of the lSth Symposilun
of Malaysid ChemlcalElaileeB
Proceedings
A STUDY OF D}NAMIC BEHAVIOUR OF PROTON
EXCHANGE MEMBRANE FUEL CELL STACK
RoslinaAbdullah', Hxmdani Saidi
Unit,Udvelsili TeknologiMalaysia,Ciiy Campuq
Membrane
Reseaxch
54100KualaLumpur,Nlalaysia.
'Co(espondingauthor.Phone:+603-26154598,Fa{: +603'26945021
Emailiaroslina@ur'nkl.utm.my
ABSTR-{CT
The proton erchange membran€tue1 cell (PEMFC) stack has shown promise as the
leading candidatefof use as a non-polluting power source.lt dischaxg€swater as wrste,
opemtesat low temperaturesfor quick start-up,andusesa solid Pol]'ner as an €lectrolyte
which reducesboth consLrclion and safetycomplications.In order io study the dynamic
b€haviow of PEMFC stack, dynamic model is d€veloped using MATLAB, a high
performanceteclmicat computing sofilvareThe model is basedon pbysical laws having
cl€ar significant in replicating the tuel ceil system and can easily be used lo set up
differefi operationalsiralegi€s-It consistsof several submodelswhich are integnted to
€ach other. The periomances of the tuel cell stack such as thermodvnamicefficiency,
pressure and humidity profile afe also d€scrib€d As a whole, the outpul from the
aswell as
canbe variedto meettheneedsof individualinvestigations
modelingtechnique
for the disiribution results.
K€ywordsrBehaviourOf PEMFC,DynamicMode| lnt€grationOf SeveralSubmodels,
Performance,Individual lnvestigationAnd Dist.ibuiion Results.
I lNl RoDt ( Tlo\
Fuel cel1sconstit te lhe most efficient energytransducersknown to modem technology;
they arc rwice as €fficient as batte es.Fu€l cells are electrochemicaldeviceslhat convef
a tueL'senergydirectly to elect.ical ene.gy,operaiingmuch like coniinuousbatlerieswhen
suppliedwith ftel to the anode(negativ€elecirode)and oxidant (e.9, ai) to the cathode
(positive electode). Forhrnately, fliel cells do not follow the naditionai extraction of
energyin the form of combuslionheat, conversionof heat energyto mechanicalenergy,
and finally tuming mechanicalenergyinto electricity- Instead,th€y chemically combine
the moleculesof a tuel and oxidizer without buming, directly producingelecrricitv and
dispensingwith the inefficienciesandpollution offiaditional combustiotr.
The dev€lopmentof tuel cell technologyis catatyzedby the fact that the global energv
use is ircreasing steadjly and eNironnenlal problems related to energyproduction and
transportationare growing.At the same time, the efficienci€s of conventional energy
conv€rsion process€s are approaching their thermodynamic limils. Morc efficient
solutionsarc thus needed.
The efficiency of tuel cels is not limited by the Camoi limitations of heat engines
High efficiency makes fuel cells attractive for a iarge variety of applications,inchding
pow€r production,residentialenergysyst€msandpossibly
road vehicles,decentralised
compactsu€
In matryapplicalions,
like pofiableelectronics.
even smallerapplications
andthe lack of1ocal emissionsalso increasethe attractivenessoffuel cells
Chemical
Engineers
Proce€dhgs
orlhe18thS)dposlunofMalaysia!
2 METHODOLOGY
2.1DYNAMIC SIMULATION
To study the dynamic performance of tuel cell stack, the modeling methodology
incoiporates an explicit finite difference scheme.For lhis puryose,lhetuel cell stack is
divided ilto elementswhos€ size is determinedby the desiredaccuacy ofxhe resultsand
the num€rica1stability of the calculations.Thepropefiies ol each computationalelement
are assumedbe spatialty unifom and changewith time. The finite differcnce schemeis
usedio calculate the temperatureonly.The remainingpropediesar€ calculaledusing ihe
temperatureand various relationships.This requiresthal the electrochemicalkiletics and
gasdlnamic be treatedwith st€adystatefonnulations.Assumptionis madelo simplify the
resulting equaiionsand reduc€the computationalrequLremenlsofmodel developedrlsing
thismethodologyThe srability citerion, an expressionusedto detenninethe sizerangefor the el€ments
and time stepsneededfor numerical stability, is derived using an energybalanceon an
is
element.Theexpression
At :!
