Program for North American
Mobility in Higher Education
Introducing Process Integration for Environmental Control
in Engineering Curricula
MODULE 12: “Heat and Mass Exchange
Networks Optimization”
1
PURPOSE OF MODULE 12
What is the purpose of this module?
This module is intended to convey and illustrate the basic principles
and methodology of heat and mass networks optimization. It is
applied to chemical engineering, especially touching the petroleum
and paper industry. At the end of the module, the student should
be able to understand the main concepts of the heat and mass
exchange network and apply it to real world context.
2
STRUCTURE OF MODULE 12
What is the structure of this module?
Module 12 is divided in 3 “tiers”, each with a specific goal:

Tier 1: Basic concepts

Tier 2: Application examples

Tier 3: Open-ended problems in a real world context
These tiers are intended to be completed in order. Students are
quizzed at various points, to measure their degree of
understanding, before proceeding.
Each tier contains a statement of intent at the beginning, and a quiz
at the end.
3
Tier I
BASIC CONCEPTS
4
TIER 1 - STATEMENT OF INTENT
The goal of Tier 1 is to provide the basic
principles and solution methods for heat and
mass exchange networks optimization with
emphasis on retrofit, heat transfer and
mass transfer analogy and optimization
techniques.
5
TIER 1 - CONTENTS
Tier 1 is broken down into three sections:
1.1 Optimization of heat exchanger networks
(HEN) by Pinch Analysis
1.2 Optimization of mass exchange networks
1.3 Application of optimization techniques to
heat and mass exchange networks
analysis
At the end of this tier there is a short multiple
answer Quiz.
6
1.1 OPTIMIZATION OF HEAT
EXCHANGER NETWORKS
(HEN) BY PINCH ANALYSIS
7
1.1 OPTIMIZATION OF HEAT EXCHANGER
NETWORKS (HEN) BY PINCH ANALYSIS







Principles of Pinch Analysis
Methodology
Special problems in heat exchangers
network design
Pinch analysis and energy integration
Special case of heat exchange
Retrofit design
Pinch software
8
INTRODUCTION
One important goal in our industry today:
Minimize the utilities consumption
(fuel, steam and cooling water)
Methods based on thermodynamic analysis,
that have the objective of minimizing the
utilities consumption, are based on fundamental
concepts that help to understand the problem of
heat exchange.
9
WHAT IS PINCH TECHNOLOGY?
Pinch Technology provides a systematic
methodology for energy saving in processes
and total sites. The methodology is based on
thermodynamic principles
10
WHAT IS THE ROLE OF PINCH TECHNOLOGY IN
THE OVERALL PROCESS DESIGN?
The Onion Diagram


Utilities
Heat Exchanger Network
Separator

Reactor

Site-wide Utilities
The design of the process starts with
the reactors (the core)
Once feeds, products, recycle
concentrations and flowrates are
known, the separators (the second
layer) can be designed
The basic process heat and material
balance is now in place and the heat
exchanger network (the third layer)
can be designed
The remaining heating and cooling
duties are handled by the utility
systems (the fourth layer)
Pinch Analysis starts with the heat
and material balance for the process at
this boundary
11
THE PHASES OF PINCH ANALYSIS
PROCESS
DATA EXTRACTION OF
HOT AND COLD
STREAMS FROM
PROCESS FLOWSHEET
SIMULATION
DATA EXTRACTION
TARGETING
DESIGN
UTILIZATION OF OF
DETERMINATION
HEURISTICS
TO
ENERGY
TARGETS
CONCEIVE
HEAT
(NEEDS
FORAHEATING
EXCHANGER
NETWORK
AND COOLING)
TO REACH ENERGY
TARGETS AT A MINIMUM
COST
OPTIMIZATION
12
DATA EXTRACTION



Extraction of information required for Pinch
Analysis from a given process flowsheet
ant the relevant heat and material balance
Data extraction is THE KEY link between
process and pinch analysis
The quality of data extraction has a direct
influence on the quality of the final result of
the analysis
13
WHAT ARE WE SEARCHING FOR?


Thermal data must be extracted from the
process
This involves the identification of process
heating and cooling duties
14
DEFINITIONS (1-2)



Hot streams are those that must be cooled
or available to be cooled. e.g. product
cooling before storage (heat sources)
Cold streams are those that must be
heated. e.g. feed preheat before a reactor
(heat sinks)
Utility streams are used to heat or cool
process streams when heat exchange
between process streams is not practical or
economic (e.g cooling water, air,
refrigerant)
15
DEFINITIONS (2-2)
For each hot and cold stream identified,
the following thermal data is extracted:
 TS : supply temperature, the temperature at
which the stream is available (oC)
 TT : target temperature, the temperature
the stream must be taken to (oC)
 ΔH : enthalpy change of streams (kW)
 CP: heat capacity flow rate
CP = Cp * M (kW/oC = kJ/oC kg * kg/s)
16
TYPICAL STREAM DATA
STREAM
NUMBER
1
2
3
4
STREAM NAME
FEED
REACTOR OUT
PRODUCT
RECYCLE
TS
( C)
60
270
220
160
o
TT
( C)
205
160
70
210
o
CP
o
(kW/ C)
20
18
35
50
DH
(kW)
2900
1980
5250
2500
17
NOTION OF ΔTmin (1-2)



ΔTmin is the minimum temperature difference,
imposed in the system; under this value, heat
exchange between two streams is not possible
Thus, the temperature of the hot and cold
streams at any point in exchangers must
always have at least a minimum temperature
difference (ΔTmin)
The selection of ΔTmin value has implications for
both capital and energy costs
18
NOTION OF ΔTmin (2-2)

In each temperature interval, each cold and hot
stream has to be separated at least by ΔTmin.
The principle of modified temperatures has to
be introduced:


for a cold stream : Tmodified = T + (ΔTmin/2)
for a hot stream : Tmodified = T - (ΔTmin/2)
19
COMPOSITE CURVES


Composite curves consist of temperatureenthalpy profiles of heat availability in the
process (the hot composite curve) and
head demands in the process (the cold
composite curve)
Composite curves allow to determine and
visualize the pinch point and the energy
targets (heating and cooling demands)
20
HOW TO DO IT?
- A stream with a constant CP
value is represented by a
straight line running from TS
to TT
- When there are a number of
hot and cold streams, the
construction of hot and cold
composites curves involves
the addition of the enthalpy
changes of the streams in the
respective temperature
intervals See Fig. (a), (b)
21
RESULT
T (oC)
Cooling required
QCmin
Heating required
Internal recuperation of heat
QHmin
Hot composite curve
TPINCH
Cold composite curve
Pinch point
H (kW)
22
PINCH GOLDEN RULES

Do not transfer heat across pinch

Do not use cold utilities above the pinch

Do no use hot utilities below the pinch
23
SUMMARY

The composite curves provide overall
energy targets
BUT...
 They do not clearly indicate how much
energy is supplied by different utility levels
SOLUTION...
 The utility mix is determined by the Grand
Composite Curve (GCC)
24
GRAND COMPOSITE CURVE

It shows the utility requirements in both
enthalpy and temperature terms

It is used to optimize the utilities network
when the utilities are available at different
quality levels

It is useful for integrating special
equipments: cogeneration, heat pump, etc.
25
GRAND COMPOSITE CURVE
QHmin
T
Heat sink
Pockets of heat
recovery
Pinch point
Heat source
QCmin
ΔH
26
DESIGN A HEAT EXCHANGER
NETWORK (HEN)

Application of heuristics to design a heat
exchanger network with the objectives of:
Reaching energy targets
Respecting pinch rules
27
DEVELOP A HEN FOR A MAXIMUM
ENERGY RECOVERY (MER) (1-2)

Divide the problem at the pinch: above the
pinch and below the pinch

Design hot-end, starting at the pinch:



Pair up exchangers according to CP and
number of streams “N” constraints
Immediately above the pinch, pair up streams
such that CPHOT  CPCOLD , NHOT  NCOLD
Add heating utilities as needed (QHmin)
28
DEVELOP A HEN FOR A MAXIMUM
ENERGY RECOVERY (MER) (1-2)

Design cold-end, starting at the pinch:



Pair up exchangers according to CP and
number of streams “N” constraints
Immediately above the pinch, pair up streams
such that CPHOT  CPCOLD , NHOT  NCOLD
Add heating utilities as needed (QCmin)
29
MINIMUM NUMBER OF HEAT
EXCHANGERS (Umin)
The minimum number of heat exchangers in a
network is given by
Umin = Nstream + Nutilities - 1
where Nstream is the total number of
streams and Nutilities the total number of
utilities in the heat exchanger network
30
SPECIAL PROBLEMS IN HEN
DESIGN

Introduction on a same stream of:



Splitting
Mixing
Elimination of loops
More opportunities
More complex
Frequently the only way of getting Umin
31
NOTION OF OPTIMAL ΔTmin



At the beginning, an arbitrary DTmin is fixed
The goal is to find an optimal DTmin for a
minimum cost
The total cost is function of the utility cost and
the heat exchanger cost


Utility cost = f(Qc, Qh)  it is an energetic cost
Heat exchanger cost = f(exchange area) 
it is a capital cost
32
ESTIMATION OF THE ENERGY
COST
Energy cost = (Costcold utility X Qc) + (Costhot utility X Qh)

where the cost unit is $/kW and Qc unit is kW
33
ESTIMATION OF HEN CAPITAL
COST (1-3)
The capital cost of a HEN depends on 3 factors:



the number of exchangers
the overall network area
the distribution of area between the exchangers
Capital cost =  + .A

where A is the exchange area and , ,  are
economical and technical factors
34
ESTIMATION OF HEN CAPITAL
COST (2-3)
Using a temperature-enthalpy diagram and the
composite curves, the estimation of the exchange
area can be obtained by:
Amin = (1/ DTLM *  qj/hj)
COMPLETER.....mettre le i!
where i: enthalpy interval
j: jth stream
DTLM: log mean temperature difference or LTMD
qj: enthalpy change of the jth stream in the interval i
hj: transfert coefficient of jth stream
35
ESTIMATION OF HEN CAPITAL
COST (3-3)
Estimation of exchange area
T (oC)
HEN AREAmin = A1 + A2 + A3 +...+ Ai
Enthalpy intervals in the
composite curves
A1
A2
A3
A4
A5
H (kW)
36
OPTIMAL ΔTmin

