
from lever arm rule as rmin ¼
•
ðFMmin Þ length
S
F min ¼ ðENþ1 Mmin Þ length ¼ 0:224 and Smin ¼ 1200 0:224 ¼
264:235 kg=hr.
To estimate the actual solvent requirement S, we adopt 30% more solvent than the minimum
required,
S
F actual ¼ 1:3 0:224 ¼ 0:291, this gives S ¼ 348.7 kg/hr. Using this, operating
mixture point M ðzSM ¼ 0:225; zBM ¼ 0:31Þ is located and RNM is extended to extract curve to
obtain E1 at ðyB1 ¼ 0:555; yS1 ¼ 0:395Þ.
418
•
•
•
Chapter 13 Extraction
To locate D point as the point of intersection of E1F and SRN, where D ¼ R0 E1 ,
E1 yB1
E1 yB1
, zSD ¼ FzSFFE
, for xFS ¼ 0, xBF ¼ 0:4 in the present problem.
zBD ¼ FzBFFE
1
1
From D, operating curve DFE1 is already drawn and from E1, tie line to raffinate curve E1R1 is
constructed with the help of xey plot beside the rectangular plot. Operating line DR1 is extended
to extract curve to locate E2. Tie line E2R2 is drawn to locate R2. The process is continued till RN is
reached. This occurs for N ¼ 9, which is on the higher side.
So we repeat the calculations with ðS=FÞ ¼ 1:75 ðS=FÞmin , which gives S ¼ 470 kg/hr.
Repeating the aforementioned procedure as shown in Fig. P13.3, we get N ¼ 5 which is reasonable.
So we adopt chloroform as the solvent with S ¼ 470 kg/hr and N ¼ 5 and select a packed tower for
the process.
1.0 B
B =
y
B
1.0
xB, yB
0.6
yB
0.8
x
0.8
0.4
P
0.6
E1min
F
E1
0.2
R'
Δ
0.0
0.2
0.4
xB
0.6
0.8
A
1.0 0.0
E2
M
E3
E4
RN
0.2
0.4
0.6
0.8
E5
S
1.0
xs, ys
FIGURE P13.3
Estimation of NTS with ðS=F Þ ¼ 1:75 ðS=F Þmin
Packed column sizing
Height.
For random packing, typically 0:4 HETP 1:2 m. So we take HETP ¼ 0.95 m, For N ¼ 5, this
gives column height H ¼ 4.75 m.
Since the feed flow rate is higher, it is expected to be the dispersed phase and the solvent is the
continuous phase in case of packed tower.
Diameter estimation
We choose random packing of 100 ceramic Berl saddle (Chapter 14) with
ε ¼ 0:69; ap ¼ 249 m2 m3 76 ft2 ft3 .
Using Eqs. 13.10 and 13.11, to predict flooding velocity and referring to Fig. P13.4 for material
balance of streams.
Feed (dispersed phase), Q ¼ 1.33 m3/hr.
Solvent (continuous phase), Q ¼ 0.315 m3/hr
13.6 Design illustrations
Acetone
Water
Chloroform
NTS = 5
S/F = 1.75 × (S/F)min = 0.391
F = 1200 kg/hr
S = 0.391 × 1200 = 470 kg/hr
kg/hr
xw/w
–
–
1.0
470 kg/hr
S (Chloroform)
–
–
470.0
1.0
470.0
ρ = 1490 kg/m3
708.5 kg/hr
Raffinate (R)
xw/w
kg/hr
Acetone 0.049
Water 0.939
Chloroform 0.012
37.7
662.3
8.5
QS = 0.315 m3/hr
Acetone
Water
Chloroform
419
1.000 708.5
ρ = 987.3 kg/m3
μ = 0.874 cP
QR = 0.72 m3/hr
xw/w
1200 kg/hr
F (Feed)
kg/hr
0.4
0.6
–
480
720
–
1.0
1200
961.5 kg/hr
Extract (E)
Acetone
Water
Chloroform
xw/w
kg/hr
0.46
0.06
0.48
442.3
57.7
461.5
1.00
961.5
ρ = 1036.6 kg/m3
QE = 0.927 m3/hr
ρ = 901.9 kg/m3, μ = 0.745 cP
QF = 1.33 m3/hr
FIGURE P13.4
Process flow diagram with ðS=F Þ ¼ 1:75 ðS=F Þmin
rc ¼ 93:01772 lb=ft3 ; mc ¼ 1:2337 lb=ðft hrÞ
Dr ¼ 36:714 lb=ft3 ; s ¼ 4:5532 dyne=cm
0.2 s
mc
a 1.5
D¼
¼ 21.24
rc
ε
Dr
C ¼ exp 8.8082 0.0563 flnðDÞg2 0.4981 lnðDÞ ¼ 877
i.e.,
C¼
Us;d 1 þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2
ðQc =Qd Þ rc Us;d 1 þ ð0:315=1:33Þ 93:01772
¼ 877
¼
76 1:2337
amc
At flooding condition
Us;d ¼ 410:5 ft=hr and Us;c ¼ Us;d ð0:315 = 1:33Þ ¼ 97:2 ft=hr
Considering 50% of flooding velocities, operating velocities are
Us;d ¼ 205:3 ft=hr and
Us;c ¼ Us;d ð0:315 = 1:33Þ ¼ 48:6 ft=hr
i.e., total operating velocity ¼ 253.9 ft /hr (77.4 m/hr).
Based on the above, tower cross section ¼ (1.33 þ 0.315)/(77.4) ¼ 0.0213 m2, i.e., D ¼ 0:165 m.
Even this operating velocity of 77.4 m3/(m2 hr) is much higher than the operating velocity in the
range 20e30 m3/(m2 hr).
3
420
Chapter 13 Extraction
We try with a standard diameter of 0.3 m, that gives the operating velocities as
Us;d ¼ 1:33 p 0:32 4 ¼ 18:82 m sec and Us;c ¼ 0:315 p 0:32 4 ¼ 4:46 m sec,
and this is within range.
Final selected tower diameter D ¼ 300 mm
Ratio of tower diameter to packing size z12 : 1. This is above 8:1 and is acceptable.
Tower packed height is 4.75 m, and therefore shall require a redistributor midway. As such
redistributors are warranted in random packed towers after 2e3 m.
Direct catalytic air oxidation of toluene to benzoic acid in liquid phase is carried out with
acetic acid as solvent and the toluene conversion is about 75%. Typically the reactor is an air sparged
pressurised system charged with toluene as feed, acetic acid as solvent and cobalt acetate as catalyst
dissolved in it. At end of the batch time, the charge is drained in a pool of cold water and cooled further
when benzoic acid crystals form and settle down at 15 C and is filtered off. If no water is added, the
acid, water and toluene remain as the liquid phase. On addition of water, two liquid phases form and
some of the acetic acid gets transferred to the aqueous phase that forms below the hydrocarbon phase
(toluene phase).
Problem 13.2.
Reactor charge is of 250 L of toluene and 250 L of acetic acid and for 75% conversion of toluene,
the final composition based on stoichiometric calculation is
Component
kg
%w/w
Toluene
54.2
15.55
Acetic acid (HAc)
262.5
75.32
Water
31.81
9.13
Total
348.51
100
Design the single-stage contacting process for separating the unreacted toluene for reuse. Since the
acetic acid is to be recovered from the aqueous phase by distillation, the aqueous phase should contain
minimum of 80% w/w acetic acid. The equilibrium data for tolueneeacetic acidewater system at
15 C is given in Table P13.3 (J. Chem. Thermodynamics 57 (2013) 76e81).
We note that the feed point lies in the miscible range of the ternary system and therefore to separate
acetic acid from toluene, additional water is required to bring the mixture point within the dome of
immiscibility where two liquid layers form with acetic acid primarily in the aqueous phase.
The rectangular ternary plot for tolueneeacetic acidewater system at 15 C (288.2 K) may be
constructed from data in Table P13.3. We also note that toluene and water are practically immiscible
and so the equilibrium data are redrawn as XeY plot (where X ¼ xB =xA and Y ¼ yB =ys ). It is nearly
linear with slope, m ¼ 16.719. The plot is not shown here.
Due to the negligible mutual solubility of toluene and water, the concentration of water in the
extract phase and that of toluene in the raffinate phase are neglected and we use Kremser equation
(Eq. 13.4a) for single-stage extraction, i.e., N ¼ 1 to find the additional amount of water required. The
Kremser equation
13.6 Design illustrations
Table P13.3 Equilibrium data for tolueneeacetic acidewater system.
S [ water, B [ HAc, A [ Toluene
Aqueous phase (fraction w/w)
Toluene phase (fraction w/w)
T [ 288.2 K
ys
yB
yA
xs
xB
xA
0.7875
0.2098
0.0027
0.0005
0.0123
0.9871
0.7472
0.2505
0.0023
0.0006
0.0181
0.9813
0.6885
0.3086
0.0029
0.0006
0.0269
0.9725
0.6552
0.3376
0.0072
0.0007
0.0323
0.9670
0.6034
0.3875
0.0090
0.0010
0.0411
0.9579
0.5446
0.4450
0.0104
0.0012
0.0534
0.9454
0.5252
0.4636
0.0113
0.0018
0.0580
0.9402
0.4448
0.5370
0.0182
0.0025
0.0765
0.9210
0.7921
0.2064
0.0015
0.0009
0.0124
0.9868
0.7321
0.2657
0.0022
0.0010
0.0220
0.9770
0.6898
0.3068
0.0034
0.0012
0.0281
0.9707
0.6227
0.3682
0.0091
0.0017
0.0396
0.9587
0.6055
0.3853
0.0092
0.0017
0.0427
0.9556
0.5317
0.4559
0.0125
0.0024
0.0586
0.9390
0.5049
0.4822
0.0129
0.0027
0.0664
0.9308
0.4452
0.5355
0.0193
0.0034
0.0816
0.9150
0.7857
0.2124
0.0019
0.0012
0.0160
0.9828
0.7354
0.2568
0.0073
0.0013
0.0239
0.9748
0.6904
0.3028
0.0068
0.0016
0.0313
0.9671
0.6334
0.3598
0.0067
0.0023
0.0417
0.9560
0.5988
0.3939
0.0073
0.0029
0.0488
0.9483
0.5322
0.4587
0.0091
0.0043
0.0657
0.9300
0.5030
0.4847
0.0123
0.0042
0.0734
0.9224
0.4490
0.5361
0.0149
0.0057
0.0909
0.9034
T [ 298.2 K
T [ 313.2 K
421
422
Chapter 13 Extraction
ln
N ¼1 ¼
XF YS =m
1
1
þ
1
XR YS =m
ε
ε
lnε
F XR
on rearrangement is ε ¼ XXR Y
.
S =m
Based on Table P13.3 and Fig. P13.5, XF ¼ 262:5=54:2 ¼ 4:84; YE ¼ 80=20 ¼ 4; and
XR ¼ YE =m ¼ 4=16:719 ¼ 0:24
rε ¼
XF XR
4:84 0:24
¼ 25:56
¼
XR YS =m 0:24 1=16:719
and
m F 0 16:719 54:2
¼ 35:45 z 35:5 kg
¼
25:56
ε
Since the feed already contains 31.81 kg water, an additional amount of (35.5e31.81) ¼
3.69e3.7 kg of water is needed as solvent. The material balance of the system along with relevant
stream properties is shown in Fig. P13.5.
S0 ¼
Feed
kg
Toluene (A) 54.2
Acetic acid (B) 262.5
Water
(S) 31.81
348.51
% w/w
ρ kg/m3
mw
μ (cP)
15.55
75.32
9.13
100.00
867
1050
997
92
60
18
0.6
1.33
1.3
Raffinate (0.51 volume fraction)
3
m
kg
0.0625
54.2
Toluene
**
0.11476
Acetic Acid 120.46
Water
–
–
0.17726
174.66
Solvent
kg
% w/w
Toluene
Acetic acid
Water
–
–
3.7
3.7
–
–
100.00
100.00
Based on
ln(μ) = Σ ln(μi),
i
kg
mol
mol.
fr.
0.589
2.010
–
2.599
0.227
0.773
–
1.000
Extract (0.49 volume fraction)
kg
–
Toluene
Acetic acid 142.04*
35.51
Water
177.55
% w/w
m3
kg
mol
mol.
fr.
–
80
20
100
0–
0.135
0.036
0.171
–
2.37
1.97
4.34
–
0.546
0.454
1.000
μ R = 1.11 cP, μ E = 1.363 cP
μ = μ υ E x μ υ R = (1.363)0.51x (1.11)0.49 = 1.227cP
R
m
E
* (35.51 x 80/20)
** (262.5 – 142.04)
FIGURE P13.5
Material balance and relevant physical properties.
Total liquid volume ¼ 500 þ 3.7 ¼ 503.7 L ¼ w0.504 m3.
Considering tank diameter D ¼ H (liquid height), we get D ¼ 0:862 m.
From Table 17.8, we adopt D ¼ 900 mm. This would lower H, but to make a conservative estimate,
we use H ¼ 900 mm for power calculation.
For agitating the mixture, a standard 90 RPM flat six-blade turbine agitator with disc is chosen. Its
dimensions following the nomenclature of Fig. 13.7 are
13.6 Design illustrations
423
DI ¼ 0:4 900 ¼ 360 mm, WI ¼ D5I ¼ 72 mm, Ddisc ¼ 23 DI ¼ 48 mm,
NI ¼ 90 rpm ¼ 1.5 rps
D ¼ 90 mm, t
L1 ¼ 0:25DI ¼ 90 mm, H1 ¼ D3 ¼ 300 mm, Wb ¼ 10
gap ¼ 0:1 Wb ¼ 9 mm,
No. of baffles ¼ 4
Agitator power estimate from Fig. 13.9
mm ¼ 1:227cP ¼ 0:001227 Pa sec; rm ¼ ð348:51 þ 3:7Þ=0:504 ¼ 699:3 kg=m3
rReI ¼ D2I NI rm =mm ¼ 1:107 105
and
NP ¼ P=D5I NI3 rm ¼ 5:2
as read from Fig. 13.9 (Curve 1).
Shaft power, P ¼ NP D5I NI3 rm ¼ 74:2 W.
Estimated motor power consumption ¼ 1:4 Pz105 W. This is a low value as the system viscosity is low and the mixer volume is not high. Using a ½ HP motor to drive the agitator
(1 HP ¼ 746 W) is suggested.
Mixing time estimate
Corresponding to ReI ¼ 1:107 105
2
fmix ¼ tmix
1
1
NI D2I 3 g6 D2I
1
3
H 2 D2
¼ 2.8
as read from Fig. 13.10 for turbine agitators.
1
tmix ¼ fmix 3
1
H 2 D2
2
1
1
NI D2I 3 g6 D2I
¼ 2:8 3
0:92 0:92
2
1
1
ð1:5 0:362 Þ3 9:816 0:362
¼ 7:7 sec
The mixing time is also quite low as the volume as well as the viscosity of the system is low. For
clear separation of phases, a practical settling time of 30 min is suggested. However, the same can be
estimated from the liquideliquid separator calculations discussed in Chapter 17.
Design steps for rotary disc contactor
The procedure to design RDC based on pilot plant test subsequently scaled to actual plant size is as
follows:
1) Pilot plant tests are performed using plant liquids usually in columns typically of diameter
0.075e0.15 m and height (number of compartments) sufficient to accomplish the desired
separation.
2) The pilot plant is run at different agitation speed N over the entire range of total throughput
ðUd þ Uc Þ to determine concentration of streams (after they reach equilibrium), holdup (on
stopping the tower) and flooding point at each throughput (by increasing N till the column floods).
3) The combination of specific throughput and agitation speed which gives the optimum
performance in terms of separation is estimated and from the data thus obtained, the slip velocity
424
Chapter 13 Extraction
N 3 D5
Uc
Us ¼ Uad þ1a
and specific power input ¼ H1 D2r at optimum is estimated (a is dispersed phase
holdup and Uc and Ud are the superficial velocities of the continuous and dispersed phase). The
flooding velocity of continuous phase Uc;F is determined at aF (the dispersed phase holdup at
s expðaF Þ
flooding) as Uc;F ¼ U
.
ðUd =Uc Þ=aF
4) The design slip velocity Us;design is taken as 0:7 0:8Us as a safe operating value and continuous
phase velocity Uc is determined as Uc ¼ Us;design ð1 aÞ Uad ð1 aÞ.
5) The tower cross-sectional area is then determined as Qc =Uc and from the diameter thus estimated
the other geometric parameters are determined from Table 13.5 referring to Fig. 13.3C.
6) The rotor speed of the actual tower Nplant is obtained by scaling pilot plant data at constant
specific power input, i.e.,
3 5
3 5
N Dr
N Dr
¼
2
H1 D pilot
H1 D2 plant
7) Column height Hplant ¼ NTU ðHTUÞeff where HTUeff is the effective height of a transfer unit
considering axial dispersion, i.e., ðHTUÞeff ¼ HTU þ HDU and HTU¼HTUpilot and HDU the
height of diffusion unit accounting for axial mixing, is obtained in terms of Peclet number of
continuous Pec and dispersed phase Ped as
HDU ¼
H1
H1
þ
Pec Ped
The individual Peclet numbers are
3:3
1
Ec ð1 aÞ
1
1
aUc
4:2 105
Ud
¼
and
¼
Pec
H1 Uc
Ped Pec ð1 aÞUd
D2
a
Where Ec and Ed , the diffusion coefficient of the continuous and dispersed phase, are
Ec ¼ 0.5H1 Uc þ 0.012Dr NH1 ðDs =DÞ2
4:2 105 Ud 3:3
E d ¼ Ec
D2
a
2
Axial mixing is very severe at lower velocity Q
Q1 > 10.
Design of new systems without pilot data can be made considering that flow capacity Ud þ Uc and
HETS increases with decrease in N and Dr and increase in Ds and H1 . HETS passes through a minimum with increase in N.
Further reading
425
Further reading
Wankat, P. C. (2006). Separation process engineering (3rd ed.). Pearson Education.
Treybal, R. E. (1963). Liquid extraction (2nd. Ed). McGraw-Hill Classic Textbook Reissue Series.
Koncsag, C. I., & Barbulescu, A. (2011). Liquid-liquid extraction with and without a chemical reaction. In Mass
transfer in multiphase systems and its applications. IntechOpen.
Perry, R. H., Chilton, C. H., & Kirkpatrick, S. D. (Eds.). (1963). Chemical engineers’ handbook (4th ed.). New
York: McGraw-Hill.
Geankoplis, C. J. (2003). Transport processes and separation process principles:(includes unit operations).
Prentice Hall Professional Technical Reference.
CHAPTER
Column and column internals for
gaseliquid and vapoureliquid
contacting
14
14.1 Introduction
The terms columns and towers are synonymous. These are continuous interphase mass transfer
equipment introduced in Chapter 8 (Interphase Mass Transfer, Table 8.1). As mentioned, towers for
vapoureliquid and gaseliquid contacting can be spray towers, bubble columns, packed towers and
tray towers. Spray columns and bubble columns in contrast to the rest do not have any special contacting internals. Their fluid inlet/exit arrangements and distribution is common with the packed and
tray towers. This chapter focuses on the tray and packed towers e the most common industrial
equipment for gaseliquid contacting. Tower design aims to enhance effective contact between the
process streams and reduce entrainment while minimising pressure drop. In addition, the design must
be consistent with the economics dictated by the process and type of construction.
Tray internals promote formation of vapour bubbles, and mass transfer occurs across the bubble
surface in a liquid pool on the tray. Some internals are used to improve physical separation as well as
other miscellaneous purposes including routing / diversion of phases. Schematic of a tray tower typical
for fractionation service is shown in Fig. 14.1A. Trays in a tower are perforated and the perforations
may or may not be fitted with attachments. This treatise focuses on the basic types of vapoureliquid
and gaseliquid tray towers namely sieve tray, bubble cap and valve tray. Fig. 14.2 shows the tray
construction features namely tray support ring (TSR) welded to the shell and major and minor beams
supporting the tray from bottom. The tray is built in suitable sections, one of which acts as a manway.
