Using Pinch Analysis to Optimize the Heat Exchanger Network of a
Regenerative Rankine Cycle for an Existing Modern Chemical Power
Plant
by
Stephanie Barnes
A Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING
Major Subject: MECHANICAL ENGINEERING
Approved:
_________________________________________
Professor Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
December, 2013
i
© Copyright 2013
by
Stephanie Barnes
All Rights Reserved
ii
CONTENTS
LIST OF TABLES ............................................................................................................ vi
LIST OF FIGURES ......................................................................................................... vii
DEFINITIONS ............................................................................................................... viii
ACRONYMS .................................................................................................................... ix
NOMENCLATURE .......................................................................................................... x
ACKNOWLEDGMENT .................................................................................................. xi
ABSTRACT .................................................................................................................... xii
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 .................................................................................................... 3
1.4
Problem Statement .............................................................................................. 3
1.5
Previous Work .................................................................................................... 4
2. Theory .......................................................................................................................... 5
2.1
Second Law of Thermodynamics ....................................................................... 5
2.2
Enthalpy Discussion?? ........................................................................................ 5
2.3
Problem Table Analysis ...................................................................................... 5
2.4
Composite Curves ............................................................................................... 6
2.4.1
Shifted Composite Curve ....................................................................... 7
2.5
Grand Composite Curve ..................................................................................... 8
2.6
ΔTmin ............................................................................................................... 10
2.7
Targeting for Multiple Utilities ........................................................................ 10
2.8
Trade Offs ......................................................................................................... 11
2.9
Design of the Heat Exchanger Network ........................................................... 13
3. Methodology .............................................................................................................. 14
iii
3.1
Overview........................................................................................................... 14
3.2
Assumptions ..................................................................................................... 14
3.3
Data Extraction ................................................................................................. 14
3.4
Problem Table ................................................................................................... 17
3.4.1
Heat Cascades ...................................................................................... 17
3.5
Composite Curves ............................................................................................. 18
3.6
Grid Diagram .................................................................................................... 18
3.7
HEN design ....................................................................................................... 19
3.8
3.7.1
Area of Heat Exchangers ..................................................................... 19
3.7.2
Cost?..................................................................................................... 19
How to use design for utilities .......................................................................... 19
4. Results and Discussion .............................................................................................. 20
4.1
Problem Table ................................................................................................... 20
4.2
Heat Cascade .................................................................................................... 21
4.3
Pinch Points and Utility .................................................................................... 22
4.4
Composite Curves ............................................................................................. 22
4.5
Grand Composite Curve ................................................................................... 23
4.6
Retrofit Heat Exchanger Network .................................................................... 24
4.6.1
Splitting the Cross Pinch Heat Exchanger ........................................... 25
4.6.2
Utility Design ....................................................................................... 25
5. Conclusion ................................................................................................................. 26
6. References.................................................................................................................. 27
6.1
Works Cited ...................................................................................................... 27
6.2
Additional References Consulted ..................................................................... 28
7. Appendices ................................................................................................................ 29
7.1
Guide to Excel File ........................................................................................... 29
7.2
Raw Data and Intermediate Steps ..................................................................... 29
iv
7.3
Millstone Unit III Heat and Mass Balance ....................................................... 31
v
LIST OF TABLES
Table 1 Millstone Unit III Heat Exchanger Network ...................................................... 15
Table 2 Input Stream Data ............................................................................................... 16
Table 3: Problem Table ................................................................................................... 20
Table 4: Heat Cascade ..................................................................................................... 21
Table 5: Raw Data from Millstone Unit III Heat and Mass Balance .............................. 29
Table 6: Combined Data for HEN used in Analysis........................................................ 30
vi
LIST OF FIGURES
Figure 1: Millstone Unit III Power Plant Schematic [Dominion] ..................................... 2
Figure 2 Hot and Cold Composite Curves ......................................................................... 7
Figure 3 Shifted Composite Curves .................................................................................. 8
Figure 4 Pg 10 March – Construction of the Grand Composite Curve ............................ 9
Figure 5 Grand Composite Curve Example....................................................................... 9
Figure 6 Multiple Utility Targeting March pg 11 ............................................................ 11
Figure 7: Grid Diagram Example [Bi] ............................................................................. 18
Figure 8: Grid Diagram with Cross Pinch Heat Transfer Example {Bi] ......................... 19
Figure 9: Hot and Cold Composite Curves...................................................................... 22
Figure 10: Shifted Hot and Cold Composite Curves ....................................................... 23
Figure 11: Grand Composite Curve ................................................................................. 24
Figure 12: Grid Diagram ................................................................................................. 25
Figure 13: Millstone Unit III Heat and Mass Balance ..................................................... 31
vii
DEFINITIONS
viii
ACRONYMS
The following is a list of acronyms and abbreviations that are used throughout this paper.