To arrive to an optimum DTmin, the total annual
cost (the sum of total annual energy and capital
cost) is plotted at varying values (see next page).
Three key observations can be made:



an increase in DTmin values result in higher energy
costs and lower capital costs
a decrease in DTmin values result in a lower energy
costs and higher capital costs
an optimum DTmin exists where the total annual
cost of energy and capital costs is minimized
37
ENERGY-CAPITAL COST TRADE
OFF (OPTIMAL ΔTmin)
Annualized cost
Total cost
Energy cost
Capital cost
Optimum DTmin
DTmin
38
RETROFIT DESIGN

For a new process: the application of pinch
concepts is relatively easy:

low uncertainty for data extraction

low constraints in the process

For an existing process: the application of pinch
concepts is more complicated:

technical, geographical and economical
constraints
39
DATA EXTRACTION FOR A
RETROFIT DESIGN



Data is extracted from the existing process
and indeed from a simulation that has to be
validated on-site
Validate a simulation is difficult: it can take up
to one year! The cost is too high!
Data are less reliable and the quality of the
pinch analysis decreases
40
HEN IN RETROFIT DESIGN

There is already in the process violation of
the golden rules

Some exchangers are already installed, used
or not, have to be taken into account
 important for the investment/capital cost

The geographical constraints are important
for fitting of equipment in a limited space
41
OPTIMAL ΔTmin IN RETROFIT
DESIGN

New factors have an influence on the
determination of the optimum ΔTmin:




Geographical constraints that have an impact
on the capital cost
Investments already realized for the actual
network
Preservation of the efficiency of the actual
network
In some cases, we can use Δtmin in the
actual HEN or use a ΔTmin from similar
processes
42
OPTIMAL ΔTmin IN RETROFIT
DESIGN
Industrial sector
Oil refining
Petrochemical
Chemical
Low temperature
processes
Experience DTmin values
20 – 40 oC
10 – 20 oC
o
10 – 20 C
3 – 5 oC
43
PINCH SOFTWARES


Super Target (Linhoff March)
Pinch Express (Linhoff March)
Aspen Pinch (Aspentech)

Hint (Angel Martin, freeware)



available on www.heatintegration.com
These softwares include the basic concepts of
pinch analysis and optimization tools can be
integrated
44
1.2 OPTIMIZATION OF MASS
EXCHANGE NETWORKS
45
1.2 OPTIMIZATION OF MASS EXCHANGE
NETWORKS



Heat transfer and mass transfer analogy
Equipment configurations
The three types of mass exchange
networks analysis
46
HEAT TRANSFER AND MASS TRANSFER
ANALOGY


There is an analogy between the exchange
potentials (temperature differences and
concentration differences) and the
quantities that are exchanged (enthalpy
and mass)
Parameters such flux, transfer coefficient,
exchange rate and other nondimensional
numbers appear in the two fields, have
similar roles, but the way they are
expressed are sometimes really different
47
HEAT TRANSFER AND MASS TRANSFER
ANALOGY
Source: Manousiouthakis, 1999
48
MASS EXCHANGE NETWORK


Mass exchange operations are important to
limit or eliminate sources of industrial
pollution
In process integration, mass exchange
operations are used to transfer selectively
some undesirable species starting from
process streams (called rich streams) to
mass separating agents (MSA) that act as
receiving streams (called lean streams)
49
MASS EXCHANGER


Definition: a mass transfert unit by direct or
indirect contact that use a MSA (lean
phase) to remove selectively some
compounds (for example pollutants) from a
rich phase (for example a waste stream)
Mass exchangers are present in processes
of absorption, adsorption, liquid-liquid
extraction, desorption, etc.
50
TYPES OF EXCHANGE EQUIPMENTS (1-2)
1. Exchange by direct contact
Rich stream
2. Exchange by mixing of miscible
phases non-redistributed
Lean stream
Dilution water
Main stream
of the process
51
TYPES OF EXCHANGE EQUIPMENTS (2-2)
3. Exchange by direct contact of
non-miscible phases
Washing water
Used water
Treated stream
Contaminated stream
52
TYPES OF MASS EXCHANGE
NETWORK

Mass pinch

Water pinch
53
MASS PINCH




Optimization of the mass exchanger network
by a method similar to the thermal pinch
Entity exchanged: chemical specie or group
of species (e.g. contaminant or undesirable
product in the stream of the main process)
The donor streams (analogues to hot
streams) are the rich streams
The receiving streams (analogues to cold
streams) are the lean streams
54
Concentration
Concentration
HOW TO DO IT?
Mass to exchange
Concentration
Concentration
Mass to exchange
Mass to exchange
Mass to exchange
55
RESULT
Concentration
Need of MSA
Internal exchange of material
Need of MSA
Rich composite curve
Pinch
Lean composite curve
concentration
Pinch point
Mass to exchange
56
WATER PINCH


Water pinch can be used to guide water and
effluent management decisions while at the
same time improving the efficiency of the
processes
It is a tool for the rational analysis of the
water networks to identify bottlenecks and
where recycle/reuse loops should be located
57
WHAT IS THE RESULT?


The procedure enables the minimum
amount of water to be determined by
considering the introduction of recycle loops
and reuse cascades
It highlights the operations that should be
investigated for the improvement of their
internal efficiencies of water management
58
LIMITING WATER PROFILE

Wastewater
minimization application

Graphic of concentration
(C) versus mass load
(m)
59
DOMAINS OF APPLICATION (1-4)


The mass-exchange operations are
necessary for pollution prevention
The realm of mass exchange includes the
following applications:


Absorption : a liquid solvent is used to remove
selected compounds from a gas using their
preferential solubility (e.g. desulfurization of flue
gases by alkaline solutions or ethanolamines,
recovery of volatile-organic compounds using light
oils, removal of ammonia from air using water)
see next page...
60
DOMAINS OF APPLICATION (2-4)


Adsorption : the ability of a solid adsorbent to
adsorb specific component from a gaseous or a
liquid solution onto its surface (e.g. activated carbon
used to remove a mixture of benzene-toluenexylene from the underground water, separation of
ketones from aqueous wastes of an oil refinery,
recovery of organic solvent from the exhaust gases
of polymer manufacturing facilities)
Extraction : a liquid solvent is used to remove
selected compounds from another liquid using their
preferential solubility of the solutes in the MSA (e.g.
wash oils used to remove phenol and PCBs from
the aqueous wastes of synthetic-fuel plants and
chlorinated hydrocarbons from organic wastewater)
61
DOMAINS OF APPLICATION (3-4)


Ion exchange : cation and/or anion resins are used
to replace undesirable anionic species in liquid
solutions with nonhazardous ions (e.g. cationexchange resins contain nonhazardous, mobile,
positive ions (sodium, hydrogen) which are attached
to immobile acid groups (sulfonic, carboxylic); these
resins are used to eliminate various species
(dissolved metal, sulfides, cyanides, amines,
phenols, and halides) from wastewater)
Leaching : a selective solution of specific
constituents of a solid mixture is brought in contact
with a liquid solvent (e.g. separating metals from
solid matrices and sludge)
62
DOMAINS OF APPLICATION (4-4)

Stripping : desorption of volatile compounds from
liquid or solid streams using a gaseous MSA (e.g.
recovery of volatile organic compounds from
aqueous wastes using air, removal of ammonia from
the wastewater of fertilizer plants using steam,
regeneration of activated carbon using steam or
nitrogen
63
MULTI-COMPONENT EXCHANGE


Multi-component mass integration

Tool to find the minimum utility cost for mass
exchanger networks with multicomponent targets
The unit operations are mass-exchangers

Framework:





1st and 2nd laws of thermodynamics
Infinite DimEnsional State Space (IDEAS)
Conservation of mass
Mass cascades from high to low chemical potential
for each component
Concepts:

composition interval diagrams, mass exchange
diagrams for each component
64
1.3 APPLICATION OF
OPTIMIZATION TECHNIQUES
TO EXCHANGE NETWORKS
ANALYSIS
65
1.3 APPLICATION OF OPTIMIZATION
TECHNIQUES TO EXCHANGE NETWORKS
ANALYSIS




Introduction
Review of optimization techniques
Mathematical programming
Combinatory optimization algorithms
66
INTRODUCTION

Many problems in plant operation, design, location
and scheduling involve variables that are not
continuous but instead have integer values. For
example, decision variables such as:



To install or not a new piece of equipment
What is the optimum number of stages in a distillation
column?
Should we use reactor 1 or reactor 2?
OPTIMIZATION IS NECESSARY!
67
3 DIFFERENT APPROACHES

Heuristics approach (intuition, engineering
experience)

Thermodynamic approach (physical insight)

Mathematical programming approach
68
REVIEW OF OPTIMIZATION TECHNIQUES
3 groups

Mathematical programming





Combinatory optimization algorithms




Linear programming (LP)
Non-linear programming (NLP)
Mixed-integer linear programming (MILP)
Mixed-integer non-linear programming (MINLP)
Branch and bound
Simulated annealing
Genetic algorithms
Fuzzy logic and heuristics
69
WHAT IS A MATHEMATICAL
PROGRAM?
A mathematical program is an optimization
problem of the form:

Maximize f(x): x in X, g(x)  0, h(x) = 0,

where X is a subset of Rn and is in the domain
of the real-valued functions, f, g and h.
The relations, g(x)  0 and h(x) = 0 are called
constraints, and f is called the objective
function.

70
WHAT IS MATHEMATICAL
PROGRAMMING ? (1-2)
Mathematical programming is the study or use of the
mathematical program. It includes any or all of the
following:




Theorems about the form of a solution, including
whether one exists;
Algorithms to seek a solution or ascertain that none
exists;
Formulation of problems into mathematical
programs, including understanding the quality of
one formulation in comparison with another;
Analysis of results, including debugging situations,
such as infeasible or anomalous values;
71
WHAT IS MATHEMATICAL
PROGRAMMING ? (2-2)
It includes any or all of the following:



Theorems about the model structure, including
properties pertaining to feasibility, redundancy
and/or implied relations (such theorems could be to
support analysis of results or design of algorithms);
Theorems about approximation arising from
imperfections of model forms, levels of aggregation,
computational error, and other deviations;
Developments in connection with other disciplines,
such as a computing environment.
72
MATHEMATICAL PROGRAMMING
LP:
optimization technique where constraints and objective function
are expressed by linear functions in relation to continuous
variables
MILP: optimization where constraints and objective function are
linear in relation to mixed variables: discrete and continuous
NLP:
optimization technique where constraints and objective
function are expressed by non-linear functions
MINLP: optimization technique where constraints and objective
function are non-linear in relation to mixed variable: discrete
and continuous
73
Number of continuous parameters to optimize
APPLICATION FIELDS FOR OPTIMIZATION
TECHNIQUES
NLP
MINLP
Heuristics
Simulated annealing
Fuzzy logic
Genetic algorithms
Exhaustive research
Number of discrete parameters to optimize
74
COMBINATORY OPTIMIZATION
ALGORITHMS
 Branch and bound
 Simulated annealing
 Genetic algorithms
75
BRANCH AND BOUND
 Approach developed for solving discrete and
combinatorial optimization problems.


