No. of Unitsfg Target

7/29/2019 No. of Unitsfg Target

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No.ofunitstarget Module:04 Lecture14

Module 04:Targeting

Lecture14: No.ofunitstarget

KeyWords:HEN,Subset,Loop,Separatecomponent,MER designThefixedcostofaheatexchangernetwork(HEN)dependsuponthenumberofheatexchanger

itemploys.

Thus,

there

exists

apossibility

that

aHEN

with

minimum

no.

of

heat

exchanger

will

cost less. Thus there exists a strong incentive to reduce the number of heat exchangers (

matchesbetweenhotandcoldstreams)inaHEN.Thefirststeprequiredforthisprocessforits

initiation isto identifythenumberofheatexchangersaHENwillrequirefromthenumberof

Hot,ColdandUtilitystreamsithandles.

Letusexplaintheproblemwithanexample.Fig.4.23showstheflowsheetofapalmoilrefinery

[1,2].

Fig.4.23Flowsheetofapalmoilrefinery


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Theflowsheetusesthreeheatexchangers,threecoolersandfourheatersmaking10units in

all.Nowthequestioniswhether10unitsaretheminimumnumberofunits,oradesignercan

reduceit withouthamperingthefunctionalityoftheprocess?

ThestreamtablefortheaboveproblemisgiveninTable4.14:

Table4.14 Streamdataforpalmoilrefinery(Fig.4.23)forTmin=10C

Stream

SerialNo.

StreamType CP

(KW/K)

ActualTemperatures Enthalpy,H

kW

Ts(0

C) Tt(0C)

1 Hot1 10.99 120 86 373.66

2 Hot2 6.04 260 160 604

3

Hot3

13.13

230

702100.8

4 Hot4 6.56 160 50 721.6

5 Cold1 11.83 50 97 556.01

6 Cold2 14.89 104 124 297.8

7 Cold3 5.69 86 230 819.36

PTAanalysisoftheproblemshowsthatitisathresholdproblemandneedsonlycoolingandno.

heating. The minimum cooling load required for the above system computed using PTA is

2126.89. The heat loads of different streams along with cold utility load is shown within the

circles representing the streams in Fig.4.24. The predicted cold utility load is also shown

similarly.

Coldutility

2126.89kW

Hot1

373.66

kW

Hot2

604kW

Hot3

2100.8

kW

Hot4

721.6

kW

Cold1

556.01

kW

Cold2

297.8

kW

Cold3

819.36

kW

721.697.76

297.8306.2249.81123.85

2003.04

HX2 HX1HX3HX4HX5HX6HX7

Fig.4.24 Schematicmatchingofheatloadsforstreamtabledata,Table4.14


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Notethatthecomplete system is inenthalpybalance(i.e.thetotal loadofcoldstreamsplus

cold utility is equal to the total load of hot streams). If we presume that temperature

constraintswillallowanymatchtobemadebetweenhotstreamsandcoldstreams including

cold

utility,

then

we

can

match

the

whole

of

cold

streams

3

(total

819.36

units)

with

Hot

streams3&4, leavingaresidualheatloadof2003.04unitsonHot3.MatchingHot3&Hot4

withCold3 andmaximizing the loadon thismatchso thatCold3& Hot4 istickedoff the

2003.4residualheatavailablewithHot3 issent tocoldutilitywhichrequires2126.89units.

Cold2 istickedoffbymatchingwithHot2 leaving306.2unitsofheat in it. Theremaining

heatinHot2alongwith249.81unitsofheatfromHot1ispassedtoCold1toTickitoff. This

leaves 123.85 units of heat with Hot1 which is passed to cold utility. This heat along with

2003.04unitsofheatfromHot3ticksoffcoldutility.Sofollowingtheprincipleofmaximizing

loads,that istickingoffstreamorutility loadsorresiduals, leadstoadesignwithatotalof

seven matches (connections between streams and utilities show matches are denotedby HX

withanumber).This is infact istheminimumforthisproblem.Noticethat it isone lessthan

thetotal

number

of

streams

plus

utilities

in

the

problem.