Acronym
Definition
GCC
Grand Composite Curve
SCC
Shifted Composite Curve
HEN
Heat Exchanger Network
SG
Stream Generator
LP
Low Pressure
HP
High Pressure
ix
NOMENCLATURE
The following is a list of nomenclature used throughout this paper:
Symbol
Description
Unit
mCp
Heat Capacity Flowrate
MBtu/hr/F
dH
Heat Load
MBtu/hr
Tmin
Minimum Temperature Difference Between Hot and Cold F
Composite Curves
TS
Supply Temperature
F
TT
Target Temperature
F
TSS
Shifted Supply Temperature
F
TTS
Shifted Target Temperature
F
M dot
Mass flow rate
lb/hr
H
Enthalpy
Btu/lb
x
ACKNOWLEDGMENT
Type the text of your acknowledgment here.
xi
ABSTRACT
Type the text of your abstract here.
xii
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
preheats the feedwater from the condenser, using the waste heat/steam from the turbines,
before it 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.
1.2.1
Millstone III Unit Overview
Figure 1 shows a simplified version of the Millstone III unit nuclear power plant. The
unit uses a pressurized water reactor, which prevents boiling in the reactor, to transfer
heat to a steam generator, which produces steam that flows through a high pressure and
three low pressure turbines to turn a turbine generator shaft to generate 1290 MW of
power. The steam exits the high pressure turbine, enters a moisture separator steam
1
reheater that separates “approximately 10% of the moisture from the steam.”
(Dominion). The steam gets reheated and is dry enough to flow through three low
pressure turbines. After exiting each low pressure turbine, the steam enters a condenser
below each low pressure turbine that condenses the steam into water. The condensate
and feed system transfers the water from the exit of the condenser back to the steam
generator. The feedwater is reheated prior to entering the steam generator by six closed
feedwater heaters.
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 1: Millstone Unit III Power Plant Schematic [Dominion]
Excess steam from the turbines is used as a heating element in six closed feedwater
heaters. Excess steam from the three low pressure turbines and the high pressure turbine
enters four closed feedwater heaters (#3-6) and two closed feedwater heaters (#1-2),
respectively. The closed feedwater heaters are used to heat the working fluid (water)
before it enters the steam generator, which significantly increases plant efficiency. The
closed feedwater heaters contain U-shaped tubes inside a shell and do not allow the
steam and water to mix. The temperature of the feedwater is increased after going
2
through each fclosed eedwater heater.
Feedwater pumps “enable the feedwater to
overcome the steam pressure in the boiling device.”
The smaller the temperature
difference between the input and output of the steam generator, the less external heating
work is that must be done by the reactor. (Dominon)
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 chemical 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” (Kemp pg 2).
“The principle is to predict what should be achieved (targeting), and to then set out to
achieve it (design)” (Linnhoff & Tjoe).
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 thermal efficiency of 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.
3
1.5 Previous Work
Linnhoff / march paper
Pinch analysis has been used to optimize new heat exchanger networks in power plants
as well as retrofit existing HENs. (Singh and Crosbie sized and integrated a heat
exchanger into an existing HEN at a gas processing plant).
Energy pinch, water pinch, hydrogen pinch (READ PINCH GUIDE ON WEBSITE Pg
38)
4
2. Theory
2.1 Second Law of Thermodynamics
Pinch analysis is based on the second law of thermodynamics. The second law of
thermodynamics describes the spontaneous processes that exist in irreversible (nonideal) cycles. The Clausius Statement of the second law of thermodynamics states: “it is
impossible for any system to operate in such a way that the sole result would be an
energy transfer by heat from a cooler to a hotter body.” [Moran pg 216] 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.”
