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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
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© Copyright 2013
by
Stephanie Barnes
All Rights Reserved
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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 !Tmin and Trade Offs..................................................................................... 10
2.8 Design of the Heat Exchanger Network .........................................................12
3. Methodology..........................................................................................................13
3.1 Overview.......................................................................................................13
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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 andExternal 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
4.7.1 Effect of Number of Heat Exchangers on the External UtilityRequirements.....................................................................................31
4.7.2 Effect of Supply and Target Temperatures on the External Utility
Requirements.....................................................................................31
4.7.3 Results...............................................................................................32
4.8 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
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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
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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..........................................19Table 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 11: 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
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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................................................................57
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
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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 .....................................................................8Figure 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
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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.
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ACRONYMS
The following is a list of acronyms and abbreviations that are used throughout this paper.
Acronym DefinitionGCC Grand Composite Curve
SCC Shifted Composite Curve
HEN Heat Exchanger Network
SG Stream Generator
LP Low Pressure
HP High Pressure
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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
Composite Curves
°F
TS Supply Temperature °F
TT Target Temperature °F
TSS Shifted Supply Temperature °F
TTS Shifted Target Temperature°F
m Mass flow rate lb/hr
H Enthalpy Btu/lb
TW Supply Temperature of Stream W of Figure 18 °F
mW
Mass flow rate of Stream W of Figure 18 lb/hr
mTot
Total Mass flow rate of combined streams lb/hr
T V
Supply Temperature of Stream V of Figure 18 °F
mV Mass flow rate of Stream V of Figure 18 lb/hr
T HP1
Output Steam Temperature from High Pressure Turbine
supplied to the First Point Heater of Figure 18
°F
m HP1
Mass flow rate of steam from High Pressure Turbine
supplied to the First Point Heater of Figure 18
lb/hr
!h Change in enthalpy Btu/lb
dmcv
dt
Rate of change of mass within a control volume lb/hr
min Mass flow rate into a control volume lb/hr
mout
Mass flow rate out of a control volume lb/hr
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ACKNOWLEDGMENT
I would like to thank my parents for their continued support and encouragement
throughout my college career and my professors who have helped me expand my
engineering knowledge. I would also like to thank Professor Ernesto Gutierrez-Miravetefor his support during the duration of this project.
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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 heaterswas evaluated using the data from the Millstone Unit III heat balance and software
provided with [3]. The pinch temperature (shifted) was determined to be 466 °F, using
the Problem Table method and construction of the composite curves. 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.
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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 shows a simplified version of the Millstone unit III nuclear power plant. Theunit 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 1,290 MW of power.
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Figure 1: Millstone Unit III Diagram [2]
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The secondary loop will be the focus of this project and is shown in Figure 2. The steam
exits the HP 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 LP
turbines. After exiting each LP turbine, the steam enters a condenser below each LP
turbine that condenses the steam into water. The condensate and feed system transfers
the water from the exit of the condenser back to the SG. The feedwater is reheated prior
to entering the SG by six closed feedwater heaters. [2]
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 LP turbines and the HP 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
SG, which significantly increases plant efficiency. The closed feedwater heaters containU-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 SG
operates at. The smaller the temperature difference between the input and output of the
SG, the less external heating work must be done by the reactor. [2]
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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
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
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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.
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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 (non-
ideal) 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 hotstreams 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.
min " m
out =
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.
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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 temperature-
enthalpy diagram, called the composite curve. The plot can be shifted, using the shiftedtemperatures, 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]
mCp =
m
7936.64144
"
# $
%
& '
(h
0.42992261
"
# $
%
& '
T SS ) T TS ( ) *
0.94781742
1.8 [2]
dH = mCp T TS " T SS ( ) [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
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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 !Tmin below hot stream and 1/2 !Tmin 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]
Figures 3, 4, and 5 have been constructed using the software provided with [3].
Figure 3: Hot and Cold Composite Curves
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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.
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 !Tmin is maintained (by
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using !Tmin /2 less than hot temperatures & !Tmin /2 greater than cold temperatures) at
all points. The x-axis of the GCC shows the utility heating or cooling required.
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 !Tmin 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 !Tmin
because this is the most constrained area of the HEN.
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As shown in Figure 6, the heat exchanger area is roughly inversely proportional to the
temperature difference. However, low values of !Tmin 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 !Tmin must be selected for the best cost savings. The optimum !Tmin 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 !Tmin [8].