Discrete optimization problems are problems in which
the decision variables assume discrete values from a
specified set; when this set is a set of integers, we
have an integer programming problem.
Combinatorial optimization problems, on the other
hand, are problems of choosing the best combination
out of all possible combinations. Most combinatorial
problems can be formulated as integer programs.
76
BRANCH AND BOUND
 Example: minimize a function f(x), where x is restricted to some
feasible region (defined, e.g., by explicit mathematical
constraints).

To apply branch and bound, one must have



a means of computing a lower bound on an instance of the
optimization problem
a means of dividing the feasible region of a problem to create
smaller subproblems.
there must also be a way to compute an upper bound (feasible
solution) for at least some instances; for practical purposes, it
should be possible to compute upper bounds for some set of
nontrivial feasible regions.
77
BRANCH AND BOUND
 Consider the original problem with the complete feasible region, which
is called the root problem.

The lower-bounding and upper-bounding procedures are applied to the
root problem.
 If the bounds match, then an optimal solution has been found and the
procedure terminates.
 Otherwise, the feasible region is divided into two or more regions, each
strict subregion of the original, which together cover the whole feasible
region; ideally, these subproblems partition the feasible region.
 These subproblems become children of the root search node. The
algorithm is applied recursively to the subproblems, generating a tree of
subproblems.
78
BRANCH AND BOUND
 If an optimal solution is found to a subproblem, it is a feasible solution
to the full problem, but not necessarily globally optimal. Since it is
feasible, it can be used to prune the rest of the tree: if the lower bound
for a node exceeds the best known feasible solution, no global optimal
solution can exist in the subspace of the feasible region represented by
the node. Therefore, the node can be removed from consideration. The
search proceeds until all nodes have been solved or pruned, or until
some specified threshold is meet between the best solution found and
the lower bounds on all unsolved subproblems.
79
SIMULATED ANNEALING
Definition 1: A technique which can be applied to any minimization or learning
process based on successive update steps (either random or deterministic) where
the update step length is proportional to an arbitrary set parameter which can play
the role of a temperature. Then, in analogy with the annealing of metals, the
temperature is made high in the early stages of the process for faster minimisation
or learning, then is reduced for greater stability.
Definition 2 : An algorithm for solving hard problems, notably combinatorial
optimization, based on the metaphor of how annealing works: reach a minimum
energy state upon cooling a substance, but not too quickly in order to avoid reaching
an undesirable final state. As a heuristic search, it allows a non-improving move to a
neighbor with a probability that decreases over time. The rate of this decrease is
determined by the cooling schedule, often just a parameter used in an exponential
decay (in keeping with the thermodynamic metaphor). With some assumptions
about the cooling schedule, this will converge in probability to a global optimum.
80
GENETIC ALGORITHMS (GA)
 A class of algorithms inspired by the
mechanisms of genetics, which has been
applied to global optimization (especially
combinatorial optimization problems). It
requires the specification of three operations
(each is typically probabilistic) on objects,
called "strings" (these could be real-valued
vectors): reproduction, mutation and
crossover
81
THREE OPERATIONS OF GA

Reproduction - combining strings in the population to create a new string
(offspring);
Example: Taking 1st character from 1st parent + rest of string from 2nd parent:
[001001] + [111111] ===> [011111]

Mutation - spontaneous alteration of characters in a string;
Example: Just the left-most string:
[001001] ===> [101001]

Crossover - combining strings to exchange values, creating new strings in their
place.
Example: With crossover location at 2:
[001001] & [111111] ===> [001111], [111001]
These can combine to form hybrid operators, and the reproduction and crossover
operations can include competition within populations.
82
GENERIC GA STRATEGY
0. Initialize population.
1. Select parents for reproduction and GA operators
(reproduction, mutation and crossover).
2. Perform operations to generate intermediate
population and evaluate their fitness values.
3. Select members of population to remain with
new generation.
Repeat 1-3 until some stopping rule is reached.
83
FUZZY LOGIC
 Problem-solving control system methodology that
lends itself to implementation in systems ranging
from simple, small, embedded micro-controllers to
large, networked, multi-channel PC or workstationbased data acquisition and control systems.
 It can be implemented in hardware, software, or a
combination of both.
 FL provides a simple way to arrive at a definite
conclusion based upon vague, ambiguous,
imprecise, noisy, or missing input information. FL's
approach to control problems mimics how a person
would make decisions, only much faster.
84
HEURISTICS
 The central idea of this approach is the application of
empirical rules based on the experience and the
“know-how” of the engineer.
 The advantage of this method is the exploitation of
the knowledge to simplify a problem and identify
rapidly some solutions, usually good quality solutions.
 The inconvenience of this method is that some
heuristics rules for a given problem can enter in
contradiction when used in applied problems
85
END OF TIER 1
At the end of Tier 1, you have now a global view
of the basic concepts of heat and mass exchange
networks optimization.
The next steps are the integration of all these notions in
order to solve Case Studies (Tier 2) and finally proceed to
solve real world “open Ended Problems” (Tier 3).
A short quiz and a list of bibliographic references are
completing Tier 1
86
QUIZ
Question 1
What is the objective of Pinch Analysis?

The prime objective of Pinch Analysis is to achieve financial
savings in the process industries by optimizing the ways in
which process utilities (particularly energy and water), are
applied for a wide variety of purposes.

With the application of Pinch Analysis, savings can be achieved
in both capital investment and operating cost. Emissions can be
minimized and throughput maximized.
87
QUIZ
Question 2
What is the significance of the pinch point?
The pinch point is defined as the enthalpy at which the
hot and cold composite curves are separated by the
minimum temperature difference, which corresponds with
the enthalpy of the energy cascade at which the heat flux
is zero.
88
QUIZ
Question 3
What analogy can be made between HEN and MEN?

The analogy can be made
between the exchange potentials
(temperature differences and
concentration differences) and
the quantities that are exchanged
(enthalpy and mass)
89
QUIZ
Question 4
When is it necessary to apply mass-exchange operations?



Mass-exchange operations are mainly used for
pollution prevention
It is used to remove selectively some compounds
(for example pollutants) from a rich phase (for
example a waste stream)
Mass exchangers are present in processes of
absorption, adsorption, extraction liquid-liquid,
desorption, etc.
90
QUIZ
Question 5
Why do we need to optimize chemical processes?

In many plants, we are confronted to make decisions
regarding the choice of operating conditions, the use
of an equipment, the choice between two pieces of
equipment or the determination of an optimal number
of operations. Optimization is then necessary to
make these decisions
91
QUIZ
Question 6
What optimization technique should you use if you have a
high number of continuous parameters and low number of
discrete parameters to optimize? Describe the chosen
technique.

NLP: optimization technique where constraints and
objective function are expressed by non-linear
functions
92
REFERENCES
Here is a list of the main references used to elaborate
Tier 1

Books




Douglas, J.M, Conceptual Design of Chemical
Processes, McGraw-Hill, Singapore, 1988.
Edgar, T.F., Himmelblau, D.M., Optimization of
Chemical Processes, McGraw-Hill, 1988.
El-Halwagi, M.M, Pollution Prevention through
Process Integration: Systematic Design Tools,
Academic Press, San Diego, 1997.
Smith, R., Chemical Process Design, McGraww-Hill,
New-York, 1995.
93
REFERENCES

Papers




Linnhoff, M., Introduction to Pinch Technology, 1998.
(available at www.linnhoffmarch.com)
Maia, L.O.A. et al, Synthesis of Utility Systems by
Simulated Annealing, Computers Chem. Eng., Vol. 19,
No. 4, 1995, pp. 481-488.
Maréchal, F., Advanced energy: process integration
and exergy analysis. 4. Heat exchangers network
synthesis, Ecole Polytechnique Fédérale de
Lausanne, 2002.
Courses notes, GCH6211 - Process Integration
Course, Ecole Polytechnique de Montréal, 2002.
94
REFERENCES

Websites







Pinch Analysis
www.cheresources.com/pinchtech4.shtml
Mass Exchange Network
http://www.eng.auburn.edu/users/edenmar/6460/6460
_Chapter_3.pdf
http://www.epa.gov/ORD/NRMRL/std/mtb/Manousiout
hakis2.ppt
Optimization techniques
Glossary of mathematical programming:
http://carbon.cudenver.edu/~hgreenbe/glossary/index.
php?page=nature.html
95
Program for North American
Mobility in Higher Education
Introducing Process Integration for Environmental Control
in Engineering Curricula
MODULE 12: “Heat and Mass Exchange
Networks Optimization”
96
Tier 2
APPLICATION
EXAMPLES
97
TIER 2 - STATEMENT OF INTENT
The goal of Tier 2 is to demonstrate the
application
of heat and mass networks optimization
techniques for a few case study examples
including thermal Pinch Analysis, mass exchange
networks analysis and optimization techniques
98
TIER 2 - CONTENTS
The tier 2 consists into three sections:
2.1 Application examples for Thermal Pinch Analysis
2.2 Application examples for Mass Exchange Network Analysis
2.3 Application examples for Optimization techniques
For each section we present example problem statements and then
the solution.
99
2.1 APPLICATION EXAMPLES
FOR THERMAL PINCH
ANALYSIS
100
EXAMPLE 1 - Data extraction
The Figure 1 below shows the flowsheet of an existing
46.3 MJ/h
process
90oC
RECYCLE A (PURE A)
FLOWRATE= 50 kg/hr
COLUMN 2
140oC
FEED A
o
20 C
120oC
73.1 MJ/h
ISOTHERMIC
REACTOR
REACTOR
OUTLET
160oC
20oC
120oC
COLUMN 1
51.9 MJ/h
150oC
TO STORAGE
AT AMBIENT
TEMPERATURE
T=120oC
FEED B
180oC
RECYCLE B (PURE B)
FLOWRATE= 10 kg/hr
68.2 MJ/h
Fig. 1
101
EXAMPLE 1 - Data extraction
Additional data:
Feed A
Feed B
Reactor Outlet
Product
Flowrate = 100 kg/hr
TBoiling Point = 90 oC
Hvap = 184.2 kJ/kg
Cpliq = 2.47 kJ/kgoC
Cpvap = 1.07 kJ/kgoC
Flowrate = 50 kg/hr
TBoiling Point = 180 oC
Hvap = 317.1 kJ/kg
Cpliq = 4.72 kJ/kgoC
Cpvap = 2.36 kJ/kgoC
TBoiling Point = 160 oC
Cpliq = 764.4 kJ/oC
Cpvap = 451.6 kJ/ oC
Cpliq = 468.3 kJ/oC
Cpvap = 279.5 kJ/ oC
102
EXAMPLE 1 - Data extraction