•
•
•
Sieve trays have simple circular perforations on the tray deck.
Bubble cap trays have caps covering individual vapour riser tubes fixed to the tray deck. The
assembly is submerged in the liquid pool. Vapour escapes as a chain of bubbles through slots on
the side of the caps.
Valve trays have flat or slightly curved plate concave to the deck as cover on the perforations in
the tray deck. The valve plate has three legs that pass through the hole and are bent outwards.
These restrain the plate from being lifted beyond a maximum limit by vapour flow through the
hole. The valve plate edge is also provided with three crimps that do not allow it to flush with the
deck and a small clearance (w2e3 mm) remains, through which the tray deck liquid may drain
when the tower is shutdown. Similar to the aforementioned trays, vapour escapes as a train of
bubbles through the liquid pool.
Process Equipment and Plant Design. https://doi.org/10.1016/B978-0-12-814885-3.00014-2
Copyright © 2020 Elsevier Inc. All rights reserved.
427
428
Chapter 14 Column and column internals for gas
Packed towers house a bed of packing irrigated by downflow of liquid and the vapour flows through
the rest of the void space in the bed. Small packing elements dumped randomly in the tower constitute
a ‘dumped bed’ of ‘random packing’. Towers can also have packing elements stacked regularly that
makes a ‘stacked packing’ section. A packed bed can also be blocks of ‘structured packing’ usually
sewn together with stainless steel wire and snugly fitting the tower cross section. Grid packing is
another type that has lower pressure drop, higher capacity and much lower efficiency than the other
types. Fig. 14.1B depicts a packed column.
(A)
(B) Overhead
Overhead
vapour
vapour
Demister
Reflux
Distributor
Reflux
Rectifying
section
Tray
Packed bed
(random/structured)
Feed
Feed
Stripping
section
Bed
limiter
Tray
Packing
support
Reboiled
vapour
Reboiled
vapour
Bottoms
Bottoms
FIGURE 14.1
Typical distillation column configuration for (A) tray and (B) packed column.
14.1 Introduction
429
Manway
Downcomer and weir
Calming area
Major beam
Tray
support
ring
Major beam
clamp, welded
to tower wall
Major beam
Minor beam
support clamp
Subsupport plate ring
used with angle ring
Minor beam support clamp
Peripheral ring clamps
Minor beam
support clamp
Subsupport
angle ring
FIGURE 14.2
Typical tray construction.
Considerations for choosing between packed and tray towers:
(i) Pressure drop per theoretical stage of contact for the same vapour and liquid load: pressure
drop increases in the order Structured packing (w15 mm WC) > Random packing (w30 mm
WC) > Sieve tray (w50e100 mm WC)> Valve tray > Bubble cap tray.
(ii) Capacity: Lower pressure drop can be translated into higher throughput or capacity of the
tower and revamp for capacity augmentation of existing tray towers with some of the trays
replaced by packed sections of structured packing is common.
(iii) Energy consumption: Lower pressure drop in packed towers allows the tower bottom pressure
to be lower. This translates into higher volatility difference between key components in the
lower part of the tower, thus requiring lower bottom temperature, reflux flow, condenser and
reboiler heat loads, all of these lead to lower energy input.
(iv) Maintenance and inspection: Towers are drained prior to maintenance shutdown. Complete
draining of packing is more difficult as compared to trays. Any hazard due to the presence of
the remaining liquid needs to be handled carefully by washing with utility water/steaming.
(v) Material of construction: Often packing material is cheaper compared to trays. This is
particularly relevant for corrosive services, e.g., ceramic packing elements are resistant to
corrosion by acid and alkali.
(vi) Liquid holdup: Packed tower has lower holdup than tray tower and is, therefore, a preferred
choice for (i) batch distillation to produce higher yield of distillate and (ii) thermally unstable
substances as the lower residence time deters its decomposition. On the other hand, for cases
where higher residence time is desirable, e.g., chemical reactions, absorption, etc., tray towers
430
Chapter 14 Column and column internals for gas
are favoured. High liquid holdup on tray as well as downcomer also dampens composition
fluctuations. The liquid holdup and residence time on a tray are primarily decided by height of
the outlet weir.
(vii) Change in feed composition: Corrective action for changes in feed composition can be made
more easily in tray towers by altering the reflux ratio and/or relocating the feed stage.
(viii) Foaming and emulsion formation tendency: This is higher on trays due to higher vapour
velocity while passing through tray perforations/slots.
(ix) Tower diameter: Tray towers are preferred for large diameter, while packing is a suitable
option for low throughput. It is difficult to inspect/maintain tray columns smaller than
1000 mm diameter due to limited space. In such cases, either an oversized tower or tray
cartridges fitted inside the column are suitable options. The latter option often does not have
perfect sealing at the wall that may lead to lower tray efficiency. Large diameter e packed
towers often suffer from maldistribution of vapour and liquid flow leading to lower efficiency
compared to tray towers. Large diameter tray design needs to ensure that the difference in
liquid depth across the flow path (on cross-flow trays) is within limit to minimise channelling
of vapour from areas with lower liquid depth. Multipass trays and cascade trays are design
options to reduce the difference in liquid depth.
(x) Temperature cycles: Cyclic and large temperature variation from cold start-up condition to
high operating temperatures damage (squeeze/crush) packing due to differential expansion and
contraction over the thermal cycles. Packed towers may not be suitable for such services.
(xi) Presence of solid: Systems with solids are better handled in tray towers than in packed columns
as the velocities are higher. Higher velocity and agitation tends to keep the particles suspended
rather than allowing them to settle down and clog the system. Cleaning of trays is much easier.
Solids often clog the liquid distributor in packed towers.
(xii) Heat removal capacity: Coils can be incorporated on trays to allow heat addition or removal.
(xiii) Weight: Usually tray towers weigh less than packed towers. This may reduce foundation cost.
(xiv) Liquid flow rate: High liquid rates in packed section reduce the contact efficiency, particularly
in structured packing. With options of cascade and multipass trays, tray towers can handle
higher liquid rates more efficiently.
(xv) Turndown (or turndown ratio): There are two definitions of ‘Turndown’ in literature and one is
the inverse of the other. In this book, turndown is defined as the ratio of normal operating
(intended) vapour throughput to the minimum allowable vapour flow rate without significant
loss of tray efficiency. Expectedly, this ratio is above one. A design with a higher ‘turndown’
suggests feasibility of operating the tower (without significant loss in separation efficiency) up
to a lower throughput limit. The turndown range of tray towers is higher. Packed towers do not
perform satisfactorily at lower liquid rates. Typically below 60% of design capacity, their
performance gets affected primarily due to improper distribution of liquid from the distributor.
(xvi) Flexibility in operation: Tray towers can handle liquid load over a wide range, while gas load
must lie within a relatively narrow range for achieving the design tray efficiency, only valve
trays allow greater operational flexibility. On the other hand, packed towers are extremely
flexible as far as gas load is concerned but require a minimum liquid load. This often excludes
their use in vacuum operation.
14.2 Tray towers
431
14.2 Tray towers
Fig. 14.1A shows the important features of a typical cross-flow tray tower commonly employed for
fractionation. Vapour and liquid are in countercurrent flow in the tower with vapour bubbles rising
through the perforations on the horizontal trays to the tray above and liquid flowing downwards
through the ‘downcomer’ connecting consecutive trays. However, on the individual trays shown, the
two phases exhibit cross flow since the vapour emerging from the perforations rises through the liquid
which flows across the tray from below the downcomer skirt at one end to the exit weir at the other end.
It crosses the weir and enters the downcomer to the tray below. It is worth noting that the liquid flow
area across a tray is nonuniform, increasing towards the central region.
Mass transfer is achieved across vapour bubbles rising through the pool of liquid on the tray.
Turbulence during contact promotes mass transfer and increases efficiency of contacting. However,
beyond a limit of turbulence, entrainment of liquid droplets and froth carryover reduce stage efficiency.
The vapour dispensers on the tray floor can have various layout patterns and various types of fitments
as described in the following section. Besides vapour dispersers (perforations, bubble caps and valves),
other components of the tray are as follows:
-
TSR, a circular ring welded with the tower shell
Bolting bars welded with tower shell
Downcomer apron/skirt bolted on bolting bars
Tray decks fitted on TSR and support beams
Tray support trusses/beams which support tray segments
Tray towers are often retrofitted with intermediate packed sections mainly to increase capacity.
The above description pertains to contacting trays, each of which provide one stage of vapoure
liquid contact. In addition, the chimney trays, that are noncontacting trays, are used for side stream
withdrawal from tray as well as packed towers as discussed later.
14.2.1 Contacting trays
Contacting trays are classified based on arrangement for vapoureliquid contacting and liquid flow path
on the trays.
Countercurrent and cross-flow trays refer to liquid flow relative to the rise of vapour bubbles. Sieve
tray without downcomer, also known dual-flow tray, is the only type of countercurrent tray. In this
case, vapour and liquid pass through tray deck perforations in opposite direction and the tray occupies
the entire tower cross section, thus providing slight vapour capacity advantages. There are no weirs,
baffles or other attachments, and typically 15%e30% of the tower cross section is the total perforated
area. The liquid forms a random pattern while draining and does not form a continuous streamlet from
each hole. Liquid holdup and interfacial area are strong functions of vapour rate that limit the operating
range (of vapour and liquid flow rates) with reasonable tray efficiency. These are also sensitive to load
changes. Due to their simplicity and lower efficiency, this tray option although cheapest (on unit cross
section basis) is used for small diameter columns and only when few stages are required. Additional
trays are provided to take care of poor efficiency. A unique advantage of counterflow trays is their selfcleaning ability which is particularly advantageous in fouling, solid-contaminated and corrosive
services.
432
Chapter 14 Column and column internals for gas
Cross-flow trays are the most common tray type and due to the longer liquid path has the highest
tray efficiency. The simplest cross-flow
arrangement, and consequently the cheapest
to fabricate, is the single-pass tray
Single-pass, multipass, cascade and reverse flow trays
(Fig. 14.3A). It has a segmental downcomer at
one side of the tray. The downcomer of
consecutive trays is fitted on opposite sides
such that liquid from the downcomer of the
upper tray flows across the tray to the downcomer at the other end as shown in Fig. 14.3A. Since the
flow across the tray is due to gravity, the depth of liquid reduces progressively along its travel path.
A large gradient is undesirable as this leads to lower resistance to the flowing vapour at lower liquid
depth (close to its downcomer). As a result, the vapour stream tends to flow preferentially or ‘channel’
from this zone instead of passing uniformly through the entire tray cross section. The gradient of liquid
level/depth on the tray depends on liquid flow rate and length of liquid path.
Towers that handle liquid with very low viscosity and low liquid to vapour flow rate have small
liquid gradient per unit length of liquid path. Such towers use reverse flow trays (Fig. 14.3B), where
despite the longer path, the gradient limit is not exceeded. In this case, the downcomers are all located
on one side of the tower and the liquid is forced to flow around a central baffle at the far side which
reverses its flow direction. The reverse flow tray provides more cap area at the expense of downcomer
area and is advantageous only for very low liquid/vapour ratios. These trays are used in air separation
towers.
Requirement of reduction in gradient has led to development of multipass trays and cascade trays.
These two types are encountered only in large diameter towers and are generally decided by the liquid
loading. When liquid load is high with respect to vapour, multipass trays are suggested and for even
higher liquid loads, the cascade type (with intermediate weirs) is recommended.
Towers fitted with two-pass trays have different layout of consecutive trays. One has two downcomers at opposite sides and the other has a single downcomer located centrally as shown in
Fig. 14.3C. This arrangement repeated in consecutive pair of trays splits the total liquid flowing on a
tray into two streams which halves not only the liquid load per unit tray width but also the travel length
of each liquid path. As a result, double pass trays provide considerably more liquid capacity and lower
liquid gradient as compared to single-pass trays. However, they cost slightly more than a single-pass
tray of the same diameter and due to the shorter liquid path, tray efficiency is lower as compared to
single-pass ones. An odd number of passes is not recommended because of problems in liquid distribution. Higher number of passes, though possible, is not too common.
Cascade trays have the tray deck in more than one level (usually two). The elevated deck and the
lower deck have their individual exit weir to ‘step’ the tray floor at two elevations, thus further cutting
down the liquid path in each section. Though the liquid flow rate on each deck is the same, reduction in
travel path reduces the gradient. Fig. 14.3D shows a typical cascade tray.
Tray types can be selected based on the information provided in Table 14.1.
14.2 Tray towers
(A)
(B)
(C)
Column
shell
433
(D)
Side downcomer
Seal
pan
Central
downcomer
FIGURE 14.3
Cross-flow tray with the liquid flow path marked (A) single-pass, (B) reverse flow, (C) two-pass and
(D) cascade tray.
Tray components: The different components of a tray are described in the following subsections.
Downcomer
This is the conduit for the passage of liquid between trays. A level of liquid accumulated in the
downcomer (downcomer backup) provides seal against vapour short circuiting through the downcomer
passage. Typically, the design backup is about half the tray spacing. It is also important to ensure that
the vapour bubbles disengage from the aerated liquid within the residence time in the downcomer and
only clear liquid flows out to the lower tray. For liquids with foaming tendency, the downcomer backup
should be kept low.
Common downcomer types are as follows:
•
•
•
•
Segmental downcomer e most common for medium to lager size towers (>300 mmf), as this
provides maximum utilisation of tower area for downflow and results in high liquid flow capacity.
Stepped apron downcomer e used to provide higher downcomer backup and increased active tray
area. Narrower cross section at the lower portion provides extra resistance to liquid downflow
resulting in higher downcomer backup.
Pipe downcomer e usually for low liquid flows. It is cheaper than segmental downcomer in small
diameter columns (<450 mm) but leads to reduced active tray area.
Envelope downcomer e has an enveloped construction located in the segmental area. The
envelope cross section can be square, rectangular or trapezoidal. These are used when liquid flow
rate is slightly more than that for pipe downcomers.
The downcomer apron is the internal wall of the segmental downcomer. This is also referred to as
the downcomer skirt. Sometimes the wall is inclined to provide a wider area at the downcomer top to
favour vapour disengagement (particularly in foaming systems). Increased backup level, if required, is
achieved by using a narrower cross section at the bottom that provides additional resistance to liquid
flowing down and out of the downcomer. The resistance depends on the frictional drop in the
downcomer and the ‘form friction’ loss as the liquid passes through the clearance below the downcomer apron is usually dominant. Downcomer backup and head loss of liquid leaving the downcomer
can be reduced, if required, by increasing the clearance under the downcomer apron.
434
Chapter 14 Column and column internals for gas
In case the resistance is insufficient to provide the requisite downcomer backup, the designer incorporates an inlet weir on the tray below, slightly away from the apron. This adds
further resistance to the liquid outflow path and ensures required backup and sealing.
However, inlet weir increases the possibility of plugging due to solid deposits from
Inlet weir
liquid and possibility of weeping due to impact of liquid on tray. So these are used
only if essential. If provided, the inlet weir should be 25e37 mm higher than the top
of the bubble cap slot and at least two 18 25 mm slots flush with the tray surface needs to be
provided to avoid dirt accumulation upstream of the weir. Tray designs with recessed seal pans prevent
vapour flow through the downcomer, but this is uncommon as the recessed design tends to accumulate
‘muck’. The seal pan is designed to avoid liquid back pressure and minimise restrictions to liquid flow.
The bottom tray must have a downcomer seal to prevent upflow of reboiled vapours through it.
Outlet weir
A straight weir formed as an upper extension of the downcomer apron is the simplest and most popular
design. A minimum of 6 mm liquid height above weir is kept in design for adequately uniform liquid
distribution. Triangular or rectangular notched weirs are recommended to improve distribution for low
liquid load. Typically, notch depth is limited to 12 mm to provide greater capacity in case higher loads
are encountered. Weir height can be adjusted to ensure a positive seal of the slots and force the vapour
to contact the liquid in bubble cap trays. This ensures good vapoureliquid contact at low and high flow
rates of both the phases. Increasing weir height increases tray efficiency at the expense of increased
pressure drop and entrainment.
Liquid bypass baffles
These are used at tray edge to guide the liquid flow path to minimise liquid bypassing of the ‘active’
tray area. These are also called redistribution baffles and are mostly used on reverse flow trays where
higher chances of maldistribution lead to low tray efficiency.
Bottom tray seal pan
These seal the downcomer of the bottom tray to prevent upflow of reboiled vapours. The downcomer of
the bottom tray is usually kept 150 mm longer than that on other trays in order to prevent vapour surges
or pressure pulses from breaking the seal. The seal pan is designed to prevent liquid back pressure and
minimises restrictions to liquid flow.
Weep holes
The tray deck is usually provided with small ‘weep holes’, typically 3 mm or slightly more in diameter.
When the tower operation is stopped, the liquid inside the tower gradually drains through these holes to
the tower bottom. Typical design draining time for towers is within 8 hours. Weep holes are located on
the tray deck below the downcomer and also at appropriate locations to ensure draining of the residual
liquid as completely as possible from the idle tower. Correctly sized weep holes neither allow
excessive weeping nor vapour passage during operation. Sieve trays and valve trays do not require
weep holes in absence of inlet weir. This is because liquid draining continues in these trays after
stopping of tower operation.
14.2 Tray towers
435
Vapour disperser elements
Based on vapour disperser elements, cross-flow trays are classified as sieve tray with downcomer,
bubble cap tray and valve tray. The vapour disperser element can be a simple hole/orifice on the tray
deck as in case of ‘sieve tray’ or more elaborate arrangements as in ‘bubble cap’ and ‘valve tray’.
These are arranged on the tray in triangular or in rotated square pitch.
Both bubble cap and valve trays are available from several manufacturers worldwide. Most often
the preliminary tray designs are vetted by the vendors who supply the tray components. Prominent tray
manufacturers like M/s Sulzer, M/s Koch-Glitsch, etc., have their own proprietary designs, claiming
advantages of high efficiency, low pressure drop and lower fouling rate. Their designs include variations of the basic design described below.
Bubble cap
In bubble cap trays, each perforation is fitted with a riser tube through which the vapour rises. An
inverted cup is fitted over the riser tube. Though the round bell-shaped bubble caps are popular, there
are several noncircular designs that are rectangular or oval. Sectional view of a single bubble cap
shown in Fig. 14.4 illustrates the operation. Vapour from the tray below flows through the risers and
reverses its direction to flow through the annular space between the riser and the cap before finally
emerging through slots on the cap apron. The slots are rectangular or trapezoidal with the narrower
side up (shown in the figure). Both shapes give good performance but usually rectangular slots give
slightly higher capacity, while trapezoidal slots give slightly better performance at low vapour rates.
Triangular slots are too limited in capacity although they perform better at low vapour rate. It is not
essential for all bubble cap designs to have slots but, typically, the round bell-shaped cap with trapezoidal slots, shroud ring and removable mounting is most popular.
The entire assembly remains submerged in the flowing liquid and the vapour ideally emerges as a
train of small bubbles. The ensuing vapour depresses the liquid level while passing through the slots
either as bubbles (at low vapour rate) or continuous streams (channelling at high vapour rate). Fig. 14.5
shows a bubble tray and different cap designs. Large volume of published data and experience for
bubble cap trays allows the designer to work with confidence.
Vapour flow
Trapezoidal slot
ds/2
Dynamic slot
seal (hss)
Outlet weir
elevation (hw)
Liquid flow
hs
ds
hriser
hs
Static slot seal
Slot opening (hso)
(partial)
Shroud ring height
hsc
dr
deap
FIGURE 14.4
Sectional view of a single bubble cap illustrating its working.
436
Chapter 14 Column and column internals for gas
FIGURE 14.5
(A) Typical single-pass bubble cap tray with segmental downcomer and (B) several designs of bubble caps.
Shroud rings provide structural strength to the end of cap. The ring may rest on the floor or may
have three 6 mm short legs for dirty service. The legs allow fouling or sediment to
be washed out of tray and also provide some additional cap action under extremely
loaded condition (a condition of obvious lower efficiency with vapour exit below
Shroud ring
the shroud ring).
