A study of dynamic behaviour of proton exchange membrane fuel cell stack

Proceedings of the lSth Symposilun of Malaysid Chemlcal ElaileeB

A STUDY OF D}NAMIC BEHAVIOUR OF PROTON

EXCHANGE MEMBRANE FUEL CELL STACK

Roslina Abdullah', Hxmdani Saidi

Membrane Reseaxch Unit, Udvelsili Teknologi Malaysia, Ciiy Campuq 54100 Kuala Lumpur, Nlalaysia.

'Co(esponding author. Phone: +603 -261 54598, Fa{: +603 '26945021 Emaili aroslina@ur'nkl.utm.my

ABSTR-{CT

The proton erchange membran€ tue1 cell (PEMFC) stack has shown promise as the leading candidate fof use as a non-polluting power source. lt dischaxg€s water as wrste, opemtes at low temperatures for quick start-up, and uses a solid Pol]'ner as an €lectrolyte which reduces both consLrclion and safety complications. In order io study the dynamic b€haviow of PEMFC stack, dynamic model is d€veloped using MATLAB, a high performance teclmicat computing sofilvare The model is based on pbysical laws having cl€ar significant in replicating the tuel ceil system and can easily be used lo set up differefi operational siralegi€s- It consists of several submodels which are integnted to €ach other. The periomances of the tuel cell stack such as thermodvnamic efficiency, pressure and humidity profile afe also d€scrib€d As a whole, the outpul from the modeling technique can be varied to meet the needs of individual investigations as well as for the disiribution results.

K€ywordsr Behaviour Of PEMFC, Dynamic Mode| lnt€gration Of Several Submodels, Performance, Individual lnvestigationAnd Dist.ibuiion Results.

I l N l R o D t ( T l o \

Fuel cel1s constit te lhe most efficient energy transducers known to modem technology; they arc rwice as €fficient as batte es. Fu€l cells are electrochemical devices lhat convef a tueL's energy directly to elect.ical ene.gy, operaiing much like coniinuous batleries when supplied with 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 energy in the form of combuslion heat, conversion of heat energy to mechanical energy, and finally tuming mechanical energy into electricity- Instead, th€y chemically combine the molecules of a tuel and oxidizer without buming, directly producing elecrricitv and dispensing with the inefficiencies and pollution offiaditional combustiotr.

The dev€lopment of tuel cell technology is catatyzed by the fact that the global energv use is ircreasing steadjly and eNironnenlal problems related to energy production and transportation are growing.At the same time, the efficienci€s of conventional energy conv€rsion process€s are approaching their thermodynamic limils. Morc efficient solutions arc thus needed.

Proce€dhgs orlhe 18th S)dposlun ofMalaysia! Chemical Engineers

2 METHODOLOGY

2.1 DYNAMIC SIMULATION

To study the dynamic performance of tuel cell stack, the modeling methodology incoiporates an explicit finite difference scheme. For lhis puryose,lhe tuel cell stack is divided ilto elements whos€ size is determined by the desired accuacy ofxhe results and the num€rica1 stability of the calculations.The propefiies ol each computational element are assumed be spatialty unifom and change with time. The finite differcnce scheme is used io calculate the temperature only.The remaining propedies ar€ calculaled using ihe temperature and various relationships. This requires thal the electrochemical kiletics and gas dlnamic be treated with st€ady state fonnulations. Assumption is made lo simplify the resulting equaiions and reduc€ the computational requLremenls ofmodel developed rlsing this

methodology-The srability citerion, an expression used to detennine the size range for the el€ments and time steps needed for numerical stability, is derived using an energy balance on an element. The expression is

At :! ioVC) iil

I r n c " ) : r m ( , r . - I l , R ) l

wiih At is the time slep used for the finite differenc€ calc lations.p is the average density ofthe element ma1erial, V is the voiume of the elemed while C is the themai capacitance ofthe element matenals. C" and m are the specific heat at constant pressure and mass flow rate respectively ofthe fluids in the element and R represent lhe thennal resNtances of the thennal and surface.s. As seen in equation (1), L're stability ofthe fidte dif€rence caiculations depends on material properiies, fluid proPedies (if any exists in the element), l h e e s , s u n c e o t l \ e s u n o u r d i n g e l e m e l r . a n d r ' r , e

2.2 FUEL CELL SYSTEM MODEL

It r€q.rires four flow systems (figure l) which are hy&ogen supply system,air supply system, cooling system and humidificalion system. To simplified the model, it is assumed that the siack tempemture is constant. A11 the variables associated with the lumped anode volume are denoted with a subscripi (an.). The cathode supply manifold (sm) lumps a1l the volumes associated with pipes and connection between the compressor and the stack cathode (ca) flow field. The cathode retum manifold (1m) represents the llunped votune ofpipes downstream of the stack cathode. Another assumplion is that the properlies of the flow €xiting a volume are the same as lhose ofthe eas inside the volume. Subscripts (cp) ard (cm) denote variables associated wi$ the compressor and compressor motor, rcspectivelY.