Extract the stream data needed to perform a pinch
analysis from the flowsheet given in Figure 1
103
EXAMPLE 1 - Solution
46.3 MJ/h
TEMPERATURE
VARIATION
90oC
RECYCLE A (PURE A)
FLOWRATE= 50 kg/hr
COLUMN 2
Feed A
140oC
51.9 MJ/h
20oC
120oC
73.1 MJ/h
ISOTHERMIC
REACTOR
REACTOR
OUTLET
160oC
20oC
Feed B
120oC
COLUMN 1
150oC
TO STORAGE AT
AMBIENT
TEMPERATURE
T=120oC
180oC
RECYCLE B (PURE A)
FLOWRATE= 10 kg/hr
68.2 MJ/h
Identification of all the streams where there is a change in the temperature
and or enthalpy
104
EXAMPLE 1 - Solution
STREAM 6
HOT
46.3 MJ/h
90oC
RECYCLE A (PURE A)
FLOWRATE= 50 kg/hr
Feed A
STREAM 1
COLD
Cpliq = 2.47
Cpvap = 1.07
STREAM 5
HOT
COLUMN 2
140oC
73.1 MJ/h
20oC
20oC
120oC
120oC
STREAM 2
COLD
Cpliq = 4.72
Feed B
ISOTHERMIC
REACTOR
T=120oC
REACTOR
OUTLET
160oC
STREAM 3
COLD
CPliq = 764.4
180oC
RECYCLE B (PURE A)
FLOWRATE= 10 kg/hr
COLUMN 1
150oC
STREAM 4
COLD
51.9 MJ/h
STREAM 7
HOT
CPliq = 468.3
TO STORAGE
AT AMBIENT
TEMPERATURE
68.2 MJ/h
105
EXAMPLE 1 - Solution
The stream data for the process are given in the following table
(streams 1 to 3).
Stream
Tin
(0C)
Tout
(0C)
CP
1. COLD
20
90
91
90
91
120
2.47 kJ/kgoC
Hvap = 184.2 kJ/kg
1.07 kJ/kgoC
2. COLD
20
120
4.72 KJ/Kg0C
3. COLD
120
160
764.4 Kj/0C
106
EXAMPLE 1 - Solution
The stream data for a process are given in the following table
(streams 4 to 7).
Stream
Tin ( 0C)
Tout ( 0C)
Information needed
for Pinch Analysis
4. Cold
179
180
Vap. Heat
68.2 MJ / h
5. Hot
140
139
Cond. Heat
73.1 MJ / h
6. Hot
90
89
Cond. Heat
46.3 MJ / h
7. Cold
149
150
Vap. Heat
51.9 MJ / h
107
EXAMPLE 2 - Composite curves and
HEN design
The stream data for a process are given in the table
below
Stream
Tin ( 0K)
Tout ( 0K)
CP (kW/ 0K)
1. Cold
311
478
1139
2. Cold
339
455
1292
3. Cold
366
478
1303
4. Hot
522
394
1662
5. Hot
578
339
1330
108
EXAMPLE 2 - Composite curves and
HEN design
The hot utility is steam at 509 K and the cold utility is
water at 311 K

Plot the composite curves for the above system
and determine QH,min, QC,min and the pinch
temperature for DTmin = 24 K

Design a network that features the minimum
number of units for maximum energy recovery
109
EXAMPLE 2 - Solution
Step 1 - Define temperature intervals

Hot stream :

interval temp. = actual temp. – 1/2 D Tmin
Cold stream :
interval temp. = actual temp. + 1/2 D Tmin
Stream
Actual temperature
TS / TT ( 0K)
Interval temperature
TS / TT ( 0K)
1. Cold
311 / 478
323 / 490
2. Cold
339 / 455
351 / 467
3. Cold
366 / 478
478 / 490
4. Hot
522 / 394
510 / 382
5. Hot
578 / 339
566 / 327
110
EXAMPLE 2 - Solution
Step 2 - Interval thermal balance
Interval temp
566
510
490
467
382
378
351
327
323
Flux
5
4
3
2
1
Interval
DTi (oC)
--56
20
23
85
4
27
24
4
Cpcold-Cphot
(kW/ oC)
DHi (kW)
Surplus/deficit
-13.3
-29.92
-5.5
7.42
24.04
11.01
-1.91
11.39
-744.8
-598.4
-126.5
630.7
96.16
297.27
-45.84
45.56
surplus
surplus
surplus
deficit
deficit
deficit
surplus
deficit
111
EXAMPLE 2 - Solution
Step 3 - Heat energy cascades
566 K
HOT UTILITY
0 kW
HOT UTILITY
0 kW
-744.8
744.8
-744.8
744.8
Heating utility = 0 kW
510 K
-598.4
1343.2
-598.4
1343.2
-126.5
1469.7
-126.5
1469.7
630.7
839
630.7
839
96.16
742.84
96.16
742.84
297.27
445.57
297.27
445.57
-45.84
491.41
-45.84
491.41
45.56
445.85
45.56
445.85
490 K
467 K
382 K
Pinch point at 566 K (where
the energy flux between 2
intervals is 0 kW)
378 K
351 K
Cooling utility = 446 kW
327 K
323 K
COLD
UTILITY
COLD
UTILITY
112
EXAMPLE 2 - Solution
Step 4 - Composite curves
113
EXAMPLE 2 - Solution
Step 5 - Network design
EXHAUST ALL HOT STREAMS
WITH COLD STREAMS
EXHAUST ALL COLD STREAMS
WITH HOT STREAMS
RESPECTING THE FOLLOWING
RULES:
- CPHOT  CPCOLD
- ΔTmin respected between streams
114
EXAMPLE 2 - Solution
Step 5 - Network design - below the pinch point
554
578
554
578
CP / DH
11.39 / 1902.13
311
1
12.92 / 1498.72
339
2
13.03 / 1459.36
366
3
16.62 / 2127.36
478
E1
1498.72
E4
380
1285.57
478
E3
394
421
522
511
4
E5
446.28
13.30 / 3178.7
455
182.79
411
339
578
5
E2
COLD UTILITY
1902.13
115
EXAMPLE 2 - Solution
Step 5 - Network design



Above the pinch point, 0 heat exchanger are
necessary
Below the pinch point, 5 heat exchangers are
necessary
In total, 5 heat exchangers are necessary for this
network



Min Number of HX for MER = Umin MER = Umin above + Umin
below
Umin above = 0
Umin below = N – 1 = 6 – 1 = 5 where N is the total number of
streams including utilities
116
EXAMPLE 3 - Composite curves
and HEN design
The stream data for a process are given in the table below
Stream
TS
( 0C)
TT
( 0C)
CP
(KW/ 0C)
1. Hot
170
88
2.3
2. Hot
278
90
0.2
3. Hot
354
100
0.5
4. Cold
30
135
0.9
5. Cold
130
205
2.0
6. Cold
200
298
1.8
117
EXAMPLE 3 - Composite curves and
HEN design
The hot utility is to be supplied by a hot oil circuit at 380oC
and the cold utility by a cooling media at 20oC. For a DTmin
of 10oC:

Plot the composite curves and determine QH,min,
QC,min and the pinch temperature

Design a network that features the minimum
number of units for maximum energy recovery,
Umin MER.
118
EXAMPLE 3 - Solution
Step 1 - Define temperature intervals
Stream
Actual temp.
TS / TT (0C)
Interval temp.
TS / TT (0C)
1. Hot
170 / 88
165 / 83
2. Hot
278 / 90
273 / 85
3. Hot
354 / 100
349 / 95
4. Cold
30 / 135
35 / 140
5. Cold
130 / 205
135 / 210
6. Cold
200 / 298
205 / 303
119
EXAMPLE 3 - Solution
Step 2 - Interval thermal balance
Interval temp
349
303
273
210
205
165
140
135
95
85
83
35
Flux
3
2
6
1
5
4
Interval
DTi (oC)
--46
30
63
5
40
25
5
40
10
2
48
Cpcold-Cphot
(kW/ oC)
DHi (kW)
Surplus/deficit
-0.5
1.3
1.1
3.1
1.3
-1
-0.1
-2.1
-1.6
-1.4
0.9
-23
39
69.3
15.5
52
-25
-0.5
-84
-16
-2.8
43.2
surplus
deficit
deficit
deficit
deficit
surplus
surplus
surplus
surplus
surplus
deficit
120
EXAMPLE 3 - Solution
Step 3 - Heat energy cascades
349oC
HOT UTILITY
0 kW
HOT UTILITY
152.8 kW
-23
23
-23
175.8
39
-16
39
136.8
69.3
-85.3
69.3
67.5
15.5
-100.8
15.5
52
52
-152.8
52
0
-25
-127.8
-25
25
-0.5
-127.3
-0.5
25.5
-84
-43.3
-84
109.5
-16
-27.3
-16
125.5
-2.8
-24.5
-2.8
128.3
43.2
-67.7
43.2
85.10
o
303 C
Heating utility = 153 kW
o
273 C
o
210 C
o
205 C
165 oC
o
140 C
135 oC
Pinch point at 165oC (where
the energy flux between 2
intervals is 0 kW)
95 oC
85 oC
83 oC
Cooling utility = 85 kW
35 oC
COLD
UTILITY
COLD
UTILITY
121
EXAMPLE 3 - Solution
Step 4 - Composite curves
T (oC)
DTmin
Hpinch
H (kW)
122
EXAMPLE 3 - Solution
Step 5 - Network design
H (kW)
m.cp (kW/oC)
EXHAUST ALL HOT STREAMS
WITH COLD STREAMS
EXHAUST ALL COLD STREAMS
WITH HOT STREAMS
RESPECTING THE FOLLOWING
RULES:
- CPHOT  CPCOLD
- ΔTmin respected between streams
123
EXAMPLE 3 - Solution
Step 5 - Network design - above the pinch point
CP/DH
21.6
0.2/21.6
0.5/92
2
3
278
354
170
90
E1
2
174
170
205
2/90
160
5
HOT UTILITY
1.8/176.4
298
E4
213
E2
212
E3
200
6
152.8
Heating utility calculated with energy cascade = 153 kW
Cooling utility calculated with energy cascade = 85 kW
124
EXAMPLE 3 - Solution
Step 5 - Network design - below the pinch point
CP/DH
COLD UTILITY
1
144
170
103
88
E7
34.1
2
170
COLD UTILITY
90
E8
16
3
170
2.3/188.6
E9
0.2/16
COLD UTILITY
100
0.5/35
35
135
E6
30
4
0.9/94.5
130
5
2.0/60
94.5
160
E5
60
125
EXAMPLE 3 - Solution
Step 5 - Network design