[Moran pg 217] The hot streams cannot transfer all of their energy to heat the cold
stream. There must be some waste heat as a result of the heat transfer process.
2.2 Enthalpy Discussion??
Steam data is plotted on a temperature-enthalpy diagram. The plot can be shifted
because we only care about the change in enthalpy.
CP=heat capacity flowrate = mass flow x specific heat
The heat available in the interval is (CPa+CPb)*(T2-T1)
Heat Load Q=dH=MCp x (Ts-Tt) amount of enthalpy change in the process stream
MORE
2.3 Problem Table Analysis
The problem table method is developed to “allow for the maximum possible amount of
heat exchange within each temperature interval (Pg 21, Kemp).” Shifted temperatures
(1/2 ΔTmin below hot stream and above cold stream) are used to ensure that Tmin exists
between all hot and cold streams. (See table 2.3 Kemp)
5
The heat cascade uses the surplus heat from one hot utility and moves it into the next
interval.
The minimum utility requirements are determined from the heat cascade
diagram. “The total heat recovered by heat exchange is found by adding the heat loads
for all the hot streams and all the cold streams. Subtracting the cold and hot utility
targets from these values gives the total heat recovery by two separate routes (Pg 24,
Kemp).”
Rules: Don’t transfer heat across the pinch, don’t use cold utilities above the pinch, don’t
use hot utilities below the pinch. If you were to transfer heat across the pinch, you
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” (Pinch Analysis Guide pg 26).
2.4 Composite Curves
The composite curve is a way to incorporate all of the hot and cold streams onto a
temperature-enthalpy (or heat content H) diagram. The heat flow is determined by
multiplying the mass flow rate (lb/hr) by the change in enthalpy (Btu(IT)/lb). The hot
and cold composite curves are plotted separately and “the overlap between the
composite curves represents the maximum amount of heat recovery possible within the
process. The “overshoot” at the bottom of the hot composite represents the minimum
amount of external cooling required and the “overshoot” at the top of the cold composite
represents the minimum amount of external heating (Pg 20 Kemp).”
The hot and cold composite curves are separated by ΔTmin. The location of the minimum
temperature difference between the curves is the pinch point. The complete overlap of
the curves (overlaps for the same range of heat flow) represents the maximum heat
recovery possible.
The extension of the cold composite curve on the upper right
represents the minimum hot utility requirement and the extension of the hot composite
6
curve on the lower left represents the minimum cold utility requirement for the given
ΔTmin (March pg 7).
The slope of the T-H diagram is mCp. (Hint Online slides)
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 2 Hot and Cold Composite Curves
“The temperature difference between cold and hot streams, in any heat exchanger of the
process, is close to the ΔTmin value when the composite curves are almost parallel.”
(Pinch Analysis Guide pg 27)
2.4.1
Shifted Composite Curve
The composite curves are also plotted using the shifted temperatures.
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. The opposite is true for below the
pinch. Moving a composite curve horizontally does not change the stream data because
the x-axis represents a change in enthalpy.
7
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 3 Shifted Composite Curves
2.5 Grand Composite Curve
The grand composite curve (GCC) is a graph of the net heat flow (utility requirement)
versus the shifted temperature. The GCC is used for “setting multiple utility targets”
(March pg 10). The shifted composite curves ensure that ΔTmin is maintained (by using
ΔTmin /2 less than hot temps & ΔTmin /2 greater than cold temps) at all points. The
composite curves touch at the pinch in the shifted composite curve (SCC). The x-axis
of the GCC shows the utility heat or cooling required.
8
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 4 Pg 10 March – Construction of the Grand Composite Curve
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 5 Grand Composite Curve Example
The pinch point is the location where the new heat flow is 0. “The values of net heat
flow at the top and bottom end are the heat supplied to and removed from the cascade,
and thus tell us the hot and cold utility targets (Pg 26 Kemp).” The curve also tells us
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.
9
2.6 ΔTmin
“Only the heat exchangers at the pinch need to operate at delta T values down to delta T
min (Pg 20, Kemp)”. “A zero temperature difference would require an infinitely large
heat exchanger (Pg 18 Kemp).”
