No. of Unitsfg Target
Transcript of 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