Step by Step for Designing an Optimum Heat Exchanger Network · Pinch Analysis (PA); one of the...

Step by Step for Designing an Optimum Heat ExchangerNetworkEman M.Gabr

[email protected] Petroleum Research Institute

Abstract

Features of energy crisis became more complicated due to shortage of non- renewablesources of energy. While energy requirements increase parallel to technologyprogress. Energy researchers always apply energy targeting methodology to reduceutilities consumption. Designing a Heat Exchangers Network [HEN] by application ofpinch analysis is an effective technique for energy integration. I can say that this workis specific and simple course for designing a HEN through case study application.Where 8 alternatives Grass roots HEN designs with 66% of utilities saving areconcluded. Minimization of units and cost, process control and operability areimportant factors for choosing the suitable HEN design. Revamping of the existingprocess to maximize energy recovery with least alterations and cost took place; wherenet annual saving reached to 1,400,000 $.

Graphical AbstractWhat is the idea of Heat Exchanger Network??

Figure (1) the Idea of HENThrough two streams from any process

Transferring Heat Load from Source (hot stream H) to Sink (cold stream C)Replacement both Cooler and Heater by a Heat Exchanger

*Corresponding author: Eman Gabr / Assistant Professor (Head Manager of Reactor Engineering andProcesses Laboratory) Egyptian petroleum Research Institute. E-mail: [email protected]

H1 0 0 ?C 4 0 ?C C P =3 kw/?C

2 0 ?CC6 0 ?C CP =4.5 kw/?C

CoolerQ C =180 kw

H eat erQH =180 kw Heat

E xchangerQ =180 kw

H1 0 0 ?C 4 0 ?C

2 0 ?CC6 0 ?C

B efo re En ergy In te g ration A fte r E n erg y In te g rat io n

International Journal of Scientific & Engineering Research Volume 9, Issue 7, July-2018ISSN 2229-5518 827

IJSER © 2018http://www.ijser.org

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Index Terms: Heat recovery, Energy saving, Pinch Analysis, Minimum utilities

Heat Exchanger Network HEN, Cost estimation, Optimum HEN.

1-Introduction

As population increase and technologydevelop; demand for energy increase whilein the same time we suffer from shortageof non-renewable sources, all these factorscomplete the energy crisis. Heat exchangernetwork (HEN) is an important techniquefor maximizing heat recovery in theindustrial chemical process and reducingexternal heating and cooling utilities.Extensive research has been done toimprove HENs design and synthesis overthe past 40 years [1].Pinch Analysis (PA); one of the mostmethods used to design (HEN) andintegrate heat since it introduced byLinnhoff and Flower [2] & Linnhoff andHinmarsh [3]. [Ahmad &Linnhoff andAhmad] [4,5] introduced the“Supertargeting” procedure for thedesign of near-optimal heat exchangernetwork which systematicallyconsiders the energy capital trade off.This method involves searching for theoptimum approach temperature thatyields the lowest total annual cost for aHEN designing.The effect of ∆Tmin contribution oncost was modified by Sun et al [6]where economical balance and analysisbetween the capital and operating costsfor a given ∆Tmin took place. Theeffect of heat – exchangers'specifications as material ofconstruction, equipment type and rateof pressure on the HEN cost hasmodified by [Hall, Ahmad and Smith][7].A methodology for determinationoptimum loads of multiple utilities totrade- off the capital and energy cost of

HEN was proposed by Shenoy et al.[8].Akbarnia, Amidpour, and Shadaram[9] added piping costs to the heatexchanger capital cost which improvesthe accuracy of capital cost 'estimation

and detects the optimum point fordesigning.Kravanja and Glavič [10] proposed asimultaneous optimization for HENcost targeting method based on processflow sheets using rigorous models anddetailed cost for HEN functions. Thenonlinear programming NLP model isa combination ofpinch technology and mathematicalprogramming and can be used to HENsynthesis with a large number ofstreams.Mixed-integer-linear programming(MILP) transportation method; wasformulated by Shethna, Jezowski, andCastillo [11] to optimize heatexchanging area, number of units andutilities load in order to achieveoptimum cost target for HEN.Reza, Reza, and Hassan [12]developed a mathematical modelwhich affected by specifications shelland tube heat exchanger (materials ofconstruction and heat transfercoefficients) in annual costoptimization of HEN.The MILP-MINLP Methodology byYee and Grossmann [13] was the basemodel for MO_MINLP simultaneousflexibility and operability technique fordesigning a flexible HEN. Where thisHEN; can maximize energy recovery



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although, there is deviation of thestreams 'conditions [14, 15, and 16].