Above the pinch point, 4 heat exchangers are
necessary
Below the pinch point, 5 heat exchangers are
necessary
In total, 9 heat exchangers are necessary for this
network



Min Number of HX for MER = Umin MER = Umin above + Umin
below
Umin above = N – 1 = 5 – 1 = 4
Umin below = N – 1 = 6 – 1 = 5 where N is the total number of
streams including utilities
126
EXAMPLE 4 - GCC
Using the given energy
cascade, draw the
grand composite
curve associated
GCC?
From Int. Energy Agency
127
EXAMPLE 4 - Solution
From Int. Energy Agency
128
EXAMPLE 5 - A complete
problem
The stream data for a process are given in the table below
Stream
TS (0C)
TT (0C)
CP (MW/0C)
1. Hot
327
40
3.0
2. Hot
220
160
4.8
3. Hot
220
60
1.8
4. Hot
160
45
12.0
5. Cold
100
300
3.0
6. Cold
35
164
2.1
7. Cold
85
138
10.5
8. Cold
60
170
1.8
9. Cold
140
300
6.0
129
EXAMPLE 5 - A complete problem
At the correct setting of the capital-energy trade-off,
D Tmin = 26oC



Plot the composite curves for the above system
and determine QH,min, QC,min and the pinch
temperature
Plot the grand composite curve of the process
Design a network to achieve the target without
violating D Tmin = 26oC
130
EXAMPLE 5 - Solution
Step 1 - Define temperature intervals
Stream
Actual temp.
TS / TT (0C)
Interval temp.
TS / TT (0C)
1. Hot
327 / 40
314 / 27
2. Hot
220 / 160
207 / 147
3. Hot
220 / 60
207 / 47
4. Hot
160 / 45
147 / 32
5. Cold
100 / 300
113 / 313
6. Cold
35 / 164
48 / 177
7. Cold
85 / 138
98 / 151
8. Cold
60 / 170
73 / 183
9. Cold
140 / 300
153 / 313
131
EXAMPLE 5 - Solution
Step 2 - Interval thermal balance
Interval temp
Flux
Interval
DTi (oC)
1
314
313
207
183
177
153
151
147
113
98
73
48
47
32
27
2
3
9
4
5
7
8
6
--1
106
24
6
24
2
4
34
15
25
25
1
15
5
CpcoldCphot
(MW/ oC)
DHi
(kW)
Surplus/
deficit
-3
6
-0.6
1.2
3.3
-2.7
7.8
0.6
-2.4
-12.5
-14.7
-16.8
-15
-3
-3000
636 000
-14 400
7200
79 200
-5400
31 200
20 400
-36 000
-322 500
-367 500
-16 800
-225 000
-15 000
surplus
deficit
surplus
deficit
deficit
surplus
deficit
deficit
surplus
surplus
surplus
surplus
surplus
surplus
132
EXAMPLE 5 - Solution
Step 3 - Heat energy cascades (1 of 2)
314 oC
HOT UTILITY
0 kW
HOT UTILITY
751 200 kW
-3000
3000
-3000
742 200
636 000
-633 000
636 000
118 200
-14 400
-618 600
-14 400
132 600
7200
-625 800
7200
125 400
79 200
-705 000
79 200
46 200
-5400
-699 600
-5400
51 400
31 200
-730 800
31 200
20 400
20 400
-751 200
20 400
0
Heating utility = 751 200 kW
313 oC
207 oC
o
183 C
177 oC
o
153 C
o
151 C
o
147 C
133
EXAMPLE 5 - Solution
Step 3 - Heat energy cascades (2 of 2)
147 oC
20 400
-751 200
20 400
0
-36 000
-715 200
-36 000
36 000
-322 500
-392 700
-322 500
358 500
-367 500
-25 200
-367 500
726 000
-16 800
-8400
-16 800
742 800
-225 000
216 600
-225 000
967 800
-15 000
231 600
-15 000
982 800
113 oC
o
98 C
Pinch point at 113oC (where
the energy flux between 2
intervals is 0 kW)
o
73 C
48 oC
o
47 C
Cooling utility = 982 800 kW
32 oC
o
27 C
COLD
UTILITY
COLD
UTILITY
134
EXAMPLE 5 - Solution
Step 4 - Composite curves
ΔΤmin
135
EXAMPLE 5 - Solution
Step 5 - Grand composite curve
136
EXAMPLE 5 - Solution
Step 6 - Network design
H (kW)
m.cp (kW/oC)
EXHAUST ALL HOT STREAMS WITH
COLD STREAMS
EXHAUST ALL COLD STREAMS WITH
HOT STREAMS
RESPECTING THE FOLLOWING
RULES:
- CPHOT  CPCOLD
- ΔTmin respected between streams
137
EXAMPLE 5 - Solution
Step 6 - Network design - above the pinch point
CP/DH
3000 / 603 000
1
4800 / 288 000
2
1800 / 169 200
3
12 000 / 408 000
4
3000 / 600 000
300
327
220
164
220
126
E6
E5
160
126
E4
H1
224.4
168
169200
E1
134
102000
138
100
H2
127.4
H3
111000
1800 / 126 000
170
100
5
102000
134400
10 500 / 399 000
160
E2
226800
2100 / 134 400
126
E3
100
6
7
288000
100
H4
8
126000
6000 / 960 000
300
H5
153000
274.5
603000
174
204000
9
140
138
EXAMPLE 5 - Solution
Step 6 - Network design - below the pinch point
1
CP/DH
COLD UTILITY
102
126
C1
40
3000 / 258 000
60
1800 / 118 800
45
12 000 / 972 000
186 000
3
4
COLD UTILITY
126
C2
113
126
101.5
COLD UTILITY
118 000
C3
294 000
100
E3
35
6
2100 / 136 500
7
10 500 / 157 500
8
1800 / 72 000
136 500
100
E2
85
157 500
100
E1
60
72 000
139
EXAMPLE 5 - Solution
Step 6 - Network design



Above the pinch point, 11 heat exchangers are
necessary
Below the pinch point, 6 heat exchangers are
necessary
In total, 17 heat exchangers are necessary for this
network



Min Number of HX for MER = Umin MER = Umin above + Umin
below
Umin above = N – 1 = 12 – 1 = 11
Umin below = N – 1 = 7 – 1 = 6
where N is the total number of streams including utilities
140
2.2 APPLICATION EXAMPLE
FOR MASS EXCHANGE
NETWORK ANALYSIS
141
EXAMPLE 1
Recovery of benzene from gaseous emission of
a polymer production facility (Source: Pollution
prevention through process integration, El
Halwagi, M.M)
A simplified flowsheet of the copolymerization
process can be found next
142
EXAMPLE 1
COPOLYMERIZATION PROCESS WITH A BENZENE RECOVERY MEN
Inhibitors + Special
Additives
Extending
Agent
S1
Catalytic
Solution
(S2)
Monomers
Monomers
Mixing Tank
Additive Mixing
Column
First Stage
Reactor
Solvent
Makeup
Recycled Solvent
Second Stage
Reactor
Gaseous
Waste (R1)
Separation
Copolymer
(to
Coagulation
and
Finishing)
Unreacted Monomers
143
EXAMPLE 1
Data of rich stream for the benzene removal example


Stream
Description
R1
Off-gas from
product separation
Flowrate
Gi, kg mol/s
0.2
Supply composition
(mole fraction) ysi
0.0020
Target composition
(mole fraction) yti
0.0001
Candidate MSA’s :
Two process MSA’s and one external MSA
Process MSA’s :
Additives (S1) : The additives mixing column can be used as a absorption
column by bubbling the gaseous waste into the additives
Liquid catalytic solution (S2) : The equilibrium data for benzene in the two
process MSA’s are given by:
y1 = 0.25x1
y1 = 0.50x2
For control purpose, the minimum allowable composition difference for S1 and
S2 should not be less than 0.001.
144
EXAMPLE 1
Data of process lean streams for the benzene removal example
Stream
Description
S1
S2
Additives
Catalytic solution
Upper bound on
flowrate Lcj
kg mol/s
0.08
0.05
Supply composition
of benzene (mole
fraction) x sj
0.003
0.002
Target composition
of benzene (mole
fraction) xtj
0.006
0.004

The external MSA, S3, is an organic oil which can be regenerated using flash
separation. The operating cost of the oil (including pumping, makeup and
regeneration) is $0.05/kgmole of recirculating oil
The equilibrium relation for transferring benzene from the gaseous waste to
the oil is given by:
y1 = 0.10x3
Data for the external MSA for the benzene removal example
Stream
Description
S3
Organic oil
Upper bound on
flowrate Lcj
kg mol/s
infinite
Supply composition
of benzene (mole
fraction) x sj
0.0008
Target composition
of benzene (mole
fraction) xtj
0.0100
145
EXAMPLE 1
SIMPLIFIED FLOWSHEET OF THE COPOLYMERIZATION PROCESS
Additive (Extending
Catalytic
Solution S2 Agent, Inhibitors and
Special Additives S1
Oil
Makeup
Benzene
Regeneration
To
atmos
phere
Monomers
Monomers
Mixing Tank
Oil
S3
Gaseous
Waste R1
Benzene Recovery MEN
First Stage
Reactor
Solvent
Makeup
Recycled Solvent
Second Stage
Reactor
Separation
Copolymer
(to
Coagulation
and
Finishing)
Unreacted Monomers
146
EXAMPLE 1



