Using Pinch Analysis to Optimize the Heat Exchanger Network of a
Regenerative Rankine Cycle for an Existing Modern Nuclear Power
Plant
by
Stephanie Barnes
A Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING
Major Subject: MECHANICAL ENGINEERING
Approved:
_________________________________________
Professor Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
December, 2013
i
© Copyright 2013
by
Stephanie Barnes
All Rights Reserved
ii
CONTENTS
LIST OF TABLES ............................................................................................................ vi
LIST OF FIGURES ........................................................................................................ viii
DEFINITIONS ................................................................................................................. ix
ACRONYMS ..................................................................................................................... x
NOMENCLATURE ......................................................................................................... xi
ACKNOWLEDGMENT ................................................................................................. xii
ABSTRACT ................................................................................................................... xiii
1. Introduction.................................................................................................................. 1
1.1
Background ......................................................................................................... 1
1.2
Regenerative Rankine Cycle............................................................................... 1
1.2.1
Millstone III Unit Overview .................................................................. 1
1.3
Pinch Analysis .................................................................................................... 4
1.4
Problem Statement .............................................................................................. 4
1.5
Previous Work .................................................................................................... 4
2. Theory .......................................................................................................................... 6
2.1
Second Law of Thermodynamics ....................................................................... 6
2.2
Conservation of Mass ......................................................................................... 6
2.3
Heat Capacity...................................................................................................... 7
2.4
Problem Table Analysis ...................................................................................... 7
2.5
Composite Curves ............................................................................................... 8
2.5.1
Shifted Composite Curve ....................................................................... 9
2.6
Grand Composite Curve ..................................................................................... 9
2.7
ΔTmin and Trade Offs ........................................................................................ 10
2.8
Design of the Heat Exchanger Network ........................................................... 12
3. Methodology .............................................................................................................. 13
3.1
Overview........................................................................................................... 13
iii
3.2
Assumptions ..................................................................................................... 13
3.3
Data Extraction ................................................................................................. 14
3.4
Problem Table ................................................................................................... 19
3.4.1
Heat Cascades ...................................................................................... 19
3.5
Composite Curves ............................................................................................. 20
3.6
Grid Diagram .................................................................................................... 20
3.7
Effect of the Number of Heat Exchangers on the External Utility Requirements
.......................................................................................................................... 22
3.8
Effect of the Minimum Temperature Difference on the Pinch Point and
External Utility Requirements.......................................................................... 22
4. Results and Discussion .............................................................................................. 23
4.1
Problem Table ................................................................................................... 23
4.2
Heat Cascade .................................................................................................... 25
4.3
Pinch Points and Utility .................................................................................... 27
4.4
Composite Curves ............................................................................................. 28
4.5
Grand Composite Curve ................................................................................... 29
4.6
Retrofit Heat Exchanger Network .................................................................... 30
4.7
Targeting Improvements to the External Utility Requirements ....................... 31
4.8
4.7.1
Effect of Number of Heat Exchangers on the External Utility
Requirements........................................................................................ 31
4.7.2
Effect of Supply and Target Temperatures on the External Utility
Requirements........................................................................................ 31
4.7.3
Results .................................................................................................. 32
Effect of the Minimum Temperature Difference on the Pinch Point and
External Utility Requirements.......................................................................... 34
5. Conclusion ................................................................................................................. 35
6. References.................................................................................................................. 36
6.1
Works Cited ...................................................................................................... 36
6.2
Additional References Consulted ..................................................................... 37
iv
7. Appendices ................................................................................................................ 38
7.1
Guide to Excel File ........................................................................................... 38
7.2
Millstone Unit III Heat and Mass Balance ....................................................... 39
7.3
Raw Data and Intermediate Steps ..................................................................... 40
7.4
Other Cases Evaluated ...................................................................................... 42
7.4.1
Case 2 ................................................................................................... 42
7.4.2
Case 3 ................................................................................................... 45
7.4.3
Case 4 ................................................................................................... 47
7.4.4
Case 5 ................................................................................................... 50
7.4.5
Case 6 ................................................................................................... 53
7.4.6
Case 7 ................................................................................................... 55
7.4.7
Case 8 ................................................................................................... 57
7.4.8
Case 9 ................................................................................................... 59
7.4.9
Case 10 ................................................................................................. 61
7.4.10 Case 11 ................................................................................................. 64
v
LIST OF TABLES
Table 1: Millstone Unit III Heat Exchanger Network ..................................................... 15
Table 2: Input Stream Data for Analysis ......................................................................... 18
Table 3: Shifted Temperatures and Heat Capacity Flowrate ........................................... 19
Table 4: Problem Table ................................................................................................... 24
Table 5: Net Heat Capacity Flowrate and Heat Load (Calculated and Software) ........... 25
Table 6: Heat Cascade ..................................................................................................... 26
Table 7: Heat Loads per Interval (Calculated and Software) .......................................... 27
Table 8: External Utilities for Various HEN Designs ..................................................... 32
Table 9: External Utilities for Various Minimum Temperature Differences .................. 34
Table 10: Raw Data from Millstone Unit III Heat and Mass Balance ............................ 40
Table 12: Combined Data for HEN used in Analysis for Case 1 .................................... 41
Table 12: Net Heat Capacity Flowrates ........................................................................... 41
Table 13: Intermediate Calculations for Heat Capacity and Heat Load .......................... 42
Table 14: Input Stream Data for Case 2 .......................................................................... 42
Table 15: Calculated Stream Data for Case 2 .................................................................. 43
Table 16: Problem Table for Case 2 ................................................................................ 43
Table 17: Heat Cascade for Case 2 .................................................................................. 44
Table 18: Input Stream Data for Case 3 .......................................................................... 45
Table 19: Calculated Stream Data for Case 3 .................................................................. 45
Table 20: Problem Table for Case 3 ................................................................................ 46
Table 21: Heat Cascade for Case 3 .................................................................................. 46
Table 22: Input Stream Data for Case 4 .......................................................................... 47
Table 23: Calculated Stream Data for Case 4 .................................................................. 47
Table 24: Problem Table for Case 4 ................................................................................ 48
Table 25: Heat Cascade for Case 4 .................................................................................. 49
Table 26: Input Stream Data for Case 5 .......................................................................... 50
Table 27: Calculated Stream Data for Case 5 .................................................................. 50
Table 28: Problem Table for Case 5 ................................................................................ 51
Table 29: Heat Cascade for Case 5 .................................................................................. 52
Table 30: Input Stream Data for Case 6 .......................................................................... 53
vi
Table 31: Calculated Stream Data for Case 6 .................................................................. 53
Table 32: Problem Table for Case 6 ................................................................................ 54
Table 33: Heat Cascade for Case 6 .................................................................................. 54
Table 34: Input Stream Data for Case 7 .......................................................................... 55
Table 35: Calculated Stream Data for Case 7 .................................................................. 55
Table 36: Problem Table for Case 7 ................................................................................ 56
Table 37: Heat Cascade for Case 7 .................................................................................. 56
Table 38: Input Stream Data for Case 8 .......................................................................... 57
Table 39: Calculated Stream Data for Case 8 .................................................................. 58
Table 40: Problem Table for Case 8 ................................................................................ 58
Table 41: Heat Cascade for Case 8 .................................................................................. 58
Table 42: Input Stream Data for Case 9 .......................................................................... 59
Table 43: Calculated Stream Data for Case 9 .................................................................. 59
Table 44: Problem Table for Case 9 ................................................................................ 60
Table 45: Heat Cascade for Case 9 .................................................................................. 60
Table 46: Input Stream Data for Case 10 ........................................................................ 61
Table 47: Calculated Stream Data for Case 10 ................................................................ 61
Table 48: Problem Table for Case 10 .............................................................................. 62
Table 49: Heat Cascade for Case 10 ................................................................................ 63
Table 50: Input Stream Data for Case 11 ........................................................................ 64
Table 51: Calculated Stream Data for Case 11 ................................................................ 64
Table 52: Problem Table for Case 11 .............................................................................. 65
Table 53: Heat Cascade for Case 11 ................................................................................ 65
vii
LIST OF FIGURES
Figure 1: Millstone Unit III Diagram [2] ........................................................................... 2
Figure 2: Millstone Unit III Power Plant Schematic [2].................................................... 3
Figure 3: Hot and Cold Composite Curves........................................................................ 8
Figure 4: Shifted Composite Curves.................................................................................. 9
Figure 5: Grand Composite Curve Example ................................................................... 10
Figure 6: Utility Use, Heat Exchanger Area, and Cost Variation with Delta Tmin [3] .... 11
Figure 7: Effect of Delta Tmin on Composite Curves ....................................................... 12
Figure 8: Simplified Schematic of the Millstone Unit III HEN ...................................... 14
Figure 9: Hot and Cold Stream Example from the Original Millstone Unit III HEN ..... 16
Figure 10: Hot and Cold Stream Data for the HEN used for Analysis ............................ 16
Figure 11: Hot and Cold Stream Example After Combining Streams ............................ 17
Figure 12: Grid Diagram Example .................................................................................. 21
Figure 13: Grid Diagram with Cross Pinch Heat Transfer Example ............................... 21
Figure 14: Hot and Cold Composite Curves.................................................................... 28
Figure 15: Shifted Hot and Cold Composite Curves ....................................................... 29
Figure 16: Grand Composite Curve ................................................................................. 30
Figure 17: Grid Diagram ................................................................................................. 30
Figure 18: Millstone Unit III Heat Balance ..................................................................... 39
Figure 19: GCC for Case 2 .............................................................................................. 45
Figure 20: GCC for Case 3 .............................................................................................. 47
Figure 21: GCC for Case 4 .............................................................................................. 50
Figure 22: GCC for Case 5 .............................................................................................. 53
Figure 23: GCC for Case 6 .............................................................................................. 55
Figure 24: GCC for Case 7 .............................................................................................. 57
Figure 25: GCC for Case 8 .............................................................................................. 59
Figure 26: GCC for Case 9 .............................................................................................. 61
Figure 27: GCC for Case 10 ............................................................................................ 64
Figure 28: GCC for Case 11 ............................................................................................ 66
viii
DEFINITIONS
Pinch Point
The location of the smallest difference between hot and
cold streams in a heat transfer network.
Supply Temperature
The temperature at the inlet of a heat exchanger.
Target Temperature
The temperature goal at the outlet of the heat exchanger.
Stream
Fluid that must be heated or cooled.
Heat Capacity Flowrate
Mass flowrate multiplied by the enthalpy of the fluid for
the given temperature range.
Heat Load
The maximum amount of heat that could be transferred to
or from a stream.
Composite Curve
Graph of temperature versus enthalpy for the cold and hot
stream data.
Grand Composite Curve
Graph of the combination of the hot and cold composite
curves, used to determine external utility requirements.
Utility
An external source of heating or cooling that does not use
energy from the streams in the system.
ix
ACRONYMS
The following is a list of acronyms and abbreviations that are used throughout this paper.
Acronym
Definition
GCC
Grand Composite Curve
SCC
Shifted Composite Curve
HEN
Heat Exchanger Network
SG
Stream Generator
LP
Low Pressure
HP
High Pressure
x
NOMENCLATURE
The following is a list of nomenclature used throughout this paper:
Symbol
Description
Unit
mCp
Heat Capacity Flowrate
MBtu/hr/F
dH
Heat Load
MBtu/hr
Tmin
Minimum Temperature Difference Between Hot and Cold F
Composite Curves
TS
Supply Temperature
F
TT
Target Temperature
F
TSS
Shifted Supply Temperature
F
TTS
Shifted Target Temperature
F
mÝ
Mass flow rate
lb/hr
H
Enthalpy
Btu/lb
TW
Supply Temperature of Stream W of Figure 18
F
ÝW
m
Mass flow rate of Stream W of Figure 18
lb/hr
ÝTot
m
Total Mass flow rate of combined streams
lb/hr
TV
Supply Temperature of Stream V of Figure 18
F