2- Pinch Analysis Technique

We can consider the first “red” bookby Linnhoff et al. [17]; is the first stepfor prevalence of heat integration topicin research sector. This User Guide; isstill the massively cited in the literatureand is considered as the beginningoverview for energy integration.Where application of Pinch AnalysisTechnique (PAT); provides searcherswith catalogue for solving the problemof process integration. The techniqueproved integration successfullythrough heat exchanger networksynthesis, heat recovery targeting, andselecting multiple utilities [18].In (PAT) utilities integration andenergy recovery realized by

transforming the process streams intothe Composite Curves (CCs) [19].From (CCs), we can estimate theminimum external requirements of hotand cold utilities which are the non-overlapping segments of the cold andhot composite curvesMaximum heat recovery represents in(CCs) by the overlap region betweenhot and cold composites curves. CCsplay an important role in processdesign; for designing a Heat ExchangerNetwork (HEN) directly. The GrandComposite Curved (GCC) and theProblem Table Algorithm (PTA) arefurther development for heatintegration techniques. Whereminimum utilities and so on minimumemissions can be concluded [20].

2-1 Principles of Pinch Analysis

Pinch Technology provides asystematic methodology for energy

saving in processes and total sites. Themethodology is based onthermodynamic principles, the basisequations are:

T

H

T ∆

H ∆

Slope = 1/CP

CP=m Cp∆H = m Cp ∆T= CP ∆TCP = ∆H / ∆T

Where:m: mass flow rateCp: specific heat (physical property)CP: Heat Capacity flow rate∆H: Enthalpy Change∆T: Temperature Change

Figure (2) Presentation of hot stream on T-H diagram

2-2 Steps of Pinch Analysis Technique

1) Identification of hot, cold, utilitystreams in the process.

2) Extraction of thermal data forprocess streams and utilities.

3) Selection of Initial ∆Tmin value.

4) Estimation of minimum hot andcold utilities and defining ofpinch point by:

· Construction ofComposite Curves



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· Problem Table Algorithm5) Design of Heat ExchangerNetwork [HEN].6) Estimation of minimum energycost target.

7) Estimation of the capital costtarget.8) Identification of the optimum∆Tmin value.9) Design of the optimum HeatExchanger Network [HEN].

2-3 Estimation of minimum utilities

Maximum energy recovery for anyprocess leads to minimization of therequired external heating and coolingloads. Estimation of minimum hot andcold utilities through pinch analysis bytwo techniques (composite curve&problem table) is done as a beginningstep for HEN designing.

2-3-1 construction of CompositeCurve

Transferring of all hot streams whichpresented in T-H diagram into onecurve depending on Summation thestreams loads of the same interval; this

curve named as hot composite curve.By repeating this step with coldstreams; we get also cold compositecurve. The overlap region is the energyrecovery limits while the non overlapare the required heating and cooling.We can move composite curveshorizontally to change temperaturedifference which affects on utilities'loads and heat transfer area. Whiledetecting ∆Tmin value is realizingmaximum energy recovery andminimum utilities [21].See Figures (3 &4)

Figure (3) Construction of Composite Curves



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Figure (4) Definition of Pinch Point & control of ∆Tmin by sliding cold composite curve

2-3-2 Problem Table

It is an analytical method forestimation of minimum utilities and itsadvantage no need for especial utensilas graph paper and scissor.Steps of problem table method:• Divide the process into intervals• Limits of intervals are shifted

temperatures (hot streamstemperatures – 1/2 ∆Tmin) & (coldstreams temperatures + 1/2 ∆Tmin )

• Schematic representation of thestreams with a vertical temperaturescale took place through intervalboundaries (shifted temperaturesSi).See Figure (5)

• Enthalpy balances of every intervali, limited by shifted temperatures(Si & Si+1) can easily be calculatedas:

ΔHi = (Si–Si+1) (∑CPHot – ∑CPCold)i

• The positive magnitude ofenthalpy balance equation

named interval case as"surplus" while the negativenamed as "deficit" to produce afeasible network design basedon the assumption that all"surplus" intervals rejected heatto cold utility, and all "deficit"intervals took heat from hotutility.