Valve
In case of valve trays, holes usually of about 30e40 mm diameter with a maximum up to 150 mm
are punched on the tray. Each hole is fitted with a movable discetype cover (valve) plate which adjusts
the vapour exit cross-section below the valve plate. This arrangement prevents liquid from leaking to
the lower plate at low gas loads and avoids excessive pressure drop across the valve at high gas loads
(by greater opening of the valves). The valves have legs protruding through the hole. The leg ends are
twisted outwards so that the rising vapour can lift the valve up to a limit of around 25 mm or so. In
14.2 Tray towers
437
caged type valve trays, there is an external cage guiding and limiting the valve lift. The layout of a
valve tray is no different from a bubble cap tray. Fig. 14.6 shows the most common type of valve with
integrated legs mounted on tray deck, and Fig. 14.7 illustrates its working.
Vapour from below emerges from the valve, forming a stream of bubbles in the cross-flowing
liquid pool. With increase in vapour flow, the valve lift is more and the area for vapour escape
into the liquid pool increases. At lower vapor flow rates, the lift is less which still allows a steady
flow of bubbles through a smaller opening. Thus, the quality of vapoureliquid contact remains
almost the same over a wide range of vapour flow and the valve trays can operate with almost the
same efficiency near (within 5%e10%) incipient flooding condition as well as for low and intermediate loading. This leads to the important advantage that valve trays have a higher turndown ratio
compared to other trays (sieve and bubble caps) with the same vapour exit area and enables minimum quality of off-specification product during start-up and operation with minimum utility
requirement over a wide range of feed rate. In addition, there is more effective utilisation of column
and auxiliary equipment and improved product quality along with reduced reflux ratio resulting in
utility (cost) savings. The modern mechanical design virtually eliminates sticking problems which
enables rapid draining, decreases shutdown time and simplifies maintenance. Worker comfort is
improved as the top of the disk is smooth and flat and there are no sharp projections above the tray
deck. However, the disk has three crimps that prevent the valve to sit flatly on the deck and seal the
hole. Instead, a gap of w2 mm remains between the deck and the valve. This avoids sticking of the
valve disk to the deck. It also allows draining of deck liquid through the opening and eliminates the
need of ‘weep holes’ on valve trays.
FIGURE 14.6
Typical valve with integrated legs mounted on tray deck.
438
Chapter 14 Column and column internals for gas
FIGURE 14.7
Working of a simple tray valve.
14.2.2 Choice of tray type
Selection of the tray type crucially affects the performance and economics of the tower. For a particular
service, i.e., vapour and liquid load and their properties, the optimum tray design is unique. It is usually
not economic to have different designs for the individual trays in a tower. However, it is not uncommon
to come across different design of trays for the stripping and the rectification section. A typical
example is the use of disc and doughnut trays in the stripping section of FCC unit fractionator, while
the rest of the trays are bubble cap or/and valve trays. The special types of ‘disc and doughnut’ trays
handle heavy hydrocarbon liquid containing more than 10% w/w catalyst fines. In case of plant retrofit
design, trays of a different design may be used to increase capacity or improve performance for
specific set of trays in the tower.
A comparison of the different tray types mentioned above is summarised in Table 14.1 to facilitate
selection of tray type.
14.2 Tray towers
439
Table 14.1 Comparison of the different tray types.
Tray type
Feature
Sieve tray
without
downcomer
Sieve tray with
downcomer
Bubble cap
Valve tray
Vapour passage
Through holes on
tray deck and then
through liquid
Through holes on
tray deck and then
through cross
flowing liquid
Through risers into
bubble caps, out
through slots and
then through cross
flowing liquid
Through holes on
tray deck and then
through cross
flowing liquid after
lifting the valves
Liquid passage
Through holes
countercurrent to
vapour flow onto
tray below
Across tray deck
over outlet weir
through downcomer
to the tray below
Across tray, over
caps, outlet weir
and downcomer to
the tray below
Across tray, over
valves, outlet weir
and downcomer to
the tray below
Capacity
Similar to sieve
tray
As high as bubble
caps in design
region but falls to
unacceptable
performance at
lower capacity
Moderately high
High to very high
Efficiency
w40% or less,
decreases at lower
rate
w40% or less,
decreases at lower
rate
High (w70%)
High (w70%),
often higher than
bubble cap
Turndown ratio
Lower than sieve
tray with
downcomer
Unsuitable for
variable liquid
operation
w2e3:1
Not suitable for
operation under
variable liquid
load
10:1
Can operate up to
extremely low
liquid rates with
marginal drop in
tray efficiency
Usual range of
flexibility is
50%e120% of
vapour load and
15%e130% of
liquid load
4e5:1
Special designs
claim even 10
Entrainment
Low to moderate
Moderate
About 3 times of
sieve trays
Moderate
Pressure drop
Lowest
Low (between
bubble cap and
valve tray)
High
Intermediate
(higher than sieve
tray
Recent designs
give same as sieve
trays
Continued
440
Chapter 14 Column and column internals for gas
Table 14.1 Comparison of the different tray types.dcont’d
Tray type
Feature
Sieve tray
without
downcomer
Sieve tray with
downcomer
Bubble cap
Valve tray
Cost
Cheapest
Cheap
High
2e3 times the cost
of sieve trays
20% more than
sieve tray
Maintenance
Low
Low
Relatively high
Low to moderate
Fouling tendency
Very low
Suitable where
fouling is
extensive and for
slurry handling
Low
High, tends to
accumulate solids
Low to moderate
Effects of
corrosion
Very low
Low
High
Low to moderate
Availability of
design information
Some information
available
Open literature
Open literature
Proprietary but
sufficient
information
available in open
literature
Main applications
Capacity revamps
where efficiency
and turndown can
be sacrificed.
Highly fouling and
corrosive services
Most towers when
turndown not
critical
Extremely low
flow conditions
where leakage
must be minimised
Most towers
when turndown is
important
Application
Handles suspended
crystals and small
solid materials and
polymer-forming
materials
Holes get plugged
in salting out
systems
Good in vacuum or
low pressure drop
design
Systems where
high capacity near
design rates to be
maintained in
continuous
services
Handles suspended
solid particles.
Holes become
plugged in salting
out systems
All services except
extremely coking,
polymer formation
or other high
fouling conditions
Services where
tray must remain
wet and maintain a
vapour seal
All services except
extremely coking,
polymer formation
or other high
fouling conditions
Also used when
throughput varies
over a wider range
Miscellaneous
Unstable at times
for large diameter
(>2.5 m) towers
14.2 Tray towers
441
14.2.3 Tray construction
Trays can be fixed or removable. Fixed trays are welded to the shell. These are difficult and expensive
to maintain and are rarely used.
Removable trays can be
- Set of trays in the form of a cartridge which is lowered inside the tower from the top. As already
mentioned, these do not perform very satisfactorily due to leakage through the shell clearance and
are also expensive to maintain.
- Trays fixed by flanges between tower sections. These are used for small diameter towers, usually
D < 750 mm, and are expensive to fabricate and difficult to maintain.
- For D > 1200 mm, trays are typically in sections that are taken inside through the manholes and
assembled inside by bolting. Fitting of the valves/bubble caps is carried out inside the tower.
Whenever sections are joined, bolts fixing the tray sections with the backing strip/truss have to be
placed along the joining line. This reduces the number of valve/cap/holes that could otherwise be
accommodated in that space. The shape as well as the size of the tray sections is carefully
designed to accommodate maximum number of disperser elements. Tray manway section can
typically be 450 500 mm or larger, depending on the manhole size on the tower. The second
largest dimension of the tray section should obviously be such that it can be introduced through
the manhole. Design value of hydraulic load is 600 N/m2 live load on tray þ 3000 N/m2 over
downcomer seal area. An additional 1500 N concentrated load is imposed on any structural
member during construction and maintenance.
14.2.4 Efficient operation of contacting tray
Tower internals are designed to operate with maximum efficiency for specific vapour and liquid flow
rates on individual trays. A properly designed tray must ensure the following:
•
•
•
•
Good vapoureliquid contact
Sufficient liquid holdup for efficient mass transfer
Sufficient area and spacing to keep entrainment and pressure drop within limits
Sufficient downcomer area for unaerated liquid flow between trays
Net result of the closely coupled operation of all trays gives the performance of the tower.
Maloperation of one tray affects the performance of the adjoining trays. Hence, the individual trays
need to operate within ranges of vapour and liquid flow rate where tray efficiency as well as effect on
the neighbouring trays is within acceptable (design) limits. The tray is designed for a specific pressure
difference at the design point and is expected to operate with limited fluctuations around the mean
value. Under this condition, the vapour flow is close to uniform through the openings on the tray.
The range of satisfactory operation of a tray is usually represented on a two-dimensional plot with
liquid and vapour flow rates as the abscissa and ordinate, respectively. This is referred to as ‘tray
performance range diagram’. Fig. 14.8 shows the nature of diagram for typical sieve trays with the
hatched area denoting the ‘area of satisfactory operation’. In order to arrive at the smallest tray size
(diameter), the design point needs to be close to the upper limits of vapour as well as liquid flow rates
(say at ‘A’ in the figure). This enables maximum utilisation of tray capacity and effectively results in a
low tower diameter. Usually 10% to 15% overdesign with respect to vapour and liquid flow is
considered as a reasonable design point.
E
e n xce
t r a ssi
i n m ve
en
t
Chapter 14 Column and column internals for gas
G
Entra
inme
nt
B
Satisfactory
operation zone
A
C
Weeping
Excessive weeping
Dumping
D
F
mer
nco
Dow oding
flo
Vapour flow rate
442
E
Liquid flow rate
FIGURE 14.8
Typical nature of performance range diagram for a sieve tray with downcomer.
As shown in the figure, the range of satisfactory operation is bounded by the maloperations of
excessive entrainment, downcomer flooding and entrainment flooding, excessive weeping and dump
point. So in order to establish the range, a designer needs to understand the maloperations mentioned.
Keeping the liquid flow rate (on the sieve tray) constant at ‘A’, if the vapour flow rate decreases
below a limit, there is increased liquid flow through the openings. When the flow exceeds the minimum
tolerable limit, the liquid level on the tray falls. The condition denoted as operating point ‘C’ is termed
‘weeping’. In this case, the entire liquid drains through the sieve holes before reaching the outlet weir.
A further decrease of vapour flow leads to ‘excessive weeping’ say at operating point ‘D’ where the
tray operation and contacting becomes unstable. At still lower vapour flow rates, there is nonuniform
and fluctuating flow through the holes. The pressure drop across the tray fluctuates and is so low that it
cannot support the liquid level. The liquid, under this condition, ‘dumps’ on the tray below and no
liquid reaches the downcomer. The dumping condition corresponds to point ‘E’. Tray operation at
conditions of excessive weeping and dumping results in poor quality of vapoureliquid contacting and
a fall in tray efficiency below acceptable limit.
At vapour flow rates above the design point ‘A’, the contact time between the phases decreases,
consequently decreasing tray efficiency and increasing entrainment of fine liquid droplets to the upper
tray. Intermixing of liquid carried from a lower tray to an upper tray reduces product enrichment,
resulting in a lower separation efficiency of the tower. A small amount of liquid entrainment is unavoidable at normal throughput and the efficiency remains acceptable up to a limiting vapour flow rate.
At higher vapour flows (say at point ‘B’), the vapour emerging from the perforations entrain substantial
liquid droplets (and froth) and the efficiency drops sharply. This is the ‘entrainment flooding’ limit.
The onset of flooding is detected by a steep increase in pressure drop and a sharp decline in efficiency.
Keeping the vapour flow rate same, if the liquid flow rate is increased, the liquid level and the froth
above it in the downcomer keep on increasing. The level on the tray also increases but to a lesser
extent. At a limiting flow rate, the tray downcomer runs almost full of liquid. This is the condition of
‘downcomer backup flooding’. On further increase in liquid flow rate, the countercurrent flow of liquid
14.3 Tray design
443
entering downcomer and disengaging gas/vapour rising from the downcomer chokes the downcomer
entry and liquid starts accumulating on the tray. This condition, described as ‘downcomer choke
flooding’, is marked as ‘F’ in the figure. Exceeding this limit floods the entire tray and destabilises
operation. This is characterised by froth carryover and pulsating flow of vapour through an undesirably
high depth of liquid on the tray resulting in decreased vapoureliquid contact and reduced tray
efficiency.
At liquid flow rate lower than ‘A’, the liquid depth on the tray is less and liquid entrainment is more.
The limiting range is marked as ‘excessive entrainment’ in the figure and corresponds to the design
vapour flow rate with a much lower liquid flow rate. The onset of ‘excessive entrainment’ is marked as
‘G’ on the figure.
Though the performance range diagram (Fig. 14.8) has been shown for sieve tray with downcomer,
the limiting phenomena represented at the boundary of the shaded region are not very different for
other cross-flow trays. However, the shape of the shaded area may differ as discussed in subsequent
sections.
The additional malfunctions for contacting trays not shown in Fig. 14.8 are as follows:
(a) Pulsing occurs for (i) low and unsteady vapour rate, (ii) low slot opening (<13 mm) and (iii) low
dynamic liquid seal. Under this condition, the liquid pulses or surges even to the point of
‘dumping’ the liquid down through the risers to the tray below. This is avoided by maintaining a
steady vapour rate and a good slot opening to take care of reasonable upsets.
(b) Blowing occurs for extremely high vapour rates regardless of liquid flow rate. This causes large
vapour streams or continuous bubbles to be blown through liquid leading to poor vapoureliquid
contact, reduced tray efficiency and increased entrainment. Low slot seals contribute to blowing.
(c) Coning happens when liquid seal over slot is low and vapour rate is so high that it completely
forces the liquid away from the cap, thus bypassing the liquid entirely. This may also happen in
valve trays. A suitable bubble cap tray design is expected to recommend adequate dynamic slot
seal to prevent this action.
14.3 Tray design
Tray design is a two-step process. A preliminary design is first worked out for the flow rates and
properties of the vapour and liquid it has to handle. This step arrives at the estimate of the following
items, as applicable to the chosen tray type:
•
•
•
•
•
Diameter and spacing which are interrelated (tray diameter is based on vapour and liquid load,
tray type and tray spacing)
Tray layout e bubbling and downcomer area, number of passes, weir height
Fractional perforated area and number and diameter of perforations
Downcomer skirt clearance
Details of bubble cap (slot area and other dimensions)/valve tray
The second step is to firm up the values from the previous step and generate detailed (dimensioned)
drawings for the tray and tray fittings. This includes the details of the segmental construction, fixing
arrangements of the segments with each other and tower wall and fixing of downcomer with tray and
tower wall.
444
Chapter 14 Column and column internals for gas
The effect of tray design variables are compiled in Table 14.2, and the definitions of different area
terms used in design of bubble cap tray are listed below.
A is the tower cross-sectional area
Adc is the downcomer area
Aa , the active tray area is the area where aeration occurs, and for cross-flow single-pass trays, it is
the space between the two downcomers, i.e., Aa ¼ A 2Adc for a single-pass tray
AN , the net tray area is the area available for vapour disengagement. For single-pass cross-flow
trays, AN ¼ A Adc without splash baffle. If a splash baffle is used at the outlet weir, the active
area Aa is available for vapour disengagement and AN ¼ Aa ¼ A 2Adc
An;L is the net open liquid area of one tray ¼ area of tray e (area occupied by bubble caps þ area
of downcomer at tray inlet)
Ao is the total area of all active holes per tray
Ao;tray is the net perforated area of the tray marked in Figs. 14.12 and 14.15 which contains the
vapour disperser elements (bubble caps, valves, sieve holes) and is the tower area minus
(i) downcomer areas, (ii) two calming zones e upstream of the outlet weir and downstream of the
downcomer apron feeding the tray, (iii) clearance of typically 40e50 mm from the tray periphery
to accommodate the tray fixing bolts and (iv) area blocked by backing strips
Acap is the sectional area of tray contained within OD of one bubble cap
Ar is the total riser area on a tray
Table 14.2 Effect of tray parameters.
Parameter
Effect of increasing parameter value (D advantage; L disadvantage)
Liquid flow path
D High tray efficiency
D Cheaper
High hydraulic gradient and possible tray instability
Active area, Aa
D Reduced chances of entrainment flooding and higher interfacial area due to low
vapour velocity
Perforated area, Ao
D Low pressure drop
D Decreased entrainment beyond a limiting value
Higher chance of weeping
Higher chance of unstable operation
Hole size, do
D Less easily fouled
D Lower pressure drop
þ Lower entrainment
Poor gas dispersion
Higher weeping tendency
Downcomer area, Adc
D Low liquid velocity
D Good froth collapse
Lower utilisation of tower area for vapour throughput
Downcomer apron
clearance, hdc;clearance
þ Reduced liquid backup in downcomer
Increased chances of vapour passage through downcomer
Weir height, hw
Increased pressure drop, liquid holdup and weeping tendency
14.3 Tray design
445
Tray spacing
Tray spacing is important for normal operation as well as surging, foaming and pulsing conditions.
It is a function of tower diameter and operating conditions. Lower tray diameter increases vapour
velocity and entrainment. To limit entrainment, higher tray spacing may be required. Thus, an inverse
relationship exists between tray diameter D and tray spacing TS. Tray spacing is also higher for higher
frothing and entrainment tendency of the liquid. Typically, 450 TS 750 mm. Values of 450, 600,
750 mm (1800 , 2400 , 3000 ) are commonly used.
Additional considerations to decide suitable tray spacing are as follows:
•
•
•
•
•
•
•
•
•
•
•
•
•
Minimum residence time required in downcomer.
TSz twice backup height of liquid in downcomer hL;dc from downcomer flooding considerations.
Theoretical optimum tray spacing may be based on tray dynamic considerations which gives the
minimum tower cost.
Mechanical factors, e.g., sufficient space to facilitate inspection and repairs. For D 1500 mm,
TS 600 mm is recommended to allow workmen to crawl between trays. TSz450 mm is
sufficient for D 1200 mm, since personnel entry is not envisaged in narrow towers.
In cryogenic columns, e.g., in oxygen plants, tray spacing as low as 75 mm (300 ) is common as the
system viscosity and surface tension values are substantially low. However, the main advantage of
low tray spacing in cryogenic columns is reduction in heat inleak to the system, which results in
substantial decrease of operating cost.
Available headroom restriction if the tower has to be fitted inside existing buildings.
Number of trays, e.g., in fractionation requiring large number of trays, smaller tray spacing is
recommended to avoid the other option of splitting the tower into two columns. Fractionators with
a very few trays may be provided with tray spacing more than 600 mm.
TS is usually different at the feed zone, side stream draw (chimney tray) and vapour return inlet
locations. This is required to handle flashing/separation of vapour and liquid streams.
TSz1:5 times the regular spacing or minimum 750 mm on draw off trays and trays where feed or
circulating (or external) reflux stream are introduced.
Twice the regular tray spacing (minimum 1200 mm) wherever the tower diameter changes.
A minimum of 1500 mm, wherever the number of liquid passes per tray changes.
Minimum TS is 1200 mm where manholes are provided. One manhole is to be provided after 8 to
10 trays.
Additional 150 mm over the normal tray spacing whenever the downcomer is provided with a
separate seal pan.
Tower height
Overall height for tray towers are based on the following considerations:
•
•
•
•
Estimated number of actual trays and the adopted tray spacing decided from the considerations
discussed above.
Extra space for vapour feed.
Extra space to accommodate internal liquid feed pipes if the tower loading is high at the feed
zone.
Minimum 1500 mm spacing above chimney tray. Chimney height is based on residence time in
the chimney tray and controllability of the chimney tray level (usually 150 mm from minimum
operating level (LLL e low low level) to maximum operating level (HHL e high high level)).
446
•
Chapter 14 Column and column internals for gas
Minimum 300 mm clearance should be provided between chimney hat top to the bottom of the
upper tray.
Tower top dome height up to TTL (tangent length) may be twice the regular spacing of the tray or
minimum 1200 mm from the top tray deck.