ÝV
m
Mass flow rate of Stream V of Figure 18
lb/hr

THP1
Output Steam Temperature from High Pressure Turbine F






supplied to the First Point Heater of Figure 18
ÝHP1
m
Mass flow rate of steam from High Pressure Turbine lb/hr
supplied to the First Point Heater of Figure 18
h
Change in enthalpy
Btu/lb
dmcv
dt
Rate of change of mass within a control volume
lb/hr
Ýin
m
Mass flow rate into a control volume
lb/hr
Ýout
m
Mass flow rate out of a control volume
lb/hr


xi
ACKNOWLEDGMENT
I would like to thank my parents for their continued support and encouragement
throughout my college career. I would also like to thank my professors who have helped
me learn. I would like to thank Professor Ernesto Gutierrez-Miravete for his support
during the duration of this project.
xii
ABSTRACT
This project uses pinch analysis techniques to analyze the heat transfer characteristics
and efficiency of a typical Regenerative Rankine cycle, used in the Millstone Unit III
nuclear power plant. The heat exchanger network, consisting of six feedwater heaters
was evaluated using the data from the Millstone Unit III heat balance. The pinch
temperature (shifted) was determined to be 466F. The minimum hot and cold utility
requirements are 1,641 MBtu/hr and 370,852 MBtu/hr, respectively, as determined by
the software and 1,642 MBtu/hr and 371,225 MBtu/hr as determined by hand
calculations. The optimum minimum temperature difference between the hot and cold
streams was determined to be 50 F. Additional cases were evaluated to determine the
effect of minimum temperature difference, supply and target temperatures, and the
number of heat exchangers in the network on the external utility requirements. Case 11
provided the most significant decrease in the cold utility requirement. Deleting the 5th
and 6th point heaters decreased the cold utility requirement from 370,852 MBtu/hr to
37,228 MBtu/hr, as determined by the software, while keeping the hot utility at 1,641
MBtu/hr.
This would greatly reduce the external energy costs by utilizing the most
energy within the system from the turbine exhausts and waste from other components.
xiii
1. Introduction
1.1 Background
Vapor power systems are commonly used to generate electricity. In nuclear power
plants, a controlled nuclear reaction generates heat energy, which is released to a
working fluid (i.e. reactor coolant) to transform feedwater into steam, via a steam
generator. The steam flows through a secondary plant to power a turbine that generates
electricity. The steam leaves the turbine and is sent through a condenser and feedwater
is pumped back in the steam generator. The Rankine cycle is an ideal vapor power cycle
without irreversibilities that are present in real power plants.
Real power plants
encounter losses (expansion through the turbine, work input to pumps, frictional losses
through pipes, etc.) and modifications to the Rankine cycle are made to improve plant
performance.
1.2 Regenerative Rankine Cycle
The Regenerative Rankine cycle has features that improve the thermal efficiency of the
power plant when compared with the Rankine cycle. The Regenerative Rankine cycle
uses heat available from the output of the turbines to preheat the feedwater from the
condenser, before the feedwater enters the steam generator. Modern power plants use
open or closed feedwater heaters to increase the average temperature of the feedwater
without using an external heat source. Regenerative rankine cycles are common in
modern power plants because they increase the thermal efficiency and power generation
of the plant, while reducing cost. [1]
1.2.1
Millstone III Unit Overview
Figure 1: Millstone Unit III Diagram [2]
shows a simplified version of the Millstone III unit nuclear power plant. The unit uses a
pressurized water reactor, which prevents boiling in the reactor, to transfer heat to a
steam generator in a secondary loop, which produces steam that flows through a high
pressure and three low pressure turbines that turn a turbine generator shaft to generate
1290
MW
of
1
power.
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Figure 1: Millstone Unit III Diagram [2]
2
The secondary loop will be the focus of this project and is shown in Figure 2. The steam
exits the high pressure turbine, enters a moisture separator steam reheater that separates
moisture from the steam. The steam gets reheated and is dry enough to flow through
three low pressure turbines. After exiting each low pressure turbine, the steam enters a
condenser below each low pressure turbine that condenses the steam into water. The
condensate and feed system transfers the water from the exit of the condenser back to the
steam generator. The feedwater is reheated prior to entering the steam generator by six
closed feedwater heaters. [2]
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Figure 2: Millstone Unit III Power Plant Schematic [2]
Excess steam from the turbines is used as a heating element in six closed feedwater
heaters. Excess steam from the three low pressure turbines and the high pressure turbine
enters four closed feedwater heaters (#3-6) and two closed feedwater heaters (#1-2),
respectively. The closed feedwater heaters are used to heat the working fluid (water)
before it enters the steam generator, which significantly increases plant efficiency. The
closed feedwater heaters contain U-shaped tubes inside a shell and do not allow the
steam and water to mix. The temperature of the feedwater is increased after going
through each closed feedwater heater. Feedwater pumps operate at high pressure to
overcome the pressure that the steam generator operates at. The smaller the temperature
3
difference between the input and output of the steam generator, the less external heating
work must be done by the reactor. [2]
1.3 Pinch Analysis
Optimizing the thermal efficiency and overall cost of a power plant can be determined
by pinch analysis. Linnhoff & Flower developed pinch analysis, at the ETH Zurich &
Leeds University, in 1978. Pinch analysis is a means of optimizing a power plant by
using the heat energy from the streams, instead of using external heating and cooling
methods (heat exchanger, furnace, cooler, etc.), to increase the thermal efficiency of the
plant and minimize energy costs. Streams are any flow paths that do not change in
chemical composition. Pinch analysis can be used for designing new, or retrofitting
existing, power plants.
Pinch analysis utilizes energy targets, which “are absolute thermodynamic targets,
showing what the process is inherently capable of achieving if the heat recovery, heating
and cooling systems are correctly designed.” [3] “The principle is to predict what should
be achieved (targeting), and to then set out to achieve it (design).” [4]
1.4 Problem Statement
This project will analyze a Regenerative Rankine cycle, based on the Millstone Unit III
nuclear power plant, using pinch analysis. The pinch point, or most constrained point in
the design, will be determined, as well as the minimum external hot and cold utility
requirements to meet the targeted heat exchanges. Modifications to the heat exchanger
network will be evaluated and a recommendation for retrofitting the components of the
power plant or improvements to increase efficiency and reduce cost will be made.
1.5 Previous Work
Pinch analysis has been used to optimize new HENs in power plants as well as retrofit
existing HENs. Linnhoff and March wrote papers about the fundamentals of pinch
analysis, focusing on retrofitting and new designs. [5] also discusses the PinchExpress
4
software used to perform the analysis. [6] sized and integrated a heat exchanger into an
existing HEN at a gas processing plant. Bi and Chang wrote a paper about retrofitting an
existing HEN, where cross pinch heat transfer is evaluated [7]. The analysis also
includes a cost analysis for the new HEN. [8] discusses the energy pinch, water pinch,
and hydrogen pinch.
5
2. Theory
2.1 Second Law of Thermodynamics
Pinch analysis is based on the second law of thermodynamics. The second law of
thermodynamics describes the spontaneous processes that exist in irreversible (nonideal) cycles. The Clausius Statement of the second law of thermodynamics states: “it is
impossible for any system to operate in such a way that the sole result would be an
energy transfer by heat from a cooler to a hotter body.” [1] A hot stream cannot be used
to heat a cold stream to a temperature hotter than the hot stream. The Kelvin-Planck
Statement of the second law states: “it is impossible for any system to operate in a
thermodynamic cycle and deliver a new amount of energy by work to its surroundings
while receiving energy by heat transfer from a single thermal reservoir.” [1] The hot
streams cannot transfer all of their energy to heat the cold stream. There must be some
waste heat as a result of the heat transfer process.
2.2 Conservation of Mass
In this analysis, each feedwater heater is considered to be a control volume. The law of
conservation of mass for a closed system (control volume) is used for each feedwater
heater as follows.
mÝin  mÝout 
dmcv
dt
[1}
For a steady state system, the mass flow rate entering the control volume is equal to that
exiting the control
volume. For the control volumes that have multiple hot streams
entering the feedwater heaters, the mass flowrates are added together to determine the
total inlet flow. The sum of all of the inlet stream flowrates must be equal to the outlet
stream flowrate since mass cannot be destroyed.
6
2.3 Heat Capacity
Enthalpy is the total energy of a system, which is determined by the sum of the internal
energy and the product of pressure and volume. Steam data is plotted on a temperatureenthalpy diagram, called the composite curve. The plot can be shifted, using the shifted
temperatures, to determine the pinch point because only the change in enthalpy between
the inlet and outlet streams is needed.
The heat capacity flowrate and the heat load are used to determine the heat transfer
characteristics of the system and the required external utilities.
The heat capacity
flowrate and the heat load are calculated for all of the temperature intervals, using
Equations 2 and 3. The heat capacity flowrate is the mass flowrate multiplied by the
enthalpy of the fluid for the given temperature range. Either the actual or shifted
temperatures can be used in Equations 2 and 3 because the calculation involves only a
temperature difference. A discussion on shifted temperatures is included in section 2.4.
The heat load is the difference in enthalpy between the supply and target stream
properties and is the maximum amount of heat that could be transferred to or from a
stream in a given temperature range. The heat load is important because it determines
how much heat transfer is possible between given streams and how much external
heating or cooling is required. The conversion factors used in the heat capacity flowrate
equation are listed in Appendix 7.2. [1, 3]