• Beginning of external heatingof zero and accumulating ofintervals loads ascending todefine the highest deficit valuewhich represent minimum hotutility (QH).

• Cascading the process intervalwith (QH) with accumulating ofintervals loads will finalconclude minimum cold utility(QC) which is the load of lastinterval [22]

Pinch

Pinch point defined as the temperature correspondingto the shortest distance between hot and coldcomposite curves

Heat Recovery



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Figure (5) Vertical Representation of Streams on Shifted Temperatures Intervals

3- Design of Heat Exchanger Network

After classification the process intostreams with its thermal and physicalproperties, estimation of minimumutilities and defining pinch point.Now we can begin the more interestingpart which is HEN designing. Thepinch separates the process into twosubnetwork designs; above and belowpinch.To achieve maximum energy

recovery we must apply these nextsteps:

1. Do not transfer heat across thepinch point.

2. Do not use hot utility below thepinch point.

3. Do not use cold utility above thepinch point.

4. Begin with pinch match and moveaway.

5. Pinch matches obey this rule:· CPhot<=CPcold (above pinch)· CPhot>=CPcold (below pinch)

Algorithm of HEN designing is shown in Fig. 6

Figure (6) Sequences for designing HEN above pinch (a) and below pinch (b)

Si = (Thin – 1/2 ∆Tmin) Thin

Si+1= (TCout + 1/2 ∆Tmin) TCout

Si+2= (Thout - 1/2 ∆Tmin) Thout

Si+3 = (TCin + 1/2 ∆Tmin) TCin

hi

Cj



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4- Economic Analysis of HEN Design

By applying pinch analysis technique,we can get many alternative designsfor the same process. Economicbalancing by cost estimation of every

design helps us to reach to theoptimum one.Cost Estimation Equations are:

Ann.Overall Cost of HEN = Ann.Capital Cost + Ann.Operating Cost

Ann.Capital Cost = Capital cost of Units / life time

Capital cost of unit = ƒ [A] …… (A Ξ heat transfer area)

A = Q / U * ΔTlm

Where:Q = heat load of the unit1 / U = 1 / hi + 1 / hj …….. (hΞ heat transfer coefficient)

ΔTlm = (T1 – t2) – (T2 – t1) /ln (T1 – t2) / (T2 – t1)Life time = 6 yearsCost of piping = 8% Installed cost of Equipment

i

j

T1

t2

T2t1

v Capital cost:

Effect of ∆Tmin on heat transfer area and capital cost is shown as next diagram:

· Capital cost affected by number of units and minimum number of units for anyHEN can be estimated by next equation:

Nmin = Nh +Nc +Nu -1Where:

Nmin = Minimum Number of UnitsNh = Number of hot streamsNc = Number of cold streamsNu = Number of utilities

v Operating Cost

NuTotal Operating Cost = ∑ Qu * Cu

u=1

Where: Qu = Duty of utility U, kW



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Cu = Unit cost of utility U, $ / KW.yr

Nu = Total Number of utilities

5- Application of Pinch Analysis Technique on a case study

I applied Pinch technique on a casestudy with a plant flowsheet shown inFigure (7). Where:

• The feed is heated to the reactiontemperature.

• The reactor effluent is furtherheated, and the products areseparated in a distillation column.

• The reboiler and condenser useexternal utilities for controlpurposes.

• The overhead and bottomsproducts are cooled and sent forfurther processing.

Classification the process into streamswith its thermal and physical propertiesis shown in table (1)As a beginning for HEN design Irepresent the streams in the form ofgrid diagram as shown in Figure (8)where the actual consumption ofexternal utilities is:Heating load = 14000 KwCooling load = 13800 KwCost of hot utility = 140.2 $/ KW.yrCost of cold utility = 7.1 $/ KW.yr

H

H

C

C

H

C

Reactor FeedC1

Reactor EffluentC2

20 ᵒC 160 ᵒC

Reac

tor

120 ᵒC

OverheadProduct

H1

BottomProduct

H2

180ᵒC

260 ᵒC

20ᵒC

280ᵒC60ᵒC

Col

umn

Figure (7) A Typical Plant Flowsheet of the case study



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Table (1): Streams data of the case study