Construct the pinch diagram of this process
Find where the pinch point is located and
what is the excess capacity of the process
MSA’s
Find the outlet composition of the additivesmixing column (S1)
147
EXAMPLE 1 - SOLUTION
1. Construct the pinch diagram (1 of 4)
148
EXAMPLE 1 - SOLUTION
1. Construct the pinch diagram (2 of 4)
Representation of the
two process MSA’s
149
EXAMPLE 1 - SOLUTION
1. Construct the pinch diagram (3 of 4)
150
EXAMPLE 1 - SOLUTION
1. Construct the pinch diagram (4 of 4)
151
EXAMPLE 1 - SOLUTION
2. Interpret de results of the pinch diagram
(1 of 3)


Pinch is located at the corresponding mole
fractions (y, x1, x2) = (0.0010, 0.0030,
0.0010)
The excess capacity of the process MSA’s is
1.4X10-4 kgmole benzene/s
152
EXAMPLE 1 - SOLUTION
2. Interpret de results of the pinch diagram
(2 of 3)

There are infinite combination of L1 and x1out
that can be used to remove the excess
capacity of S1 according to the following mass
balance:


Benzene load above the pinch to be remove by
S1=L1(x1out - x1S) i.e 2.4X10-4 = L1(x1out - 0.003)
Since the additives-mixing column will be used for
absorption, the whole flowrate S1 (0.08 kgmole/s)
should be fed to the column. The outlet composition
of S1 is 0.0055.
153
EXAMPLE 1 - SOLUTION
2. Interpret de results of the pinch diagram (3 of 3)
Graphical
identification of x1out
154
2.3 APPLICATION EXAMPLES
FOR OPTIMIZATION
TECHNIQUES
155
EXAMPLE 1 - Linear programming (LP)
A process consists of the following set of hot and cold
process streams:
Stream
Tin( 0C)
Tout( 0C)
F Cp (kW 0C-1)
H1
95
75
5
H2
80
75
50
C1
30
90
10
C2
60
70
12.5
Example taken from Floudas and Ciric (1989)
This example features constant flow rate heat
capacities, one hot and one cold utility being steam
and cooling water, respectively.
156
EXAMPLE 1 - Linear programming (LP)
Assumption: the costs of hot utility i (Ci) and cold
utility j (Cj) are equal to 1, for the minimum utility
consumption.
Formulate
the
linear
programming
(LP)
transshipment model, and solve it to determine the
minimum utility cost.
157
EXAMPLE 1 - SOLUTION
The temperature interval partitioning along with the
transshipment representation is shown in Figure 1.
QS
(120)
(90)
50
TI - 1
H1
(95)
25
250
R1
(65)
C1
100
200
TI - 2
50
(90)
25
H2
250
R2
(60)
62.5
TI - 3
(80)
R3
(50)
62.5
C2
TI - 4
(60)
(30)
QW
Figure 1.
158
EXAMPLE 1 - SOLUTION
Then, the LP transshipment model for minimum utility
consumption takes the form:
min QS + QW
s.t. R1 – QS = -312.5
R2 – R1 = -87.5
R3 – R2 = -50
QW – R3 = 75
QS, QW, R1, R2, R3 ≥ 0
159
EXAMPLE 1 - SOLUTION
This model features four equalities, five variables and
has linear objective function constraints. Its solution
obtained via GAMS/MINOS (General Algebraic
Modeling System / Modular Incore Nonlinear
Optimization System) is:
QS = 450
QW = 75
R1 = 137.5
R2 = 50
R3 = 0
160
EXAMPLE 1 - SOLUTION
Since R3 =0, there is a pinch point between TI – 3
and TI - 4. hence, the problem can be decomposed
into two independent subnetworks, one above the
pinch and one below the pinch point.
Remind that when we have one hot and one cold
utility, it is possible to solve the LP transshipment
model by hand. This can be done by solving the
energy balances of TI – 1 for R1, TI – 2 for R2, TI – 3
for R3, and TI – 4 for QW which become
161
EXAMPLE 1 - SOLUTION
R1 = QS – 312.5
R2 = R1 – 87.5 = QS – 400
R3 = R2 – 50 = QS – 450
QW = R3 + 75 = QS – 375
Since R1, R2, R3, R4 ≥ 0 we have
QS ≥ 312.5
QS ≥ 400
QS ≥ 450
QS ≥ 375
162
EXAMPLE 1 - SOLUTION
The objective function to be minimized becomes
QS + QW = 2*QS – 375
Then, we seek the minimum QS that satisfies all the
above four inequalities. This is
QS = 450
163
EXAMPLE 2
Etching of copper is achieved through ammoniacal
solution and etching efficiency is higher for copper
concentrations in the ammoniacal solution between
10 - 13 w/w%. To maintain the desired copper
concentration in the solution, copper must be
continuously removed. Copper must also be removed
from the rinse water, with which the etched printed
circuits are washed out, for environmental and
economic reasons.
164
EXAMPLE 2
Thus, two rich streams in copper must be purified up
to concentrations dictated by environmental
regulations and process economics. Mass flow rate
data and concentration specifications are given in
table I.
Stream
No.
Description
Mass flow rate
Gi (Kg/s)
Initial
concentration
Yis
Target
concentration
yit
R1
Ammoniacal solution
0.25
0.13
0.10
R2
Rinse water
0.10
0.06
0.02
Table I. Rich streams of copper recovery problem
165
EXAMPLE 2
A simplified representation of the etching process is
illustrated in Fig 1.
Etchant
Makeup
Etchant
Spent Echant
Etching
Line
Etched Boards
Rinse
Bath
Printed
Circuit
Boards
R2
Rinse Water
Rinse
Water
Makeup
Mass
Exchange To solvent
Regeneration
Network
S1
S2
Treated Rinse Water
R2
Regenerated Etchant
R1
Fig. 1. Recovery of streams of copper in an etching plant.
166
EXAMPLE 2
Two extractants are proposed for copper recovery,
LIX63 (an aliphatic α- hydroxyoxime, S1) and P1 (an
aromatic
β-hydroxyoxime,
S2).
The
initial
concentrations in copper of the available lean
streams, an upper bound on their final concentration
and their costs are given in table II.
Stream
Description
Initial
concentration
xjs
Maximum outlet
concentration
xjT, up
Cost
(US$/Kg)
Ann. Cost
(US$/Kg)
S1
L1X63
0.030
0.07
0.010
88,020
S2
P1
0.001
0.02
0.120
1,056,240
Table II. Lean streams of copper recovery problem
167
EXAMPLE 2 - SOLUTION
Within the ranges of copper concentrations of
interest, the copper transfer between the given rich
and lean streams is governed by the following linear
equilibrium relations (Henry equation):
R1 - S1 : y1* = 0.734 x1* + 0.001
R2 - S1 : y2* = 0.734 x1* + 0.001
R1 - S2 : y1* = 0.111 x2* + 0.008
R2 - S2 : y2* = 0.148 x2* + 0.013
168
EXAMPLE 2 - SOLUTION
Two types of contactors are considered:
• a perforated plate column for S1 (LIX63)
• a packed tower for S2 (P1)
Where y1*, y2* and x1*,
x2* are the copper
concentrations of R1, R2 and S1, S2, respectively, at
equilibrium.
169
EXAMPLE 2 - SOLUTION
The annualized investment cost of a plate-column is
based on the number of plates NSt which is
determined through Kremser equation.