Ý
m
h



7936.64144 0.42992261 0.94781742
mCp 

1.8
TSS  TTS 
dH  mCpTTS  TSS 
[2]
[3]

2.4 Problem Table Analysis

The problem table method is developed to “allow for the maximum possible amount of
heat exchange within each temperature interval.” [3] The method is used for existing
7
systems so that any hot and cold streams can be matched together. There would be little
flexibility for improvement of a heat exchanger network if streams that are already
matched via the current heat exchanger network were used in the analysis. Shifted
temperatures (1/2 ΔTmin below hot stream and 1/2 ΔTmin above cold stream) are used to
ensure that Tmin exists between all hot and cold streams to adhere to the Second Law of
Thermodynamics. [3, 5]
2.5 Composite Curves
The composite curve is a way to incorporate all of the hot and cold streams onto a
temperature-enthalpy diagram. Figure 3 shows the change in enthalpy, for the given
temperature range, as shown in Equation 3. The maximum amount of heat recovery and
hot and cold utilities can be found from the hot and cold composite curves, as shown in
Figure 3. The maximum amount of heat recovery, from the excess steam from the
turbines and from the cold feedwater, is the area of overlap between the hot and cold
composite curves (from the upward arrow at the start of the cold composite to the
downward arrow at the end of the hot composite). The gap between the start of the hot
and cold composite curves is the minimum cold utility required and the gap between the
end of the hot and cold composite curves is the minimum hot utility required. [3, 5]
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Figure 3: Hot and Cold Composite Curves
8
2.5.1
Shifted Composite Curve
The composite curves are also plotted using the shifted temperatures, as shown in Figure
4. The shifted composite curves touch at the pinch point. The problem is divided on
either side of the pinch point. Above the pinch point, the cold flow is greater than the
hot flow and the hot utilities must be supplied to make up the difference. As shown in
Figure 4, the cold composite extends farther along the x-axis (heat flow) than the hot
composite, therefore requiring a heating duty. Below the pinch point, the hot flow is
greater than the cold flow and cold utilities must be supplied. As shown in Figure 4, the
cold composite curve trails the hot composite, requiring an external cooling duty. Using
shifted temperatures does not affect the values of the heat recovery, cooling duty or
heating duty, as seen by comparing Figure 3 and Figure 4, because the hot composite is
being shifted down and the cold composite is being shifted up by the same value.
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Figure 4: Shifted Composite Curves
2.6 Grand Composite Curve
The grand composite curve, shown in Figure 5, is a graph of the net heat flow (utility
requirement) versus the shifted temperature. The GCC is used for “setting multiple
utility targets.” [5] The shifted composite curves ensure that ΔTmin is maintained (by
9
using ΔTmin /2 less than hot temperatures & ΔTmin /2 greater than cold temperaturs) at all
points. The x-axis of the GCC shows the utility heating or cooling required.
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Figure 5: Grand Composite Curve Example
The pinch point is the location where the net heat flow is zero. The net heat flow values
at the two endpoints of the graph are the external heating and cooling duties that are
required for optimum heat transfer within the HEN. The curve also shows the
temperatures at which heating and cooling are required. When the pinch occurs at one
end of the curve, it is referred to as a threshold problem.
2.7 ΔTmin and Trade Offs
The minimum temperature difference between the hot and cold composite curves affects
the pinch temperature, the required external utilities, and the size of the heat exchangers.
However, only the heat exchangers that exist at the pinch point need to operate at ΔTmin
because this is the most constrained area of the HEN.
10
As shown in Figure 6, the heat exchanger area is roughly inversely proportional to the
temperature difference. However, low values of ΔTmin can result in large and costly heat
exchangers. The hot utility required increases as the heat exchanger area decreases.
While there are cost savings involved with decreasing the physical area of the heat
exchanger, there are high energy costs associated with an increase in hot utilities. The
optimum ΔTmin must be selected for the best cost savings. The optimum ΔTmin can be
selected by matching the capital cost and the energy cost to determine the minimum cost
for new designs. The point at which the energy cost and the heat exchanger cost (surface
area) are equal identifies the optimal ΔTmin [8].
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Figure 6: Utility Use, Heat Exchanger Area, and Cost Variation with Delta T min [3]
As ΔTmin is increased, the difference between the hot and cold composite curves
increases, which increases the heat required by external utilities, as shown in Figure 7.
The heating and cooling duties increase as the hot and cold composite curves are
separated by a larger ΔTmin.
11
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Figure 7: Effect of Delta Tmin on Composite Curves
2.8 Design of the Heat Exchanger Network
Many variables exist when performing a retrofit pinch analysis. The pinch point is
determined and cross-pinch heat transfer in the existing network is identified.
To
improve the network design, cross-pinch heat transfer should not exist. Correcting this
problem involves using new heat exchangers, of different areas, in the network. In some
cases it is best to combine two existing heat exchangers and design a new heat exchanger
to handle the mass flowrates and heat exchange requirements of multiple streams. Other
times it is best to add an additional heat exchanger in the network. Additional heat
exchangers and redesigned heat exchangers are costly for existing power plants,
depending on the area of the heat exchanger. However, it is worthwhile when the cost
from energy savings exceeds the one time cost of the new heat exchanger(s).
12
3. Methodology
3.1 Overview
The pinch analysis performed for this project is divided into three major steps: (1)
extraction of stream data (temperature, flow, and heat capacity data) from the Millstone
Unit III heat and mass balance, (2) selection of Tmin and calculation of the pinch point
and minimum utility requirements, (3) determining areas of cross-pinch heat transfer and
modifying the heat exchanger network.
An excel spreadsheet template, provided with [3] was used for the first two steps of the
analysis. The user enters Tmin, the supply and target temperatures, the mass flow rates,
and the change in enthalpy. Typical ΔTmin values for different types of plants can be
found in various texts. ΔTmin for chemical plants ranges from 10-20 C. [3, 5, 8] The
program calculates the heat load, whether the stream is hot or cold, and the shifted
temperatures based on the supplied Tmin. The problem was evaluated as two systems,
one above the pinch and one below the pinch. The analysis was also verified by hand
calculations.
3.2 Assumptions
A simplified Millstone Unit III HEN consisting of six feedwater heaters, as shown in
Figure 8, was evaluated. In the analysis, it is assumed that the flow from the condenser
is that which enters the 6th point heater. The main condenser is considered a permanent
utility because of the cooling water from the Long Island Sound and was therefore, not
included in the analysis. Weighted average supply and target temperatures, enthalpy,
and flowrates are used when streams are combined. The weighted average is based on
the mass flowrates of the individual streams, and will be discussed in section 3.3.
13
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 8: Simplified Schematic of the Millstone Unit III HEN
3.3 Data Extraction
Data is extracted from the heat and mass balance in Appendix 7.2 for all areas of the
plant that need heating or cooling. In this analysis, the HEN consisting of six feedwater
heaters, shown in Figure 8, was evaluated for simplicity. A ΔTmin of 50 F was used for
this analysis.
In the input stage, the heating and cooling demands of the streams are included without
any reference to the existing heat exchangers. [5] Typically, the analysis does not match
specific hot and cold streams so the analysis is not constrained. However, the analysis
performed was simplified with only one cold stream that feeds through all of the
feedwater heaters. Therefore, it is apparent that one cold stream is heated by, and cools,
all of the hot streams.
For an existing plant, the heat exchangers and the plant layout should not be used at first.
Utility streams (cooling water, steam, etc.) are not to be included in the data extraction
phase unless they cannot be replaced. [3] The original heat exchanger network design
parameters, extracted from
Figure 18: Millstone Unit III Heat Balance
, are presented in Table 1.
14
Table 1: Millstone Unit III Heat Exchanger Network
Hot Stream
Heat Exchanger
Cold Stream
Number
Ts (F)
Tt (F)
Ts (F)
Tt (F)
1st Point
491
380
369
442.8
2nd Point
379
334
326.7
365.6
3rd Point
346
292
282
297.9
4th Point
297
266
222.9
288.1
5th Point
231
174
158.3
222.9
6th Point
163
158
101
158.3
Figure 9 is an example of the streams associated with the 1st point heater (of Table 1)
from the Millstone Unit III HEN, shown in
Figure 18: Millstone Unit III Heat Balance
. The figure shows a control volume of the hot and cold streams entering and exiting.
The weighted average supply and target temperatures are those listed in Table 1. The
figure can also be used to describe the 2nd through 6th point heaters with their original
temperatures from Table 1. Treating each heater as its own control volume would
significantly constrain the analysis. Therefore, the six cold streams for each of the heat
exchangers listed in Table 1 were combined into one stream for this analysis, using only
the supply temperature for the 6th point heater and the target temperature for the 1st point
heater. The HEN with supply and target temperatures used for the analysis is shown in
Figure 10 and Table 2.
The analysis was done using one cold stream (from the
condenser to the SG (Stream 1 of Table 2)) and six hot streams (one stream for each
closed feedwater heater (Streams 2 through 7 of Table 2)).
15
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decompressor
are needed to see this picture.
Figure 9: Hot and Cold Stream Example from the Original Millstone Unit III HEN
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 10: Hot and Cold Stream Data for the HEN used for Analysis
The 1st through 4th point heaters have a combination of streams that flow through the
heat exchanger to heat the feedwater stream, as shown in
Figure 18: Millstone Unit III Heat Balance
. For example, the 1st point heater from the Millstone Unit III heat balance has three hot
stream supplies (W, V, and HP 1) that combine in the heater into one target stream, as
shown in Figure 9. The input streams are combined to simplify the analysis, as shown in
Figure 10 and Figure 11.
16
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 11: Hot and Cold Stream Example After Combining Streams
The supply temperatures for the 1st through 4th point heaters, in this analysis, are
weighted averages based on the mass flow rates. For example, the supply temperature
for the 1st point heater (Stream 2 of Table 2) was determined by multiplying the
temperature of each hot supply stream by the mass flowrate, divided by the total
combined mass flowrate, and taking the sum of this result for all of the supply streams to
the heater, as shown in equation 4. The total mass flowrates for streams 2 through 5 of
Table 2 are a combined sum of the individual stream flowrates that enter the feedwater
heater, as described above for the 1st point heater (See Table 11 of Appendix 7.3 for
intermediate steps and details). The average supply and target temperatures used in the
analysis are shown in Table 2, along with the mass flowrate for each stream and
enthalpy change.
m
 m
m
Ý 
Ý 
Ý 
Ts  TW  W  TV  V  THP1 HP1 
ÝTot 
ÝTot 
ÝTot 
m
m
 m
[4]
 73,748lbm /hr 
1,540,778lb /hr 
1,247,218lb /hr 
Ts  525F 
 525F 
 448F 
 491F
2,861,744lbm /hr 
2,861,744lb /hr 
2,861,744lb /hr 