The surface area required for heat exchange is given by A=Q/U*deltaTLM. U is the
overall heat transfer coefficient, delta TLM is the log mean temperature difference, Q is
the heat transferred in the exchanger, and A is the surface area. Text assumes a value of
0.1 kW/m^2 K for U)
Delta TLM = (see pg 36 of Kemp)
The heat exchanger area is roughly inversely proportional to the temperature difference.
Low values of ΔTmin can result in large and costly heat exchangers.
QuickTime™ and a
decompressor
are needed to see this picture.
2.7 Targeting for Multiple Utilities
Using the grand composite curve to target for multiple utilities helps reduce utility costs.
For example, in Figure b, MP and cooling water are used to reduce the amount of HP
10
steam and refrigeration required. In this figure b, a horizontal line is drawn from the yaxis at the temperature of MP steam until it hits the GCC. This is the MP steam target.
The remaining heating utility is satisfied by HP steam. The points where MP, HP, CW,
and Ref touch the GCC are called utility pinches. “Heat transfer across a utility pinch
represents inefficiency. For the process pinch, the inefficiency is an increase in overall
energy use above the target value. For a utility pinch, the inefficiency is a shift in heat
load from a cheaper utility level to a more expensive one.” (Pinch Guide pg 32).
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 6 Multiple Utility Targeting March pg 11
“The general objective is to maximize the use of cheaper utility levels and minimize the
use of the expensive utility levels. (March pg 9).” “It is preferable to use LP steam
instead of HP steam, and cooling water instead of refrigeration” (March pg 9). LP steam
use can replace part of the HP steam use for heating purposes until the ΔTmin is
difference between the hot composite curve and the cold composite curve is reached.
Each time a new utility is added, the composite curve will change shape.
2.8 Trade Offs
There is a trade off between the capital costs and energy costs. The optimum ΔTmin
can be selected by the intersection of the capital cost and the energy cost graphs to
determine the minimum cost in new designs. If the energy cost and the heat exchanger
cost (surface area), the optimal ΔTmin can be determined (Pinch Analysis Guide pg 27).
11
“There is a correlation between the value of ΔTmin in the exchanger and the total utility
load on the system (Pg 18, Kemp).” As ΔTmin is increased, the difference between the
hot and cold composite curves increases, which increases the heat required by external
utilities, as shown in Figure 3.7.
QuickTime™ and a
decompressor
are needed to see this picture.
Pg 14 of March
12
QuickTime™ and a
decompressor
are needed to see this picture.
Pg 27 Pinch Analysis Guide
2.9 Design of the Heat Exchanger Network
13
3. Methodology
3.1 Overview
The pinch analysis performed for this project is divided into four major steps: (1)
extraction of steam 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, (4) designing the hot and cold utility systems and
modifying the heat exchanger network as necessary. [Kemp]
An excel spreadsheet, developed by Gabriel Norwood (Kemp) was used for the first two
steps of the analysis. The user enters Tmin, the supply and target temperatures, the mass
flow rate, and the change in enthalpy. Typical ΔTmin values for different types of plants
can be found in various texts. ΔTmin for chemical plants ranges from 10-20 deg C.
(Linhoff, Kemp, Pinch Guide). 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
In the analysis, it is assumed that the flow from the condenser is that which enters the
6th point heater. A weighted average supply and target temperatures, enthalpy, and
flowrates are used when streams are combined.
The HEN consisting of six feedwater heaters was evaluated. The main condenser is
considered a permanent utility because of the cooling water from the Long Island Sound.
3.3 Data Extraction
Data is extracted from the heat and mass balance in Appendix 7.3 for all areas of the
plant that need heating or cooling. In this analysis, the HEN consisting of six feedwater
heaters was evaluated for simplicity. A ΔTmin of 50 F was used for this analysis.
14
In the input stage, the heating and cooling demands of the streams are included without
any reference to the existing heat exchangers (March pg 5). “The assumption in the data
extraction flow-sheet is that any process cooling duty is available to match against any
heating duty in the process.” (March pg 5). This analysis “does not consider matching
constraints between specific hot and cold streams” (March pg 14).
The effective stream temperatures are more important than the actual stream
temperatures in the data extraction phase (March pg 50).
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. [Kemp] The original heat exchanger network
design parameters are presented in Table 1.