14.3.1 Bubble cap tray design
A simplified view of the complex fluid dynamics of a bubble cap tray is presented in Fig. 14.9. The tray
cross section can be divided into three zones e entry calming zone, active area and exit calming zone
denoted by AB, BC and CD in the figure. The entry zone marks the clearance between downcomer
apron and the first row of bubble caps. Usually this distance is small and the flowing liquid is clear and
unaerated, although at times aeration may occur right after the downcomer apron.
The bubble caps occupy the active area BC, also known as bubbling area Aa . In a properly designed
tray, intense vapoureliquid contact results in a highly turbulent frothy mixture that provides large
interfacial area for enhanced mass transfer and high tray efficiency. The height of the aerated mass is hf
(not marked on the figure) and the effective hydrostatic head hL is the height of the ‘settled’ clear liquid
of density rL. If the mass of the vapour portion is neglected, the relative forth density rrel is
rrel ¼
hL rf
¼
hf
rL
(14.1)
and the residence time of vapour tV and liquid tL are
tV ¼
hf Aa ð1 rrel Þ
hL ð1 rrel Þ
¼
rrel
QV
UVa
(14.2a)
hf Aa rrel
hL
¼
QL
ULa
(14.2b)
and
tL ¼
In the above expressions, Q denotes volumetric flow rate and Ua is the velocity based on active
area, in consistent units. Subscripts L and V denote the liquid and vapour phases. Although the density
of froth decreases with height above the tray deck, a height average density rf is used for convenience.
Beyond C, the froth begins to collapse as it flows towards the outlet weir at point D. The length of
exit calming section to be provided, i.e., distance CD, depends on foam stability and is lower if an exit
splash baffle (for foam breakup) is provided. In highly foaming systems, such an exit splash baffle is
mounted upstream of the exit weir with clearance of 12e15 mm from the tray deck. The weir restricts
the passage of froth and clear liquid flows under the splash baffle to the outlet weir. For most
vapoureliquid systems, foaming is not excessive and a small calming section is sufficient. Nevertheless, some foam may be carried into the downcomer by the liquid and secondary foam may also be
generated due to liquid splashing. A froth level hfd in the downcomer is present as vapour disengages
from the froth. The tray spacing must consider the height of frothy liquid in the downcomer to avoid
vapour carryover to the lower tray which not only increases pressure drop but also decreases plate
efficiency. The liquid from the weir at D is thrown over into the downcomer, the distance beyond the
weir where liquid strikes the downcomer material is designated as dtw . The liquid depth is not uniform
across the tray and a gradient D exists to overcome the flow resistance due to bubble caps and aerated
mass. D is measured as the difference between equivalent height of clear liquid at inlet hLi and outlet
hLo side of tray. Vapour while rising through the riser of bubble caps and flowing through the annular
14.3 Tray design
447
space depresses the liquid level as it emerges through the slots. The ‘slot opening’ hso (shown in
Fig. 14.4) is the height through which the liquid gets depressed below the top of the slots. The distance
from the top of the slot to the ‘equivalent’ liquid level hss is the ‘dynamic slot seal’. The term
‘equivalent’ is used to indicate that the liquid on the tray is aerated and the height is with respect to
unaerated liquid.
Liquid droplets may also be entrained by the vapour phase. Some liquid entrainment with the
vapour leaving the tray is inevitable. As mentioned above, excessive entrainment lowers plate efficiency as liquid carryover from a tray with higher proportion of less volatile component(s) to a tray
with higher proportion of more volatile component(s) reduces the effect of fractionation. Less-volatile
components in the feed carried upwards by the vapour contaminate the distillate. Excessive entrainment or liquid backup in the downcomer causes flooding as already discussed. In all cases, the effect is
reduction of tray efficiency.
Splash
baffle
(optional)
Straight
downcomer
apron
Froth
Clear
liquid
dtw
Vapour
with mist
Froth
Recessed
seal pan
TS
hfd
Disengaging
space
Clear
liquid
Δ
hLi
hL,dc
how
hLo
hw
D
C
Tapered
downcomer
apron
B
A
No seal
pan
AB, CD – calming
zone
BC – active area
FIGURE 14.9
Tray hydraulics parameters for a bubble cap tray.
448
Chapter 14 Column and column internals for gas
Layout of tray is also shown in Fig. 14.15, which is the same for both bubble cap and sieve trays.
The performance range diagram depicting the safe operating zone for a typical bubble cap tray is
presented in Fig. 14.10 for gas and liquid loads expressed with respect to the active tray area. The zone
of satisfactory operation is bounded by the limit of different tray dynamic factors namely excessive
entrainment, overloaded slots, flooding, insufficient residence time, excessive throw over weir, poor
vapour distribution, dumping and vapour pulsation. Tower operation beyond the upper limits for gas
and liquid flow as shown in Figs. 14.8 and 14.10 is unacceptable and would lead to unstable operation
with severe flow fluctuations. However, operation below the lower limits may be permissible to certain
extent. Even if operation in this zone does not encounter severe flow problems, there is fall in tray
efficiency. Generally, the design operating conditions should be selected to ensure a safe margin from
the border curves and for most well-designed bubble cap tray columns, the efficiency curve is more or
less flat for vapour loads between 15% and 85% of flooding velocity.
Flo
odi
ng
Po
dis or v
tri ap
bu ou
m
tio r
pin
n
g
Satisfactory
operation zone
Insufficient slot submergence
with low weir height
Insufficient residence
Time; Excessive throw
over weir
Overloaded
slots
Du
Vapour flow rate
Excessive
entrainment
Liquid flow rate
FIGURE 14.10
Typical nature of bubble cap tray performance diagram.
Tower diameter
Two classical methods of estimating bubble cap tray diameter are as follows:
(a) Souders and Brown (I&EC, V.26, p.98, 1934) suggested estimation of tray/tower diameter, D (in
m) from vapour flow rate mV (kg/s) and maximum allowable vapour mass flux mV;max (kg/hr$m2)
using the following expression:
1=2
4
mV
D¼
(14.3)
p mV;max =3600
where mV;max is obtained from Eq. 14.4 in kg/hr$m2 based on total tower area (not the active area).
mV;max ¼ CfrV ðrL rV Þg1=2
(14.4)
14.3 Tray design
449
rL ; rV (kg/m3) are the density of liquid and vapour, respectively, and the C factor is a function of
liquid surface tension s (dynes/cm) and tray spacing TS (mm). The function, generally depicted
graphically, can be expressed as Eq. 14.5 which, estimates C (in m/hr)
C ¼ 0:3048 Kcorr fa lnðsÞ þ bg
(14.5)
Constants a and b for selected tray spacing are listed in Table 14.3a, and the value of the correction
factor Kcorr for different cases is given in Table 14.3b. The minimum and the maximum predicted
values of C for each tray spacing are also mentioned in Table 14.3a.
Tray diameter, thus estimated, is then rounded off based on Table 17.8.
Table 14.3a Variation of constants a and b with tray spacing.
Valid predicted range of C
TS
a
Minimum
m/hr (ft/hr)
b
Maximum
m/hr (ft/hr)
900 mm (3600 )
124.00
363.4
24.4 (80)
213.36 (700)
750 mm (3000 )
121.78
337.3
18.3 (60)
213.36 (700)
600 mm (2400 )
119.59
285.6
5.5 (18)
213.36 (700)
500 mm (2000 )
112.51
232.3
0
213.36 (700)
450 mm (1800 )
107.22
198.4
0
202.7 (665)
Table 14.3b Correction factor Kcorr for different applications.
Kcorr
Application
General case of fractional distillation and others
1
Absorbers
0.55
Fractionating section of absorber oil stripper
0.8
Petroleum columns
0.95
Stabiliser column or stripper column
1.15
It is important to note that
- the method is a generalisation based on standard bubble cap tray design and layout
- C factor may vary along the tower and needs to be estimated for the top, bottom and
intermediate position in order to evaluate the maximum diameter required
- mV;max is based on the total tower cross section. To take care of uncertainties in the design
conditions, it may be divided by a factor of 1.05e1.25 to arrive at a more conservative
(higher) tray diameter. The factor can be in the range 1.05e1.15 for towers operating in the
pressure range 0.35e17 kg/cm2(g), i.e., 5 to 250 psig.
450
Chapter 14 Column and column internals for gas
(b) Fair and Mathews (Petrol. Refiner, April 1958, p. 153) developed a generalised correlation of
flooding in bubble cap trays to estimate tower diameter. The graphical relationship correlates
dimensionless liquidevapour flow parameter FLV with vapour capacity parameter Csb for
different tray spacing under incipient flooding conditions where
rffiffiffiffiffiffi
m L rV
FLV ¼
(14.6)
mV rL
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rV
Csb ¼ UfV;n
(14.7)
ðrL rV Þ
mL and mV are the mass flow rates (kg/s) of the liquid and vapour; rV and rL are the density (kg/m3 at
tray pressure and temperature) of vapour and the liquid and Uf V;n is the superficial velocity (m/s) of
vapour at flooding condition based on net tray area (An) available for liquid disengagement, i.e., tower
area (A) minus the area of the downcomer (Adc) of that tray for a single-pass cross-flow tray. Unusual
baffling effects can reduce this area.
The graph is based on liquid surface tension of 20 dynes/cm and the correlation equation is
lnðCsb Þ ¼ a3flnðFLV Þg3 þ a2flnðFLV Þg2 þ a1flnðFLV Þg þ a0 1.1880
(14.8)
The constants a0, a1, a2 and a3 as function of tray spacing are listed in Table 14.4 for liquid
surface tension of 20 dynes/cm. When ss20 dynes=cm, the value of Csb is corrected by
multiplying with ðs=20Þ0:2 .
Table 14.4 Constants in Eq. 14.2 for different tray spacing.
a3
a2
a1
a0
300 mm (1200 )
0.0157
0.1863
0.7713
2.7708
450 mm (1800 )
0.0178
0.2027
0.8161
2.5493
600 mm (2400 )
0.0172
0.2071
0.8609
2.3289
900 mm (3600 )
0.0182
0.2156
0.8951
2.1038
Tray spacing mm (in)
Fair’s correlation is 15% accurate for (a) nonfoaming liquids with s ¼ 20 dynes=cm,
(b) bubble trays with weir height below 15% of tray spacing and (c) bubbling area covering most
of the area between the weirs.
It is also applicable to towers with large tray spacing (above 450 mm) when the process of
blowing the liquid off the tray is important. When tray spacing is smaller, the height of the two
phase layer and not the blow off process is decisive for the highest feasible gas load. For safe
operation, the froth level must always be less than the tray spacing.
It may be noted that experimental determination of true flooding point is difficult and so the
‘maximum capacity’ is usually decided by the ‘incipient flooding condition’. As stated above,
flooding in distillation tower can be initiated either on the tray (entrainment flooding) or in the
downcomer (downcomer flooding).
14.3 Tray design
451
The following steps during design is followed for finding the flooding velocity UfV and the tray
diameter D (m) corresponding to j%
flooding
ofthe tray.
Input: mL ðkg=sÞ; mV ðkg=sÞ; rL kg m3 ; rV kg m3 , j(%), sðdynes=cmÞ, TSðmmÞ
1. Compute: FLV from Eq. 14.6, this is a dimensionless number.
2. Calculate Csb from Eq. 14.8 corresponding to the value of FLV for the chosen tray spacing
from Table 14.4. Note that Csb is not same as C in case of SouderseBrown method that
considers negligible entrainment and involves total tower area for calculations.
3. Calculate the vapour velocity based on net tray area as
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
j
ðrL rV Þ
0:2
UV;n ¼
(14.9)
ðs=20Þ Csb
100
rV
This corresponds to j% flooding condition on tray and UV;n is in m/s.
Typically, j is 70% for tower diameter up to 2 m and 80% for higher diameters.
Considering downcomer area to be k% of the tray area, the tray diameter D (m) for vapour flow
rate mV (kg/s) is given by the following expression:
1=2
4ðmV =rV Þ
1
D¼
(14.10)
pð1 k=100Þ UV;n
Typically, as a first trial, the weir length can be considered to be 0:77D equivalent to
Adc ¼ 0:12A, i.e., k is w12%.
For accurate design, sizing is required for the top tray, bottom tray, above and below every feed
and side stream withdrawal or point of heat transfer and at maximum vapour and liquid loading
points. The largest diameter is adopted for design. However, for large columns, e.g., crude
distillation columns, different tower diameter for different sections may be more economic as the
material savings in such constructions is high.
After estimation of tower diameter, the bubble cap size and type and tray layout is decided and
the tray hydraulic limits are checked.
Check for entrainment
Fig. 14.11 shows the effect of flow parameter on entrainment. As a rough guide, the acceptable upper
limit of fractional entrainment (j) is 0.1. The total amount entrained (in kg mol/hr) for liquid flow rate
NL kg mol/hr is
e¼
jNL
1j
(14.11)
and the decreased tray efficiency Eactual due to entrainment is
Eactual ¼ Emv
1
1 þ eEmv =NL
(14.12)
where Emv is the local Murphree (vapour) tray efficiency.
It can be seen from the figure that entrainment is not significant for lower tray flooding percentages
and in such cases the check for j may be omitted.
452
Chapter 14 Column and column internals for gas
1.0
0.8
0.6
0.5
0.4
Per cent
flood
0.3
95
ψ, moles entrained/mole gross downflow
0.2
90
80
0.1
0.08
70
0.06
0.05
60
50
0.04
40
0.03
0.02
0.01
0.008
0.006
0.005
0.004
0.003
0.002
0.001
0.01
0.02
0.03 0.04
0.06 0.080.1
0.2
0.3
FLυ
FIGURE 14.11
Effect of flow parameter FLV
mL
¼m
V
qffiffiffiffi
rV
rL
on j for bubble cap tray.
14.3 Tray design
453
Tray passes
A guide for tentative selection of tray passes is given in Table 14.5.
Table 14.5 Guide for tentative selection of tray passes.
Estimated tower
diameter (mm)
Typical range of liquid flow rate (m3/hr)
Reverse flow
Cross flow
Double pass
920
0e7
7e200
1220
0e9
9e68
1830
0e14
14e91
91e159
2410
0e14
14e113.5
113.5e182
Cascade (double pass)
3050
0e14
14e113.5
113.5e205
205e318
3660
0e14
14e113.5
113.5e227
227e363
4580
0e14
14e113.5
113.5e250
250e410
6100
0e14
113.5e250
250e455
A quick estimate of the number of passes required for a particular liquid loading is obtained by
m =hr
considering a limit of 62e116 ðm weir
with the preliminary estimate of weir length often being
lengthÞ
3
76% of tower diameter.
Outlet weir
With segmental downcomer, the optimum weir length lw is around 60%e85% of the tower diameter
and this fixes the area of the downcomer. A good initial guess for weir length with segmental
downcomer on single-pass cross-flow trays is 76% of tower diameter, and the downcomer area is
10%e12% of the tower cross-sectional area. For double pass trays, the optimum side weir length is
50%e60% of tower diameter, typically taken as 62%D as first guess and the central weir length
is taken as 97%D. This is checked against the limit of weir loading (62.5e116.3 m3 per hr per m of
weir length) mentioned above and the number of passes or the tray diameter is altered, if required.
From Fig. 14.4
Weir height ¼ Cap skirt clearance ðtypically w 25 mmÞ þ Shroud ring height ðw 6 mmÞ þ
Slot height þ Static seal ðtypically w10 to 12 mmÞ
(14.13)
(1.5e300 )
Typically, weir height hw is 40e90 mm
for columns above atmospheric pressure
(Table 14.19) with the usual recommended being 40e50 mm. Minimum hw is 12 mm. For vacuum
operation, a lower hw of 6e12 mm (0.25e0.500 ) is adopted to ascertain low pressure drop across tray.
454
Chapter 14 Column and column internals for gas
Height over weir
Head due to liquid crest over the outlet weir (how ) depends on liquid flow rate per unit length of the
weir and is given by the Francis’ weir flow formula. For a segmental downcomer, how (in mm liquid) is
expressed as
mL 2=3
how ¼ 750
(14.14)
rL l w
where mL is in kg/s, lw ðtypically w0:76DÞ is in m and rL is in kg/m3. Due to constriction of liquid flow
by column wall, the weir crest is higher in this case as compared to flow over an open weir. This is
accounted for in Eq. 14.14 by using a higher value of the constant in the standard Francis formula.
A minimum height of overflow over weir is usually set at approximately 5 mm and this corresponds
to a minimum weir load (QL/lw) of 2 m3 per hr per m of weir length.
Though the trays are levelled accurately while fixing, a few millimetres of offset may set in over the
period of use. In fact during installation, the acceptable offset limit is 3 mm. To account for this,
designers often ensure minimum crest level of 10 mm at the lowest liquid rate to ensure steady flow
over the weir. The value may be considerably lower in small diameter towers, and at high liquid loads,
entrainment of liquid by gas may determine the minimum liquid load. In case the liquid flow rate over
L , a multipass tray is adopted. This parameter is more
weir obtained from design is greater than 5e8 s:m
important for vacuum than for high pressure systems.
Downcomer area
Depending on the ratio (lw =D), the area ratio of the segmental downcomer area to tray area (Adc/A) and
maximum downcomer width to tray diameter (wdc =D) get fixed by the geometrical relationship.
For,
c ¼ ðwdc = DÞ
Downcomer width as % of tray diameter ¼ 50 1 cos sin1 ðcÞ
Downcomer area as % of tray area ¼ ð50 = pÞ 2 sin1 c sin 2 sin1 c
(14.15)
(14.16)
(14.17)
For double-pass trays, the area of central downcomer may be estimated approximately as a rectangle with length D and width 200e300 mm (800 e1200 ) as decided by the designer. This leads to a small
over estimate of w2%.
Downcomer apron seal ¼ hw hdc;clearance
(14.18)
where hw ¼ height of weir and hdc;clearance ¼ downcomer apron clearance. The recommended
downcomer apron seal, hw -hdc;clearance is 12 mm (0.500 ), 25 mm (100 ) and 38 mm (1.500 ) for weir to
apron distance of 1.8 m (600 ), 1.8e3.6 m (600 e1200 ) and 3.6 m (1200 ), respectively.
Adc;clearance the downcomer apron clearance/liquid flow area under downcomer skirt is given as
Adc;clearance ¼ hdc;clearance lw
(14.19)
14.3 Tray design
455
Cap size
Though it is possible to custom design bubble caps, the common practice is to adopt a standard design
from Table 14.6. The most popular cap nominal size is 100 mm (400 ) OD for D 1:2 m. Caps of size
75 mm (300 ) and 125 mm (600 ) are also common in smaller (0.75e1.5 m) and larger column diameters.
Smaller caps provide larger slot area and more flexible arrangement resulting in less wastage and
liquid distribution areas particularly in smaller towers. They are also more easily covered by liquid
which causes improved mass transfer and higher efficiency. On the other hand, larger bubble caps are
cheaper for the same tray area and incur lower pressure gradients.
Generally, 100 mm (400 ) caps serve as good general purpose units for small as well as large diameter
towers. So towers with diameter in the range 750e3000 mm is first evaluated using 100 mm (400 ) cap and
if there are points of poor performance, cap size is changed and the performance re-evaluated.
Number of caps
Caps are fixed on the active tray area. The maximum number of caps that can be fitted on a tray
depends on (1) pitch, (2) clearances kept on the tray to accommodate the bolting arrangement for
fixing the deck to the tray fixing ring, (3) clearance for fixing bolts to fix the backing strips for the tray
segments, tray support trusses and beams and (4) calming zone on the tray. Fig. 14.12 shows the
unutilisable area for (1) and (3). The net perforated area of the tray contains the bubble caps and is the
tower area minus (i) downcomer areas, (ii) two calming zones, upstream of the outlet weir and
downstream of the downcomer apron feeding the tray, and (iii) clearance of 35e40 mm from the tray
periphery to accommodate the tray fixing bolts. The tray layout arrangement is the same for sieve
plates.
For a pitch of P mm, number of caps accommodated per m2 of net perforated area of tray Ao;tray can
6
6
210
pffiffi
be estimated from geometry as 10
for triangular pitch.
2
P2 for square pitch and
3P
Following the estimate, the actual number of caps nc on a tray is arrived at graphically by drawing
the tray layout. During the layout, caps that are too close to the tray periphery and the junction of the
segments or the support bars are removed. This brings down the actual number from the estimate based
on geometry.