The same procedure was followed to determine the supply enthalpy for the heaters that

have multiple supply streams. The combined supply enthalpy for the 1st point heater is
calculated as follows:
17
m
 m
m
Ý 
Ý 
Ý 
Hs  HW  W  HV  V  H HP1 HP1 
ÝTot 
ÝTot 
ÝTot 
m
m
 m
[5]
 73,748lbm /hr 
1,540,778lb /hr 
1,247,218lb /hr 
Hs 1,198Btu /lb
 518Btu /lb
1,146Btu /lb
 809Btu /lb
2,861,744lbm /hr 
2,861,744lb /hr 
2,861,744lb /hr 

Table 2: Input Stream Data for Analysis

Stream
Name
Supply
Target
Temperature Temperature
dT Min / 2 Mass Flowrate
Enthalpy
Change
°F
°F
°F
lb/hr
Btu(IT)/lb
1
98
442.8
25
10085320.000
202
2
491
380
25
2861744.000
455
3
379
334
25
3444389.000
173
4
346
292
25
3983700.000
171
5
297
266
25
4566511.000
146
6
231
174
25
675020.000
968
7
163
158
25
571554.000
928
The shifted temperatures are then calculated by subtracting half of Tmin from the hot
stream supply and target temperatures. The shifted supply temperature for stream 2 of
Table 2 is calculated as follows.
TSS Hot  TS 
Tmin
50F
 491F 
 466F
2
2
[6]
The supply shift temperature for the cold stream (Stream 1 of Table 2) is calculated by
adding half
 of Tmin to the supply temperature as follows.
TSSCold  TS 
Tmin
50F
 98F 
 123F
2
2
[7]
Table 3 shows the shifted temperatures for the hot and cold streams, along with the net
heat capacity
 flowrates, which will be addressed in section 3.4.
18
Table 3: Shifted Temperatures and Heat Capacity Flowrate
Stream
Supply Shift (°F)
Target Shift (°F)
mcp net (MBtu/hr/°F)
1
123
467.8
-912
2
466
355
1810
3
354
309
2055
4
407
267
1947
5
272
241
3319
6
206
149
1769
7
138
133
16370
3.4 Problem Table
To make the problem table, the shifted temperatures are ranked in decreasing order,
starting from the highest temperature, as shown in Table 4 of section 4.1. The heat
capacity flowrate and the heat load are calculated for all of the temperature intervals,
using equations 1 and 2.
The calculations for the first interval (between shifted
temperatures 467.8 °F and 466 °F) are provided below. The net heat capacity flowrates
are shown in Table 3. The intermediate calculations for the problem table and heat loads
can be found in Table 13 of Appendix 7.3. [7]
10085320lb /hr  202Btu /lb 



 7936.64144 0.42992261 0.94781742
mCp 

 911.7986MBtu /hr /F
1.8
123F  467.8F 
dH  911.7986MBtu /hr /F 467.8  466  1641.2375MBtu /hr