  mG  y in  m x in  b mG 

ln  1 

 out
in
L  y  mx  b
L 


N St 
 mG 
ln 

 L 
The cost of packed tower is based on the overall
height of the column:
G
H OR 
K y ( y  y* )
HTotal  H R x N R
170
EXAMPLE 2 - SOLUTION
The annualized investment costs are given in table III
Cost of plate column
4 552 NSt $ / Yr
Cost of packed column
4 245 H $ / Yr
Table III. Capital cost data for copper recovery problem
(Papalexandri et al., 1994)
171
EXAMPLE 2 - SOLUTION
The obtained mass exchange network for copper
recovery is illustrated in Fig 2. the model was solved
in 3GBD (Generalized benders decomposition)
S
S
iterations.
0.278 kg/s
0.019 kg/s
1
2
xs = 0.030
xs = 0.001
N2 = 4
R2
1
N3 = 1
1
yT = 0.020
0.100 kg/s
ys = 0.060
xT = 0.020
N1 = 1
R1
1
0.250 kg/s
ys = 0.130
yT = 0.100
xT = 0.070
Fig 2.
172
EXAMPLE 2 - SOLUTION
It features 3 mass exchangers in series and a total
annualized cost of $15,933/yr, with $52,591/yr
corresponding to operating cost.
A flexibility analysis (Grossmann and Floudas, 1987)
of the proposed MEN reveals that it is flexible to
operate in the whole uncertainty range of GR.
173
EXAMPLE 3
Problem statement & solution structure
System closure in pulp and paper mills
One can formulate the problem as having two types of
white water streams:
•Sources: white water streams that are produced in
different operations and are available to be used in
other operations. They are characterized by fiber, fine
and contaminant concentrations and by flow rate.
•Demands: white water streams that are required by
operations, and on which limiting concentrations in
fibers, fines and, contaminants are imposed.
174
EXAMPLE 3
Problem statement & solution structure
The objective is to establish a white water network
configuration such that all demands are satisfied and
yet optimization goals such as minimized fresh water
consumption, fiber loss degree of contamination are
met. The method consists of encoding structure
elements in the general framework of a genetic
algorithm problem and relating network characteristics
to linear programming problem. A superstructure is
formed by respecting the following rules:
175
EXAMPLE 3
Problem statement & solution structure
•Each source stream and fresh water enters a splitter
in which it can be divided into several streams that are
directed to various demands while the excess is sent
to the waste water effluent.
•Before each demand there is a mixer, which gathers
all the streams coming from the different sources;
wastewater effluents are also collected into a single
stream.
176
EXAMPLE 3
Problem statement & solution structure
This form of superstructure is encoded as follows.
Each individual configuration of the superstructure is
characterized by chromosome in which each gene
represents a potential connection between a splitter
and a mixer. The value of a gene is one or zero
indicating the existence or absence of connection. All
possible configurations for a given set of sources and
demands can thus be represented by a set of
chromosomes
in
a
unique
one-to-one
correspondence. Figure 1 shows an example of a
structure and corresponding code.
177
EXAMPLE 3
Problem statement & solution structure
Splitters
Mixers
S1
D1
S2
D2
S3
D3
S4
Waste
Fresh Water
1 1 0 0
1 1 1 1
1 1 0 0
0 0 1 0
Figure 1: example of coding for a system of 4 sources and 3 demands
178
EXAMPLE 3
Problem statement & solution structure
Knowing the number of sources and demands the
number of genes and hence, the length of
chromosomes is determined. For example if there are
m sources and n demands, the number of genes will
be (m+1)(n+1). This includes the genes needed to
take into account fresh water as a source stream and
the effluent stream as a demand.
Overall and component material balances are written
for each splitter and mixer for any structure
considered.
179
EXAMPLE 3
Problem statement & solution structure
The balance equations constitute constraints of the
optimization problem with specified objective function.
A linear or non-linear programming problem is thus
formed and is solved to give the value of the objective
function for the given structure. The optimization of
the network is treated a two levels; at the master
problem level a set of feasible structures is proposed
by GA and at slave problem level the proposed
structures
are
optimized
by
mathematical
programming methods to obtain the optimal value of
the objective function.
180
EXAMPLE 3
Problem statement & solution structure
This value in turn is passed to the master problem by
means of an adaptation index to be used in the
generation of new structures. At the end of the
iterative procedure a set of structures is available that
have near optimal objective function values.
181
EXAMPLE 3
Problem statement & solution structure
Genetic algorithm procedure (GA)
The GA implemented follows the classical iterative
procedure introduced by Goldberg (1989):
Generation of the initial population
Evaluation of the fitness of the initial population
Iteration of the following sequence until total number
of generations is reached
182
EXAMPLE 3
Problem statement & solution structure
Generation of the offspring population
Selection of surviving individuals
Synthesis of offspring obtained by cross-over
Mutation of individuals
End of search
The initial population consists of 20 structures that
have been created randomly by assigning to the
genes.
183
EXAMPLE 3
Problem statement & solution structure
For each generation subsequently generated, a fixed
fraction is conserved in the offspring generation and
the rest of the population is created by crossover of
randomly selected pairs of individuals (Figure 2). In
crossover the chromosomes are cut and recombined
at a randomly selected crossover point (CP)
184
EXAMPLE 3
Problem statement & solution structure
The individuals interchange chromosome sections
and two new individuals are thus created. In mutation
one gene is selected randomly and its value is
changed.
CP
Muted Gene
CP
P1
P2
Before mutation
1 1 0 1 0 1
E1
E2
After mutation
1 1 0 1 1 1
Crossover
Mutation
Figure 2. Crossover and mutation operations
185
EXAMPLE 3
Problem statement & solution structure
Each interesting solution given by the program in the
final population is compared with the base case of the
mill by PS. The necessary changes to be made are
extracted from the solution and a scenario is
formulated. This scenario is executed in the mill
simulation and the changes in concentration of the
different species in important points of the process
are determined. Figure 3 shows the flow of
information at different stages of the overall
procedure.
186
EXAMPLE 3
Problem statement & solution structure
PROBLEM DEFINITION
Process
Simulation
Superstructure
Master problem
Genetic Algorithm
Mass
Balance
Demand
Constraints
OPTIMIZATION
Objective
Function
Superstructure
Adaptation
Index
Retained
Solutions
Feasibility
IMPLEMENTATION
Engineering
Figure 3.General structure of procedure
187
EXAMPLE 3
Problem statement & solution structure
In this process four sources of water and three
demands are identified. The specification of the
sources and demands are given on table I
Sources
Available flowrate (L/min)
Fines
concentration (%)
Contaminant
concentration (ppm)
S1
500
0.3
100
S2
2000
0.1
110
S3
400
0.5
110
S4
300
0.5
60
Demands
Required flowrate (L/min)
Limiting fines
concentration (%)
Limiting contaminant
concentration (ppm)
D1
1200
0.5
120
D2
800
0.4
105
D3
500
0.1
80
Table I
188
EXAMPLE 3
Problem statement & solution structure
The initial configuration of the process is given on
figure I, the demands D2 and D3 are satisfied by fresh
water and all the sources are sewered except a
fraction of source 2, used to satisfy demand 1. The
goal is to find the optimal configuration of the water
network, minimizing the fresh water consumption.
189
EXAMPLE 3
Problem statement & solution structure
1200
Pulp
D1
Fresh Water
800
Fresh Water
500
D2
D3
Pulp
S1
S2
S3
S4
waste
500
waste
800
waste
400
waste
300
Flow sheet general diagram
190
EXAMPLE 3 - Solution (GA)
Splitters
500
Mixers
1200
S1
D1
2000
S2
800
D2
400
S3
500
300
D3
S4
2000
Fresh 1300
Water
Sewer
Superstructure
191
EXAMPLE 3 – Solution (GA)
The initial solution of the process is given on table II.
The fresh water consumption is 122 L/min, it is 90%
reduced from the initial data (1300 L/min)
Splitters
D1
S1
D2
D3
Waste
500
S2
540
290
S3
390
10
S4
270
348
30
Fresh
water
122
Table II
822
S1
Mixers
500
1200
2000
S2
S3
S4
800
D1
D2
400
500
300
D3
822 Waste
Fresh 122
Water
First solution
192
EXAMPLE 3 – Solution (GA)
The second solution of the process is given on table
III. The fresh water consumption is 172 L/min.
D1
S1
D3
S1
764
S3
400
S4
300
Splitters
Waste
500
S2
Fresh
water
D2
364
872
136
S4
Table III
500
1200
2000
S2
S3
36
Mixers
800
D1
D2
400
500
300
D3
872 Waste
Fresh 172
Water
Second solution
193
EXAMPLE 3 – Solution (GA)
On table IV are compared the first and second
solutions of the process using a Genetic Algorithms
Water consumption
(L/min)
Fibers Waste
g/min
GA1
122
0.822
GA2
172
0.872
Table IV
194
REFERENCES
•El-Halwagi, MM and Manousiouthakis, V.,
“Synthesis of Mass Exchange Networks”, AIChE
Journal, 35,(8), 1233-1244, (1989)
•El-Halwagi, MM and Manousiouthakis, V.,
“Simultaneuos Synthesis of Mass Exchange and
Regeneration Networks, AIChE Journal, 36,(8), 1209,
(1990a)
•Floudas C. A. and Paules IV G. E. “A mixed-integer
non linear programming formulation for the synthesis
of heat-integrated distillation sequences”, Comp.
Chem. Eng., 12, 259-372, (1998)
195
REFERENCES
•Garrard A., Fraga E. S., “Mass exchange network
synthesis using genetic algorithms” Computers and
Chemical Engineering, 22, (12), 1837-1850, (1998).
•Goldberg D.E., “Genetic Algorithms in Search,
Optimization, and Machine Learning” Ed. Addison
Wesley, (1997).
•Jacob, J., H. Kaipe, F. Couderc and J.Paris, “Water
network analysis in pulp and paper processes by
pinch and linear programming techniques”, Chem.
Eng. Communication, 189, (2), 184-206 (2002b).
196
REFERENCES
•Shafiei S., Domenech S., Koteles R., Paris J.,
“System Closure in Pulp and Paper Mills: Network
Analysis by Genetic Algorithm” Pulp and Paper
Canada (soumis).
197
Program for North American
Mobility in Higher Education
Introducing Process Integration for Environmental Control
in Engineering Curricula
MODULE 12: “Heat and Mass Exchange
Networks Optimization”
198
Tier 3
OPEN-ENDED PROBLEMS IN
A REAL WORLD CONTEXT
199
TIER 3 - STATEMENT OF INTENT
The goal of Tier 3 is to present an open-ended problem to
solve an industrial case study of actual heat or mass
exchange network optimization in which the student must
interpret results and evaluate a range of potential
solutions. The problem involves defining objective
functions, generating solutions, evaluating their technical
and economical feasibilities. Problem will be drawn from
actual cases in the petroleum and pulp and paper
industries.
200
TIER 3 - CONTENTS
The tier 3 is broken down into two sections:
3.1 Design of a heat and mass exchange network for
the efficient management of energy, water and
hydrogen in a selected oil refinery process.
3.2 Design of a whitewater network in an integrated
thermomecanical pulp and newsprint mill for
minimum fresh water consumption and minimum
fiber loss
201
3.1 PETROLEUM OPENENDED PROBLEM
202
PROBLEM DEFINITION
A mill is designed to eliminate the sulfuric compounds
present in a feed stream of diesel and light oil.
The mill is divided in 7 sections:







Reaction and load section
Gaz separation
Hydrogen purification
Diesel stabilization
Product cooling
Treatment with DEA
Compression of recirculated hydrogen
203
REACTION AND LOAD
SECTION




The objective of this section is to eliminate the
sulfur components and nitrogen, throught the
hydrogenation reaction in a fixed bed catalytic
reactor.
First, a stream of diesel and a stream of oil are
mixted together (MX-801***). The resultant mix is
then heated and transported to the decantation
tank (FA-801) where the aqueous phase is
remove.
The water-free mix is then heated in the three heat
exchangers (EA-802, EA-803, EA-804)
The mix is then sent to a heater to reach the
temperature of 346oC.
204
REACTION AND LOAD
SECTION


The vapor mix or charge is then transported to the
reactor (DC-801) where the reactions of
hydrogenation and the transformation of the nitrogen
and oxygen compounds are done.
The reactor effluent is then passed another time in
the three heat exchangers (EA-802, EA-803, EA804)
*** The identification equipment numbers can be founded
on the process diagram following the present
description of the process
205
GAS SEPARATION SECTION






The vapor and liquid mix is separated in a liquid
phase and a gaseous in the FA-802 tank.
The gaseous phase is cooled and a water stream
is then injected to eliminate the last impurities.
The resultant mix is then cooled in the aerocooler
EC-801
The aqueous phase is separated from the
gaseous phase rich in sulfur compounds in the
separator FC-803.
The aqueous phase is sent to the stabilization
section
The gaseous phase is sent to the DEA treatment
section
206
HYDROGEN PURIFICATION
SECTION




The hydrogen from the reformation plant is sent to a
separator (FA-805) to remove heavy compounds.
The hydrogen pass through three steps of compression
(GB-802, GB-803, GB-804)
Between each compression, the hydrogen is cooled (EC803, EC-804) and is entering a separator (FA-806, FA807) to remove the heavy compounds from the hydrogen
stream.
After the third compression, the hydrogen is at the
conditions of pressure and temperature necessary to be
utilized in the process.
207
DIESEL STABILIZATION
SECTION




The liquid phase resulting from the separation in FA802 is sent to heat exchanger EA-806.
The
preheated phase is then sent to the stabilization
tower DA-801
The liquid phase resulting from the separation in FA803 is also sent to the stabilization tower DA-801
The stabilization tower is used to separate the
lightweight hydrocarbures from the heavyweight
ones.
At the top of the tower, vapor containing sulfur
compounds exit and are condensated in EC-805.
The separation is done in FA-808.
208
DIESEL STABILIZATION
SECTION