ioVC) iil
Irn c" ): rm(,r. -Il ,
R) l
wiih At is the time slep usedfor the finite differenc€calc lations.pis the averagedensity
ofthe elementma1erial,V is the voiume of the elemed while C is the themai capacitance
ofthe elementmatenals. C" and m are the specific heat at constantpressureand mass
flow rate respectivelyofthe fluids in the elementand R representlhe thennal resNtances
As seenin equation(1), L'restabilityofthe fidte dif€rence
of the thennalandsurface.s.
caiculationsdependson material properiies,fluid proPedies(if any existsin the element),
elemelr.andr'r,e
ot l\e sunourding
lhe es,sunce
2.2 FUEL CELL SYSTEMMODEL
It r€q.rires four flow systems(figure l) which are hy&ogen supply system,airsupply
system,cooling systemandhumidificalion system. To simplified the model,it is assumed
that the siack tempemtureis constant.A11the variablesassociatedwith the lumped anode
volume are denotedwith a subscripi(an.).The cathodesupply manifold (sm) lumps a1lthe
volumes associatedwith pipes and connection between the compressorand the stack
cathode(ca) flow field. The cathoderetum manifold (1m)representsthe llunped votune
ofpipes downstreamof the stack cathode.Another assumplionis that the properliesof the
flow €xiting a volume are the sameas lhoseofthe easinside the volume. Subscripts(cp)
ard (cm) denote variables associatedwi$ the compressor and compressor motor,
rcspectivelY.
fonrt]l5d
I cP,
!rumdrns
I \\',;,,,,
FIGTIR! 1. Componentsandvoiumesin tuel ce11rcaciantsupply system
The power of ihe tuel ce1] stack dependson cunent drawn from th€ stack and stack
voltage. The tuel cell voltage is a tunction of currenl, reactan! partial pressule,
.1-5l
:ii
Chemical
Engineeis
Proceedlngs
offie 18thSymposnu!
of Malaysian
lemperatureand membranehumidity. As the curaentis drawr ftom the tuel c€11,oxygen
andhydrogenareusedin the r€action.Waterandhe3t are also generated.
2,3 FIIEL CELL STACKMODEL
The ftel cel stack model containsfour interacting sub-modelswhich are stack voltage
mod€I, anode flow model, cathodeflow modei and membranehydration mode1.It is
assumedthat the stack temperatureis constantat 80"C (353.15 K). The voltage model
containsan equationto calculatestackvoltage basedon fue] cel1pressure,temperature,
reactantgas partial pressureand membranehumjdity. The dynamically varying pressure
andrelative humidiry of the reactantgasflow inside the stackflow channelsare calculated
in the cathodeand th€ anodeflow models.
2.3.1StackYoltageModel
The stackvoltage is calculatedas a functior of stack current, cathodepressure,reactani
pafial Fessures,tuel cell temperatureandmembranehumidily. Fuel cell voltageis
Vfc =E-Vact-Vohm
(:2)
Vconc
ohmicand
wilh E is the opetrcircuitcircuitwhileVact, Vdhm and Vconcareactivation,
overvoltages,
which reprcsentlossesdue to variousphysicalor chemical
concenirarion
factors.
2.3.1.1ActivationOvervoltage
It arisesffom the need to move elecfons, to break , and to form chemical bond at the
cathodeand anode - The relation between the activation ovewoltage and the cunent
density is describedby rhe Tafel equationwhich is however not valid for small curent
d€nsiry.Therefore,the Tafel equationis approximatedby expression
vacr:vo
Va (l - e-cri)
(3)
The calculationfor Vo and Va is basedon eiectrochenical,kinetics and therrnodlnamic
2.3.1.2Olmic Overvoliage
It arises&om the rcsistanceof the polymer membraneto the 'transfer of protons' and the
ofthe electlodes
andconaollerplatesto the 'tansfer ofelectrons'.Th€voltage
resistance
drop that conespondsto the otmic resistanceis proponional to the cu(ent density
( 1)
v *,=i & m
with i is curent andR.bnis ohmic resistance
2.3.1.3 Concentration
Overvotag€
It resultslrom the increasedloss at high curent density)€.g., a sigificant &op in reaclant
concentation due to both hig:hreacrantconsumptionand he3d loss ar high flow laie. An
equalionthat approximatesthe voltagedrop from concentrationlossesis given by
vconc = i ( c2 x i,/i ,"")"r
(5)
This ierm is ignored is some models,becauseil is not desirableto operatethe stack at
regionswhere Vconc is high. However, this term needsto be included, if the siack will
operateat high cunent density. c2, c3 and i.", are constantsthat d€pendon temperature
andreactantpartial pressure.