3.4.1
Heat Cascades
The heat cascade uses the surplus heat from one hot utility and moves it into the next
interval so that the heat from the system is not wasted.
The minimum utility
requirements are determined from the heat cascade diagram.
Starting from a zero heat input at the highest temperature in the Problem Table, the net
heat change (dH) is added to each temperature interval to form a heat cascade. The heat
19
cascade was evaluated and determined to be infeasible because the cascade contains
negative heat flows.
The minimum heat flow (largest negative value) from the infeasible heat cascade is now
added to the hot utility in a new cascade. This causes the net heat flows in the new
cascade to increase by the largest negative value from the infeasible cascade, making the
minimum value in the new cascade equal to zero. The minimum value (should be zero)
is the pinch point. The heat added to the first interval is the hot utility requirement and
the heat removed from the final interval is the cold utility target. [3] The intermediate
steps to construct the heat cascade are provided in Table 13 of Appendix 7.3. The
results of the heat cascade will be provided and discussed in section 4.2.
3.5 Composite Curves
The composite curve is a graph of temperature versus heat flow. The shifted composite
curve is then made using the shifted temperatures for both the hot and cold streams. To
generate the GCC, the net heat flow (right side of the feasible heat cascade) is plotted on
the horizontal axis and the shifted temperature is plotted on the vertical axis. The
composite curves generated for this analysis can be found in sections 4.4 and 4.5 of the
results section.
3.6 Grid Diagram
The grid diagram is another way to visualize the streams in the analysis. The grid
diagram “represents the countercurrent nature of the heat exchange.” [3] The grid
diagram is a useful visual tool to apply the rules of pinch analysis. Some of the rules for
a successful pinch analysis are: do not transfer heat across the pinch, do not use cold
utilities above the pinch, and do not use hot utilities below the pinch. [3, 5, 8] If one
were to transfer heat across the pinch, one would have to “replace this cross-pinch heat
with an equivalent amount of hot utility above the pinch, and we would increase our
consumption of cold utility below the pinch (air, cooling water, etc.) by the same
amount.” [8]
20
As shown in Figure 12, streams 1 and 2 (boxes) are hot streams and streams 3 and 4 are
cold streams. The circles represent current heat exchangers between two streams.
QuickTime™ and a
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Figure 12: Grid Diagram Example
For a retrofit analysis, the current streams and heat exchangers are depicted on the grid
diagram. The location of the pinch is drawn, as shown in Figure 13. If there is a current
heat exchanger that transfers heat across the pinch, the heat exchanger is split into two
(one above the pinch and one below the pinch as shown by circles “1” and “1a” in
Figure 13).
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 13: Grid Diagram with Cross Pinch Heat Transfer Example
21
The heat exchangers that were split are then combined with another heat exchanger on
the same side of the pinch or a new heat exchanger is created.
3.7 Effect of the Number of Heat Exchangers on the External Utility
Requirements
Multiple cases were analyzed to determine the effect of the number of heat exchangers
and the temperatures of the streams. The results will be addressed in section 4.7. The
base case of the six feedwater heaters and the one cold stream, from Figure 10 was the
foundation for each case.
3.8 Effect of the Minimum Temperature Difference on the Pinch Point
and External Utility Requirements
The effect of the minimum temperature difference was analyzed using the pinch analysis
software and will be addressed further in section 4.8. Minimum temperature differences
of 10 F, 30 F, 40 F, 48 F, 50 F, and 70 F were evaluated.
22
4. Results and Discussion
4.1 Problem Table
The problem table is provided in Table 4 and was constructed based on the method
described in section 3.4. The heat capacity flowrate and the heat load are calculated for
each interval, using Equations 2 and 3. The heat capacity flowrates of all the streams that
exist within the given temperature interval are added together to determine the net heat
capacity flowrate, shown in column four of Table 4. For example, in interval 2 of Table
4, the shifted temperature range is from 466 F to 355 F. Streams 1 and 2, of Table 2,
exist within the temperature interval, so the net heat capacity flowrate is the sum of the
heat capacity flowrates for streams 1 and 2. Table 12 in Appendix 7.3 shows the heat
capacity flowrates for each stream. Table 13 in Appendix 7.3 shows the intermediate
calculations for the heat capacity flowrates and heat loads for each interval in Table 4.
Table 5 shows the net heat capacity flowrates and heat loads for each interval and
compares them to the values obtained using the software.
23
Table 4: Problem Table
Shift
Temperature
°F
467.8
Interval
T(i+1)-Ti
mCpnet
dH
°F
MBtu(IT)/hr/°F
MBtu(IT)/hr
1
1.8
-912
-1641
demand
2
111
898
99731
surplus
3
1
-912
-912
demand
4
33
1132
37346
surplus
5
12
3078
36941
surplus
6
37
1035
38294
surplus
7
5
4354
21770
surplus
8
26
2407
62586
surplus
9
35
-912
-31913
demand
10
57
857
48864
surplus
11
11
-912
-10030
demand
12
5
15459
77293
surplus
13
10
-912
-9118
demand
466
355
354
321
309
272
267
241
206
149
138
133
123
24
Table 5: Net Heat Capacity Flowrate and Heat Load (Calculated and Software)
Interval
1
2
3
4
5
6
7
8
9
10
11
12
13
Temperature
(F)
467.8 to 466
466 to 355
355 to 354
354 to 321
321 to 309
309 to 272
272 to 267
267 to 241
241 to 206
206 to 149
149 to 138
138 to 133
133 to 123
Temperature
Difference
(F)
2
111
1
33
12
37
5
26
35
57
11
5
10
mcp net
(Mbtu/hr/
F)
-912
898
-912
1143
3090
1035
4353
2407
-912
857
-912
15458
-912
mcp net
(Mbtu/hr/F)
from software
-912
898
-912
1132
3078
1035
4354
2407
-912
857
-912
15459
-912
dH
(Mbtu/hr)
-1642
99680
-912
37720
37077
38277
21767
62574
-31928
48838
-10035
77290
-9122
dH (Mbtu/hr)
from software
-1641
99731
-912
37346
36941
38294
21770
62586
-31913
48864
-10030
77293
-9118
The theoretical calculations for the heat capacity flowrates and the heat load, shown in
Table 5, were calculated using Equations 2 and 3 and are very close to those determined
from the software. The slight error could be due to differences in conversion factors and
rounding (number of decimal places).
Overall, the results from the software are
considered valid based on the hand calculations.
4.2 Heat Cascade
The heat cascade is drawn from the problem table. The heat loads (of Table 4) are in the
boxes of Table 6 and the heat load for each interval is added to that of the previous
interval. Table 6 shows the heat cascade calculated by the software program. [3] The
heat cascade on the left hand side of Table 6 is infeasible because there is a negative net
heat load. The minimum heat flow (largest negative value) from the infeasible heat
cascade is now added to the hot utility in a new cascade. The feasible heat cascade does
not include any negative heat flows. The temperature at which there is no heat flow is
the pinch point.
25
Table 6: Heat Cascade
QuickTime™ and a
decompressor
are needed to see this picture.
Table 7 compares the heat loads for the infeasible and feasible heat cascades from the
software and those calculated by hand. The error between the hand calculations and the
software is a carryover of the error from the heat load calculations in Table 5 and
rounding differences.
26
Table 7: Heat Loads per Interval (Calculated and Software)
Shift
Temperature
(F)
467.8
466
355
354
321
309
272
267
241
206
149
138
133
123
Infeasible
cascade
(MBtu/hr)
0
-1642
98038
97126
134846
171923
210200
231967
294541
262612
311450
301415
378706
369583
Infeasible
cascade
(software)
(MBtu/hr)
0
-1641
98090
97178
134523
171465
209759
231528
294114
262201
311065
301035
378328
369210
Feasible
Cascade
(MBtu/hr)
1642
0
99680
98768
136488
173565
211842
233609
296183
264254
313092
303057
380348
371225
Feasible
Cascade
(software)
(MBtu/hr)
1641
0
99731
98819
136165
173106
211400
233169
295755
263842
312706
302676
379970
370852
4.3 Pinch Points and Utility
The pinch temperature (shifted) is 466F and is highlighted in yellow in Table 4 and
Table 7. The hot pinch is 491F and the cold pinch is 441F and are calculated using
Equations 6 and 7.
The minimum hot and cold utility requirements are 1,641 MBtu/hr and 370,852
MBtu/hr, respectively, as determined by the software and 1,642 MBtu/hr and 371,225
MBtu/hr, respectively as determined by hand calculations. The hot utility is fairly low
because there are six hot streams heating up the one cold stream. The cold utility is
relatively high because the base case analysis, using Figure 10, was done with the exact
supply and target temperatures from Figure 18. However, the target temperatures of the
hot streams do not need to be fixed because they are not used to heat up any other
streams. The cold stream is the only stream in the analysis that has a fixed target
temperature. Changes to the hot stream target temperatures are evaluated and discussed
in Section 4.7.
27
4.4 Composite Curves
The pinch point is also determined graphically by using the shifted composite curve.
The hot and cold composite curves are shown in Figure 14.
Hot and Cold Composite Curves
600
Actual Temperature (ЎF)
500
400
300
200
100
0
0
100000
200000
300000
400000
500000
600000
700000
800000
Heat Flow (Mbtu(IT)/hr)
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 14: Hot and Cold Composite Curves
The shifted hot and cold composite curves are shown in Figure 15. The point where the
hot and cold shifted composite curves touch is the pinch point. ΔTmin is redistributed in
the shifted composite curves by subtracting 1/2 ΔTmin from the hot stream temperatures
and adding1/2 ΔTmin to the cold stream temperatures. This allows the hot and cold
composite curves to shift and touch at the pinch point for easier visual interpretation of
the results.
28
Shifted Hot and Cold Composite Curves
500
450
Shifted Temperature (ЎF)
400
350
300
250
200
150
100
50
0
0
100000
200000
300000
400000
500000
600000
700000
800000