COver headproductH1

H2Bottomproduct C

180 C 20 C

280 C 60 C

C1ReactorFeed

20 CH

H

160 C

C2Reactoreffluent

120 C260 C

CP KW / C

45

30

40

60

Hot Pinch(150 C)

Cold Pinch(120 C)

Q =7200 KW

Q=6600 KW

Q=5600 KW

Q=8400 KW

Actual Cooling Load = 13800 KWActual Heating Load = 14000 KW

Figure (8) Grid Diagram of the Flowsheet

5-1 Estimation of Minimum Hot and Cold Utilities

· With ∆Tmin of 30ᵒC; minimum hot and cold utilities of the process estimated bygraphical composite curve as shown in Figure (9).

Where [QHmin = 4750 KW, QCmin = 4550 KW, Thp= 150 ᵒC and Tcp = 120ᵒC]

· The Analytical problem table method got the same results of minimum utilitiesand pinch point as shown in Figures (10, 11) and Table (2)



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Qhmin

4750 KW

Qcmin

4550 KW

Pinchpoint

Tmin = 30 C

0 5000 10000 15000 20000Enthalpy KW

300

250

200

150

100

50

0

Tem

pera

ture

C

Thp=150 C

Tcp=120 C

Figure (9) Estimation of Minimum Utilities by Composite Curve

TB = Si =Th – ½ TminTB = Si = Tc + ½ Tmin

TB + ½ Tmin CTB

1

2

3

4

5

6

7

275

265

175

165

135

45

35

5

H1

290

280

190

180

150

60

50

20

H2

C1

C2

Ts=120 C

Ts=20 C

Ts=280 C

Ts=180 C

Tt=20 C

Tt=60 C

Tt=260 C

Tt=160 C

CP=60

CP=40

CP=30

CP=45

C

Figure (10) Representation of Streams on Boundary Intervals



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Table: (2) Definition and Calculation of Enthalpy Change for Every Interval

BoundaryPinch pointThp=150 CTcp= 120 C

ΔH=600KW

2700

700

750

-3150

-50

-1350

ΔH=600KW

2700

700

750

-3150

-50

-1350

275 C

265

175

165

135

45

35

5

O KW

-600

-3300

-4000

-1600

-1550

-200

QHmin = 4750 KW

4150

1450

750

0

3150

3200

QCmin = 4550 KW

Figure (11) Estimation of minimum Utilities by Problem Table Algorithm through heat CascadePrinciple

5-2 Designing of Subnetworks for the Case Study

By applying pinch technique sequencesfor HEN designing as mentionedbefore in text 3, four subnetworksalternatives are concluded .Two above

Pinch. See Figures (12-a) & (12-b) andthe other two subnetworks weredesigned below pinch point. SeeFigures (12-c) & (12-d).

Temperature TC

IntervalNO Ti - Ti+1 ∑CPcold - ∑CPhot ΔHi

Surplus orDeficit

275

265

175

165

135

45

35

5

1 10 60 600 Deficit

2 90 30 2700 Deficit

3 10 70 700 Deficit

4 30 25 75 Deficit

5 90 -35 -3150 Surplus

6

7

10

30

-5

-45

-50

-1350

Surplus

surplus



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5-3 Synthesis of HEN Designs by Subnetworks Combination

By combination between every two subnetworks (above –below); I got fouralternatives HEN designs for the case study, Figures (13-a, 14-a, 15-a, and 16-a). Allthe designs achieved minimizing of utilities but differed in matching and number ofunits. As a result of combination; loops appear due to match repeating between thesame streams as represented in Figures by purple dashed line. In this case;modification of design by breaking the loop is required by replacement the 2 H.E with1 to minimize the units 'number and so on reduce capital cost as shown in Figures (13–b, 14-b, 15-b and 16-b) .The summary of the economic analysis of the modifieddesigns is shown in table (3); where HEN of Fig.15-b has the least cost.