Table 1 Millstone Unit III Heat Exchanger Network
Hot Stream
Heat Exchanger
Cold Stream
Number
Ts (F)
Tt (F)
Ts (F)
Tt (F)
1st Point
491
380
369
442.8
2nd Point
379
334
326.7
365.6
3rd Point
346
292
282
297.9
4th Point
297
266
222.9
288.1
5th Point
231
174
158.3
222.9
6th Point
163
158
101
158.3
The 1st through 4th point heaters have a combination of streams that flow through the
exchanger to heat the feedwater stream. The input streams are combined to simplify the
analysis. The supply temperatures for the 1st through 4th point heaters are weighted
averages based on the mass flow rates. For example, the supply temperature for the 1 st
point heater (stream 2 of Table 2) was determined by the following:
15
m
 m
m
Ý 
Ý 
Ý 
Ts  TW  W  TV  V  THP1 HP1 
ÝTot 
ÝTot 
ÝTot 
m
m
 m
(Equation 1)
 73,748lbm /hr 
1,540,778lbm /hr 
1,247,218lbm /hr 
Ts  525F 
 525F 
 448F 
 491F
2,861,744lbm /hr 
2,861,744lbm /hr 
2,861,744lbm /hr 

The same procedure was followed to determine the enthalpy the combined streams.

Table 2 Input Stream Data
Stream
Name
Supply
Target
Temperature Temperature
dT Min
Contrib
Mass Flowrate
Enthalpy
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
432
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 adding half of Tmin to the cold stream
supply and target temperatures. The shifted supply temperature for stream 2 of Table 2
is calculated as follows.
TSS  TS 
Tmin
50F
 491F 
 466F
2
2
(Equation 2)
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.
TSS  TS 
Tmin
50F
 98F 
 123F
2
2
(Equation 3)
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)). The mass flowrates for streams 2 through 5 of Table 2 are a
16
combined sum of the individual stream flowrates that enter the feedwater heater (See
Table 6 of Appendix 7.2 for intermediate steps and details).
3.4 Problem Table
To make the problem table, the shifted temperatures are ranked in decreasing order,
starting from the highest temperature. The heat capacity flowrate (mCp) and the heat
load (dH) are calculated for all of the temperature intervals. The calculations for the first
interval (between shifted temperatures 467.8F and 466F) are provided below. The
following conversion factors are used in the heat capacity flowrate equation.
1 kJ/kg = 0.42992261 Btu/lb
1 kJ = 0.94781742 Btu
T(R) = 1.8T(K)
1 kg/s = 7936.64144 lb/hr



Ý
m
h



7936.64144 0.42992261 0.94781742
mCp 

1.8
TSS  TTS 
(Equation 4)
10085320lb /hr  202Btu /lb 



 7936.64144 0.42992261 0.94781742

 911.7986MBtu /hr /F
 mCp 
1.8
123F  467.8F 
dH  mCpTTS  TSS 

(Equation 5)
dH  911.7986MBtu /hr /F 467.8  466  1641.2375MBtu /hr


3.4.1
Heat Cascades
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 cascade is typically 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. “All the net heat flows in the cascade now
17
increase by this amount and the minimum value becomes 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.
[Kemp]
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 –not the
boxed numbers) is plotted on the horizontal axis and the shifted temperature is plotted on
the vertical axis.
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” [section 2.3.2
Kemp]. As shown in Figure 7, streams 1 and 2 (boxes) are hot streams and streams 3
and 4 are cold streams. The circled numbers represent current heat exchangers between
two streams. The circles with “H” and “C” represent external heating and cooling
utilities.
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 7: Grid Diagram Example [Bi]
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 8. If there is a current
18
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 the green circles in Figure 8).
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 8: Grid Diagram with Cross Pinch Heat Transfer Example {Bi]
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 HEN design
3.7.1
Area of Heat Exchangers
3.7.2
Cost?
3.8 How to use design for utilities
Selecting the minimum number of heat exchanger units can be determined by Umin = N1 where N is the total number of process and utility streams in the HEN (March pg 13).
Process improvements for reducing the hot utility target include increasing the hot
stream above the pinch and decreasing the cold stream above the pinch. The cold utility
is reduced by the opposite.