Heat Flow (Mbtu(IT)/hr)
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 15: Shifted Hot and Cold Composite Curves
4.5 Grand Composite Curve
The grand composite curve is shown in Figure 16. The utility requirements can also be
obtained from the grand composite curve.
29
Grand Composite
500
450
400
Shifted Temperature (ЎF)
350
300
250
200
150
100
50
0
0
50000
100000
150000
200000
250000
300000
350000
400000
Net Heat Flow (Mbtu(IT)/hr)
Figure 16: Grand Composite Curve
4.6 Retrofit Heat Exchanger Network
The grid diagram is shown in Figure 17. The current heat exchangers, with their
corresponding cold and hot streams, are depicted by black circles with arrows between
the streams. There are no streams that cross through the pinch point.
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 17: Grid Diagram
30
4.7 Targeting Improvements to the External Utility Requirements
Multiple cases were analyzed to determine the effect of the number of heat exchangers
and the supply and target temperatures of the streams on the external utility
requirements.
4.7.1
Effect of Number of Heat Exchangers on the External Utility Requirements
The following cases were selected for evaluation to determine the effect of the number
of heat exchangers on the external utility requirements. The purpose of reducing the
number of heat exchangers is to determine if improvements could be made to the current
HEN to reduce the cold utility requirement. As discussed in section 4.3, the hot and cold
utility requirements were determined to be 1,641 MBtu/hr and 370,852 MBtu/hr,
respectively using the HEN of Figure 10. The thought was that reducing the number of
heat exchangers would decrease the cold utility required to cool the hot streams for the
heat exchangers that are removed.
In case 2, the 6th point heater was deleted and the hot stream 7 was combined with the
hot stream 6. In case 3, the 5th and 6th point heaters were deleted and streams 5, 6, and 7
were combined to go through the 4th point heat exchanger. Case 4 deleted the 1st point
heat exchanger, closest to the pinch point and combined streams 2 and 3 through the 2nd
point heat exchanger. Case 5 deleted the 1st point heat exchanger and the 6th point heat
exchanger and combined streams 2 and 3 and 6 and 7, respectively. Case 7, combined
the 1st & 2nd point and 3rd, 4th, 5th, and 6th point heaters, into two heat exchangers. In this
case, all of the output from the high pressure turbine entered the combined 1st and 2nd
heaters and all of the output from the three low pressure turbines entered one heater.
Case 11 deleted the 5th & 6th point heaters entirely, with the thought of possibly
redirecting the heat & flow through the condenser or elsewhere.
4.7.2
Effect of Supply and Target Temperatures on the External Utility
Requirements
The following cases were selected for evaluation to determine the effect of supply and
target temperatures on the external utility requirements. The purpose of changing the
31
target temperatures of the hot streams was to require less heat transfer from the cold
stream to the hot streams (i.e. requiring a smaller temperature difference between hot
supply and target streams). The exit temperature of the hot stream is not the driving
factor for the HEN. The cold stream must be heated to its target temperature to maintain
the plant efficiency to enter the SG.
Cases 6, 8, and 9 increased the supply temperatures for the hot streams of Figure 10
because with a larger temperature difference between the hot and cold streams, more
heat could be transferred to the cold stream. Case 10, changed the target temperatures of
the hot streams (made supply & target temperatures as close as possible for all the hot
streams), so that the cold stream wouldn’t have to transfer that much heat to the hot
stream to cool it.
4.7.3
Results
The results for the cases presented above are shown in Table 8. The full analysis for each
case can be found in Appendix 7.4.
Table 8: External Utilities for Various HEN Designs
Case
Pinch
Minimum
Temperature (F)
Utility (MBtu/hr)
Utility (MBtu/hr)
2
466
1,641
370,917
3
466
1,641
370,548
4
447
18,965
366,897
5
447
18,965
366,962
6
447
18,965
366,592
7
447
18,965
366,252
8
465
2,553
349,840
9
467
729
348,016
10
466
1,641
320,096
11
466
1,641
37,228
32
Hot Minimum
Cold
The target temperatures for the base case were directly input from Figure 10. However,
the target temperatures for the hot streams are flexible. The main goal is to heat the cold
stream to 442.8 F before entering the steam generator. The hot streams that heat the
one cold stream have fixed supply temperatures, from the output of the turbines, but the
target temperatures can change. Some of the supply temperatures are dependent on the
target (output) temperatures of the hot streams because the output streams are combined
for a supply stream of another heat exchanger.
The results of cases 2 through 5, and 7, did not improve the cold utility requirements
significantly because the analysis was done to maintain the conservation of mass and
redistribute the hot streams from the heat exchangers that were removed to other heat
exchangers in the network. After realizing why this method was unsuccessful, case 11
was performed to determine how removing two heat exchangers and not redirecting their
hot supply streams to other heat exchangers would affect the utility requirements. This
action decreased the hot streams by two, which significantly decreased the cold utility
required.
The results were as expected; the cold utility requirement decreased
significantly due to the one cold stream not needing to cool two hot streams.
The minimum cold utility requirement does not change much between cases 2 through 9
because the target temperatures for the hot streams were not changed. The analysis
assumes that the hot streams must be cooled to the specified target temperature.
However, this is not necessary because the cold stream is the only stream that must be
heated to a specified temperature. The target temperatures for the hot streams were
changed in Case 10 to be close to the supply temperatures. Enthalpy values were
changed as the temperatures were adjusted.
The cold utility still did not change
significantly in this case. The hot utility increases in Cases 4, 5, and 7 as expected
because the heating capacity of the heat exchangers was removed.
33
4.8 Effect of the Minimum Temperature Difference on the Pinch Point
and External Utility Requirements
The minimum temperature difference is important to optimize the efficiency and cost of
the HEN. “A zero temperature difference would require an infinitely large heat
exchanger.” [3] The ideal minimum temperature difference for the base case (Figure 10)
was found to be 50 F. As shown in Table 9, the minimum temperature difference is the
driving variable for the pinch point. In this analysis, the hot and cold utilities do not
change with a temperature difference less than 50 F. Decreasing ΔTmin can greatly
increase the heat exchanger cost. Since the minimum utility requirements do not change
up until a ΔTmin of 50 F, it is not worth the extra cost to use heat exchangers capable of
a smaller minimum temperature difference between streams. The utility requirements
significantly increased as ΔTmin was increased above 50 F, which would cost less for
the heat exchanger, but more for the energy associated with the utilities. Therefore, the
optimal minimum temperature difference for the base case is 50 F.
Table 9: External Utilities for Various Minimum Temperature Differences
ΔTmin
Pinch
Minimum Hot Utility Minimum
(F)
Temperature (F)
(MBtu/hr)
Utility (MBtu/hr)
10
486
0
369,210
30
476
0
369,210
40
471
0
369,210
48
467
0
369,210
50
466
1,641
370,852
70
456
19,877
389,088
34
Cold
5. Conclusion
In conclusion, pinch analysis techniques were used to evaluate the external utility
requirements for the Millstone Unit III heat exchanger network, consisting of six
feedwater heaters. The problem table, heat cascades, shifted composite curve, and the
grand composite curves were constructed to determine the pinch temperature and the
utility requirements. The pinch temperature (shifted) was determined to be 466F. The
minimum hot and cold utility requirements are 1,641 MBtu/hr and 370,852 MBtu/hr,
respectively, as determined by the software and 1,642 MBtu/hr and 371,225 MBtu/hr as
determined by hand calculations.
The optimum minimum temperature difference between the hot and cold streams was
determined to be 50 F for the base case of Figure 10. Ten additional cases were
analyzed to determine the effect of the number of heat exchangers and the supply and
target temperatures of the streams on the utility requirements. The utility requirements
contribute to the efficiency and cost optimization of the power plant. The larger the
utility requirements, the more expensive the cost due to energy costs. Case 11 provided
the most significant decrease in the cold utility requirement. Deleting the 5th and 6th
point heaters decreased the cold utility requirement from 370,852 MBtu/hr to 37,228
MBtu/hr, as determined by the software, while keeping the hot utility at 1,641 MBtu/hr.
To provide adequate cost savings, it is recommended that the 5th and 6th point heaters be
deleted and the exhaust from the turbines that enters the 5th and 6th point heaters be
directed elsewhere, such as the main condenser.
This would also increase the
temperature of the fluid leaving the condenser (entering the first feedwater heater),
which would decrease the hot utility required to heat the fluid to 442.8 F when entering
the SG.
35
6. References
6.1 Works Cited
[1] Moran, Michael J., and Howard N. Shapiro. Fundamentals of Engineering
Thermodynamics. New York: Wiley, 2008. Print.
[2] Dominion. Nuclear Media Guide, Information on Millstone Power Station.
Waterford: Dominion, 2012. Dominion, 2012. Web. 19 Aug. 2013.
[3] Kemp, Ian E. Pinch Analysis and Process Integration - A User Guide on Process
Integration for the Efficient Use of Energy. 2nd ed. Oxford: Elsevier, 2007. Print.
[4] Tjoe, T. N., and Bodo Linnhoff. "Using Pinch Technology for Process Retrofit."
Chemical Engineering 28 (1986): 47-60. Web.
[5] March, Linnhoff. Introduction to Pinch Technology. 1998. Targeting House
Gadbrook Park, England.
[6]