Figure (13- a) First alternative HEN design, combination between (12-a) and (12-d)

H1

H2

C2

Thp = 150 C

Tcp = 120 C

1350 KW

1600 KW2301 KW

180 C

280 C 203.3 C

160 C

142.5 C180.85 C

QHmin = 4750 KW

260 C

CP KW/ C

45

30

40

60

C1

Pinchmatch

CPhot ≤CPcold

1300 KW

C1

Thp = 150 C

Tcp = 120 C

4550 KW

2700 KW

121.11 C 20 C

60 C

20 C

CP KW/ C

45

30

40

PinchmatchCPhot ≥Cpcold

H1

H2

C2

Thp = 150 C

Tcp = 120 C

1350 KW

3901 KW

180 C

280 C

160 C

185. C

4500 KW

260 C

CPKW/ C

45

30

40

60

C1

Pinchmatch

CPhot ≤CPcold

153.75 C

250 KW

4000 KW

C1

Thp = 150 C

Tcp = 120 C

1850 KW

2700 KW

61.1 C 20 C

60 C

20 C

CP KW/ C

45

30

40

PinchmatchCPhot ≥Cpcold

1300 KW

H1

H2

1350 KW

1600 KW2301 KW

180 C

280 C 203.3 C

160 C

142.5 C180.85 C

QHmin = 4750 KWQCmin = 4550 KW

260 C

CP KW/ C

45

30

40

60

C1

Thp = 150 C

Tcp = 120 C

4550 KW

2700 KW

121.11 C 20 C

60 C

20 C

CP KW/ C

45

30

40

Qhmin=4750 KW

No of Units = 7

No of Units = 7

Qcmin= 4550 KW

Qcmin= 4550 KWQcmin= 4550

Figures (12-a) & (12-b) Subnetworks above pinch

Figures (12-c) & (12-d) Subnetworks below pinch



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Figure (13-b) First alternative HEN design after loop breaking

Figure (14-a) Second alternative HEN design, combination between (12-b) and (12-c)

Figure (14-b) Second alternative HEN design after loop breaking

1300 KW

H1

H2

1350 KW

2301 KW

180 C

280 C 203.3 C

160 C

142.5 C180.85 C

QHmin = 4750 KWQCmin = 4550 KW

260 C

CP KW/ C

45

30

40

60

C1

4550 KW

4300 KW

121.11 C 20 C

60 C

20 C

C2

4000 KW

H1

H2

C2

Thp = 150 C

Tcp = 120 C

1350 KW

3901 KW

180 C

280 C

160 C

185. C

4500 KW

260 C

CP KW/ C

45

30

40

60

153.75 C

250 KW

C1

1850 KW

2700 KW

61.1 C 20 C

60 C

20 C

5350 KW

H1

H2

C2120 C

3901 KW

180 C

280 C

160 C

185. C

4500 KW

260 C

CP KW/ C

45

30

40

60

153.75 C

250 KW

C1

1850 KW

2700 KW

61.1 C 20 C

60 C

20 C

No of Units = 7QHmin = 4500 + 250 = 4750 KWQcmin = 2700 +1850= 4550 KW

No of Units = 6

No of Units = 6QHmin = 4500 + 250 = 4750 KWQcmin = 2700 +1850= 4550 KW



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Figure (15-a) Third alternative HEN design, combination between (12-b) and (12-d)

Figure (15-b) Third alternative HEN design after loop breaking

Figure (16-a) Fourth alternative HEN design, combination between (12-a) and (12-c)

1300 KW

H1

H2

C2

1350 KW

3901 KW

180 C

280 C

160 C

185. C

4500 KW

260 C

CP KW/ C

45

30

40

60

153.75 C

250 KW

C1

Thp = 150 C

Tcp = 120 C

4550 KW

2700 KW

121.11 C 20 C

60 C

20 C

2650 KW

H1

H2

C2

3901 KW

180 C

280 C

160 C

185 C

4500 KW

260 C

CP KW/ C

45

30

40

60

153.75 C

250 KW

C1

4550 KW

2700 KW

121.11 C 20 C

60 C

20 C

4000 KW

H1

H2

1350 KW

1600 KW2301 KW

180 C

280 C 203.3 C

160 C

142.5 C180.85 C

QHmin = 4750 KWQCmin = 1850 + 2700= 4550 KWNo of Units = 7

260 C

CP KW/ C

45

30

40

60

C1

1850 KW

2700 KW

61.1 C 20 C

60 C

20 C

4750 KW

No of Units = 7QHmin = 4500 + 250 = 4750 KWQcmin = 4550 KW

No of Units = 6 QHmin = 4500 + 250 = 4750 KWQcmin = 4550 KW

Thp = 150 ᵒC

Thp = 120 ᵒC



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Figure (16-b) Fourth alternative HEN design after loop breaking