Figure 6: Utility Use, Heat Exchanger Area, and Cost Variation with Delta Tmin [3]
As !Tmin 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 !Tmin.
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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).
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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 !Tmin values for different types of power plants can be found in various texts. !Tmin 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.
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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 !Tmin 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, are presented in Table 1.
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Table 1: Millstone Unit III Heat Exchanger Network
Hot Stream Cold StreamHeat Exchanger
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. 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)).
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Figure 9: Hot and Cold Stream Example from the Original Millstone Unit III HEN
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. 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.
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Figure 11: Hot and Cold Stream Example After Combining Streams
The supply temperatures for the 1
st
through 4
th
point heaters, in this analysis, areweighted 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.
T s= T
W
mW
mTot
"
# $
%
& ' +T V
mV
mTot
"
# $
%
& ' +T HP1
m HP1
mTot
"
# $
%
& ' [4]
T s= 525°F
73,748lbm /hr
2,861,744lbm /hr
"
# $
%
& ' +525°F
1,540,778lb /hr
2,861,744lb /hr
"
# $
%
& ' + 448°F
1,247,218lb /hr
2,861,744lb /hr
"
# $
%
& ' = 491°F
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:
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H s= H
W
mW
mTot
"
# $
%
& ' + H V
mV
mTot
"
# $
%
& ' + H HP1
m HP1
mTot
"
# $
%
& ' [5]
H s=1,198 Btu / lb
73,748lbm /hr
2,861,744 lbm /hr
"
# $
%
& ' + 518 Btu /lb
1,540,778lb /hr
2,861,744 lb /hr
"
# $
%
& ' +1,146 Btu / lb
1,247,218lb /hr
2,861,744 lb /hr
"
# $
%
& ' = 809 Btu / lb
Table 2: Input Stream Data for Analysis
Supply
Temperature
Target
Temperature
dT Min / 2 Mass Flowrate
Enthalpy
Change
Stream
Name
°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.
T SS Hot
= T S " #T
min
2= 491°F "
50°F
2= 466°F [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.
T SS Cold
= T S
+ "T
min
2= 98°F +
50°F
2=123°F
[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.
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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]
mCp =
10085320lb
/hr
7936.64144"
# $ %
& '
202 Btu
/lb
0.42992261"
# $ %
& '
123F ( 467.8F ( ) )
0.94781742
1.8= (911.7986 MBtu /hr /F
dH = "911.7986 MBtu /hr /F 467.8 " 466( ) = "1641.2375 MBtu /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
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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]
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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.
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).
Figure 13: Grid Diagram with Cross Pinch Heat Transfer Example
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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 UtilityRequirements
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.
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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 intermediatecalculations 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.
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.
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Table 4: Problem Table
Shift
TemperatureInterval T(i+1)-Ti mCpnet dH
°F °F MBtu(IT)/hr/°F MBtu(IT)/hr
467.8
1 1.8 -912 -1641 demand
466
2 111 898 99731 surplus
355
3 1 -912 -912 demand
354
4 33 1132 37346 surplus
321
5 12 3078 36941 surplus
309
6 37 1035 38294 surplus
272
7 5 4354 21770 surplus
267
8 26 2407 62586 surplus
241
9 35 -912 -31913 demand
206
10 57 857 48864 surplus
149
11 11 -912 -10030 demand
138
12 5 15459 77293 surplus
133
13 10 -912 -9118 demand
123
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Table 5: Net Heat Capacity Flowrate and Heat Load (Calculated and Software)
Interval
Temperature
(°F)
Temperature
Difference
(°F)
mc p net
(Mbtu/hr/
°F)
mc p net
(Mbtu/hr/°F)
from software
dH
(Mbtu/hr)
dH (Mbtu/hr)
from software
1
467.8 to 466
2
-912
-912
-1642
-1641
2
466 to 355
111
898
898
99680
99731
3
355 to 354
1
-912
-912
-912
-912
4
354 to 321
33
1143
1132
37720
37346
5
321 to 309
12
3090
3078
37077
36941
6
309 to 272
37
1035
1035
38277
38294
7
272 to 267
5
4353
4354
21767
21770
8
267 to 241
26
2407
2407
62574
62586
9
241 to 206
35
-912
-912
-31928
-31913
10
206 to 149
57
857
857
48838
48864
11
149 to 138
11
-912
-912
-10035
-10030
12
138 to 133
5
15458
15459
77290
77293
13
133 to 123
10
-912
-912
-9122
-9118
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.