Singh, Kamel, and Raymond Crosbie. "Use of Pinch Analysis in Sizing and
Integrating a Heat Exchanger into an Existing Exchanger Network at a Gas
Processing Plant." The Journal of the Association of Professional Engineers of
Trinidad and Tobago 40.2 (2011): 43-48. Print.
[7]
Bi, Bao-Hong, and Chuei-Tin Chang. "Retrofitting Heat Exchanger Networks
Based on Simple Pinch Analysis." Ind. Eng. Chem. Res. 49 (2010): 3967-971.
Web.
[8] Pinch Analysis: For the Efficient Use of Energy, Water, and Hydrogen. N.p.:
Canada, 2003. Print.
36
6.2 Additional References Consulted
Bakhtiari, Bahador, and Serge Bedard. "Retrofitting Heat Exchanger Networks Using a
Modified Network Pinch Approach." Applied Thermal Engineering 51 (2012):
973-979. Science Direct. Web. 17 Aug. 2013.
Linnhoff, B., and E. Hindmarsh. "The Pinch Design Method for Heat Exchanger
Networks." Chemical Engineering Science 38.5 (1983): 745-63. Print.
Rossiter, Alan P. Using Spreadsheets for Pinch Analysis. Tech. no. 96D. N.p.:
Unpublished, 2004. Print.
Zebian, Hussam, and Alexander Mitsos. "A Double-pinch Criterion for Regenerative
Rankine Cycles." Energy 40.2 (2012): 258-70. Print.
37
7. Appendices
7.1 Guide to Excel File
The following are the tabs in the excel file:
INDEX – Table of Contents
INPUT – Input Stream Data for the Heat Exchanger Network
PT – Problem Table and Heat Cascade
CC – Hot and cold composite curves
SCC – Shifted composite curves
GCC – Grand composite curves
GRID – Network grid diagram, shifted temperatures
AS – Stream data plot, actual temperatures
AT – Interval tables (heat loads and temperatures), actual temperatures
SS – Stream data plot, shifted temperatures
ST – Interval tables (heat loads and temperatures), shifted temperatures
DTMIN – Variation of hot and cold utility targets and pinch temperature with ∆Тmin.
A1 – Intermediate calculations
A2 – Plot raw data
38
7.2 Millstone Unit III Heat and Mass Balance
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 18: Millstone Unit III Heat Balance
39
7.3 Raw Data and Intermediate Steps
Table 10: Raw Data from Millstone Unit III Heat and Mass Balance
Stream
Description
from LP 1
from LP 2
from LP 3
from LP 4
HP 1
HP 2
W to 1st pt
V to 1st pt
A to 2nd pt
waste
from
1st pt
waste
from
2nd pt
waste
from
3rd pt
waste
from
5th pt
waste
from
6th pt
Input H
(Btu/lb)
1241
1200
1110
1054
1146
1089
1198
518
1192
Output
H
(Btu/lb(
261
235
142
126
354
305
354
354
305
Change H
(Btu/lb)
980
965
968
928
792
784
844
164
887
Supply
Temp (F)
426
335
231
163
448
373
525
525
538
Target
Temp
(F)
292
266
174
158
380
334
380
380
334
Flow
(lb/hr)
539308
582815
675020
571554
1247218
570935
73748
1540778
11711
354
305
49
380
334
2861743
305
261
44
334
292
3444392
261
235
26
292
266
3983696
142
56
86
174
98
675021
126
56
70
158
98
785742
40
Table 11: Combined Data for HEN used in Analysis for Case 1
Stream
Description
Condenser
to SG
1
Total
W+V+HP1
flow
2
Total A +
2nd pt +
waste from
1st pt
Total 3rd pt
(LP1)+ 2nd
pt waste
3
4
Total waste
from 3rd pt
+ LP2
5
From LP 3
6
7
From LP 4
Output
H
(Btu/lb
)
Change
H
(Btu/lb)
56
258.1
809
Supply
Temp (F)
Target
Temp
(F)
202.1
98
442.8
354
455
491
380
479
305
174
379
432
261
171
381
235
1110
1054
Input H
(Btu/lb)
Supply
Shift (F)
Target
Shift
(F)
Cold
123
467.8
2861744
Hot
466
355
334
3444389
Hot
354
309
346
292
3983700
Hot
407
267
146
297
266
4566511
Hot
272
241
142
968
231
174
675020
Hot
206
149
126
928
163
158
571554
Hot
138
133
Flow
(lb/hr)
Stream
Type
10085320
Table 12: Net Heat Capacity Flowrates
Stream
mcp net (Mbtu/hr/F)
1
Supply Shift (F)
123
Target Shift (F)
467.8
2
466
355
1810
3
354
309
2055
4
407
267
1947
5
272
241
3319
6
206
149
1769
7
138
133
16370
41
-912
Table 13: Intermediate Calculations for Heat Capacity and Heat Load
Temperature
Temperature
(F)
Interval
1
467.8 to 466
2
466 to 355
3
355 to 354
4
354 to 321
5
321 to 309
6
309 to 272
7
272 to 267
8
267 to 241
9
241 to 206
10
206 to 149
11
149 to 138
12
138 to 133
13
133 to 123
mcp net
(Mbtu/hr/F)
dH (Mbtu/hr)
-912
-912 * 2
-912 + 1810
898 * 111
-912
-912 * 1
-912 + 2055
1143 * 33
-912 + 2055 +
1947
-912 + 1947
3090 * 12
4353 * 5
26
-912 + 3319 +
1947
-912 + 3319
35
-912
-912 * 35
57
-912 + 1769
857 * 57
11
-912
-912 * 11
-912 + 16370
15458 * 5
-912
-912 * 10
Difference (F)
2
111
1
33
12
37
5
5
10
1035 * 37
2407 * 26
Conversion Factors for heat capacity flowrate calculations (from [1])
1 kJ/kg = 0.42992261 Btu/lb
1 kJ = 0.94781742 Btu
T(R) = 1.8T(K)
1 kg/s = 7936.64144 lb/hr
7.4 Other Cases Evaluated
7.4.1
Case 2
Table 14: Input Stream Data for Case 2
Stream
Name
Supply
Temperature
Target
Temperature
dT Min / 2
Mass Flowrate
1
2
3
4
5
6
°F
98
491
379
346
297
200
°F
442.8
380
334
292
266
167
°F
25
25
25
25
25
25
lb/h
10085320.000
2861744.000
3444389.000
3983700.000
4566511.000
1246574.000
42
Enthalpy
Change
Btu(IT)/lb
202
455
173
171
146
950
Table 15: Calculated Stream Data for Case 2
Stream Name
Heat Flow
1
2
3
4
5
6
MBtu(IT)/hr
314388.1611
200940.4215
91956.7107
105125.4499
102887.4717
182753.9621
Stream
Type
Supply
Shift
Target
Shift
COLD
HOT
HOT
HOT
HOT
HOT
°F
123.0
466.0
354.0
321.0
272.0
175.0
°F
467.8
355.0
309.0
267.0
241.0
142.0
Table 16: Problem Table for Case 2
Shift
Temperature
°F
467.8
Interval
T(i+1)-Ti
mCpnet
dH
°F
MBtu(IT)/hr/°F
MBtu(IT)/hr
1
1.8
-911.7986
-1641.2375
demand
2
111
898.4755
99730.7757
surplus
3
1
-911.7986
-911.7986
demand
4
33
1131.6838
37345.567
surplus
5
12
3078.4514
36941.4173
surplus
6
37
1034.969
38293.8522
surplus
7
5
4353.9197
21769.5984
surplus
8
26
2407.1521
62585.9543
surplus
9
66
-911.7986
-60178.7083
demand
10
33
4626.2002
152664.6079
surplus
11
19
-911.7986
-17324.1736
demand
466
355
354
321
309
272
267
241
175
142
123
43
Table 17: Heat Cascade for Case 2
Infeasible
Cascade
▼
PINCH
-1641.2375
▼
99730.7757
▼
-911.798611
▼
37345.56701
▼
36941.41727
▼
38293.85224
▼
21769.5984
▼
62585.95432
▼
60178.70833
▼
152664.6079
▼
17324.17361
▼
Feasible
Cascade
▼
0
-1641.2375
98089.5382
97177.73959
134523.3066
171464.7239
209758.5761
231528.1745
294114.1288
233935.4205
386600.0284
369275.8548
44
-1641.2375
▼
99730.7757
▼
-911.798611
▼
37345.56701
▼
36941.41727
▼
38293.85224
▼
21769.5984
▼
62585.95432
▼
60178.70833
▼
152664.6079
▼
17324.17361
▼
1641.2375
0
99730.7757
98818.97709
136164.5441
173105.9614
211399.8136
233169.412
295755.3663
235576.658
388241.2659
370917.0923
Grand Composite
500
450
400
Shifted Temperature (ЎF)
350
300
250
200
150
100
50
0
0
50000
100000 150000 200000 250000 300000 350000 400000 450000
Net Heat Flow (Mbtu(IT)/hr)
Figure 19: GCC for Case 2
7.4.2
Case 3
Table 18: Input Stream Data for Case 3
Stream
Name
Supply
Temperature
Target
Temperature
dT Min / 2
Mass Flowrate
1
2
3
4
5
°F
98
491
379
346
277
°F
442.8
380
334
292
245
°F
25
25
25
25
25
lb/h
10085320.000
2861744.000
3444389.000
3983700.000
5813085.000
Table 19: Calculated Stream Data for Case 3
Stream Name
Heat Flow
1
2
3
4
5
MBtu(IT)/hr
314388.1611
200940.4215
91956.7107
105125.4499
285271.854
Stream
Type
Supply
Shift
Target
Shift
COLD
HOT
HOT
HOT
HOT
°F
123.0
466.0
354.0
321.0
252.0
°F
467.8
355.0
309.0
267.0
220.0
45
Enthalpy
Change
Btu(IT)/lb
202
455
173
171
318
Table 20: Problem Table for Case 3
Shift
Temperature
°F
467.8
T(i+1)Ti
°F
mCpnet
dH
MBtu(IT)/hr/°F
MBtu(IT)/hr
1
1.8
-912
-1641
demand
2
111
898
99731
surplus
3
1
-912
-912
demand
4
33
1132
37346
surplus
5
12
3078
36941
surplus
6
42
1035
43469
surplus
7
15
-912
-13677
demand
8
32
8003
256094
surplus
9
97
-912
-88444
demand
Interval
466
355
354
321
309
267
252
220
123
Table 21: Heat Cascade for Case 3
Infeasible
Cascade
Feasible
Cascade
9
30.7757
0
PINCH
-1641.2375
▼
99730.7757
▼
-911.798611
▼
37345.56701
▼
36941.41727
▼
43468.69714
▼
13676.97917
▼
256094.2985
-1641.2375
▼
99730.7757
▼
-1641.2375
98089.5382
-911.798611
▼
37345.56701
▼
36941.41727
▼
43468.69714
▼
13676.97917
▼
256094.2985
97177.73959
134523.3066
171464.7239
214933.421
201256.4419
46
0
99730.7757
98818.97709
136164.5441
173105.9614
216574.6585
202897.6794
▼
88444.46527
▼
▼
88444.46527
▼
457350.7403
368906.2751
458991.9778
370547.5126
Grand Composite
500
450
400
Shifted Temperature (ЎF)
350
300
250
200
150
100
50
0
0
100000
200000
300000
400000
500000
Net Heat Flow (Mbtu(IT)/hr)
Figure 20: GCC for Case 3
7.4.3
Case 4
Table 22: Input Stream Data for Case 4
Stream
Name
Supply
Temperature
Target
Temperature
dT Min / 2
Mass Flowrate
1
2
3
4
5
6
°F
98
472
346
297
231
163
°F
442.8
372
292
266
174
158
°F
25
25
25
25
25
25
lb/h
10085320.000
3444390.000
3983700.000
4566511.000
675020.000
571554.000
Table 23: Calculated Stream Data for Case 4
Stream Name
Heat Flow
1
2
MBtu(IT)/hr
314388.1611
271617.8775
Stream
Type
Supply
Shift
Target
Shift
COLD
HOT
°F
123.0
447.0
°F
467.8
347.0
47
Enthalpy
Change
Btu(IT)/lb
202
511
171
146
968
928
3
4
5
6
105125.4499
102887.4717
100836.3529
81852.2036
HOT
HOT
HOT
HOT
321.0
272.0
206.0
138.0
267.0
241.0
149.0
133.0
Table 24: Problem Table for Case 4
Shift
Temperature
°F
467.8
Interval
T(i+1)-Ti
mCpnet
dH
°F
MBtu(IT)/hr/°F
MBtu(IT)/hr
1
20.8
-912
-18965
demand
2
100
1804
180438
surplus
3
26
-912
-23707
demand
4
49
1035
50713
surplus
5
5
4354
21770
surplus
6
26
2407
62586
surplus
7
35
-912
-31913
demand
8
57
857
48864
surplus
9
11
-912
-10030
demand
10
5
15459
77293
surplus
11
10
-912
-9118
demand
447
347
321
272
267
241
206
149
138
133
123
48
Table 25: Heat Cascade for Case 4
Infeasible
Cascade
▼
18965.41111
PINCH
▼
180438.0164
▼
23706.76389
▼
50713.48
▼
21769.5984
▼
62585.95432
▼
31912.95139
▼
48863.83203
▼
10029.78472
▼
77293.21059
▼
-9117.98611
▼
Feasible
Cascade
▼
18965.41111
18965.41111
0
357049.1806
▼
180438.0164
▼
23706.76389
▼
50713.48
▼
21769.5984
▼
62585.95432
▼
31912.95139
▼
48863.83203
▼
10029.78472
▼
77293.21059
▼
347931.1945
-9117.98611
▼
0
18965.41111
161472.6053
137765.8414
188479.3214
210248.9198
272834.8741
240921.9227
289785.7548
279755.97
49
180438.0164
156731.2525
207444.7325
229214.3309
291800.2852
259887.3338
308751.1659
298721.3812
376014.5917
366896.6056
Grand Composite
500
450
400
Shifted Temperature (ЎF)
350
300
250
200
150
100
50
0
0
50000
100000
150000
200000
250000
300000
350000
400000
Net Heat Flow (Mbtu(IT)/hr)
Figure 21: GCC for Case 4
7.4.4
Case 5
Table 26: Input Stream Data for Case 5
Stream
Name
Supply
Temperature
Target
Temperature
dT Min / 2
Mass Flowrate
1
2
3
4
5
°F
98
472
346
297
200
°F
442.8
372
292
266
167
°F
25
25
25
25
25
lb/h
10085320.000
3444390.000
3983700.000