Table (3) Economic Analysis of the HEN Designs

5-4 Revamping of the Case Study through Heat Recovery Technique

As a new design (grass-root) for the case study; all the last alternatives HEN designscan be used according to availability and operability conditions. While the revampingtechnique depends on choosing the least alterations HEN design compared to theexisting. That's guarantees minimizing added capital cost. So The HEN design ofFigure (14-b) is our pivot for existing process revamping. The modification is onlyadding two heat exchangers represented by yellow circles as shown in Figure (17).Maximum energy recovery realized where external heating reduced from 13800 to4750 KW and external cooling reduced from 14000 to 4550 KW. The summary ofeconomic analysis due to revamping is shown in Table (4); where the net saving isaround 1,400,000 $/y

20 o C 160 ᵒC

120 ᵒC

HH1

H2

C1

C2

4750 KW

3651 KW

5600 KW 1600 KW

2950 KW

55.6 o C 20 ᵒC

60 ᵒC158.3 o C

180.6 ᵒC

180 ᵒC

280 ᵒC

260 ᵒC

CP KW/ᵒC

45

30

40

60

Figure 13-b Figure 14-b Figure 15-b Figure 16-b

Capital Cost$/y

141665.7 134423.7 130550.9 168335.2

Capital Cost*C.I $/y

153000.0 145177.6 140995.0 181802.02

Cost of Hotutility $/y

665950 665950 665950 665950

Cost of Coldutility $/y

32305 32305 32305 32305

Operating Cost$/y

698255 698255 698255 698255

Overall Cost$/y

851255 843433 839220 880057

QHmin = 4750 KW, QCmin = 4550 KW, NO of Units = 5



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H

H

C

C

H

C

Reactor FeedC1

Reactor EffluentC2

20 C 160 C

Reac

tor

120 ºC

OverheadProduct H1

BottomProduct H2

180 C

260ºC20 C

150 ºC 60 ºCC

olum

n

H.E

5350 KW153.75 C

61.1 C

1850 KW

250 KW

185 ºCH.E

3901 KW4500 KW

2700 KW280 ºC

QHact.= 13800 KW, QHmin = 4750 KWQcact.= 14000 KW, Qcmin = 4550 KW

Figure (17) The flowsheet of the case study after revamping

Table (4) Economic Analysis for Revamping the Case study



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Conclusion

This study is a summary of pinch analysis to design Heat Exchanger Network HENstep by step. Designing of HEN is an effective technique for maximizing energyrecovery and so on minimizing external utilities. It's proved its validity throughapplication on a case study where percentage of utilities' saving reached to (65% &68%) for hot utility and cold utility respectively. The process revamping got excellentresults where maximization of saving realized by least alterations represented inadding two heat exchangers and the net annual saving reached to 1,382,893 $ which isgreat.

Recommendation

This technique is recommended for any chemical process where energy saving is aninternational target for all countries (rich or poor). We need to reduce energyconsumption to save money and protect environment.

Acknowledgment

The author acknowledges Egyptian Petroleum Research Institute for continuouslysupport.

Nomenclature

Qhmin: Minimum hot utility (kW)Qcmin: Minimum cold utility (kW)∆Tlm: Minimum temperature difference log meanThp: hot pinch point (ᵒC)Tcp: cold pinch point (ᵒC)TB: Boundary temperature (ᵒC)Ts: Supply temperature (ᵒC)Tt: Target temperatureA: heat exchanger area (m2)hi: heat transfer coefficient of hot stream (kW/m2 ᵒC)hj: heat transfer coefficient of cold stream (kW/m2 ᵒC)U: Overall heat transfer coefficient (kW/m2 ᵒC)Nmin = Minimum Number of UnitsNh = Number of hot streamsNc = Number of cold streamsNu = Number of utilitiesH: enthalpy (kW)CP: heat capacity flow rate (kW/ᵒC)T1: Inlet temperature of hot stream (ᵒC)T2: outlet temperature of hot stream (ᵒC)t1: inlet temperature of cold stream (ᵒC)t2: outlet temperature of cold stream (ᵒC)∆Tmin: minimum temperature difference approach

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Step by Step for Designing an Optimum Heat Exchanger Network · Pinch Analysis (PA); one of the...

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