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Table 6: Heat Cascade
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.
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Table 7: Heat Loads per Interval (Calculated and Software)
Shift
Temperature
(°F)
Infeasible
cascade
(MBtu/hr)
Infeasible
cascade
(software)
(MBtu/hr)
Feasible
Cascade
(MBtu/hr)
Feasible
Cascade
(software)
(MBtu/hr)
467.8 0
0
1642
1641 466 -1642
-1641
0
0
355 98038
98090
99680
99731
354 97126
97178
98768
98819
321 134846
134523
136488
136165
309 171923
171465
173565
173106
272 210200
209759
211842
211400
267 231967
231528
233609
233169
241 294541 294114 296183 295755
206 262612
262201
264254
263842
149 311450
311065
313092
312706
138 301415
301035
303057
302676
133 378706
378328
380348
379970
123 369583 369210 371225 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 otherstreams. 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.
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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.
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. !Tmin is redistributed in
the shifted composite curves by subtracting 1/2 !Tmin from the hot stream temperatures
and adding1/2 !Tmin 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.
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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.
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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.
Figure 17: Grid Diagram
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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 HP turbine entered the combined 1 st and 2nd heaters and
all of the output from the three LP 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
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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
Temperature (°F)
Minimum Hot
Utility (MBtu/hr)
Minimum Cold
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 2,553 349,8409 467 729 348,016
10 466 1,641 320,096
11 466 1,641 37,228
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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.
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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 !Tmin can greatly
increase the heat exchanger cost. Since the minimum utility requirements do not change
up until a !Tmin 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 !Tmin 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
!Tmin
(°F)
Pinch
Temperature (°F)
Minimum Hot Utility
(MBtu/hr)
Minimum Cold
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
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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 thegrand composite curves were constructed, using software provided with [3], 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 6
th
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. Overall, deleting the 5th
and 6th point heaters would decrease the energy costs
associated with cold external utilities and the initial cost of the heat exchangers.
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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.
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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.
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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 temperaturesAS – 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 !! min.
A1 – Intermediate calculations
A2 – Plot raw data
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7.2 Millstone Unit III Heat and Mass Balance
Figure 18: Millstone Unit III Heat Balance
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7.3 Raw Data and Intermediate Steps
Table 10: Raw Data from Millstone Unit III Heat and Mass Balance
Stream
Description
Input H
(Btu/lb)
Output
H
(Btu/lb(
Change H
(Btu/lb)
Supply
Temp (F)
Target
Temp
(F)
Flow
(lb/hr)
from LP 1
1241
261
980
426
292
539308
from LP 2
1200
235
965
335
266
582815
from LP 3
1110
142
968
231
174
675020
from LP 4
1054
126
928
163
158
571554
HP 1
1146
354
792
448
380
1247218
HP 2
1089
305
784
373
334