Area fractions over tray
The typical distribution of areas (depicted in Fig. 14.12) as % of tower cross-sectional area is provided
in Table 14.7. The area of different tray components based on the bubble cap chosen (from Table 14.6),
the number of caps (nc) per tray and the tray diameter (D) is summarised in Table 14.8. The maximum
liquid flow path is typically 30%D.
Typical dimensions of bubble cap tray internals are summarised below:
•
•
•
Perforated area is approximately 10%e14% of active area; holes are either drilled or punched
depending on the plate thickness.
For most applications, round bell-shaped cap with trapezoidal slots, shroud ring and removable
mounting is recommended.
Shroud ring of height 6 mm (1/400 ) is recommended for all caps.
Table 14.6 Standard design of industrial bubble caps.
Material
Alloy steel
75
100
150
75
100
150
US standard gauge
12
12
12
16
16
16
OD, mm
79
104
155
76
102
152
ID, mm
OD e 2 2:78
OD e 2 2:78
OD e 2 2:78
OD e 2 1:59
OD e 2 1:59
OD e 2 1:59
456
Nominal size, mm
Carbon steel
Cap
20
26
39
20
26
39
Slot shape
Trapezoidal
Trapezoidal
Trapezoidal
Trapezoidal
Trapezoidal
Trapezoidal
Bottom, mm
8.5
8.5
8.5
8.5
8.5
8.5
Top, mm
4.2
4.2
4.2
4.2
4.2
4.2
Slot height, mm
25
32
38
25
32
38
Height of shroud
ring, mm
6
6
6
6
6
6
12
12
12
16
16
16
OD, mm
53
69
104
51
67
102
ID, mm
OD e 2 2:78
OD e 2 2:78
OD e 2 2:78
OD e 2 2:78
OD e 2 2:78
OD e 2 2:78
Slot width
Riser
US standard gauge
Cap standard heights, mm
13 mm skirt height
57
2.5
63.5
57
2.5
63.5
25 mm skirt height
70
76
83
70
76
83
38 mm skirt height
83
89
95
83
89
95
Riser slot seal, mm
13
13
13
13
13
13
2
Cap area, mm
p OD2
4
Area ratios
Reversal/riser
1.5
1.52
1.49
1.58
1.57
1.52
Annular/riser
1.15
1.25
1.2
1.26
1.33
1.25
Slot/riser
1.89
1.69
1.25
1.89
1.69
1.25
Slot/cap
0.67
0.62
0.50
0.71
0.65
0.52
Chapter 14 Column and column internals for gas
No. of slots
14.3 Tray design
457
End wastage
area
Downcomer
seal area
Downcomer
area
Net tray
Perforated
area
Outlet
weir
Downcomer
edge / inlet
weir / seal
pan edge
Calming
zone
Calming
zone
Flow path
length
FIGURE 14.12
Tray layout showing useable spaces for a single-pass cross-flow tray.
Table 14.7 Estimate of different areas as % of tower cross section.
Downflow area
Tower diameter
(m)
Cross
flow
920
10e20
Double
pass
1220
Liquid distribution area
Cross
flow
Double
pass
Cascade double
pass
End
wastage
10e25
10e30
8e20
7e22
1830
20e30
5e12
15e20
5e18
2410
18e27
4e10
12e16
4e15
3050
16e24
3e8
9e13
20e30
3e12
3660
14e21
3e6
8e11
15e25
3e10
4580
12e18
2e5
6e9
12e20
2e8
6100
10e15
5e7
9e15
2e6
458
Chapter 14 Column and column internals for gas
Table 14.8 Area estimate of different parts of a cross-flow tray.
Per tray
Per cap
Side downcomer
Riser area
Ariser(1)
Ar ¼ Ariser nc (4)
Slot area
As(1)
(2)
Active area
(3)
10
0.12A
12
76
hdc;clearance lw
hdc;clearance lw
pD 2 A
dc
4
pD2 A
dc
4
Tower area, p4 D2
Net area
% of tower area
As nc (4)
Downcomer area
Liquid flow area
under downcomer
skirt
Central
downcomer, if
present
100
88 (for no splash baffle)
76 with splash baffle
(1) Directly from Table 14.6; (2) already discussed; (3) calculated as tray area minus downcomer areas and area lost due to
clearances from weir, calming zone and tower wall; (4) nc ¼ no. of bubble caps per tray.
•
•
•
•
•
•
•
•
•
Recommended range for skirt height is 12e38 mm (0.500 e1.500 ). A minimum height of 12 mm
(0.500 ) provides for vapour overload, avoids excessive liquid gradient and provides space for
settling of solids, if required.
Rotated square and triangular pattern with pitch (centre to centre distance) minimum twice the
hole diameter; normal range is 2.5e4 times do . Pitch can also be 1.25 times the cap diameter.
Typically, the recommended cap spacing, measured between outside diameter of adjacent caps is
25e75 mm (100 e300 ). Triangular pitch can accommodate more caps for the same area.
Slots are usually rectangular, trapezoidal or triangular in shape. Rectangular and trapezoidal slots
have better loading characteristics and are therefore preferred. Slot widths ranging from 3 to
12 mm (1/800 e1/200 ) are employed. Higher tray efficiency is obtained with narrow slots and
fabrication is cheaper for wider slots. Based on this, 6 mm (1/400 ) mean slot width is a suitable
compromise. Slot heights range from 12 to 50 mm (1/200 e200 ). Low slot height limits slot capacity,
while other tray dynamic factors become controlling at larger heights. Based on cap size specified
in Table 14.6, recommended slot height range is 25e38 mm (100 e1.500 ). High slot seals are
practical for high pressure operations. The slot seal is to be kept low to limit pressure drop in
vacuum operations.
Riser height is determined by skirt clearance and riser slot seal. Recommended riser slot seal, i.e.,
vertical distance between top of riser and top of slots is 38 mm (1.500 ).
A reversal area greater than riser or annular area avoids flow restriction. For round bubble caps,
the optimum reversal area is about 1.35 times the average of riser and annular area.
Width of entry and exit calming zones is usually 75 mm for tower diameter up to 1500 and
100 mm for higher diameters.
Typical plate thickness is 5 mm for carbon steel and 3 mm for stainless steel decks. Typical
material of construction used for tray deck is SS410S.
Segmental downcomer with a straight outlet weir is recommended.
The feed tray and the draw off trays are designed with their specific features discussed
in Section 14.6.
14.3 Tray design
459
Liquid gradient across tray
Liquid gradient, d mm per row of caps on the tray (perpendicular to liquid flow direction), uncorrected for
vapour velocity, is related to height of clear liquid (in mm) on tray ðhlo ¼ h
w þ how
þ D =2Þ), ratio (g)
of distance between caps to cap diameter, cap skirt clearance (s mm) and
ðQ=Lw Þ
Cd
It can be obtained
from Eq. 14.20.
ðQL =lw Þ
g
0:3 s
0:5
d 1:6 d þ 3 hlo þ
¼ 0:2015 Cd
1þg
g
(14.20)
This implicit equation in d needs to be solved iteratively and the LHS in the equation is found from
Eq. 14.21. D may be taken as 25 mm as a first trial to estimate hlo ¼ hw þ how þ D=2.
ðQL =lw Þ
(14.21)
¼ exp 0:0899 flnðf Þg2 0:0238 lnð f Þ þ 2:4146
Cd
where f ¼ 4831.18 m3 s liquid flow per m of mean tray width
Actual liquid gradient D corrected for vapour velocity is obtained as
D ¼ Cv d No. of rows perpendicular to liquid flow direction
pffiffiffiffiffi
where Cv is found from Fig. 14.13 against liquid load with Vo rv as parameter.
To use the plot,
Parameter:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
QV in m3 =s
pffiffiffiffiffi
rv in kg=m3
Vo rv ¼ 0:8197 ðA in m2 Þ
(14.22)
x-axis is liquid load per ft mean tray width, gpm ¼ 4831.17 (m3/s liquid flow per m mean tray width)
and Cv is directly read from y-axis in Fig. 14.13.
Tray pressure drop (htray , mm of liquid)
Total pressure drop per tray due to vapour flow may be taken as 50e100 mm (200 e400 ) of water
column for towers at atmospheric pressure and above and 2e4 mm Hg for columns operating at
vacuum (50 mm Hg). It is the summation of the three head loss components that the vapour has to
overcome, viz,
htray ¼ hdry þ hso þ hal
hdry , the head loss for flow through dry caps (excluding slots), is expressed as
r QV 2
hdry ¼ 273:4Kc V
r L Ar
(14.23)
(14.24)
for hdry in mm, QV in m3/s and Ar (total riser area per tray) in m2.
mm can be obtained as function of r, the ratio of annulus area to riser
The dry cap coefficient Kc in m$s
area from Eq. 14.25 for round bubble caps.
Kc ¼ 0:6373 r 2 2:0386 r þ 2:0554
(14.25)
460
Chapter 14 Column and column internals for gas
Cv, VAPOR LOAD CORRECTION FACTOR
1.4
1.3
Vo ρ v
1.2
1.9
1.1
1.2
1.1
1.0
1.0
0.9
0.8
0.8
0.6
0.7
0.6
0.5
0.4
0
10
20
30
40
50
60
70
80
90
100
LIQUID LOAD PER FOOT MEAN TRAY WIDTH, GPM
FIGURE 14.13
Correction (Cv ) for d.
From Davies, J.A. (1947). Bubble tray hydraulics. Industrial and Engineering Chemistry, 39, 774.
This equation is valid for 1:0 r 1:5.
hso the head loss through wet slots is estimated for different slot loading as follows
For slots not fully loaded, head loss accompanying vapour flow ¼ slot opening assuming clear
liquid to exist around slots (although in reality the liquid is aerated).
n For loaded slots, head loss ¼ height of slot opening which can be obtained from Table 14.6.
n For overloaded slots, QV > QV;max , hso ¼ hs þ Height of shroud ring if the cap design has a
clearance under the skirt and for caps flush with tray floor, the increased pressure drop is
n
hso;overloaded
¼
hso
Qv ;overloaded 2
.
Qv ;max
Estimation of % slot opening is discussed in the following section.
% Slot opening
Slot opening at vapour load QV is obtained from Fig. 14.14 which presents slot opening (% of slot
height in mm) as function of QV QV;max for different slot types (shape and size details in Table 14.6).
The maximum vapour capacity QV;max in m3/s is calculated using Eq. 14.26.
1
QV;max ¼ 0:060478Cs As fhs ðrL rV Þ=rL g2
2
3
(14.26)
3
for As, slot area per tray in m , QV;max in m /s, hs in mm and r in kg/m .
14.3 Tray design
461
100
Rs – trapezoidal slot shape factor,
ratio of top to bottom width
Slot opening, % slot height
80
60
Rs
–
0.
00
(tr
Rs
ia
–
40
Rs
u
ng
5
0.
–
la
r)
0
1.
00
(re
ct
a
u
ng
la
r)
Maximum slot capacity formula:
Qmax – CsAs
20
hsh
ρ – ρV
L
ρV
Rs
Cs
0.00
0.50
1.00
0.63
0.74
0.79
60
80
0
0
20
40
100
Vapor load, % maximum for fully loaded slots
FIGURE 14.14
Generalised correlation for slot opening.
pffiffiffiffiffiffiffi
Cs in ðm=s mmÞ is 0.63 for triangular slot, 0.79 for rectangular slot and 0.74 for a trapezoidal slot
with bottom width nearly twice the top width.
hal , drop through aerated liquid, is expressed as
hal ¼ bhds
(14.27)
b, the aeration factor, accounts for energy loss due to bubble formation, frictional resistance to flow
through aerated mass, static head effects and difference between slot drop and slot opening, if any. It is
1=2
estimated from Eq. 14.28 from the value of FVa ¼ UVa rV
. UVa is the vapour velocity based on
3
active tray area in m/s and rV is the vapour density in kg/m .
b ¼ 0:0255 ðFVa Þ3 þ 0:1744 ðFVa Þ2 0:4282 FVa þ 0:9979
(14.28)
The dynamic slot seal,
hds ¼ hss þ how þ D=2
(14.29)
hss is the static slot seal provided in Table 14.6, how , the height of liquid crest over weir is given by
Eq. 14.14 and, D, the liquid gradient in mm is estimated from Eqs. 14.20e14.22. Typically, the mean
dynamic slot submergence of 38 mm (1.500 ) is recommended for towers operating at atmospheric
pressure. A mean submergence of 25 mm (100 ) is recommended for operation under vacuum, 50 mm
(200 ) for 50e100 psig pressure and 75 mm (300 ) for 200e500 psig pressure conditions.
462
Chapter 14 Column and column internals for gas
Check for vapour distribution
In bubble cap trays, a significant liquid gradient often causes vapour maldistribution resulting in low
tray efficiency. This effect is checked from vapour distribution ratio rvd which is the ratio of liquid
gradient D to the mean cap pressure drop ðhcap ¼ hdry þhso Þ.
The normal design limit is recommended as
ðrvd ¼ D = hcap Þ 0:5
(14.30)
In case this limit is exceeded, rvd can be minimised at the cost of increased pressure drop and
reduced capacity by blanking off some of the caps or designing caps with higher pressure drop. Low
rvd combined with low pressure drop and high capacity can be obtained by adopting wider cap spacing
and higher skirt clearance to reduce D.
Special care is required to calculate rvd for stepped caps and cascade trays. In both cases, the worst
distribution on the tray is checked by calculating rvd for extreme pairs of rows. In addition, an effective
D needs to be considered as the gradient between the corresponding rows minus the amount of stepping
for stepped caps and the difference in dynamic submergence (hss þ how þ D to the particular row) for
the rows in question for cascade trays.
Vapour velocity and corrected ‘approach to flooding’
Vapour velocity is given as the volumetric flow rate of vapour per unit tray net area or
UV;n ¼ QV =An
(14.31)
Flooding % of the tray is recalculated with the ‘vapour velocity’ obtained from Eq. 14.31 and the
tray flooding velocity (Eq. 14.7) expressed as
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðrL rV Þ
UfV;n ¼ Csb
rV
The tray diameter needs to be increased in case flooding limit is reached, which does not happen
often. The entrainment is also recalculated for the revised flooding % from Fig. 14.11.
Downcomer pressure drop (hdc;prdrop , mm of liquid)
Downcomer head loss primarily occurs when the liquid flows out on the tray through the opening
below the downcomer skirt.
It is considered to be predominantly a function of velocity (m/s) of outflow below the skirt and is
estimated using the following correlation
QL;m3 hr 2
hdc;prdrop ¼ 0:1275
(14.32)
100Ada
where hdc;prdrop is in mm of liquid, QL;m3 hr is the liquid flow rate in m3/hr and Ada is the minimum flow
area in m2, the lower value of area under downflow apron or between apron and inlet weir (if provided).
14.3 Tray design
463
Downcomer backup (hL;dc , mm of liquid, for all cross-flow trays)
Downcomer backup in terms of clear liquid level is expressed as
hL;dc ¼ hw þ how þ hdc;prdrop þ htray þ D
(14.33)
All terms on the right-hand side of Eq. 14.33 are discussed above.
An important check is
hL;dc TS=2
(14.34)
Velocity and residence time in downcomer
The two considerations for sizing of downcomer are (i) residence time and (ii) maximum allowable
velocity.
Residence time in downcomer tdc is calculated from liquid flow rate and clear liquid volume in
downcomer as
tdc ¼
Adc hL;dc
QL
(14.35)
The minimum residence time needs to lie within 3e7 s, the higher limit is for foaming systems.
The maximum velocity of clear liquid in the downcomer is limited by choking in the downcomer
and disengagement of vapour bubbles from the liquid. The recommended range of maximum
downcomer velocity is 0.06e1.5 m/s (0.2e0.5 ft/s) with the typical value being around 0.1 m/s.
Downcomer throw over the weir
Liquid throw over weir (dtw ) is the distance from the top of the weir to the level of aerated mass in
downcomer. Throw of liquid over weir into downcomer is not important in case of segmental
downcomers.
For multipass trays, it is important for centre and off centre downcomers where the two liquid
streams from opposite weirs are thrown towards each other. However, this is not important for the side
downcomers. In case of central downcomer, dtw is estimated as
pffiffiffiffiffiffiffiffiffiffiffiffiffi
dtw ¼ 0:8 how hff
(14.36)
where hff the height of free fall in downcomer measured from weir is
hff ¼ TS þ hw hfd
(14.37)
hfd ¼ hL;dc =rrel
(14.38)
rrel ¼ 0:5
(14.39)
and
If dtw calculated from Eq. 14.36 is greater than half the width of centre downcomer, antijump
baffles are employed.
464
Chapter 14 Column and column internals for gas
System (foaming) factors (applicable for all cross-flow trays)
The flooding of a tray due to excessive downcomer backup of liquid along with foam or due to
entrainment of foam with vapour leaving the tray are often different for specific systems and applications. In either case, this is reflected as loss of tray efficiency that needs to be taken care of while
using the generalised correlations presented so far.
Traditional flooding equations are corrected with a (derating) system factor (SF). Actual downcomer backup (including foam) is calculated by dividing the calculated backup (hL;dc ) by (SF). Some
designers also discount flooding velocity (UfV ), calculated using SouderseBrown type of equations
with the system factor (SF). System factors of some common services are listed in Table 14.9 and may
be used for the pertinent cases.
Table 14.9 System factor for different services.
SF
System
Crude/vacuum column
0.85e0.9
Crude pretopping column
0.8e0.85
H2S/CO2 (gas)- amine absorber
0.65e0.7
Glycol absorber
0.65e0.7
Amine regeneration column
0.85
Glycol regeneration column
0.85
Sour water stripper column
0.7
Caustic regeneration
0.3e0.6
Oil absorbers
0.85
Weep holes
These have a diameter of 3e5 mm. A general recommendation is to provide 275e280 mm2 of weep
hole area per m2 (4 square inch per 100 ft2) of net open liquid tray area summed over all trays in the
tower.
Alternatively, the following empirical expression can be used for bubble cap tray draining:
ð10:895N þ 1:36192Þ m0:12
An;L
l
q¼
(14.40)
1:2
deq;wh =h0
r0:25
l
where N is total number of actual trays in column, q is the draining time of the tower in minutes.
Average viscosity and density of liquid at temperature in tower is ml cP and rl gm/cm3. deq;wh (mm) is
the diameter of a circle whose area is same as the total area of all weep holes on one tray. h0 (mm) is the
lower of the bubble cap riser height and the height of overflow weir. An;L (m2) is the net open liquid
area of one tray. The accuracy of the relationship is 6% on an average. During design, the draining
time is set to a reasonable value e say typically 6e8 hours and deq;wh is calculated using Eq. 14.40.
Number of weep holes is then calculated based on a chosen weep hole diameter.
14.3 Tray design
465
14.3.2 Sieve tray design (cross-flow type e with downcomer)
A sieve tray comprises of a flat metal sheet perforated with round holes and suitably supported in the
tower. The tray is connected with one or more downcomers for liquid discharge and may contain weirs
and baffles for directing vapour and liquid flows. Fig. 14.15 depicts the schematic of the sieve tray.
A comparison with Fig. 14.9 denotes similar liquidevapour contacting action of a sieve tray and a
bubble cap tray, both having sufficient liquid submergence to prevent short circuiting of vapour. There
are, however, two differences between vapour flow in sieve tray and bubble cap trays. In sieve trays, the
vapour emerging from the sieves flow primarily in the vertical direction unlike the tortuous path
followed during flow through bubble caps and since there is no built-in liquid seal, only vapour flow
can prevent liquid weeping through the holes.
The active tray area (Ao,) is characterised by the aerated mass or froth of height hf equivalent to an
effective hydrostatic head hL . The aerated mass collapses in the calming section upstream of outlet
weir. The calming section may be provided for partial froth collapse but is generally not needed and the
overflow material is in reality aerated. The equivalent height of clear liquid hlo at the liquid exit end is
calculated as the sum of the outlet weir height and the crest of equivalent liquid falling over the weir.