4566511.000
1246574.000
Table 27: Calculated Stream Data for Case 5
Stream Name
Heat Flow
1
2
3
4
5
MBtu(IT)/hr
314388.1611
271617.8775
105125.4499
102887.4717
182753.9621
Stream
Type
Supply
Shift
Target
Shift
COLD
HOT
HOT
HOT
HOT
°F
123.0
447.0
321.0
272.0
175.0
°F
467.8
347.0
267.0
241.0
142.0
50
Enthalpy
Change
Btu(IT)/lb
202
511
171
146
950
Table 28: Problem Table for Case 5
Shift
Temperature
°F
467.8
Interval
T(i+1)-Ti
mCpnet
dH
°F
MBtu(IT)/hr/°F
MBtu(IT)/hr
1
20.8
-912
-18965
demand
2
100
1804
180438
surplus
3
26
-912
-23707
demand
4
49
1035
50713
surplus
5
5
4354
21770
surplus
6
26
2407
62586
surplus
7
66
-912
-60179
demand
8
33
4626
152665
surplus
9
19
-912
-17324
demand
447
347
321
272
267
241
175
142
123
51
Table 29: Heat Cascade for Case 5
Infeasible
Cascade
▼
18965.41111
PINCH
▼
180438.0164
▼
23706.76389
▼
50713.48
▼
21769.5984
▼
62585.95432
▼
60178.70833
▼
152664.6079
▼
17324.17361
▼
Feasible
Cascade
▼
18965.41111
0
18965.41111
161472.6053
137765.8414
188479.3214
210248.9198
272834.8741
212656.1658
365320.7737
347996.6001
52
▼
180438.0164
▼
23706.76389
▼
50713.48
▼
21769.5984
▼
62585.95432
▼
60178.70833
▼
152664.6079
▼
17324.17361
▼
18965.41111
0
180438.0164
156731.2525
207444.7325
229214.3309
291800.2852
231621.5769
384286.1848
366962.0112
Grand Composite
500
450
400
Shifted Temperature (ЎF)
350
300
250
200
150
100
50
0
0
50000
100000 150000 200000 250000 300000 350000 400000 450000
Net Heat Flow (Mbtu(IT)/hr)
Figure 22: GCC for Case 5
7.4.5
Case 6
Table 30: Input Stream Data for Case 6
Stream
Name
Supply
Temperature
Target
Temperature
dT Min
Contrib
Mass Flowrate
1
2
3
4
°F
98
472
346
277
°F
442.8
372
292
245
°F
25
25
25
25
lb/h
10085320.000
3444390.000
3983700.000
5813085.000
Table 31: Calculated Stream Data for Case 6
Stream Name
Heat Flow
1
2
3
4
MBtu(IT)/hr
314388.1611
271617.8775
105125.4499
285271.854
Stream
Type
Supply
Shift
Target
Shift
COLD
HOT
HOT
HOT
°F
123.0
447.0
321.0
252.0
°F
467.8
347.0
267.0
220.0
53
Enthalpy
Change
Btu(IT)/lb
202
511
171
318
Table 32: Problem Table for Case 6
Shift
Temperature
°F
467.8
Interval
T(i+1)-Ti
mCpnet
dH
°F
MBtu(IT)/hr/°F
MBtu(IT)/hr
1
20.8
-911.7986
-18965.4111
demand
2
100
1804.3802
180438.0164
surplus
3
26
-911.7986
-23706.7639
demand
4
54
1034.969
55888.3249
surplus
5
15
-911.7986
-13676.9792
demand
6
32
8002.9468
256094.2985
surplus
7
97
-911.7986
-88444.4653
demand
447
347
321
267
252
220
123
Table 33: Heat Cascade for Case 6
Infeasible
Cascade
▼
18965.41111
PINCH
▼
180438.0164
▼
23706.76389
▼
55888.32489
▼
13676.97917
▼
256094.2985
▼
88444.46527
▼
Feasible
Cascade
0
18965.41111
161472.6053
137765.8414
193654.1663
179977.1871
436071.4856
347627.0204
54
▼
18965.41111
18965.41111
▼
180438.0164
▼
23706.76389
▼
55888.32489
▼
13676.97917
▼
256094.2985
▼
88444.46527
▼
0
180438.0164
156731.2525
212619.5774
198942.5982
455036.8967
366592.4315
Grand Composite
500
450
400
Shifted Temperature (ЎF)
350
300
250
200
150
100
50
0
0
100000
200000
300000
400000
500000
Net Heat Flow (Mbtu(IT)/hr)
Figure 23: GCC for Case 6
7.4.6
Case 7
Table 34: Input Stream Data for Case 7
Stream
Name
Supply
Temperature
Target
Temperature
dT Min
Contrib
Mass Flowrate
1
2
3
4
°F
98
472
346
277
°F
442.8
372
292
245
°F
25
25
25
25
lb/h
10085320.000
3444390.000
3983700.000
5813085.000
Table 35: Calculated Stream Data for Case 7
Stream Name
Heat Flow
1
2
3
4
MBtu(IT)/hr
314388.1611
271617.8775
105125.4499
285271.854
Stream
Type
Supply
Shift
Target
Shift
COLD
HOT
HOT
HOT
°F
123.0
447.0
321.0
252.0
°F
467.8
347.0
267.0
220.0
55
Enthalpy
Change
Btu(IT)/lb
202
511
171
318
Table 36: Problem Table for Case 7
Shift
Temperature
°F
467.8
Interval
T(i+1)-Ti
mCpnet
dH
°F
MBtu(IT)/hr/°F
MBtu(IT)/hr
1
20.8
-911.7986
-18965.4111
demand
2
100
1804.3802
180438.0164
surplus
3
26
-911.7986
-23706.7639
demand
4
54
1034.969
55888.3249
surplus
5
15
-911.7986
-13676.9792
demand
6
32
8002.9468
256094.2985
surplus
7
97
-911.7986
-88444.4653
demand
447
347
321
267
252
220
123
Table 37: Heat Cascade for Case 7
Infeasible
Cascade
Feasible
Cascade
1
0438.0164
.6053
.0164
▼ 180
-237
76389
-23706.763
23706.76389
.76389
56
6
8
0164
▼
23706.76389
▼
55888.32489
▼
13676.97917
▼
256094.2985
▼
88444.46527
▼
▼
23706.76389
▼
55888.32489
▼
13676.97917
▼
256094.2985
▼
88444.46527
▼
161472.6053
137765.8414
193654.1663
179977.1871
436071.4856
347627.0204
180438.0164
156731.2525
212619.5774
198942.5982
455036.8967
366592.4315
Grand Composite
500
450
400
Shifted Temperature (ЎF)
350
300
250
200
150
100
50
0
0
100000
200000
300000
400000
500000
Net Heat Flow (Mbtu(IT)/hr)
Figure 24: GCC for Case 7
7.4.7
Case 8
Table 38: Input Stream Data for Case 8
Stream
Name
Supply
Temperature
Target
Temperature
dT Min
Contrib
Mass Flowrate
1
2
°F
98
490
°F
442.8
372
°F
25
25
lb/h
10085320.000
3444390.000
57
Enthalpy
Change
Btu(IT)/lb
202
511
3
400
264
25
9796785.000
258
Table 39: Calculated Stream Data for Case 8
Stream Name
Heat Flow
1
2
3
MBtu(IT)/hr
314388.1611
271617.8775
390057.3038
Stream
Type
Supply
Shift
Target
Shift
COLD
HOT
HOT
°F
123.0
465.0
375.0
°F
467.8
347.0
239.0
Table 40: Problem Table for Case 8
Shift
Temperature
°F
467.8
Interval
T(i+1)-Ti
mCpnet
dH
°F
MBtu(IT)/hr/°F
MBtu(IT)/hr
1
2.8
-911.7986
-2553.0361
demand
2
90
1390.0478
125104.3028
surplus
3
28
4258.1162
119227.2541
surplus
4
108
1956.2698
211277.1383
surplus
5
116
-911.7986
-105768.6389
demand
465
375
347
239
123
Table 41: Heat Cascade for Case 8
Infeasible
Cascade
▼
2553.036111
PINCH
▼
125104.3028
▼
119227.2541
▼
211277.1383
▼
Feasible
Cascade
0
2553.036111
122551.2667
241778.5208
453055.6591
58
▼
2553.036111
2553.036111
▼
125104.3028
▼
119227.2541
▼
211277.1383
▼
0
125104.3028
244331.5569
455608.6952
105768.6389
▼
105768.6389
▼
347287.0202
349840.0564
Grand Composite
500
450
400
Shifted Temperature (ЎF)
350
300
250
200
150
100
50
0
0
100000
200000
300000
400000
500000
Net Heat Flow (Mbtu(IT)/hr)
Figure 25: GCC for Case 8
7.4.8
Case 9
Table 42: Input Stream Data for Case 9
Stream
Name
Supply
Temperature
Target
Temperature
dT Min
Contrib
Mass Flowrate
1
2
3
°F
98
492
372
°F
442.8
372
264
°F
25
25
25
lb/h
10085320.000
3444390.000
9796785.000
Table 43: Calculated Stream Data for Case 9
Stream Name
Heat Flow
1
2
3
MBtu(IT)/hr
314388.1611
271617.8775
390057.3038
Stream
Type
Supply
Shift
Target
Shift
COLD
HOT
HOT
°F
123.0
467.0
347.0
°F
467.8
347.0
239.0
59
Enthalpy
Change
Btu(IT)/lb
202
511
258
Table 44: Problem Table for Case 9
Shift
Temperature
°F
467.8
Interval
T(i+1)-Ti
mCpnet
dH
°F
MBtu(IT)/hr/°F
MBtu(IT)/hr
1
0.8
-911.7986
-729.4389
demand
2
120
1351.6837
162202.0442
surplus
3
108
2699.8431
291583.0538
surplus
4
116
-911.7986
-105768.6389
demand
467
347
239
123
Table 45: Heat Cascade for Case 9
Infeasible
Cascade
▼
729.4388888
PINCH
▼
162202.0442
▼
291583.0538
▼
105768.6389
▼
Feasible
Cascade
▼
729.4388888
0
729.4388888
161472.6053
453055.6591
347287.0202
60
▼
162202.0442
▼
291583.0538
▼
105768.6389
▼
729.4388888
0
162202.0442
453785.098
348016.4591
Grand Composite
500
450
400
Shifted Temperature (ЎF)
350
300
250
200
150
100
50
0
0
100000
200000
300000
400000
500000
Net Heat Flow (Mbtu(IT)/hr)
Figure 26: GCC for Case 9
7.4.9
Case 10
Table 46: Input Stream Data for Case 10
Stream
Name
Supply
Temperature
Target
Temperature
dT Min
Contrib
Mass Flowrate
1
2
3
4
5
6
7
°F
98
491
462
447
418
231
163
°F
442.8
480
450
430
410
200
158
°F
25
25
25
25
25
25
25
lb/h
10085320.000
2861744.000
3444389.000
3983700.000
4566511.000
675020.000
571554.000
Table 47: Calculated Stream Data for Case 10
Stream Name
Heat Flow
1
2
3
4
5
6
7
MBtu(IT)/hr
314388.1611
152361.4185
92488.2524
105125.4499
102887.4717
98127.9384
81852.2036
Stream
Type
Supply
Shift
Target
Shift
COLD
HOT
HOT
HOT
HOT
HOT
HOT
°F
123.0
466.0
437.0
422.0
393.0
206.0
138.0
°F
467.8
455.0
425.0
405.0
385.0
175.0
133.0
61
Enthalpy
Change
Btu(IT)/lb
202
345
174
171
146
942
928
Table 48: Problem Table for Case 10
Shift
Temperature
°F
467.8
Interval
T(i+1)-Ti
mCpnet
dH
°F
MBtu(IT)/hr/°F
MBtu(IT)/hr
1
1.8
-912
-1641
demand
2
11
12939
142332
surplus
3
18
-912
-16412
demand
4
12
6796
81547
surplus
5
3
-912
-2735
demand
6
17
5272
89625
surplus
7
12
-912
-10942
demand
8
8
11949
95593
surplus
9
179
-912
-163212
demand
10
31
2254
69862
surplus
11
37
-912
-33737
demand
12
5
15459
77293
surplus
13
10
-912
-9118
demand
466
455
437
425
422
405
393
385
206
175
138
133
123
62
Table 49: Heat Cascade for Case 10
Infeasible
Cascade
▼
PINCH
-1641
▼
142332
▼
-16412
▼
81547
▼
-2735
▼
89625
▼
-10942
▼
95593
▼
-163212
▼
69862
▼
-33737
▼
77293
▼
-9118
▼
Feasible
Cascade
▼
0
-1641
140690
124278
205825
203089
292714
281773
377366
214154
284016
-1641
▼
142332
▼
-16412
▼
81547
▼
-2735
▼
89625
▼
-10942
▼
95593
▼
-163212
▼
69862
▼
327573
-33737
▼
77293
▼
318455
-9118
▼
250279
63
1641
0
142332
125919
207466
204731
294355
283414
379007
215795
285657
251921
329214
320096
Grand Composite
500
450
400
Shifted Temperature (ЎF)
350
300
250
200
150
100
50
0
0
50000
100000
150000
200000
250000
300000
350000
400000
Net Heat Flow (Mbtu(IT)/hr)
Figure 27: GCC for Case 10
7.4.10 Case 11
Table 50: Input Stream Data for Case 11
Stream
Name
Supply
Temperature
Target
Temperature
dT Min
Contrib
Mass Flowrate
1
2
3
4
°F
98
491
462
446
°F
442.8
480
450
430
°F
25
25
25
25
lb/h
10085320.000
2861744.000
3444389.000
3983700.000
Table 51: Calculated Stream Data for Case 11
Stream Name
Heat Flow
1
2
3
4
MBtu(IT)/hr
314388.1611
152361.4185
92488.2524
105125.4499
Stream
Type
Supply
Shift
Target
Shift
COLD
HOT
HOT
HOT
°F
123.0
466.0
437.0
421.0
°F
467.8
455.0
425.0
405.0
64
Enthalpy
Change
Btu(IT)/lb
202
345
174
171
Table 52: Problem Table for Case 11
Shift
Temperature
°F
467.8
Interval
T(i+1)-Ti
mCpnet
dH
°F
MBtu(IT)/hr/°F
MBtu(IT)/hr
1
1.8
-912
-1641
demand
2
11
12939
142332
surplus
3
18
-912
-16412
demand
4
12
6796
81547
surplus
5
4
-912
-3647
demand
6
16
5659
90537
surplus
7
282
-912
-257127
demand
466
455
437
425
421
405
123
Table 53: Heat Cascade for Case 11
Infeasible
Cascade
▼
PINCH
-1641
▼
142332
▼
-16412
▼
81547
▼
-3647
▼
90537
▼
-257127
▼
Feasible
Cascade
▼
0
-1641
140690
124278
205825
-1641
▼
142332
▼
-16412
▼
81547
▼
292714
-3647
▼
90537
▼
35587
-257127
▼
202177
65
1641
0
142332
125919
207466
203819
294355
37228
Grand Composite
500
450
400
Shifted Temperature (ЎF)
350
300
250
200
150
100
50
0
0
50000
100000
150000
200000
250000
Net Heat Flow (Mbtu(IT)/hr)
Figure 28: GCC for Case 11
66
300000
350000