570935
W to 1st pt
1198
354
844
525
380
73748
V to 1st pt 518 354 164 525 380 1540778
A to 2nd pt
1192
305
887
538
334
11711
waste from
1st pt
354
305
49
380
334
2861743
waste from
2nd pt
305
261
44
334
292
3444392
waste from
3rd pt 261 235 26 292 266 3983696
waste from
5th pt
142
56
86
174
98
675021
waste from
6th pt
126
56
70
158
98
785742
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Table 11: Combined Data for HEN used in Analysis for Case 1
Stream
Description
Input H
(Btu/lb)
Output
H
(Btu/lb
)
Change
H
(Btu/lb)
Supply
Temp (F)
Target
Temp
(F)
Flow
(lb/hr)
Stream
Type
Supply
Shift (F)
Target
Shift
(F)
1
Condenserto SG 56 258.1 202.1 98 442.8 10085320 Cold 123 467.8
2
Total
W+V+HP1
flow809 354 455 491 380 2861744 Hot 466 355
3
Total A +
2nd pt +
waste from
1st pt
479 305 174 379 334 3444389 Hot 354 309
4
Total 3rd pt
(LP1)+ 2nd
pt waste432 261 171 346 292 3983700 Hot 407 267
5
Total waste
from 3rd pt
+ LP2381 235 146 297 266 4566511 Hot 272 241
6
From LP 31110 142 968 231 174 675020 Hot 206 149
7
From LP 41054 126 928 163 158 571554 Hot 138 133
Table 12: Net Heat Capacity Flowrates
StreamSupply Shift (F) Target Shift (F)
mc p 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
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Table 13: Intermediate Calculations for Heat Capacity and Heat Load
Interval
Temperature
(F)
Temperature
Difference (F)
mc p net
(Mbtu/hr/F)
dH (Mbtu/hr)
1
467.8 to 466
2
-912
-912 * 2
2 466 to 355
111
-912 + 1810
898 * 111
3
355 to 354
1
-912
-912 * 1
4
354 to 321
33
-912 + 2055
1143 * 33
5
321 to 309
12
-912 + 2055 +
1947
3090 * 12
6
309 to 272
37
-912 + 1947
1035 * 37
7
272 to 267
5
-912 + 3319 +
1947
4353 * 5
8
267 to 241
26 -912 + 3319 2407 * 26
9
241 to 206
35
-912
-912 * 35
10
206 to 149
57
-912 + 1769
857 * 57
11 149 to 138
11
-912
-912 * 11
12
138 to 133
5
-912 + 16370
15458 * 5
13
133 to 123
10
-912
-912 * 10
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 FlowrateEnthalpy
Change°F °F °F lb/h 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
6 200 167 25 1246574.000 950
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Table 15: Calculated Stream Data for Case 2
Stream Name Heat FlowStream
TypeSupply
ShiftTargetShift
MBtu(IT)/hr °F °F
1 314388.1611 COLD 123.0 467.8
2 200940.4215 HOT 466.0 355.03 91956.7107 HOT 354.0 309.0
4 105125.4499 HOT 321.0 267.0
5 102887.4717 HOT 272.0 241.0
6 182753.9621 HOT 175.0 142.0
Table 16: Problem Table for Case 2
ShiftTemperature
Interval T(i+1)-Ti mCpnet dH
°F °F MBtu(IT)/hr/°F MBtu(IT)/hr
467.8
1 1.8 -911.7986 -1641.2375 demand
466
2 111 898.4755 99730.7757 surplus
355
3 1 -911.7986 -911.7986 demand
354
4 33 1131.6838 37345.567 surplus
321
5 12 3078.4514 36941.4173 surplus
309 6 37 1034.969 38293.8522 surplus
272
7 5 4353.9197 21769.5984 surplus
267
8 26 2407.1521 62585.9543 surplus
241
9 66 -911.7986 -60178.7083 demand
175
10 33 4626.2002 152664.6079 surplus
142
11 19 -911.7986 -17324.1736 demand
123
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Table 17: Heat Cascade for Case 2
Infeasible
Cascade
Feasible
Cascade
! 0 ! 1641.2375
-1641.2375 -1641.2375
PINCH ! -1641.2375 ! 0
99730.7757 99730.7757
! 98089.5382 ! 99730.7757
-911.798611 -911.798611
! 97177.73959 ! 98818.97709
37345.56701 37345.56701
! 134523.3066 ! 136164.5441
36941.41727 36941.41727
! 171464.7239 ! 173105.9614
38293.85224 38293.85224
! 209758.5761 ! 211399.8136
21769.5984 21769.5984
! 231528.1745 ! 233169.412
62585.95432 62585.95432
! 294114.1288 ! 295755.3663
-
60178.70833
-
60178.70833
! 233935.4205 ! 235576.658
152664.6079 152664.6079
! 386600.0284 ! 388241.2659
-
17324.17361
-
17324.17361
! 369275.8548 ! 370917.0923
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Figure 19: GCC for Case 2
7.4.2 Case 3
Table 18: Input Stream Data for Case 3
StreamName
SupplyTemperature
TargetTemperature
dT Min / 2 Mass FlowrateEnthalpyChange
°F °F °F lb/h 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
5 277 245 25 5813085.000 318
Table 19: Calculated Stream Data for Case 3
Stream Name Heat FlowStream
TypeSupply
ShiftTargetShift
MBtu(IT)/hr °F °F
1 314388.1611 COLD 123.0 467.8
2 200940.4215 HOT 466.0 355.0
3 91956.7107 HOT 354.0 309.0