Downcomer design must take into account secondary froth formation and allow space for froth
collapse; otherwise froth density may be too low for adequate liquid outflow resulting in decrease of
efficiency and increase in pressure drop.
The terms ‘foam’ and ‘froth’ are often interchangeably used in literature. In this book, froth is the
expanded material formed during passage of gas or vapour through a liquid and if the expansion is
related more to liquid physical properties than to method and degree of aeration, the material is ‘foam’.
In sieve tray design, ‘foamability’ is important and taken into account.
Design deliverables for cross-flow sieve trays are as follows:
•
•
•
•
•
•
•
•
•
•
Liquid flow arrangement
Active area
Area occupied by perforations
Hole size, pitch and arrangement
Hole blanking, if required
Tray baffles and calming zones
Downcomer area, type and clearance
Tray inlet arrangement
Outlet weir e type and dimensions
Tray thickness, material and tray levelness
Steps of design
Input: mL ðkg =sÞ; mV ðkg =sÞ; rL kg m3 ; rV kg m3 ; j%; sðdynes=cmÞ; TSðmmÞ
Initial guess: d0 ¼ 5 mmð3 =1600 Þ; A0 =Aa ¼ 0:1; TS ¼ 450=600 mm; Tray thickness: 2 mm;
straight weir, hw ¼ 50 mm, lw =D ¼ 0.77; segmental downcomer with Adc/A w0.12
466
Chapter 14 Column and column internals for gas
End wastage
Ao, tray
Adc
Adc
Calming zone
Wdc
Dφ
lw
Foam
level
Δ
Perforations
TS
hw
hdc, clearance
hL, dc
how
FIGURE 14.15
Schematic representation of sieve tray dynamics.
(1) Tray type and spacing
Single-pass cross-flow tray is selected from economic considerations even for large diameter
columns. TS of 300e410 mm (1200 e1600 ) is common. Higher tray spacing up to 760 mm (3000 )
may be adopted for high vacuum services and it is rarely less than 230 mm (900 ). Usually TS for
sieve plates can be 150 mm (600 ) less than for a corresponding bubble cap tray.
(2) Estimation of tower diameter
Sieve tray diameter is estimated from ‘incipient flooding’ limit which corresponds to maximum
tray capacity. Although both liquid or vapour capacity limitations can lead to ‘incipient flooding
condition’ and both are limiting at true flooding, the former is more common and should be
checked initially. The procedure presented in Section 14.3.1 can be followed and Fig. 14.16 can be
14.3 Tray design
467
used to estimate
K (analogous to Csb in Eq. 14.7) as function of liquidevapour flow
the constant
rffiffiffiffiffiffi 1
m L rV
parameter: FLV ¼
.
mV rL
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rV
(14.41)
K1 ¼ Uf V;n
ðrL rV Þ
Fig. 14.16 is based on small diameter perforations (do < 6:5 mm). Larger perforation size results
in higher entrainment. The correlation is valid under the following conditions:
(i) ðAo =Aa Þ 0:1 and (Adc/A) ¼ 0.12.
(ii) ðhw =TSÞ < 0:15
(iii) s ¼ 20 dynes=cm
(iv) Nonfoaming systems or systems with low foaming tendency
In case of foaming systems, the vapour velocity Uf V should be 75% of the value predicted
following the aforementioned procedure.
For liquid surface tension ss20 dynes=cm and ðAo =Aa Þ 0:1, the corrected value of K1 is
¼ K1 ðs=20Þ0:2
KCorrected
1
(14.42)
If ðAo =Aa Þh0:1 and ss20 dynes=cm, the corrected value of K1 is
¼ ½5ðAo = Aa Þ þ 0:5K1 ðs=20Þ0:2
KCorrected
1
(14.43)
100
Plate spacing.m
–1
K1 10
0.90
0.60
0.45
0.30
0.25
0.15
10–2
0.01
0.1
FLV
FIGURE 14.16
Flooding capacity e sieve trays.
1.0
5.0
468
Chapter 14 Column and column internals for gas
The corresponding vapour velocity at flooding, Uf V;n , based on An is given by
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðrL rV Þ
Uf V;n ¼ KCorrected
1
rV
(14.44)
Similar to bubble cap trays, An, is the net area of tray available for liquid disengagement and is
typically (A e Adc). Unusual baffling can reduce this area.
If a splash baffle is used at the outlet weir, An ¼ Aa and the velocity obtained from Eq. 14.44 is
Uf V;a .
Usually 80%e85% approach to flooding is used.
The calculated tower diameter D is rounded off based on Table 17.8 as discussed in Section
14.3.1.
The results of flooding analysis give a tentative diameter-tray spacing combination which may be
adjusted in subsequent design calculations. For significant variations in volumetric flow rates of
liquid and vapour, the limiting tower size is obtained by making separate flooding calculations
for different points in the tower. Presence of side stream draw and circulating refluxes may
warrant such situations in distillation columns. It is usually sufficient to make two estimates e
above and below the feed point and changes in vapour flow rate are adjusted by blanking off
some rows of holes, while liquid flow rate variation is addressed by adjusting liquid downcomer
area. Different column diameters for different tower sections are adopted only for significant
variations in flow rates and are economical only for large towers. This is in fact rare for sieve tray
towers.
(3) Tray layout
Sieve trays with perforation diameter do z3 12 mm (1/800 e1/200 ) are commonly employed. The
recommended size for nonfouling services is 5 mm (3/1600 ) and for
fouling liquids and liquids containing solids, larger perforations
(12.5 mm/0.500 ) are adopted. For vacuum services and systems with low
Perforation size.
surface tension, do z3 6 mm (1/8e1/400 ). Air separation towers are
typically equipped with sieve trays of 1 mm or less perforation size.
Perforations are either drilled or punched on the trays. Punching is done for 2:5 do 19 mm.
The direction of punching oriented in the direction of vapour flow is often preferred. The
minimum perforation size is generally limited by dimension of punch die which depends on
thickness and material of tray (a general thumb rule e perforation size should not be less than
sheet thickness for C-steel and 1.25 times the sheet thickness in case of stainless steel). In usual
practice, tray thickness of 12 or 14 US standard gauge is employed except for C-steel where 10
gauge thickness is used. Thus, typical perforation size is 3.2 mm (1/800 ) in 14 US standard gauge
tray thickness of 2 mm (0.07800 ) and 4.76 mm (3/1600 ) in 10 US standard gauge SS tray of
thickness 3.6 mm (0.14100 ).
Interestingly, at small perforation diameter (do 2 to 3 mm), uniform gas flow through all holes
is the limiting mechanism and the minimum gas load decreases with increasing perforation size
while for do > 2 to 3 mm, liquid weeping through tray becomes decisive and the minimum gas
load increases with increase in perforation diameter.
14.3 Tray design
469
As a preliminary estimate, pitch P is calculated by considering the net perforated area discussed
above. If the calculated pitch does not correspond to a commercial
standard, the next smaller pitch is selected and the (net) perforated
area is recalculated to determine the amount of blanking
(perforations covered with sheet metal) required. Blanking strips
Hole pitch and number
should be distributed uniformly over active area except when used
for calming zones at the weirs. Blanked area should normally not
exceed 25% of active area (to avoid excessive entrainment). In order to avoid ‘dead spots’ in the
active area, the width of the backing strip should not exceed 70% of tower diameter for small
towers and 50% for larger ones The active tray area usually encircles the perforated area at a
distance of 50e75 mm (2e300 ) from the peripheral perforations and the perforations are arranged
on a triangular pitch with liquid flow normal to the rows. Generally, 2:5d0 P 5d0 with
P ¼ 3:8do commonly preferred. For effective tray action, perforations should not be more than
65e130 mm (2.5e300 ) apart.
6
pffiffi
As mentioned in Section 14.3.1, the number of holes per m2 of net perforated area is 210
for
3 P2
triangular pitch, when P is in mm.
The net perforated area Ao;tray is the difference between active area Aa and area covered by (i) tray
supports, tray rings, etc., (ii) inlet and exit calming zones and (iii) end
wastage area. Generally, the entry and exit calming zones are 75 mm each
for D < 1:5 m and 100 mm for D > 1:5 m.
Perforation area
The acceptable range of ðAo =Aa Þ is 0.05e0.15 with the preferred value
being 0.1 and for pressure services, the range is 0.08e0.10. The ratio is
never less than 0.05 and for some critical services, the ratio can be as high
as 0.17 to 0.175, provided weeping does not occur.
Open area ratio Ro is used only to identify perforated sheet metal material and for a given section
of material, it refers to the ratio of hole area to total area. For equilateral triangular pitch,
A0
¼ 0:905 ðdo =PÞ2
A
(14.45)
Ro ¼ 0:785ðdo =PÞ2
(14.46)
Ro ¼
and for square pitch
Perforated sheet metals usually come in standard width of 900 mm (3600 ) and 1200 mm (4800 ) and
in standard lengths of 2500 mm (9600 ), 3000 mm (12000 ) and 3500 mm
(14400 ). For special requirements, other widths and lengths can be provided.
Tray support members can be spaced at 300 mm (1200 ), 400 mm (1600 ),
Tray supports
450 mm (1800 ) or 600 mm (2400 ). Using blank margins of perforated sheets as
tray support minimises wastage of metal. Generally, tray spacing and support
members employed with sectional trays need to consider accessibility
through manways. The width of support ring is 50e75 mm and the support ring does not extend
into the downcomer area.
(4) Area ratios and adjustment of flow conditions
The tower cross-sectional area A ¼ ðp=4ÞD2 is reestimated from the rounded off D for single-pass
cross-flow tray area and the area of the individual tray components are calculated as Adc ¼ 0:12A,
An ¼ 0:88A Aa ¼ 0:76A; Ao ¼ 0:1Aa . Based on these, the flow conditions are adjusted and UV; n is
calculated from Eq. 14.9 to check that j is within permissible limits (80%e85%).
470
Chapter 14 Column and column internals for gas
(5) Entrainment
Fractional entrainment j (kg moles/kg moles gross liquid flow) is determined from Fig. 14.17
corresponding to FLV and % flooding and the total amount entrained is obtained from Eq. 14.11.
j in the range 0.1e0.2 represents optimum conditions.
100 9
8
7
6
5
4
3
Percent flood
2
95
10–1 9
90
Fractional entrainmentψ
8
7
6
80
5
4
3
70
2
60
50
10–2 9
45
8
7
6
40
5
35
4
3
30
2
10–3
2
3
4
5 6 78 9
10–2
2
3
4
5 6 7 8 9
10–1
100
FLV
FIGURE 14.17
mL
Effect of flow parameter FLV ¼ m
V
qffiffiffiffi
rV
rL
on fractional entrainment j for sieve tray.
From Smith, B.D. (1963). Design of equilibrium stage processes. McGraw-Hill.
14.3 Tray design
471
Fig. 14.17 shows that at high mL =mV , sieve trays may be operated quite close to flooding point
before significant entrainment occurs. Accordingly, optimum values lose their significance under
such conditions since flood point itself cannot be predicted accurately.
(6) Tray pressure drop
The pressure drop (htray ) across the tray in mm of liquid is
htray ¼ ho þ bðhw þ how Þ
(14.47)
¼ 9:81 103 h
and in pressure units (Pa), Dptray
tray rl .
ðhw þ how Þ is the operating liquid seal at tray outlet weir in terms of clear liquid height. hw is
typically 50 mm. Table 14.19 can be referred for selection of hw under different pressure
conditions and how can be estimated from Eq. 14.14. ho , the head loss due to vapour flow through
perforations (mm of liquid) is
ho ¼ 51 ðrV = rL Þ ðUVo =Co Þ2
(14.48)
UVo , the vapour velocity (m/s) through the perforations corresponding to ho , is calculated as
UVo ¼
ðmV =rV Þ
Ao
And the orifice coefficient Co is evaluated as
Ao
Co ¼ 0:7205 Aa
m values for different
Tray thickness
Hole diameter
(14.49)
þm
(14.50)
are listed in Table 14.10.
Table 14.10 Evaluation of orifice coefficient Co .
Tray thickness
Hole diameter
m
1.2
0.8142
1.0
0.7736
0.8
0.7080
0.6
0.6733
0.2
0.6404
0:1
0.5885
472
Chapter 14 Column and column internals for gas
1=2
The aeration factor b in Eq. 14.47 is obtained from Eq. 14.51 as a function of FVa ¼ UVa rV as
b ¼ 0:5792 þ 0:4027 eð1:5806FVa Þ
(14.51)
where UVa is the vapour velocity based on active tray area in m/s and rV is the vapour density in kg/m3.
The desirable range of the variable in the above equation is 0:305 Fva 3:05.
For j > 0:1, two-phase flow increases pressure drop through perforations and the equivalent head
loss hj>0:1 is given by
j
FLV
hj>0:1 ¼ hdry 1 þ 15 (14.52)
1j
Alternatively, the hydrostatic head of aerated mass on tray, hf , corresponding to clear liquid
height hL (in mm) can also be estimated from relative froth density from the expression
hf ¼ hL =rrel
(14.53)
rrel ¼ hL =hf ¼ 2b 1
(14.54)
where the relative froth density
Typically, rrel z0:4 0:7 and for design purposes, rrel ¼ 0:5 is normally assumed. The same
value of rrel is adopted for downcomer which needs to respect
hL;dc f0:5 ðTS þ hw Þg
(14.55)
(7) Weeping
Vapour velocity at weep point is the minimum velocity for stable operation and the perforated
area is chosen to ensure that the vapour velocity is above weep point at the lowest operating flow
rate. Weeping occurs on the trays due to the (static) head of (equivalent clear) liquid hL and is
opposed by liquid surface tension and vapour flow through perforations. This gives the condition
to prevent weeping as
ðhs þ ho Þ > ðhlo ¼ hw þ how Þ
(14.56)
where the maximum depth of liquid hs (in mm) that can be sustained by surface tension is empirically
given by
hs ¼
15:806s
rL do
(14.57)
for rL in kg/m3, s in dynes/cm and do in mm.
Tray weeping may occur at part or whole of the tray. This requires the parameter ðAo =Aa Þ to be
considered along with hlo and the conditions to prevent weeping are given by the following criteria
for 0.06 < ðAo =Aa Þ < 0.14 and ðAo =Aa Þ ¼ 0:2.
(a) When 0:06 < ðAo =Aa Þ < 0:14:
n
o
(14.58)
ðho þ hs Þ > 7.433 104 ðhlo Þ2 þ 0.2358 hlo þ 3.52
14.3 Tray design
(b) When ðAo =Aa Þ ¼ 0:20:
n
o
ðho þ hs Þ > 7.655 104 ðhlo Þ2 þ 0.43676 hlo þ 5.3
473
(14.59)
Since the influence of weeping on tray efficiency depends on the fraction of total liquid
downflow that weeps, even a small amount of weeping can be relatively serious at low liquid
flow rates.
Alternately, the minimum design vapour velocity to prevent weeping can be obtained as
UV0;min ¼
K2 0:90ð25:4 d0 Þ
r0:5
V
(14.60)
where UV0;min is the minimum vapour velocity through the holes (based on hole area) in m/s,
d0 is hole diameter in mm and K2 is a constant, expressed as a function of clear liquid depth on
tray ðhlo ¼ hw þ how Þ as
K2 ¼
32:9ðhlo Þ0:62
1:044 þ ðhlo Þ0:62
(14.61)
Eq. 14.61 is valid for 14 hlo 111:5
(8) Liquid gradient across tray ðDÞ
Liquid gradient problems are much less severe in sieve tray as compared to bubble cap and valve
tray design since the resistance to liquid flow is smaller in this case. So large diameter towers
without double flow paths are possible. In normal practice, the effect of gradient is neglected
unless D > 19 mm (0.7500 ).
Nevertheless, for long flow paths and high liquid rates, liquid gradient on sieve trays needs to be
checked. It is also significant in vacuum operations where low weir height causes D to be a
significant fraction of total liquid depth. Similar to the case of bubble cap trays, the condition for
stable tray operation is given by Eq. 14.30 as ðD =ho Þ < 0:5 where ho is given by Eq. 14.48 and D
in mm of clear liquid is calculated from Eq. 14.62 with all units in m.
D¼
f lpath Uf2
9:81 Rh
103
lpath ¼ D wdc;inlet wdc;outlet
(14.62)
(14.63)
where wdc;inlet and wdc;outlet are the width (weir to wall) of the inlet and outlet downcomer and D is the
tray diameter in single-pass trays. In case of double pass, the appropriate geometry is considered as
discussed in Section 14.3.3.
Rh , hydraulic radius for cross flow of aerated mass is given as
Rh ¼ hlo lf =ð2hlo þ lf Þ
(14.64)
The average liquid flow path width for a single-pass tray is the average of tray diameter D and
weir length lw ,
lf ¼ ðD þ lw Þ=2
(14.65)
474
Chapter 14 Column and column internals for gas
Rh U f r l
The friction factor f is obtained from Reynolds number Re ¼ m
for a known weir height
l
hw as
f ¼ expð 1:0583 lnðReÞ þ cÞ
(14.66)
f is estimated by interpolating values obtained from Eq. 14.66 for known Re at two nearest hw and the
corresponding c is available in Table 14.11.
Table 14.11 Evaluation of friction factor f for known Re and hw .
hw
c
10.2 mm (0.4)
6.5411
17.8 mm (0.70 )
6.9849
25.4 mm (10 )
7.4102
38.1 mm (1.50 )
7.8915
50.8 mm (20 )
8.2246
76.2 mm (30 )
8.7058
97.6 mm (40 )
9.1054
Using consistent units, the average liquid velocity on the tray in m/s is estimated as
Uf ¼ QL =ðhlo lf Þ
(14.67)
The calculated D is checked for the acceptability condition mentioned in Eq. 14.30.
For significant D, perforations nearer to tray inlet weep before those closer to tray outlet.
(9) Downcomer dynamics
Both sieve tray and bubble cap tray employ the same downcomer design and the only difference
in liquid handling occurs in the aerated zone. Downcomer backup in terms of clear liquid is
calculated by adding the head loss terms as discussed in Section 14.3.1.
hL;dc ¼ htray þ hw þ how þ D þ hdc;prdrop
(14.33)
Evaluation of the terms on the right-hand side of Eq. 14.33 is discussed above. hL;dc is measured
from plate surface, how and hdc;prdrop are estimated from Eqs. 14.14 and 14.32 provided in Section
14.3.1 (bubble cap tray design).
An important check is
hL;dc TS=2
(14.34)
Liquid throw over weir hfd is important only for multipass trays which is not common in sieve
trays. Antijump baffles can be installed to ensure that liquid flows smoothly into the central
downcomer.
14.3 Tray design
475
14.3.3 Valve tray design
Valve trays (also known as ballast trays from M/s Koch-Glitsch) are essentially sieve plates with larger
diameter of perforations covered by flaps which get lifted with increasing vapour flow. These are
mostly proprietary items. The procedure presented here is by M/s Koch-Glitsch that has been primarily
from the Ballast Tray Design Manual (Bulletin 4900), sixth edition. The design procedure estimates
tray diameter and spacing, capacity and pressure drop. Subsequently, changes in diameter, tray
spacing, cap spacing or downcomer specifications are made to arrive at an optimised design with
maximum capacity, maximum efficiency and minimum cost. The procedure outlined claims neither a
too conservative nor a too tight design. The correlations used in the design procedure outlined below
has been developed by Carl Branan (The Process Engineer’s Pocket Handbook, Vol. 1, Gulf Pub. 1990)
Design steps:
1. Approach to flooding (j %) is taken as not more than 82% for normal services and not more than
77% for vacuum operations. Typically, 65 j 75 for D < 0:9 m. A thumb rule is j ¼ 70% for
D 2 m and j ¼ 80% for D > 2 m
2. Tray spacing, TS, typically is 600 mm (2400 )
3. Estimation of approximate tower diameter (D) for calculation of flow path length
The approximate tower diameter Dapprox in m can be estimated from the following set of
equations at known actual vapour and liquid load of Qv and QL m3/s respectively.