Thusitcanbeshownthat:

umin=N1 .( 4.8)whereumin=minimumnumberofunits(includingheatersandcoolers)and

N=totalnumberofstreams(includingutilities)


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Infact,itisusuallypossibleinheatexchangernetworkdesigntofindauminsolution.However,

certain refinements toEq.4.8 are requiredasdiscussedbelow tobroaden itsapplicability. In

Fig.4.25 (a), problem having two hot streams ( H1 & H2), two cold streams(C1& C2), Hot

utility(HU)andColdutility(CU)isshown.Inthiscase,

putting matches as before by ticking off loads or residuals leads to a design withN 1 unitswhich satisfy Eq.4.8 However, in Fig4.25(b) a design is revealed having one unit less. The

justification for the fact that the number is less than minimum is not hard to find. Even as

overalltheproblemisinenthalpybalance, thesubsetcontaining streamsH2,C1andCU are

inenthalpybalance.SimilarlyHU, H1andC2areinenthalpybalance(thisisaknownfactas

the total problem is in load balance).This means that for the given stream data set we can

designtwo

completely

separate

networks,

employing

the

Eq.4.8

to

each

subset

individually.

Thetotalnumberofunitsfortheoverallsystemistherefore(3 1)+(3 1)=4units,whichis one

lessthanfoundinFig.4.25(a).Thisconditioniscalled subsetequality,thisappearswhenfora

given stream data set it is possible to identify two subsets which are separately in enthalpy

balanceandthuscanformseparatenetworks.Sincetheflowsheetdesigner,cancontrolofthe

quantityoftheheatloadsinhisplanttosomeextent,itispossibletochangetheheatloadsso

as to create subset equality and thus create an opportunity to save a unit. Finally, in

Fig.4.25(c)amatchingscheme isshownwhichrequires oneunitmorethantheschemeshown

Loop

Fig.4.25 Subsetandloops duringmatching

HU

40

H1

80

H2

160

C1

90

C2

120

CU

70

40 80 90 70

(b)

HU

40

H1

80

H2

160

C1

90C

2

120

CU

70

Y 30Y 90 70

(c)

40Y 50+Y

HU

40

H1

80

H2

160

C1

90

C2

120

CU

70

5040 30 90 70

(a)Matches=05 Matches=04

Matches =06


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in Fig.4.25(a),thenewextraunithasbeenintroducedasthematchbetweenHUandC2 which

introduces aloop in thesystem. It issobecauseonecan traceaclosedpath through the

networkstartingfrom,sayHU,theloopcanbetracedtoC1,fromC1toH1,fromH1toC2,

andfromC2backtoHU.Though,thepresenceoftheloopintroducesanelementofflexibility

into the design it increases number of units in the system. Suppose the new extra match,

betweenHUandC2,isassignedaloadofYunits,thenthroughenthalpybalance,the loadonthe

match

between

HU

and

C1has

to

be

40

Y,

between

C1and

H

1,

50

+Y,

and

between

H

1

andC2, 30Y.FromFig(c)itcanbeinstitutivelysaidthatYcanvaryfrom0toavalueof30.WhenY=0 thematchbetweenHUandC2vanishesand whenitis30thematchbetweenH1

and C2 disappears. The flexibility introduced by loops is many times useful, particularly in

revampstudiesandcleaningoperations.