4 105125.4499 HOT 321.0 267.0
5 285271.854 HOT 252.0 220.0
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Table 20: Problem Table for Case 3
Shift
TemperatureInterval
T(i+1)-Ti
mCpnet dH
°F °F MBtu(IT)/hr/°F MBtu(IT)/hr
467.8
1 1.8 -912 -1641 demand
466
2 111 898 99731 surplus
355
3 1 -912 -912 demand
354
4 33 1132 37346 surplus
321
5 12 3078 36941 surplus
309
6 42 1035 43469 surplus
267
7 15 -912 -13677 demand
252
8 32 8003 256094 surplus
220
9 97 -912 -88444 demand
123
Table 21: Heat Cascade for Case 3
Infeasible
Cascade
Feasible
Cascade
! 0 ! 1641.2375
-1641.2375 -1641.2375
PINCH ! -1641.2375 ! 0
99730.7757 99730.7757
! 98089.5382 ! 99730.7757
-911.798611 -911.798611
! 97177.73959 ! 98818.97709
37345.56701 37345.56701
! 134523.3066 ! 136164.5441
36941.41727 36941.41727
! 171464.7239 ! 173105.9614
43468.69714 43468.69714
! 214933.421 ! 216574.6585-
13676.97917-
13676.97917
! 201256.4419 ! 202897.6794
256094.2985 256094.2985
! 457350.7403 ! 458991.9778
-88444.46527
-88444.46527
! 368906.2751 ! 370547.5126
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Figure 20: GCC for Case 3
7.4.3 Case 4
Table 22: Input Stream Data for Case 4
StreamName
SupplyTemperature
TargetTemperature
dT Min / 2 Mass Flowrate EnthalpyChange
°F °F °F lb/h Btu(IT)/lb
1 98 442.8 25 10085320.000 202
2 472 372 25 3444390.000 511
3 346 292 25 3983700.000 171
4 297 266 25 4566511.000 146
5 231 174 25 675020.000 968
6 163 158 25 571554.000 928
Table 23: Calculated Stream Data for Case 4
Stream Name Heat Flow StreamType
SupplyShift
TargetShift
MBtu(IT)/hr °F °F
1 314388.1611 COLD 123.0 467.8
2 271617.8775 HOT 447.0 347.0
3 105125.4499 HOT 321.0 267.0
4 102887.4717 HOT 272.0 241.0
5 100836.3529 HOT 206.0 149.0
6 81852.2036 HOT 138.0 133.0
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Table 24: Problem Table for Case 4
Shift
TemperatureInterval T(i+1)-Ti mCpnet dH
°F °F MBtu(IT)/hr/°F MBtu(IT)/hr467.8
1 20.8 -912 -18965 demand
447
2 100 1804 180438 surplus
347
3 26 -912 -23707 demand
321
4 49 1035 50713 surplus
272
5 5 4354 21770 surplus267
6 26 2407 62586 surplus
241
7 35 -912 -31913 demand
206
8 57 857 48864 surplus
149
9 11 -912 -10030 demand
138
10 5 15459 77293 surplus
133
11 10 -912 -9118 demand
123
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Table 25: Heat Cascade for Case 4
Infeasible
Cascade
Feasible
Cascade
! 0 ! 18965.41111
-18965.41111
-18965.41111
PINCH !
-
18965.41111 ! 0
180438.0164 180438.0164
! 161472.6053 ! 180438.0164
-
23706.76389
-
23706.76389
! 137765.8414 ! 156731.2525
50713.48 50713.48
! 188479.3214 ! 207444.7325
21769.5984 21769.5984
! 210248.9198 ! 229214.3309
62585.95432 62585.95432
! 272834.8741 ! 291800.2852
-
31912.95139
-
31912.95139
! 240921.9227 ! 259887.3338
48863.83203 48863.83203
! 289785.7548 ! 308751.1659
-
10029.78472
-
10029.78472
! 279755.97 ! 298721.3812
77293.21059 77293.21059
! 357049.1806 ! 376014.5917
-9117.98611 -9117.98611
! 347931.1945 ! 366896.6056
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Figure 21: GCC for Case 4
7.4.4 Case 5
Table 26: Input Stream Data for Case 5
StreamName
SupplyTemperature
TargetTemperature
dT Min / 2 Mass FlowrateEnthalpyChange
°F °F °F lb/h Btu(IT)/lb
1 98 442.8 25 10085320.000 2022 472 372 25 3444390.000 511
3 346 292 25 3983700.000 171
4 297 266 25 4566511.000 146
5 200 167 25 1246574.000 950
Table 27: Calculated Stream Data for Case 5
Stream Name Heat FlowStream
TypeSupply
ShiftTargetShift
MBtu(IT)/hr °F °F
1 314388.1611 COLD 123.0 467.8
2 271617.8775 HOT 447.0 347.0
3 105125.4499 HOT 321.0 267.0
4 102887.4717 HOT 272.0 241.0
5 182753.9621 HOT 175.0 142.0
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Table 28: Problem Table for Case 5
Shift
TemperatureInterval T(i+1)-Ti mCpnet dH
°F °F MBtu(IT)/hr/°F MBtu(IT)/hr
467.8
1 20.8 -912 -18965 demand
447
2 100 1804 180438 surplus
347
3 26 -912 -23707 demand
321
4 49 1035 50713 surplus
272
5 5 4354 21770 surplus
267
6 26 2407 62586 surplus
241
7 66 -912 -60179 demand
175
8 33 4626 152665 surplus
142
9 19 -912 -17324 demand
123
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Table 29: Heat Cascade for Case 5
Infeasible
Cascade
Feasible
Cascade
! 0 ! 18965.41111
-
18965.41111
-
18965.41111
PINCH !