ðDapprox Þ2 ¼ 9:925 A þ 624:03 A B þ 630:31 A B2 þ 433:11 ðBÞ1:719
Where for single pass tray,
B ¼ QL in m3 =s and A ¼ Qadj
v ¼ Qv
rffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rv
rl rv
(14.68)
(14.69)
Eq. 14.68 is valid for single pass trays for 600 mm (2400 ) TSat 80% flooding condition.
Estimation accuracy with respect to the original nomogram is 15% for 600 D 1200 mm and
for higher diameters up to 3000 mm the accuracy is w5%. The range of validity of flow rates are:
Qv < 0:85 m3/s and QL < 0:095 m3/s.
The same equation can be used for multipass trays using the values of A and B (in m3/s) from
Table 14.12.
Table 14.12 A, B to be used in Eq. 14.68 for estimation of tray diameter
Number of tray passes
Single
2 pass
4 pass
A(m3/s)
Qadj
v
Qadj
v =2
Qadj
v =4
3
B(m /s)
QL
QL =4
D(m)
Dapprox from Eq. 14.68
QL =2
pffiffiffi
2 Dapprox obtained
from Eq. 14.68
2 Dapprox obtained
from Eq. 14.68
476
Chapter 14 Column and column internals for gas
4. No. of tray passes as function of tower diameter is decided based on Table 14.13.
Table 14.13 Tray passes in valve tray towers.
Number of tray passes, NP
Dmin in m (ft)
Preferred D in m (ft)
2
1.52 (50 )
1.8 (60 )
3
2.44 (80 )
2.74 (90 )
4
3.05 (100 )
3.66 (120 )
5
4 (130 )
4.5 (150 )
5. The approximate diameter and number of tray passes NP is used to calculate flow path length,
FPL in mm from the following expression involving Dapprox in m.
750 Dapprox
NP
(14.70)
3:2808 Qadj
v þ ðQL FPLÞ=224:24
CAF ðj=100Þ
(14.71)
FPL ¼
6. Minimum active area of tray (Aa;min m2 )
Aa;min ¼
3
for Qadj
v and QL in m /s and FPL in mm, j is % approach to flooding specified in Step 1 of design,
FPL in mm is calculated from Eq. 14.70 and vapour capacity factor (CAF) is estimated as
function of tray spacing TS (in mm) and vapour density rV (in kg/m3) from Eq. 14.72.
For rV < 2.7 kg/m3 (rV < 0.17 lb/ft3),
1=6
CAF ¼ 6:412 103 SF TS0:65 rV
(14.72a)
and for rV > 2.7 kg/m3 (0.17 lb/ft3)
CAF ¼ SF 0:1392 þ ðTS = 1305:2Þ TS2 = 2560:2 103 ðTS rV Þ = 640.74 103
(14.72b)
System factor SF in Eq. 14.72 can be obtained from Table 14.14.
14.3 Tray design
477
Table 14.14 System factor for different services.
Tray SF
Downcomer SF
Nonfoaming, regular systems
1.00
1.00
Fluorine systems, e.g., BF3, Freon
0.90
0.90
Moderately foaming, e.g., oil absorbers, glycol and amine regenerators
0.85
0.85
Highly foaming, e.g., glycol and amine absorbers
0.73
0.73
Severely foaming, e.g., MEK units
0.60
0.60
Foam-stable systems, e.g., caustic regenerators
0.30 to 0.60
0.3
Service
CAF increases with increase of TS and decrease of rV . However, for a particular rV , there is a
limiting TS beyond which CAF does not increase
with tray spacing. This limiting TS in mm is
given by Eq. 14.73 for 32 rV 86:5 kg m3
TSlimit ¼ 63:284 104 r3V þ 1.4861 r2V 121.62 rV þ 3800:2
(14.73)
3
In cases of rV < 32 kg m , TSlimit ¼ 1200 mm.
7. Downcomer design velocity Udc;design (in m/s) is the maximum velocity of clear liquid in the
downcomer. It is limited by downcomer choking and disengagement of vapour bubbles from
liquid. It is taken as the smallest Udc;design value obtained from the following three equations:
Udc;design ¼ 0:17 SF
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Udc;design ¼ 6:957 103 ðrL rV Þ SF
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Udc;design ¼ 2:525 103 TS ðrL rV Þ SF
(14.74a)
(14.74b)
(14.74c)
where rL & rV are liquid and vapour density in kg/m3, TS is tray spacing in mm and SF is
specified as downcomer SF in Table 14.14 for different services.
Typically, Udc;design is recommended as 0.061e0.15 m/s (0.2e0.5 ft/s) and minimum downcomer
residence time is 3e7 s.
8. Minimum downcomer area (Adc;min m2 ) is given by
(14.75)
Adc;min ¼ QL = Udc;design j = 100
where QL is in m3/s and Udc;design is in m/s and j is the approach to downcomer flooding in %
If Adc < 0:11 p D2 4 , i.e., below
11% of tray area, then Adc;min is the smaller of (i) 2 Adc
calculated from Eq. 14.75, or (ii) 0:11 Aa;min , Aa;min estimated in Step 6.
9. Minimum tower cross-sectional area (Amin m2 ) is the larger one of that given by Eq. 14.76a and b.
Amin ¼ Aa;min þ 2 Adc;min
(14.76a)
478
Chapter 14 Column and column internals for gas
and
Amin ¼ 0.0929 Qadj
v
0:78 CAF ðj=100Þ
!
¼
0:1191 Qadj
v
CAF ð j=100Þ
!
(14.76b)
10. Minimum tower diameter D in m is recalculated from Amin obtained from Eq. 14.76 as
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
D ¼ 4 Amin =p
(14.77)
D is rounded off as per Table 17.8 and the number of passes are finalised accordingly from
Table 14.13.
The minimum cost tower will have cross section of Amin .
11. Downcomer width and area
Layout of tray areas with 1e4 passes with the downcomer width (H) and FPL marked are shown
in Fig. 14.18.
The downcomer area at the top is divided in proportion to the liquid rate received and the active
area served. In case of multipass trays, the liquid rate to the weirs in m3/hr per m of weir length is
set as equally as possible. Also the downcomer lengths are slightly adjusted to modular flow path
lengths. From Fig. 14.18, FPL can be expressed as
FPL ¼
D ð2H1 þ H2 þ 2H3 Þ
NP
(14.78)
FPL cannot be less than 405 mm (1600 ) in case of trays with manways.
Downcomer area (Adc, m2) is given as
Adc;i ¼ Hi SF D
(14.79)
where SF is the span factor fraction defined as the wall to wall distance at the midpoint of
downcomer expressed as fraction of tower diameter. Approximate values of SF for two, three and
four pass trays are shown in Tables 14.15 for H2 and H3 marked in Fig. 14.18.
Table 14.15 Span factor (SF) for different downcomers
SF
H2
# of passes
H3
2
1
-
3
-
0.95
4
1
0.885
Refer to Fig. 14.18 for nomenclature; H1 from weir length.
14.3 Tray design
H1
H1
FPL
H1
Single pass
H1
FPL
H3
FPL
H2
479
H1
FPL
Two pass
FPL
H3
FPL
H1
H1
Three pass
FPL
H3 FPL H2 FPL
H3
FPL
H1
Four pass
FIGURE 14.18
Layout of tray passes.
12. Active area (Aa )
Aa (m2) is the area available for ballast units between the inlet and outlet edges of the tray for
straight or sloped downcomers.
Aa ¼ A ð2Adc1 þ Adc3 þ 2Adc5 2Adc7 Þ
or
Aa ¼ A 2Adc;avg
(14.80)
where Adc;avg is the average Adc for odd and even trays. Sloped downcomers are used with recessed
inlet areas or draw sumps.
480
Chapter 14 Column and column internals for gas
13. Number of valves on a tray
Actual number of valves on the tray active area can only be found from a detailed layout of the
tray that considers the location of the major beam and truss lines. Truss lines are usually parallel
to the liquid flow direction but in case of trays with major beam, the truss lines are perpendicular
to the liquid path.
The approximate number of valves accommodated on a tray is thus the number of rows
multiplied by the average number of valves per row, with correction for the tray manway loss.
This is found as
(a) When truss lines are parallel to liquid flow path (for towers not having a major beam)
FPL 0:216
þ 1 NP
(14.81a)
No of rows ¼
0:5 Base
where FPL and Base are expressed in m
Valves per row ¼
WFP
0:8 ðNo. of major beams þ 1Þ
0:146 NP
(b) When truss lines are perpendicular to liquid flow path (with a major beam)
FPL 0:0445 ðNo: of TrussesÞ 0:15
No of Rows ¼
NP
0:0635
Valves per row ¼
1000 WFP
2 ðNo. of major beams þ 1Þ
Base NP
(14.81b)
(14.81c)
(14.81d)
where
FPL is the flow path length in m
WFP is the width of flow path (in m) ¼ ðAa Þ=FPL for Aa in m2
NP is the no of passes, and
Base ¼ base spacing of valves (in mm) which is the centre-to-centre distance between
valves in a row. Usually Base ¼ 76 mm (300 ). It can also be 88.9 mm (3.500 ), 101.6 mm
(400 ), 114.3 mm ( 4.500 ), 152.4 mm (600 ).
Spacing
00
For traditional round valves, orifices of 39 mm (1 17=32 ) diameter are punched in the deck in a
triangular pattern. The base pitch of the triangle (parallel to liquid flow direction) varies from 76
00
to 152 mm (300 to 600 ). The triangle height is typically 63.5 mm (2 1=2 ) except across truss lines
(joints). Truss lines are preferably parallel to liquid flow, but may be perpendicular to liquid flow
in larger towers that have at least one major beam.
The valve base pitch is inversely proportional to the required valve quantity, which is a function
of the design vapour rate. There will be approximately 130e150 valves per square meter of active
area when using a base pitch of 76 mm (300 ). A typical layout for a 1.5 m (50 ) single pass tray is
shown in Fig. 14.19.
481
1.25
4.25
2.5
11.75
9.69
14.3 Tray design
17.06
MANWAY
9.69
11.75
FLOW
25 × 1.50 = 37.50
7.00
11.25
4.25
TWR I.D. 5 FT- 0.00 IN
42.69
8.69
1.25
8.69
0.81
FIGURE 14.19
Typical layout for 50 single-pass tray.
Courtesy of Koch-Glitsch LP, Wichita, Kansas.
482
Chapter 14 Column and column internals for gas
14. Weir height is usually 50 mm (200 ) in most services. Generally, a weir height less than 19 mm
(0.7500 ) is not recommended but in vacuum towers, it can be as low as 12 mm (0.500 ). For a high
residence time, e.g., a system involving chemical reaction, hw can be 150 mm (600 ). For hw >
0:15TS, the effective tray spacing to calculate% flooding is the TS reduced by the excess weir
height over 0:15TS.
15. Pressure drop (hdry mm of liquid)
Dry tray pressure drop is the pressure drop of vapour in passing through the valves on the tray in
dry condition, similar to that of vapour flow through an orifice, where the head loss is
proportional to the square of velocity (UV;valve m/s) through the orifice.
It is taken to be the larger of the following two values calculated:
(a) Units part open:
2
hdry ¼ 1:35ðtm Þrm =rL þ K1 UV;valve
rV =rL
(14.82a)
2
hdry ¼ 273:4K2 UV;valve
ðrV = rL Þ
(14.82b)
(b) Units full open:
where tm is valve thickness in mm; rm is valve metal density, typically 8170 kg/m3 for ferrous
valves, K1 , K2 are pressure drop coefficients; UV ,valve is velocity of gas through valve in m/s, as
given by Eq. 14.84 and Avalve is total valve area per tray.
Koch-Glitsch valve type V-1 is used for most applications. It has integral leg and is suitable
for tray deck thickness up to 9.5 mm (3/800 ). The coefficients for this type of tray are
K1 ¼ 54.686 (0.2 in fps units) and K2 as function of deck thickness is listed in Table 14.16.
Table 14.16 K2 as a function of deck thickness.
Deck thickness mm
(in.)
K2
1.88 (0.074)
2.64 (0.104)
3.4 (0.134)
4.75 (0.187)
6.35 (0.25)
1.18
0.95
0.86
0.67
0.61
Alternatively,
The expression of hdry in mm of liquid head is
2
hdry ¼ 273:4 K UV;valve ðrV = rL Þ
(14.83)
where
UV;valve ¼
QV
Avalve
(14.84)
14.3 Tray design
483
Avalve is the total valve area per tray in m2, QV is the vapour flow rate in m3/s, UV;valve is in m/s and
r in kg/m3. The values of K for different tray deck thickness are given in Table 14.17.
Table 14.17 Dry tray pressure loss coefficient
for different tray thickness.
K
Tray deck thickness (mm)
2
1.05
3.25
0.82
5.8
0.58
Tray manufacturers also use equations of the form
3
hdry ¼ C1 þ C2 UV;valve =2gc
where C1 and C2 are proprietary constants.
Total tray pressure drop (htray , mm of liquid) is calculated from the following equation
htray ¼ hdry þ 554 ðQL =lw Þ2=3 þ 0:4hw
(14.85)
where hdry calculated from Eq. 14.82 is in mm, hw is weir height in mm, lw is weir length in m, QL
is in m3/s.
Downcomer pressure drop
hdc;prdrop in mm of liquid head loss for liquid outflowing from downcomer is given by
2
hdc;prdrop ¼ 177:7 UL;dc
(14.86)
UL;dc ¼ QL A
is the velocity of liquid outflow in m/s from under the downcomer onto
dc;clarance
the tray, Adc;clarance ¼ hdc;clarance lw as discussed earlier and hdc;clearance is downcomer apron
clearance, usually 40 mm for a 50 mm weir height.
16. Downcomer backup
Downcomer backup (hL;dc mm) expressed as Eq. 14.87 shall not exceed 40% TS for high vapour
density systems 48 kg/m3 (3 lb/ft3), 50% for medium vapour density systems, 16e48 kg/m3
(1e3 lb/ft3) and 60% for low vapour density systems<16 kg/m3 (1 lb/ft3), otherwise downcomer
flooding may occur before tray flooding predicted by jet flooding equation used earlier to size the
tray.
rL
hL;dc ¼ hw þ how þ htray þ hdc;prdrop (14.87)
rL rV
where
2=3
QL
how ¼ 554 lw
(14.88)
484
Chapter 14 Column and column internals for gas
A minimum how of 10 mm at the lowest liquid level is recommended for uniform liquid flow
along weir length.
17. Leakage (weeping) check
Leakage on a specific type of tray depends on liquid level on the tray and the term
UV;valve ðrV =rL Þ1=2 . The estimated vapour velocity at which no leakage occurs on a single-pass
valve tray is listed in Table 14.18 for different UV;valve ðrV =rL Þ1=2 values as function of liquid
level on tray.
Table 14.18 Insignificant leakage limits for different liquid levels on valve trays.
Liquid level, mm
(in.)
25.4
(1.0)
38.1
(1.5)
50
(2.0)
63.5
(2.5)
76.2
(3.0)
89
(3.5)
101.6
(4.0)
Limiting UV;valve ðrV =rL Þ1=2 ,
m/s (ft/s)
0.192
(0.63)
0.247
(0.81)
0.2956
(0.97)
0.34
(1.11)
0.378
(1.24)
0.4145
(1.36)
0.45
(1.48)
The values listed in table represent leakage point for a standard design and can be altered by proper
choice of ballast units. These are merely for guidance as a leakage rate of 25% of liquid on a tray in
general corresponds to 10% fall in tray efficiency.
In case at the end of the design, sufficient flexibility is not obtained, cap spacing may be increased
or cap rows may be eliminated at inlet or outlet or heavier caps may be used that have ‘zero’ initial
opening.
Typical dimensions of valve tray internals:
•
•
•
•
•
•
•
•
Typical weir height 50 mm (6e12 mm for vacuum applications)
Plate thickness: 3 mm for SS-410S tray deck
Height under downcomer: 40 mm
Downcomer liquid seal: 8e10 mm
Calming zone width: 75 mm for D < 1.5 and 100 m for D > 1.5 m
Pitch: rotated square and triangular pattern, with pitch minimum twice the hole diameter; normal
range is 2.5e4 times do
Maximum number of valves: 130 to 150 per square metre of active area
Mechanical aspects
The following are the recommendations from the M/s Koch-Glitsch Manual.
Distance of valve from weir and truss line
A gap of 108 mm (41/400 ) is kept between (i) centreline of nearest valve from outlet weir, (ii)
centreline of nearest valve from inlet edge of tray and (iii) between valve centreline and truss line
for lap joints. The distance is 83 mm (31/400 ) for butt joints. All distances may be changed in case of
special applications. Distance of valve centreline distance from tray ring should be minimum
32 mm (11/400 ).
Tower manhole ID
If the number of valves per panel is 5, 6 or 7, using 63.5 mm (21/200 ) as distance between row
centres, the manhole approximate ID is 406 mm (1600 ), 470 mm (181/200 ) and 533.4 mm (2100 ),
respectively. Large manhole diameters are important for large diameter towers as this can
substantially reduce the number of panels.
14.4 Packed tower
485
Trusses and beam(s)
Small towers have trusses parallel to liquid flow. Major support beam(s) may be required if tray
diameter is more than 3.6 m (12 ft). The beams are placed parallel to flow and the trusses are
perpendicular to it.
Truss depth and construction is based on weight of tray plus uniform load of 97.7e122 kg/m2
(20e25 lb/ft2).
Maximum allowable tray deflection is 3 mm (1/800 ) for towers up to 3.8 m (12 ft 6 in.) and 4.8 mm
(3/600 ) for higher diameters. Trusses in addition are designed to bear a point load of 113.5 kg (250
lb) on any point without exceeding tangential stress limit at extreme fibres. Explosion proof trays
are designed for 2930 kg/m2 (600 lb/ft2) loading.
Circular downpipes and rectangular ducts
These are used at transition trays, chimney trays, accumulator trays and from the bottom tray
sump to tower bottom. The collection area or the recessed sump is sized with the same
considerations as the downcomer. A sump should be minimum 380 mm (1500 ) deep. The duct
velocity is kept 0.6e0.9 m/s (2e3 ft/s).
Table 14.19 Standard dimensions on trays for different pressure services.
Service
Vacuum
Atmospheric
High pressure
TS(m)
0.4e0.6
0.4e0.6
0.3e0.4
lw (m)
0:5 0:6D
0:6 0:76D
0:85D
hw (m)
0.02e0.03
0.03e0.08
0.04e0.1
Skirt clearance hdc;clearance (m)
0:7hw
0:8hw
0:9hw
Bubble cap diameter dcap (m)
0.08e0.15
0.08e0.15
0.08e0.15
Bubble cap pitch
1:25dcap
ð1:25 1:4Þdcap
1:5dcap
0.04e0.05
Valve diameter dvalve (m)
0.04e0.05
0.04e0.05
Valve spacing (m)
1:5dvalve
ð1:7 2:2Þdvalve
Hole diameter do (m)
0.004e0.013
0.004e0.013
0.004e0.013
Hole spacing
ð2:5 3Þdo
ð3 4Þdo
ð3:5 4:5Þdo
Relative free area (%)
15e10
10e6
7.5e4.5
14.4 Packed tower
Packed towers are used as gaseliquid and liquideliquid contacting equipment. In most applications,
the fluids flow in countercurrent fashion. Mass transfer applications using gaseliquid flow in packed
bed are distillation, absorption and stripping and liquideliquid flow is involved in extraction.
Adsorption and desorption in packed bed involves a single flowing phase (gas/liquid) through a packed
bed where solute transfer takes place from (to) the fluid bulk to (from) the packed bed of adsorbent.
Apart from the mass transfer applications, packed beds are also used in regenerative heat exchangers
and packed bed reactors. These cases mostly involve a single fluid flowing through the bed.
This section focuses on design of packed bed for vapoureliquid contacting e primarily for
distillation, absorption and stripping. A packed bed contactor would comprise of the shell containing
486
Chapter 14 Column and column internals for gas
packing in one or more sections, packing support(s), liquid distributor, liquid collector and gas and
liquid entry and exit nozzles. Intermediate supports and redistributors are used in case of tall columns.
General arrangements in a typical packed tower are presented in Fig. 14.20.