This is called the plus-minus principle for process
modifications (Pinch Guide pg 37).
19
4. Results and Discussion
4.1 Problem Table
The problem table is provided in Table 3. The heat capacity flowrate and the heat load
are calculated for each interval, using Equations 4 and 5.
Table 3: Problem Table
Shift
Temperature
°F
467.8
Interval
T(i+1)-Ti
mCpnet
dH
°F
MBtu(IT)/hr/°F
MBtu(IT)/hr
1
1.8
-911.7986
-1641.2375
demand
2
59
898.4755
53010.0519
surplus
3
52
1649.3715
85767.3194
surplus
4
1
-160.9025
-160.9025
demand
5
45
1882.5799
84716.0964
surplus
6
37
-160.9025
-5953.394
demand
7
5
3158.0482
15790.2408
surplus
8
26
2407.1521
62585.9543
surplus
9
35
-911.7986
-31912.9514
demand
10
57
857.2602
48863.832
surplus
11
11
-911.7986
-10029.7847
demand
12
5
15458.6421
77293.2106
surplus
13
10
-911.7986
-9117.9861
demand
466
407
355
354
309
272
267
241
206
149
138
133
123
20
4.2 Heat Cascade
The heat cascade is drawn from the problem table. The heat loads are in the boxes of
Table 4 and the heat load for each interval is added to that of the previous interval. The
heat cascade on the left hand side of Table 4 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 with no heat flow is the pinch.
Table 4: Heat Cascade
Infeasible
Cascade
▼
PINCH
-1641.2375
▼
53010.05195
▼
85767.31943
▼
160.9025404
▼
84716.09638
▼
5953.393995
▼
15790.2408
▼
62585.95432
▼
31912.95139
▼
48863.83203
▼
10029.78472
▼
77293.21059
▼
-9117.98611
▼
Feasible
Cascade
▼
0
378328.4354
-1641.2375
▼
53010.05195
▼
85767.31943
▼
160.9025404
▼
84716.09638
▼
5953.393995
▼
15790.2408
▼
62585.95432
▼
31912.95139
▼
48863.83203
▼
10029.78472
▼
77293.21059
▼
369210.4492
-9117.98611
▼
-1641.2375
51368.81445
137136.1339
136975.2313
221691.3277
215737.9337
231528.1745
294114.1288
262201.1775
311065.0095
301035.2248
21
1641.2375
0
53010.05195
138777.3714
138616.4688
223332.5652
217379.1712
233169.412
295755.3663
263842.415
312706.247
302676.4623
379969.6729
370851.6867
4.3 Pinch Points and Utility
The pinch temperature (shifted) is 466F and is highlighted in yellow in Table 3. The hot
pinch his 491F and the cold pinch is 441F and is calculated using Equations 2 and 3.
The minimum hot and cold utility requirements are 1641.24 MBtu/hr and 370,851.69
MBtu/hr, respectively.
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 9.
Hot and Cold Composite Curves
600
Actual Temperature (ЎF)
500
400
300
200
100
0
0
100000
200000
300000
400000
500000
600000
700000
800000
Heat Flow (Mbtu(IT)/hr)
Figure 9: Hot and Cold Composite Curves
The shifted hot and cold composite curves are shown in Figure 10. The point where the
hot and cold shifted composite curves touch is the pinch point.
22
Shifted Hot and Cold Composite Curves
500
450
Shifted Temperature (ЎF)
400
350
300
250
200
150
100
50
0
0
100000
200000
300000
400000
500000
600000
700000
800000
Heat Flow (Mbtu(IT)/hr)
Figure 10: Shifted Hot and Cold Composite Curves
4.5 Grand Composite Curve
The grand composite curve is shown in Figure 11. The utility requirements can be
obtained from the grand composite curve.
23
Grand Composite
500
450
400
Shifted Temperature (ЎF)
350
300
250
200
150
100
50
0
0
50000
100000
150000
200000
250000
300000
350000
400000
Net Heat Flow (Mbtu(IT)/hr)
Figure 11: Grand Composite Curve
4.6 Retrofit Heat Exchanger Network
The grid diagram is shown in Figure 12. The current heat exchangers, with their
corresponding cold and hot streams, are depicted by black circles with arrows between
the streams. The 1st point heat crosses the pinch point and must be evaluated using the
method described in Section 3.6.