-
18965.41111 ! 0
180438.0164 180438.0164
! 161472.6053 ! 180438.0164
-
23706.76389
-
23706.76389
! 137765.8414 ! 156731.2525
50713.48 50713.48
! 188479.3214 ! 207444.7325
21769.5984 21769.5984
! 210248.9198 ! 229214.3309
62585.95432 62585.95432
! 272834.8741 ! 291800.2852-
60178.70833
-
60178.70833
! 212656.1658 ! 231621.5769
152664.6079 152664.6079
! 365320.7737 ! 384286.1848
-
17324.17361
-
17324.17361
! 347996.6001 ! 366962.0112
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Figure 22: GCC for Case 5
7.4.5 Case 6
Table 30: Input Stream Data for Case 6
StreamName
SupplyTemperature
TargetTemperature
dT MinContrib
Mass FlowrateEnthalpyChange
°F °F °F lb/h Btu(IT)/lb
1 98 442.8 25 10085320.000 202
2 472 372 25 3444390.000 511
3 346 292 25 3983700.000 171
4 277 245 25 5813085.000 318
Table 31: Calculated Stream Data for Case 6
Stream Name Heat FlowStream
TypeSupply
ShiftTargetShift
MBtu(IT)/hr °F °F
1 314388.1611 COLD 123.0 467.8
2 271617.8775 HOT 447.0 347.0
3 105125.4499 HOT 321.0 267.0
4 285271.854 HOT 252.0 220.0
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Table 32: Problem Table for Case 6
Shift
TemperatureInterval T(i+1)-Ti mCpnet dH
°F °F MBtu(IT)/hr/°F MBtu(IT)/hr
467.8
1 20.8 -911.7986 -18965.4111 demand
447
2 100 1804.3802 180438.0164 surplus
347
3 26 -911.7986 -23706.7639 demand
321
4 54 1034.969 55888.3249 surplus
267
5 15 -911.7986 -13676.9792 demand
252
6 32 8002.9468 256094.2985 surplus
220
7 97 -911.7986 -88444.4653 demand
123
Table 33: Heat Cascade for Case 6
Infeasible
Cascade
Feasible
Cascade
! 0 ! 18965.41111-
18965.41111-
18965.41111
PINCH ! -18965.41111 ! 0
180438.0164 180438.0164
! 161472.6053 ! 180438.0164
-23706.76389
-23706.76389
! 137765.8414 ! 156731.2525
55888.32489 55888.32489
! 193654.1663 ! 212619.5774
-13676.97917
-13676.97917
! 179977.1871 ! 198942.5982
256094.2985 256094.2985
! 436071.4856 ! 455036.8967
-88444.46527
-88444.46527
! 347627.0204 ! 366592.4315
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Figure 23: GCC for Case 6
7.4.6 Case 7
Table 34: Input Stream Data for Case 7
StreamName
SupplyTemperature
TargetTemperature
dT MinContrib
Mass FlowrateEnthalpyChange
°F °F °F lb/h Btu(IT)/lb
1 98 442.8 25 10085320.000 202
2 472 372 25 3444390.000 511
3 346 292 25 3983700.000 171
4 277 245 25 5813085.000 318
Table 35: Calculated Stream Data for Case 7
Stream Name Heat FlowStream
TypeSupply
ShiftTargetShift
MBtu(IT)/hr °F °F
1 314388.1611 COLD 123.0 467.8
2 271617.8775 HOT 447.0 347.0
3 105125.4499 HOT 321.0 267.0
4 285271.854 HOT 252.0 220.0
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Table 36: Problem Table for Case 7
Shift
TemperatureInterval T(i+1)-Ti mCpnet dH
°F °F MBtu(IT)/hr/°F MBtu(IT)/hr
467.8
1 20.8 -911.7986 -18965.4111 demand
447
2 100 1804.3802 180438.0164 surplus
347
3 26 -911.7986 -23706.7639 demand
321
4 54 1034.969 55888.3249 surplus
267
5 15 -911.7986 -13676.9792 demand
252
6 32 8002.9468 256094.2985 surplus
220
7 97 -911.7986 -88444.4653 demand
123
Table 37: Heat Cascade for Case 7
Infeasible