ThefeaturesdiscussedaboveandshowninFig.4.25(a),(b)&(c) canbeconvertedintoa

formulatocompute numberofheatexchangeunits, usingtheEulersGeneralNetwork

theoremappliedtoheatexchangernetwork:

umin=N+LS (4.9)where;

u=numberofheatexchangeunits(includingheatersandcoolers),N=numberofstreams(includingutilities),L=numberofindependentloops,andS=numberofseparatecomponentsNormallyadesigner wanttoavoidextraunitsbyreducingLtozero. Unlessoneislucky,there

willbenosubsetequalityinthestreamdatasetandthusthevalueofswillbe1. Thisleadsto

thenumberofunitstargetingequation:

umin=N1 (4.8)

Inthedesignofheatexchangernetworkstechniquesdiscussedabovewillbeusedtoreducethe

number of heat exchangers by allowing small energy penalty at various sections of the

networkfor tradingoffenergyagainstcapitalcost.

Examples:Afivestreamproblemistakenupcomputeno.ofunitstarget.

Table4.15Afivestreamproblemforno.ofunitstargetforTmin=10C

Stream

Number

Stream

Type

Heat Capacity

FlowRate

Source

Temperature

Target

Temperature

H,kW

(kW/

0C)

(0C)

(0C)

1 HOT1 147.74 70 10 8864.34

2 HOT2 165.85 60 33 4478

3 COLD1 50 57 60 150

4 COLD2 215 41 60 4085

5 COLD3 194.74 10 30 4479

UsingPTA theminimumhotandcoldutilitiesarecomputedasgivenbelow:


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Hotutility(HU) =822.61kW

Coldutility(CU) =5450.95kW

HotPinchTemp. =60C

Coldpinchtemp. =50C

Fromthe

table

it

appears

that

ifthe

heat

load

of

Cold

3can

be

brought

down

to

4478

there

is

a

chanceforsubsetequalityresultingS=2and therebydecreaseofno.ofunitsbyone.Forthis

case:N=7(includingHUandCUstreams);L=0andS=2

umin= N+LS=7+02=5

IfsubsetequalityisnotcreatedthenN=7,L=0andS=1.Forthiscase

No.ofunitsare:

umin=7+01=6

Targeting for the minimum number of units for a MER design

HoweveriftheaboveequationEq.4.8isappliedtoamaximumenergyrecovery(MER)design

the results will be somewhat different. For this purpose the problem of Table 4.15 is

considered. In a MER design the pinch divides the problem into two heat balanced regions.

Since these balanced regions are independent, numbers of units targeting should be applied

separatelytoeachregionasshownbelow:


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Fig.4.26showsthestreamlayoutaboveandbelowthepinch.

Thustotaluminforthenetwork=3+4=7

IfPinch

division

is

not

considered

then

no.

of

streams

including

hot

and

cold

utilities

is

=7,

S=1andL=0.

Thus,thetotalno.ofunitsfornonMERdesign=umin=7+01=6

ThusitcanbeprovedthatuminuminMER

Thenumberofunits obtained intargetingfortheMERdesignismorethatuminduetothefact

that streamsthatcrossthepincharecountedtwiceinMERdesign.Theconclusionisthatthere

isatradeoffbetweenenergyrecoveryandnumberofunitsemployedinaMERdesign.Howto

reduceno.ofunitsinaMERdesignwillbeexplainedwhenMERdesignwillbediscussed.

Fig.4.26 Process hotandcoldstreamsandutilitystream inaboveandbelowpinch

1

2

3

4

5

70C 10C

33C

33C

57C60C

60C

10C

60C 41C

HotPinch=60C Cold Pinch=50CHU

CU

AbovePinch Below Pinch

Umin=41=3 Umin=51=4


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References

1. K.K.Trivedi,E.Fouche,K.E.Parmenter,ProcessEnergyEfficiency:PinchTechnologyinHandbookofEnergyEfficiencyandRenewableEnergy,CRCPress,BocaRaton,2007,pp.

1511530.

2. SharifahR.WanAlwi,ZainuddinA.Manan,STEPAnewgraphicaltoolforsimultaneous

targeting

and

design

of

aheat

exchanger

network,

Chemical

Engineering

Journal162(2010)106121

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