At the bottom of the tower, the stream containing
mainly heavyweight hydrocarbures is divided in two
streams. The first stream is sent to the heater BA802 where it acquire the heat necessary to be
injected in the stabilization tower another time. The
second stream is sent to the heat exchanger EA806. The hydrodesulfurized and stabilized diesel is
sent to the vapor generator EA-807, and then the
diesel at a temperature of 215oC is transported to
the preheater EA-801.
209
PRODUCT COOLING SECTION



The diesel from the heatexchanger EA-801 is sent
to the heat exchanger EA-808 where it is cooled
until 153oC.
The cooled stream enters the aerocooler EC-802
and the watercooler EA-809.
After these two steps, the diesel is at the conditions
necessary to be stock.
210
TREATMENT WITH DEA
SECTION



The gaseous phase rich in sulfur compounds from
the separator FA-803 is feeded the last tray of the
absorption column DA-802. A stream of DEA
(dietanolamine) in aqueous phase is sent to the first
tray to absorb the sulphuridric acid contained in the
feed stream.
The gas obtained at the top of the column is
transported to the recirculated gas compression
section.
The amine obtained at the bottom of the column,
rich in H2S, is sent to the amine recuperation plant.
211
RECIRCULATED HYDROGEN
COMPRESSION SECTION



The gas free of H2S and rich in hydrogen is feeded
to the separator FA-804 where traces of amine can
be totally eliminated.
The gaseous phase is sent to the hydrogen
compressor GB-801 to increase its pressure
The compressed gas obtained is either mixted with
the hydrogen coming from the gas purification
section, or directly sent to the hydrodesulfurized
reactor DC-801.
212
PROCESS FLOWSHEET AND
DATA

The process flowsheet can be found at the
following link:


ProcessFlowsheet _PetroleumProb.pdf
The process data can be found at the following
link:

ProcessData_PetroleumProb.xls
213
WHAT YOU HAVE TO DO?
Perform a complete pinch analysis using the following
steps
a) Extract the hot and cold streams from the process
flowsheet and extract all the data necessary from the
data flowsheet (flowrate, temperature, enthalpy or Cp)
b) Determine QH,min, QC,min , the minimum consumption of
external utilities (energy targets)
214
WHAT YOU HAVE TO DO?
c) Propose a ΔTmin using Introduction to Pinch
Technology, 1998.of Linnhoff, M., (disponible at
www.linnhoffmarch.com) or using the experience ΔTmin
presented in the first tier - basic concepts.
d) Propose a heat exchanger network for the chosen
ΔTmin and respecting the energy targets.
e) Design a network that features the minimum number
of units for maximum energy recovery
215
3.2 PULP & PAPER OPENENDED PROBLEM
216
PROBLEM DEFINITION
An integrated newsprint mill is located in Canada. The
nominal production of the mill is 1230 odt/d (oven dried
tons per day) of paper with a feedstock of 1060 odt/d of
thermomechanical pulp (TMP) and 170 odt/d of deinked
pulp (DIP) also produced on site.
A simplified process flow diagram focusing on steam and
fresh water requirements is given in Fig.1.
217
PROBLEM DEFINITION
Fig. 1. Simplified reference process flow diagram. Abbreviations: CPH: chips pre-heather, HRU: heat recovery unit,
OM: old magazines, ONP: old newsprint, PM: paper machine.
218
PROBLEM DEFINITION
High pressure steam (16.5 bar, 540 K) is produced by
boilers burning biomass( wood residues) and natural gas
(NG). It is in part directly used to meet some mill needs
and in part depressurised through turbines and headers to
three lower pressure levels: MP (4.5 bar, 421 K), LP (3.4
bar, 415 K) and VLP (1.7 bar, 408K).
As indicated on Fig. 2, steam is then directed to the TMP,
DIP, paper making plants and other miscellaneous
operations. Steam is also exported to an adjoining saw
mill. The turbines produce 2 MWe of electricity, while the
mill purchases 125 MWe.
219
PROBLEM DEFINITION
Fig. 2. Reference steam distribution system. Abbreviations, NG: natural gas,
WM: water make-up.
220
PROBLEM DEFINITION
The two most important operations from the energy
standpoint are wood chips refining and paper drying.
Refining consists in disintegrating wood into individual
fibres by forcing the chips between two grooved disks
rotating at very high speed. In the mill analysed, the
refiners consume 83.7 MWe or 6820 kJ/odt. The
mechanical energy supplied to the refiners is largely
dissipated into heat, which evaporates whitewater injected
with the chips.
221
PROBLEM DEFINITION
The heat content of this medium steam is recovered
through heat exchanges with fresh water in the heat
recovery unit (Fig.1) since it contains wood contaminants
and cannot be reused directly. The steam from the primary
refiners is released at medium pressure (MP) but is
subsequently depressurised to low pressure (LP). The
steam from the secondary refiners (1 bar, 273 and 1.4 bar,
282 K) is not recovered currently.
Paper is dried in the end section of the paper machine by
passing the sheet of paper over a series of steam-heated
steel rolls.
222
PROBLEM DEFINITION
High-pressure steam is used at the beginning and MP in
the intermediate zone.
In the follwowing sections are refer types of operation in
the paper mill and the thermodynamic requirements.
Preheating by steam injection
The chip washing operation and the three main
whitewater chests are heated by direct contact with steam
(Fig. 1). This steam must be treated as loss by the utility
network since it is not returned to the boilers as
condensate.
223
PROBLEM DEFINITION
The thermodynamic requirement is defined by two cold
streams in order to separate mass exchange from heat
exchange. The first represents the heat required to raise
the temperature of the process stream to tank mixing
conditions. The second cold stream represents the heat
required to raise the liquid water makeup that completes
the mass balance from ambient (i.e. the water inlet
temperature) to the reservoir mixing conditions. Data are
given on Fig. 3 for the wood chip washing operation. In
the thermodynamic representation isothermal mixing is
assumed, all the process streams entering the mixer
having first been heated to the mixing temperature.
224
PROBLEM DEFINITION
Stream
Comp.
T (K)
P (bar)
m (kg/s)
1
WW
278
2
3.6
2
Steam
351
1
3.6
3
Steam
351
1
3057.3
4
Chips
278
1
15.7
5
WW
350
1
3040
Exchanger
Q (kW)
EX 1
1086
EX 2
2243
EX 3
6390
Fig. 3. Thermodynamic (reference case)
225
PROBLEM DEFINITION
Paper machine drying
There are two thermodynamic requirements for the drying
section of the paper machine: preheating the humid sheet,
and evaporating its water content which is reduced from
58% at the inlet of the drying section to 8% in the exiting
paper.
Primary and secondary refiners
Since the steam produced by evaporation of the white
water in the refiners is not returned in the steam network,
the thermodynamic requirements are identically defined
as a hot stream to be condensed and cooled to the
ambient temperature.
226
PROBLEM DEFINITION
Table 1 gives the characteristics of the hot and cold
streams for thermodynamic requirements of each of the
major energy consuming operations in the process shown
on Fig.1. Steam consumption for soot blowing and general
heating has been assimilated to process requirements
and the consumption for deaeration is treated as part of
the steam network model. The secondary refiner steam
will be recovered.
227
TABLE 1
Stream type
Tin (K)
Tout (K)
m Cp (kW/K)
Q (MW)
P
(bar)
Thermo. (chips)
Cold
278
351
31
2.2
–
Thermo. (WW)
Cold
350
351
13,595
6.4
–
Thermo. (makeup)
Cold
278
351
15
1.1
–
351
388
251
9.4
–
Representation
Wood chip washing
Preheat before primary refiners
Thermo.
Preheat before secondary refiners
Thermo. (makeup)
Cold
278
362
116
9.8
–
Thermo. (pulp)
Cold
324
362
60
2.3
–
Thermo. (FW)
Cold
278
321
591
25.7
–
Thermo. (makeup)
Cold
278
321
32
1.4
–
Thermo. (WW)
Hot
324
321
2576
6.5
–
TMP whitewater tank
228
TABLE 1 (CONTINUED)
Stream type
Tin (K)
Tout (K)
m Cp (kW/K)
Q (MW)
P (bar)
Thermo. (FW)
Cold
308
313
70
0.3
–
Thermo. (WW)
Cold
313
313
950
0.2
–
Thermo. (makeup)
Cold
278
313
1
0.03
–
Thermo. (FW)
Cold
288
308
1004
20.2
–
Thermo. (makeup)
Cold
278
308
23
0.7
–
Thermo. (WW)
Hot
309
308
4768
5.8
–
Thermo. (heating)
Cold
309
363
42
25.7
–
Thermo. (drying)
Cold
309
373
Water
1.4
–
Representation
Deinking whitewater tank
Paper machine whitewater
Drying section
229
TABLE 1 (CONTINUED)
Stream type
Tin (K)
Tout (K)
m Cp (kW/K)
Q (MW)
P (bar)
Primary refiners
Cold
421
298
Water
73.7
4.46
Secondary refiners
Cold
373
298
Water
14.3
1.00
Secondary refiners
Hot
388
298
Water
7.5
1.70
Heating
Cold
323
417
Water
30.1
3.43
Soot blowing
Cold
278
540
Water
6.0
16.52
Effluent treatment
Cold
278
417
Water
1.5
3.43
Saw mill
Cold
278
417
Water
5.1
3.43
Boilers
Cold
323
417
Water
8.3
3.43
Deareator
Cold
323
408
Water
3.8
1.70
LP level
Cold
323
417
Water
47.6
3.43
MP level
Cold
323
421
Water
8.7
4.46
HP level
Cold
323
540
Water
10.7
16.52
LP level
Hot
394
323
Water
10.2
2.03
MP level
Hot
407
323
Water
2.3
3.06
HP level
Hot
472
323
Water
3.5
15.12
Representation
Conventional representation
230
WHAT YOU HAVE TO DO?
Perform a complete Thermal Pinch Analysis

Using the hot and cold streams from the process
flowsheet reported in the table 1, determine QH,min,
QC,min , the minimum consumption of external
utilities (energy targets), and construct the grand
composite curves.

Propose a ΔTmin using Introduction to Pinch
Technology, 1998.of Linnhoff, M., (disponible at
www.linnhoffmarch.com) or using the experience
ΔTmin presented in the first tier - basic concepts.

Propose a heat exchanger network for the chosen
ΔTmin and respecting the energy targets.
231