Cascade
Feasible
Cascade
! 0 ! 18965.41111-
18965.41111-
18965.41111
PINCH ! -18965.41111 ! 0
180438.0164 180438.0164
! 161472.6053 ! 180438.0164
-23706.76389
-23706.76389
! 137765.8414 ! 156731.2525
55888.32489 55888.32489
! 193654.1663 ! 212619.5774
-13676.97917
-13676.97917
! 179977.1871 ! 198942.5982
256094.2985 256094.2985
! 436071.4856 ! 455036.8967
-88444.46527
-88444.46527
! 347627.0204 ! 366592.4315
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Figure 24: GCC for Case 7
7.4.7 Case 8
Table 38: Input Stream Data for Case 8
StreamName
SupplyTemperature
TargetTemperature
dT MinContrib
Mass FlowrateEnthalpyChange
°F °F °F lb/h Btu(IT)/lb
1 98 442.8 25 10085320.000 202
2 490 372 25 3444390.000 511
3 400 264 25 9796785.000 258
Table 39: Calculated Stream Data for Case 8
Stream Name Heat FlowStream
TypeSupply
ShiftTargetShift
MBtu(IT)/hr °F °F
1 314388.1611 COLD 123.0 467.8
2 271617.8775 HOT 465.0 347.0
3 390057.3038 HOT 375.0 239.0
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Table 40: Problem Table for Case 8
Shift
TemperatureInterval T(i+1)-Ti mCpnet dH
°F °F MBtu(IT)/hr/°F MBtu(IT)/hr
467.8
1 2.8 -911.7986 -2553.0361 demand
465
2 90 1390.0478 125104.3028 surplus
375
3 28 4258.1162 119227.2541 surplus
347
4 108 1956.2698 211277.1383 surplus
239
5 116 -911.7986 -105768.6389 demand
123
Table 41: Heat Cascade for Case 8
Infeasible
Cascade
Feasible
Cascade
! 0 ! 2553.036111
-2553.036111
-2553.036111
PINCH ! -2553.036111 ! 0
125104.3028 125104.3028
! 122551.2667 ! 125104.3028
119227.2541 119227.2541! 241778.5208 ! 244331.5569
211277.1383 211277.1383
! 453055.6591 ! 455608.6952
-105768.6389
-105768.6389
! 347287.0202 ! 349840.0564
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Figure 25: GCC for Case 8
7.4.8 Case 9
Table 42: Input Stream Data for Case 9
StreamName
SupplyTemperature
TargetTemperature
dT MinContrib
Mass FlowrateEnthalpyChange
°F °F °F lb/h Btu(IT)/lb
1 98 442.8 25 10085320.000 2022 492 372 25 3444390.000 511
3 372 264 25 9796785.000 258
Table 43: Calculated Stream Data for Case 9
Stream Name Heat FlowStream
TypeSupply
ShiftTargetShift
MBtu(IT)/hr °F °F
1 314388.1611 COLD 123.0 467.8
2 271617.8775 HOT 467.0 347.0
3 390057.3038 HOT 347.0 239.0
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Table 44: Problem Table for Case 9
Shift
TemperatureInterval T(i+1)-Ti mCpnet dH
°F °F MBtu(IT)/hr/°F MBtu(IT)/hr
467.8
1 0.8 -911.7986 -729.4389 demand
467
2 120 1351.6837 162202.0442 surplus
347
3 108 2699.8431 291583.0538 surplus
239
4 116 -911.7986 -105768.6389 demand
123
Table 45: Heat Cascade for Case 9
InfeasibleCascade
FeasibleCascade
! 0 ! 729.4388888
-729.4388888
-729.4388888
PINCH ! -729.4388888 ! 0
162202.0442 162202.0442
! 161472.6053 ! 162202.0442
291583.0538 291583.0538
! 453055.6591 ! 453785.098
-
105768.6389
-
105768.6389! 347287.0202 ! 348016.4591
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61
Figure 26: GCC for Case 9
7.4.9 Case 10
Table 46: Input Stream Data for Case 10
StreamName
SupplyTemperature
TargetTemperature