24
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 12: Grid Diagram
4.6.1
Splitting the Cross Pinch Heat Exchanger
4.6.2
Utility Design
25
5. Conclusion
26
6. References
6.1 Works Cited
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.
Dominion. Nuclear Media Guide, Information on Millstone Power Station. Waterford:
Dominion, 2012. Dominion, 2012. Web. 19 Aug. 2013.
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.
March, Linnhoff. Introduction to Pinch Technology. 1998. Targeting House Gadbrook
Park, England.
Moran, Michael J., and Howard N. Shapiro. Fundamentals of Engineering
Thermodynamics. New York: Wiley, 2008. Print.
Pinch Analysis: For the Efficient Use of Energy, Water, and Hydrogen. N.p.: Canada,
2003. Print.
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.
27
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.
Tjoe, T. N., and Bodo Linnhoff. "Using Pinch Technology for Process Retrofit."
Chemical Engineering 28 (1986): 47-60. Web.
Zebian, Hussam, and Alexander Mitsos. "A Double-pinch Criterion for Regenerative
Rankine Cycles." Energy 40.2 (2012): 258-70. Print.
28
7. Appendices
7.1 Guide to Excel File
The following tabs in the excel file:
TARGETS – Problem table, energy targets, pinch temperature and type of problem
(pinch, threshold, multiple pinch, or pinch region)
CC – Hot and cold composite curves
SCC – Shifted composite curves
GCC – Grand composite curves
GRID – Network grid diagram, shifted temperatures
AS – Stream data plot, actual temperatures
SS – Stream data plot, shifted temperatures
AT – Interval tables (heat loads and temperatures), actual temperatures
ST – Interval tables (heat loads and temperatures), shifted temperatures
DTMIN – Variation of hot and cold utility targets and pinch temperature with ∆Тmin.
7.2 Raw Data and Intermediate Steps
Table 5: Raw Data from Millstone Unit III Heat and Mass Balance
Stream
Description
from LP 1
from LP 2
from LP 3
from LP 4
HP 1
HP 2
W to 1st pt
V to 1st pt
A to 2nd pt
waste from
1st pt
waste from
2nd pt
waste from
Input H
(Btu/lb)
1241
1200
1110
1054
1146
1089
1198
518
1192
Output
H
(Btu/lb(
261
235
142
126
354
305
354
354
305
Change H
(Btu/lb)
980
965
968
928
792
784
844
164
887
Supply
Temp (F)
426
335
231
163
448
373
525
525
538
Target
Temp
(F)
292
266
174
158
380
334
380
380
334
Flow
(lb/hr)
539308
582815
675020
571554
1247218
570935
73748
1540778
11711
354
305
49
380
334
2861743
305
261
261
235
44
26
334
292
292
266
3444392
3983696
29
3rd pt
waste from
5th pt
waste from
6th pt
142
56
86
174
98
675021
126
56
70
158
98
785742
Table 6: Combined Data for HEN used in Analysis
Stream
Description
Condenser
to SG
1
Total
W+V+HP1
flow
2
Total A +
2nd pt +
waste from
1st pt
3
Total 3rd pt
(LP1)+ 2nd
pt waste
4
Total waste
from 3rd pt
+ LP2
5
From LP 3
6
7
From LP 4
Output
H
(Btu/lb
)
Change
H
(Btu/lb)
56
258.1
809
Supply
Temp (F)
Target
Temp
(F)
202.1
98
442.8
354
455
491
380
479
305
174
379
432
261
171
381
235
1110
1054
Input H
(Btu/lb)
Supply
Shift (F)
Target
Shift
(F)
Cold
123
467.8
2861744
Hot
466
355
334
3444389
Hot
354
309
346
292
3983700
Hot
407
267
146
297
266
4566511
Hot
272
241
142
968
231
174
675020
Hot
206
149
126
928
163
158
571554
Hot
138
133
30
Flow
(lb/hr)
10085320
Stream
Type
7.3 Millstone Unit III Heat and Mass Balance
QuickTime™ and a
decompressor
are needed to see this picture.
Figure 13: Millstone Unit III Heat and Mass Balance
31