+54
ChemicalEnsineen
of the l EthSynposiunof Nlalaysian
Proceedinss
2.3.2Cathode
Flow Mod€i
Thjs model capturesthe cathode air flow behavior, and is deveiop€dusing the mass
conveffationprinciple and the thernodlnamic and psychometricpropertiesof air. Several
assumptionsare made.First, all gasesobey ideai gas law and the temperatur€ofthe air
insidethe cathodeis equalto the stackt€mpemturewhich is 80oC.Ii shouldbe noted that
lhe propeniesofthe flow exiiirg the cathodesuch as temperature,presiule and humidiiy
are assumedto be the sameas those inside the cathode.Fufhermore, wh€n the relative
humidity of the gasexceeds100%,vapor condens€sinto ihe liquid for,n The iiquid water
doesnot leav€the siack andwill either evapoGtewhen the humidiry dropsbelow 100%or
accumulatein the cathode.
2.3.3AnodeFiow Model
This nod€l is qrite similar to the cathodeflow model. First assumptionis pure hydrogen
gasis assumedto be suppliedto rhe anodefrom a hy&ogen tank. Nexi, the inlel hyihogen
flow is assumed ro have 100% relative hunidiry. Hy&ogen flowmte can be
instanraneouslyadjusled by a valve while maintaining a minimum pressue difference
acrossthemembrane.
2.3.4Membrane
HydmtionModel
The water transportaffoss membraneis achiv€dthrough two distinct phenomenalirst,
the €lectro-osmolic drag phenomenonis rcsponsible for the water molecules dragg€d
acrossthe membmneftom anodeto cathodeby the hydrogenproton. Second,the gadient
of water concentrationacrossthe membran€due to differencein humidity in anodeand
cathodegasescauses"back-diffllsion"ofwater from the cathodeto anode2.4PERFORMANCE
The calculaiion for themodynamic efficiency of the tuel cell is accomplishedby dividing
the net electrical energyproducedby the energy value of the tuel used ro produce the
electricity. The ner eiectdcalenergyis calculatedby numericallyintegratingihe net power
with respectwith time. The modeling allows for €ither the higher or lower haeling value
of thefuel to be usedfor rhiscaiculation.
n=
{P
dt
(6)
with rl is the themodlnamic efficiency of the stack,P is ihe net power prcducedby ihe
stack,lry is the heatingvalu€ of the fuel andm is the massofrhe fuel usedto producethe
2.5PROPERTIES
Pressureandhumidiry plofiles are computedusing the design of the bipolarplates,output
from the at flow, the ideal gas equationand psychometricrelationship The bipolar plate
desigrl output fiom xhe air flow and the ideal gas equation are used to calculate ihe
densit and velocity of the gasesin the flow channei; both of which are required to
calculatethe pressuredrop.
2.6 CONTROLSYSTEM
The pueose of control systemis io regulalesthe enxirestack system lt determinesthe
amounlof processgasrequiredto meetpaticular load as well as calculalesthe amountof
eneryyusedto deliver the gasto the tuei cells. It is also calculatesthe amounl ofcooling
flow requiredby the stackto maintain the desirediemperaturc.If the stackis pressurized,
th€ energyrequted to pressurizethe syslemwili be calculated.The amountofthe process
gas requircd and the amount ol the water producedby the tuel cell stack is calculated
using the electrochemicalequalions
..rl
olMalavsianChemicalEn_qneds
of the lSth Svmposium
Proceedings
3 RESULT
*g**g*''*r**e**+*
#F{*r{*trtil1#':tx*r'h
resuLl
showsan exampleof distribuhon
sf:!qI}91!9ll!9q
T AB IE l . Stn e l e \a | u ere suLtfromrhemodel
Result
r'-l
- Pl- r t "1r l
1.6381L/s
0.40631L/s
4't.2%
en' c ler c v
7.468 kW
AmP
155.99
\l J \i 1 r 4 c t re rt
*
''
C 1,,.
A mor
a'
l'{GLtu 2 Drsnrbrror esJ'I HearoLrDuL
rnclionofcunerL
4 CONCLUSION
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Since
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"vtt"-. ,r'" r'"1
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rnodelwill prove to be verv usetul
".11
BIBLIOGR-A.PHY
!3iJsi'ii"3'h"t':#Ti"qi:3]-:i:'#'fr:
B:*::,H:1,',;:?1,,'+:.T#[:ff
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Chemical
Eryiree6
Proceedings
ol the18thSymposium
of Malaysjan
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,ii