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i

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



ii

© Copyright 2013

by

Stephanie Barnes

All Rights Reserved



iii

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



iv

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



v

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



vi

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
















vii
















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



viii

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 27: GCC for Case 10 .........................................................................................64

Figure 28: GCC for Case 11 .........................................................................................66



ix

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.



x

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



xi

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



xii

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.



xiii

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.



1

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.



2

Figure 1: Millstone Unit III Diagram [2]



3

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]



4

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



5

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.



6

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.



7

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



8

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



9

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



10

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.



11

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.



12

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).



13

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.



14

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.



15

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)).



16

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.



17

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:



18

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.



19

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



20

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.


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]



21

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



22

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.



23

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.



24

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



25

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.



26

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.



27

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.



28


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.



29

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.



30

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



31

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



32

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



33

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.



34

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



35

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.



36

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.



37

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.



38

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



39

7.2 Millstone Unit III Heat and Mass Balance

Figure 18: Millstone Unit III Heat Balance



40

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



41

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



42

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



43

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


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



44

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



45

Figure 19: GCC for Case 2

7.4.2 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



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



46


Shift

TemperatureInterval

T(i+1)-Ti

mCpnet dH


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


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



47


7.4.3 Case 4


StreamName

SupplyTemperature

TargetTemperature

dT Min / 2 Mass Flowrate EnthalpyChange


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


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



48


Shift


°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



49


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



50


7.4.4 Case 5


StreamName

SupplyTemperature

TargetTemperature

dT Min / 2 Mass FlowrateEnthalpyChange


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



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



51


Shift



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



52


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



53


7.4.5 Case 6


StreamName

SupplyTemperature

TargetTemperature

dT MinContrib

Mass FlowrateEnthalpyChange


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



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



54


Shift



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


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



55


7.4.6 Case 7


StreamName

SupplyTemperature

TargetTemperature

dT MinContrib



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



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



56


Shift



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


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



57


7.4.7 Case 8


StreamName

SupplyTemperature

TargetTemperature

dT MinContrib



1 98 442.8 25 10085320.000 202

2 490 372 25 3444390.000 511

3 400 264 25 9796785.000 258



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



58


Shift



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


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



59


7.4.8 Case 9


StreamName

SupplyTemperature

TargetTemperature

dT MinContrib



1 98 442.8 25 10085320.000 2022 492 372 25 3444390.000 511

3 372 264 25 9796785.000 258



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



60


Shift



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


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



61


7.4.9 Case 10


StreamName

SupplyTemperature

TargetTemperature

dT MinContrib



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



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



62


Shift



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



63


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



64


7.4.10 Case 11


StreamName

SupplyTemperature

TargetTemperature

dT MinContrib


°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



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



65


Shift



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


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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