dT MinContrib
Mass FlowrateEnthalpyChange
°F °F °F lb/h Btu(IT)/lb
1 98 442.8 25 10085320.000 202
2 491 480 25 2861744.000 345
3 462 450 25 3444389.000 174
4 447 430 25 3983700.000 171
5 418 410 25 4566511.000 146
6 231 200 25 675020.000 942
7 163 158 25 571554.000 928
Table 47: Calculated Stream Data for Case 10
Stream Name Heat FlowStream
TypeSupply
ShiftTargetShift
MBtu(IT)/hr °F °F1 314388.1611 COLD 123.0 467.8
2 152361.4185 HOT 466.0 455.0
3 92488.2524 HOT 437.0 425.0
4 105125.4499 HOT 422.0 405.0
5 102887.4717 HOT 393.0 385.0
6 98127.9384 HOT 206.0 175.0
7 81852.2036 HOT 138.0 133.0
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Table 48: Problem Table for Case 10
Shift
TemperatureInterval T(i+1)-Ti mCpnet dH
°F °F MBtu(IT)/hr/°F MBtu(IT)/hr
467.8
1 1.8 -912 -1641 demand
466
2 11 12939 142332 surplus
455
3 18 -912 -16412 demand
437
4 12 6796 81547 surplus
425
5 3 -912 -2735 demand
422
6 17 5272 89625 surplus
405
7 12 -912 -10942 demand
393
8 8 11949 95593 surplus
385
9 179 -912 -163212 demand
206
10 31 2254 69862 surplus
175
11 37 -912 -33737 demand
138
12 5 15459 77293 surplus
133
13 10 -912 -9118 demand
123
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Table 49: Heat Cascade for Case 10
Infeasible
Cascade
Feasible
Cascade
! 0 ! 1641
-1641 -1641
PINCH ! -1641 ! 0
142332 142332
! 140690 ! 142332
-16412 -16412
! 124278 ! 125919
81547 81547
! 205825 ! 207466
-2735 -2735
! 203089 ! 204731
89625 89625
! 292714 ! 294355
-10942 -10942
! 281773 ! 283414
95593 95593
! 377366 ! 379007
-163212 -163212
! 214154 ! 215795
69862 69862
! 284016 ! 285657
-33737 -33737
! 250279 ! 251921
77293 77293
! 327573 ! 329214
-9118 -9118
! 318455 ! 320096
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Figure 27: GCC for Case 10
7.4.10 Case 11
Table 50: Input Stream Data for Case 11
StreamName
SupplyTemperature
TargetTemperature
dT MinContrib
Mass FlowrateEnthalpyChange
°F °F °F lb/h Btu(IT)/lb1 98 442.8 25 10085320.000 202
2 491 480 25 2861744.000 345
3 462 450 25 3444389.000 174
4 446 430 25 3983700.000 171
Table 51: Calculated Stream Data for Case 11
Stream Name Heat FlowStream
TypeSupply
ShiftTargetShift
MBtu(IT)/hr °F °F
1 314388.1611 COLD 123.0 467.82 152361.4185 HOT 466.0 455.0
3 92488.2524 HOT 437.0 425.0
4 105125.4499 HOT 421.0 405.0
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Table 52: Problem Table for Case 11
Shift
TemperatureInterval T(i+1)-Ti mCpnet dH
°F °F MBtu(IT)/hr/°F MBtu(IT)/hr
467.8
1 1.8 -912 -1641 demand
466
2 11 12939 142332 surplus
455
3 18 -912 -16412 demand
437
4 12 6796 81547 surplus
425
5 4 -912 -3647 demand
421
6 16 5659 90537 surplus
405
7 282 -912 -257127 demand
123
Table 53: Heat Cascade for Case 11
Infeasible
Cascade
Feasible
Cascade
! 0 ! 1641
-1641 -1641
PINCH ! -1641 ! 0
142332 142332
! 140690 ! 142332
-16412 -16412
! 124278 ! 125919
81547 81547
! 205825 ! 207466
-3647 -3647! 202177 ! 203819
90537 90537
! 292714 ! 294355
-257127 -257127
! 35587 ! 37228
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Figure 28: GCC for Case 11