FIGURE 14.20
Schematic diagram of a packed tower.
Countercurrent flow of gas and liquid throughout the packing makes it more effective for mass
transfer as compared to tray towers that involve cross flow of gas and liquid on each tray. The contacting, however, is not perfect due to the nonhomogeneous structure of packing causing nonuniform
flow over the cross section. Maldistribution of liquid is usually caused by channelling and wall flow.
Appropriate packing shape and size is selected to minimise this maldistribution while ensuring high
capacity, flexibility in gas and liquid throughput combined with high but nearly constant separation
efficiency.
Packing elements are classified as
•
•
Random e these can be ‘stacked’ or ‘dumped’ to form the bed. Typical shapes are standard and
many are proprietary. Fig. 14.21 shows several such random packing elements.
Structured e these are typically blocks of suitably spaced corrugated plates. These blocks are
arranged side by side as well as in layers and are stitched with wire to form the bed. Near-vertical
alignment of different layers of vapour passage reduces form friction. The skin friction pressure
drop is contributed by the interaction between gas and liquid film on the packing surface. The
14.4 Packed tower
487
proprietary shapes of the corrugations, inter plate protrusions and surface holes are employed to
increase surface area and mass transfer. Compared to random packing, structured packing allows
a higher rate of mass transfer and lower pressure drop for the same bed height. A typical section of
structured packing from M/s Sulzer Ltd., Switzerland, is shown in Fig. 14.22.
FIGURE 14.21
Commercial random packing elements: (A) Raschig ring, (B) Lessing ring, (C) Partition ring, (D) Berl saddle,
(F) Tellerete, (G) Pall ring.
FIGURE 14.22
Structured packing from M/s Sulzer.
© Sulzer Ltd. 2019.
488
Chapter 14 Column and column internals for gas
Packing manufacturers have been evolving competitive designs to prove the superiority of their
packing over available design in terms of one or more desirable features listed below.
(a) Low weight per unit volume. This affects not only the total weight to be carried by the tower but
also the design of the tower shell itself. A packing that is dumped into the tower at random may
exert a side thrust against the walls, and if the packing has a high unit weight, this may affect the
cost of tower construction.
(b) Large active surface per unit volume
(c) Large free cross section. This is of importance because it affects the frictional pressure drop
through the tower and the power required to circulate the gas. Also, a lower free cross section
means higher gas velocity for a given throughput that may lead to an earlier onset of flooding.
(d) Large void volume permits passage of high flow rate of fluid through small tower cross section
without loading or flooding and achieve low pressure drop for gas. It is also desirable that the gas
pressure drop is predominantly due to skin and not form friction. This is important in cases like
absorption of oxides of nitrogen where sufficient time must be allowed for reactions in the gas
phase.
(e) Low liquid holdup e This is generally an advantage since it decreases the load on the tower and
removes the liquid from the tower as rapidly as possible. In some cases, it may be a disadvantage,
especially where the reaction between gas and liquid is slow or where the solubility of gas in
liquid is not reasonably high. In towers handling hazardous liquids, it is particularly desirable to
have lower amount of liquid retained as it lowers the potential hazard. Ideally the packing needs
to be irrigated with a thin layer of liquid.
(f) Inexpensive, reasonable mechanical strength and chemically inert towards the components
involved.
Design of packed tower apart from the normal features of any tower involves
-
Selection of packing e type (random/structured), shape, size and material
Packed bed details e depth, diameter and number of beds for a particular service
Arrangements for liquid distribution/redistribution and draw off, if warranted
14.4.1 Choice of packing
Packing types and size
Choice of packing affects bed depth. Raschig rings and Pall rings are most common random packings.
Saddle shapes are also popular but more expensive. As outlined earlier, structured packings are more
expensive but require lower bed depth and incur lower pressure drop.
In case of random packing, the size needs to be compatible with the tower diameter as use of large
packing size relative to tower diameter leads to poor contacting. Typically, for uniform liquid and gas
distribution, the ratio of tower diameter to packing size should be 10:1.Small size packings tend to
flood more and the liquid load has an upper limit. Typical recommended values for minimum tower
diameter and maximum liquid loading are presented in Table 14.20.
14.4 Packed tower
489
Table 14.20 Minimum tower diameter and maximum liquid loading for random packing.
Random packing
nominal size, mm (in.)
Minimum column
inside diameter, mm
Maximum liquid
loading, m3/hr per m2
19(¾)
250
0.53
25 (1)
300
0.84
38 (1½)
450
1.16
50 (2)
600
1.48
89 (3½)
1100
2.64
Retrofit designs for augmenting capacity and/or separation performance are carried out by
replacing some/all existing trays with packed (structured packing) section(s). This works because the
‘height equivalent to a theoretical plate’ (HETP) and the pressure drop are lower for structured
packing. Almost all crude distillation towers in Indian refineries using tray have today augmented
capacity and separation efficiency by replacing some of the trays with sections of structured packing. It
may also be noted that modern atmospheric cooling towers (see Chapter 7) involving counterflow of
water and air are designed with structured packing.
Table 14.21 lists the characteristics of random packings required by the designer.
Table 14.21 Packing factors for random and structured packing.
Type
Material
Fp
mL1
(ftL1)
Relative mass
transfer
coefficient
Nominal
size, mm (in)
ε
ap m2 =m3 ft2 =ft3
13 (0.5)
0.64
364 (111)
1900 (580)
1.52
25 (1)
0.74
190 (58)
587 (179)
1.2
38 (1.5)
0.73
121 (37)
312 (95)
1.0
50 (2)
0.74
92 (28)
213 (65)
0.85
13 (0.5)
0.62
466 (142)
787 (240)
1.58
25 (1)
0.68
249 (76)
361 (110)
1.36
105 (32)
148 (45)
Random packing
Raschig
rings
Berl
saddles
Ceramic
Ceramic
50 (2)
Pall rings
Metal
25 (1)
0.94
207 (63)
184 (56)
1.61
38 (1.5)
0.95
128 (39)
131 (40)
1.34
50 (2)
0.96
102 (31)
89 (27)
1.14
Continued
490
Chapter 14 Column and column internals for gas
Table 14.21 Packing factors for random and structured packing.dcont’d
ε
ap m2 =m3 ft2 =ft3
Fp
mL1
(ftL1)
Relative mass
transfer
coefficient
25 (1)
0.97
230 (70)
134 (41)
1.78
50 (2)
0.98
98 (30)
59 (18)
1.27
25 (1)
0.92
180 (55)
82 (25)
50 (2)
0.94
102 (31)
39 (12)
25 (1)
0.96
177 (54)
148 (45)
1.51
50 (2)
0.97
95 (29)
85 (26)
1.07
25 (1)
0.92
180 (55)
82 (25)
50 (2)
0.94
102 (31)
39 (12)
0.95
249 (76)
499 (152)
66 (20)
112 (34)
Flexipac 2
4
0.93
0.98
223 (68)
72 (22)
20 (6)
Gempak
2A
4A
0.93
0.91
220 (67)
452 (138)
52 (16)
105 (32)
Norton
Intalox 2T
3T
0.97
0.97
213 (65)
177 (54)
56 (17)
43 (13)
299 (91)
108 (33)
700 (213)
492 (150)
230 (70)
69 (21)
Material
Nominal
size, mm (in)
Metal
Intalox
IMTP
Metal
Nor-Pac
Plastic
Type
Hy-Pak
Metal
Plastic
Structured packing
Mellapak
250Y
500Y
Metal
Montz
B300
Sulzer CY
BX
Wire
mesh
0.85
0.90
1.98
1.94
Geankoplis, C. J., (2003). Transport processes and separation process principles (unit operations) (4th ed.). Reprinted by permission
of Pearson Education, Inc., New York, NY.
14.4.2 Liquid distribution
Ideal operation for vapoureliquid contacting is with a thin liquid layer flowing on the packing surface
while in contact with the flowing gas. The entire packing surface is wet and the liquid layer continuously gets renewed. It is important to ensure uniform liquid distribution across the bed section by
maintaining the liquid flow rate above a minimum limit. Tall columns are often fitted with liquid
redistributors as maldistribution sets in after a certain depth from the top. It is also important to remain
away from flooding, the other limit of operation.
14.4 Packed tower
491
Liquid distributor
Four basic types of distributors are as follows:
(a) Pan type (riser tube) e These have tall riser tubes (typically 100 mm) allowing the vapour to
bypass the distributor, while the liquid pool overflows through downcomers with 25 mm weir
height projecting from the pan. Schematic of pan distributor is shown in Fig. 14.23.
(b) Pipe orifice headers (gravity or pressure type) e These distributors are fixed with flanges to the
liquid inlet nozzle. The branches are fitted inside the tower. Even though holes are preferred,
slots are used as they provide more opening area. The openings point downwards and their
number per square metre is kept as uniform as possible.
(c) Trough distributors are used with the liquid overflowing from the weir wall of the trough. These
are common in large diameter towers and in cooling towers.
(d) Spray nozzle headers are used when the liquid is available at adequate pressure, is clean and the
gas velocity is not too high to cause entrainment. Nozzle pressure drop is usually kept below
1 kg/cm2 to avoid generation and entrainment of fine droplets. Sprays are located considering the
cone angle of the spray, details of which is provided by the vendor.
Distributor feed line
6 “NB, 40 sch, pipe
Blocked
end
50
250
Flange for fixing
with inlet nozzle
close to vessel wall
4 “NB, 40 sch
pipe
welded
10
300
Liquid downcomer(s)
splash
baffle
450
150
φ
600 φ
12 φ
weep
hole
Distributor
deck
25
2400 φ
FIGURE 14.23
Schematic of a typical pan type distributor.
Vapour riser(s)
4 “NB, 40 sch
pipe
welded
492
Chapter 14 Column and column internals for gas
Design guidelines e gravity-type distributors
•
•
•
•
•
Drip points to be located uniformly over tower section. For D 920 mm, 75e150 mm square
pitch and for D > 920 mm, number of points z (D/150)2.
Maximum number of points: 105 nos./m2; up to 95 in many services with random and structured
packing.
Minimum opening size: 10 mmf for carbon steel, 3 mmf for alloy steel.
Total hole/slot area is calculated based on pressure drop of 170e350 mm WC and discharge
coefficient of 0.6. This area is then distributed in different branches, etc.
Liquid distributed within a distance of 5%e10% of D from tower wall should be kept below 10%
to avoid liquid flow towards the wall. Structured packings are more prone to initial
maldistribution of liquid.
Redistributor and collector
Redistributors are usually not required in case of stacked packing as these have low channelling
tendency. Redistribution for random dumped bed is recommended after every three tower diameters
(or approximately 3e5 m) of bed depth for Raschig rings and 5 to 10 diameters (5e6 m) for saddle
packings. The gravity redistributor is similar to a chimney tray with sieves or with drip tubes and risers
for redistribution. Its inclusion typically adds about 1500 mm to column height. Beds of high efficiency packing may employ a collector above the redistributor to ensure (A) free passage of gas and
(B) mixing of liquid across the column section. A collector with a distributor increases the column
height significantly e typically by around 2500 mm.
Typically, chimney tray is used for side stream draw below packed section in distillation columns.
This also facilitates vapour redistribution. Chimney height decides the liquid residence time on a tray.
It should be sufficient to allow level variation within 150 mm on the tray and the minimum chimney
height is 225 mm from the tray floor. Minimum 300 mm clearance is kept above the chimney tray hat
up to the upper tray deck. Manholes are provided above the packed bed with preferred clearance of
1200 mm from the upper deck for a 600 mm manhole.
14.4.3 Bed support
Packing supports must offer low pressure drop and the free area of support should be higher than the
packing voidage and rarely below 65%. Typically, bed height per support plate is 3.7 m for Raschig
ring and 4.6e6.2 m for other packing shapes.
The supports could be simple grids or perforated plates with risers or other designs. These can also
be fabricated from expanded metal sheets of adequate strength. Simple grids are usually used for
smaller columns. Bigger diameter columns use profiled grids where the support is not in one plane.
This allows greater free area per tower cross section and also allows liquid and gas to pass in a
segregated fashion.
A low design pressure drop (w8 mm WC) across the support plate is considered for most applications to ensure that no liquid accumulates on the support plate.
Mechanical design of the support is based on the weight it has to carry. This includes (A) weight of
packing, (B) flooded liquid volume in the voids, (C) force due to pressure surges, if considered,
(D) weight of any redistributor, if the same is also to be supported.
14.4 Packed tower
493
14.4.4 Flooding and pressure drop in randomly packed bed
Operating region of a gaseliquid contactor is the flow rate range within which the contactor retains its
desirable mass transfer rate and operability. In trays, this region is fixed by the type of tray and its
dimensional details. In case of packed bed, the performance also depends on liquid distributor and the
effective operating region of a packed bed is very different from that of a contacting tray. At extremely
low liquid rates, the packing does not remain well irrigated, resulting in a drastic fall in mass transfer
rate. This minimum mass flux of liquid is termed as the minimum wetting rate (MWR). A similar sharp
fall is also observed at high gas and liquid rates as the operation approaches ‘flooding’. Thus, the limits
of operation of the packed bed are the approach to bed flooding at high gas and liquid flow rates and the
MWR at low liquid flows.
The liquid distributor is functionally efficient only over a limited range of liquid mass flux and its
efficacy is practically independent of the gas rate. Thus the effective operating region for a typical bed
is the common area for distributor and bed as marked in Fig. 14.24. It is clearly seen that the operating
region is actually limited by the liquid distributor and there can be a wide range of variation of gas flow
rate, whereas the range of liquid flow rate is rather narrow.
This apparent limitation may be utilised by the designer as an advantage by employing packed bed
contactors for applications where the range of gas flow is wide or is rather uncertain.
101
Superficial gas velocity, m/s - ->
Liquid distributor operating limits
Wetting limit
100
Flooding limit
10–1
10–4
10–3
10–2
10–1
Superficial liquid velocity, m/s - ->
FIGURE 14.24
Operating range of a packed column.
Bed diameter estimation based on flooding and pressure drop
Packed towers are typically used for D 1 m (3.3 ft).
Pressure drop in packed bed depends on the packing characteristics, bed diameter, gas and liquid
flow rates and their properties. The generalised pressure drop curves for randomly packed tower are
494
Chapter 14 Column and column internals for gas
shown in Fig. 14.25A and that for structured packings in Fig. 14.25B. The packing factors (Fp ) are
listed in Table 14.21. For using Fig. 14.25A and B, Fp in ft/s is noted from Table 14.21. y is liquidphase kinematic viscosity in centistokes, vG is superficial gas velocity in ft/s (1 m/s ¼ 3.281 ft/s),
rG ; rL are gas and liquid densities in lb/ft3 (1 kg/m3 ¼ 0.06243 lb/ft3). Note that though the abscissa is
dimensionless, the ordinate is not.
Validity of the generalised correlations in Fig. 14.25 requires the maximum limit of irrigation rates
to remain below the values mentioned in Table 14.22.
(A)
2.4
ΔP = (in. H2O/ft)
2.0
1.5
1.0
2.0
1.6
0.50
υG[ ρG /(ρL – ρ G)]0.5 FP 0.5ν 0.05,
1.2
capacity parameter
0.25
0.8
0.10
0.05
0.4
0.0
0.006
0.02 0.04 0.06
0.20 0.40 0.60
0.005 0.01
0.30 0.50 1.0
0.03 0.05 0.10
2.0
4.0
3.0 5.0
(GL/GG)(ρG /ρL)0.5, flow parameter
(B)
3.0
2.8
2.6
2.4
2.2
2.0
1.8
υG[ ρG /(ρL – ρG)]0.5 FP 0.5ν 0.05, 1.6
1.4
capacity parameter
1.2
1.0
0.8
0.6
0.4
0.2
0.0
ΔP = 2.0 (in. H2O/ft)
1.5
1.0
0.50
0.25
0.10
0.05
0.01
0.05
0.10
0.50
1.00
2.00
(GL/GG)(ρG /ρL)0.5, flow parameter
FIGURE 14.25
Generalised pressure drop curves for (A) random packing, (B) structured packing.
From (A) Strigle, R.F., Jr. (1987). Random packings and packed towers: design and applications. Gulf Publishing Company;
(B) Kister, H.Z. (1992). Distillation design. New York: McGraw-Hill Book Company.
14.4 Packed tower
495
Table 14.22 Upper limit of validity of irrigation rate (liquid viscosity below 3 cP) for random
packing.
Upper limit of irrigation rate, m3/hr per m2 tower
cross section
Nominal packing size, cm (in.)
1.6 (5/8)
41.5
2.5 (1)
95.5
1
3.8 (1 /2)
134.5
5 (2)
166
Each curve in Fig. 14.25 represents a value of constant pressure drop per unit bed depth as marked
thereon. The empirical correlation to estimate pressure gradient at flooding is
for Fp 197 m1 (60 ft1)
DPflood ðin: = ftÞ ¼ 0:115 ðFp Þ0:7
(14.89a)
and when Fp > 197 m 1 (60 ft1)
DPflood ¼ 2 in:=ft
(14.89b)
This allows the flooding line to be located as shown in Fig. 14.25A or B for specific packing type
and size and the design vapour velocity is calculated corresponding to j % approach to flooding. The
tower area and diameter are calculated from the gas flow rate and the design vapour velocity.
It is preferred to operate the packed bed close to loading conditions. The onset of loading is usually
around 65%e70% of flooding velocity. For absorption, the tower is designed for 50%e70% of gas
flooding velocity with the higher value adopted for higher flow parameters. For atmospheric pressure
distillation, the value is 70%e80%. For distillation and structured packing, 80% of flooding velocity is
normally used in design.
For extraction process, where both the phases are liquid, the flooding velocity can be predicted
from Crawford and Wilke correlation. This along with the approach to flooding and packed column
characteristics for extraction process is discussed in Chapter 13.
Pressure gradient
Pressure drop per unit bed length is noted from the constant pressure drop curve passing through the
intersection of the design X and Y value in Fig. 14.25. Typical recommended values for design pressure
drop for randomly packed beds in several services are shown in Table 14.23.
496
Chapter 14 Column and column internals for gas
Table 14.23 Typical design pressure drop for random packing.
Pressure drop (mm
WC/m bed depth)
Application
Absorber/regenerator e nonfoaming service
20 to 35
Absorber/regenerator e moderately foaming service
12 to 20
Fume scrubbers e water absorbent
35 to 50
Fume scrubbers e chemical absorbent
20 to 35
Fractionating towers (close to atmospheric or higher pressure)
35 to 100
Vacuum towers
12 to 35
Minimum wetting rate
The bed design must ensure that the liquid flux is above the MWR. As can be seen from Table 14.24,
MWR largely depends on the packing material.
Table 14.24 Minimum wetting rate for different packing material.
Packing material
Minimum wetting rate (MWR)
m3/hr per m2 packing surface
Unglazed ceramic
0.5
Oxidised metal (carbon steel, copper)
0.7
Surface treated metal (etched stainless
steel)
1.0
Glazed ceramic
2.0
Glass
2.5
Bright metal
3.0
PVC
3.5
Polypropylene
4.0
PTFE
5.0
14.5 Packed tower design
Process design of a packed tower involves choosing the packing type (shape), material and size;
estimation of packed section diameter and height; location and space required for liquid distributor/
redistributor and draw-off as applicable. A layer (100e120 mm) of larger packing and/or alumina balls
is sometimes placed over the active bed. This helps uniform liquid irrigation, acts partly as bed
restrainer to prevent packing carryover with vapour and clogging of nozzle.
14.5 Packed tower design
497
This is followed by design of the mechanical details of packed section, packing support, bed
restrainer and other fittings.
Inputs for the design are
•
•
•
•
Liquid and gas inflow rates, mV and mL in kg/s
Inlet compositions of both streams and desired change in concentration of transferred
component(s)
Maximum allowable pressure drop for each phase
Properties of phases, rV ; rL , densities of vapour and liquid in (kg/m3), mL , liquid viscosity in cP
(and possibly their estimation method based on composition, temperature and pressure)
Outputs from the process design are
•
•
Active bed height: Governed by the targeted change in con