FIGTIR! 1 . Components and voiumes in tuel ce11 rcaciant supply system

The power of ihe tuel ce1] stack depends on cunent drawn from th€ stack and stack voltage. The tuel cell voltage is a tunction of currenl, reactan! partial pressule,

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Proceedlngs offie 18th Symposnu! of Malaysian Chemical Engineeis

lemperature and membrane humidity. As the curaent is drawr ftom the tuel c€11, oxygen and hydrogen are used in the r€action. Water and he3t are also generated.

2,3 FIIEL CELL STACK MODEL

The ftel cel stack model contains four interacting sub-models which are stack voltage mod€I, anode flow model, cathode flow modei and membrane hydration mode1. It is assumed that the stack temperature is constant at 80"C (353.15 K). The voltage model contains an equation to calculate stack voltage based on fue] cel1 pressure, temperature, reactant gas partial pressure and membrane humjdity. The dynamically varying pressure and relative humidiry of the reactant gas flow inside the stack flow channels are calculated in the cathode and th€ anode flow models.

2.3.1 Stack Yoltage Model

The stack voltage is calculated as a functior of stack current, cathode pressure, reactani pafial Fessures, tuel cell temperature and membrane humidily. Fuel cell voltage is

V f c = E - V a c t - V o h m V c o n c ( : 2 )

wilh E is the opetr circuit circuit while Vact, Vdhm and Vconc are activation, ohmic and concenirarion overvoltages, which reprcsent losses due to various physical or chemical factors.

2.3. 1.1 Activation Overvoltage

It arises ffom the need to move elecfons, to break , and to form chemical bond at the cathode and anode - The relation between the activation ovewoltage and the cunent density is described by rhe Tafel equation which is however not valid for small curent d€nsiry. Therefore, the Tafel equation is approximated by expression

v a c r : v o V a ( l - e-cri) ( 3 )

The calculation for Vo and Va is based on eiectrochenical, kinetics and therrnodlnamic

2.3. 1.2 Olmic Overvoliage

It arises &om the rcsistance of the polymer membrane to the 'transfer of protons' and the resistance ofthe electlodes and conaoller plates to the 'tansfer ofelectrons'. Th€ voltage drop that conesponds to the otmic resistance is proponional to the cu(ent density

v * , = i & m

( 1 )

with i is curent and R.bn is ohmic resistance

2.3. 1 .3 Concentration Overvotag€

It results lrom the increased loss at high curent density) €.g., a sigificant &op in reaclant concentation due to both hig:h reacrant consumption and he3d loss ar high flow laie. An equalion that approximates the voltage drop from concentration losses is given by

vconc = i ( c2 x i,/ i ,"")"r (5)

This ierm is ignored is some models, because il is not desirable to operate the stack at regions where Vconc is high. However, this term needs to be included, if the siack will operate at high cunent density. c2, c3 and i.", are constants that d€pend on temperature and reactant partial pressure.

Proceedinss of the l Eth Synposiun of Nlalaysian Chemical Ensineen

2.3.2 Cathode Flow Mod€i

Thjs model captures the cathode air flow behavior, and is deveiop€d using the mass conveffation principle and the thernodlnamic and psychometric properties of air. Several assumptions are made. First, all gases obey ideai gas law and the temperatur€ ofthe air inside the cathode is equal to the stack t€mpemture which is 80oC. Ii should be noted that lhe propenies ofthe flow exiiirg the cathode such as temperature, presiule and humidiiy are assumed to be the same as those inside the cathode. Fufhermore, wh€n the relative humidity of the gas exceeds 100%, vapor condens€s into ihe liquid for,n The iiquid water does not leav€ the siack and will either evapoGte when the humidiry drops below 100% or accumulate in the cathode.

2.3.3 Anode Fiow Model

This nod€l is qrite similar to the cathode flow model. First assumption is pure hydrogen gas is assumed to be supplied to rhe anode from a hy&ogen tank. Nexi, the inlel hyihogen flow is assumed ro have 100% relative hunidiry. Hy&ogen flowmte can be instanraneously adjusled by a valve while maintaining a minimum pressue difference across the membrane.

2.3.4 Membrane Hydmtion Model

The water transport affoss membrane is achiv€d through two distinct phenomena lirst, the €lectro-osmolic drag phenomenon is rcsponsible for the water molecules dragg€d across the membmne ftom anode to cathode by the hydrogen proton. Second, the gadient of water concentration across the membran€ due to difference in humidity in anode and cathode gases causes "back-diffllsion"ofwater from the cathode to

anode-2.4 PERFORMANCE

The calculaiion for themodynamic efficiency of the tuel cell is accomplished by dividing the net electrical energy produced by the energy value of the tuel used ro produce the electricity. The ner eiectdcal energy is calculated by numerically integrating ihe net power with respect with time. The modeling allows for €ither the higher or lower haeling value of the fuel to be used for rhis caiculation.

n = { P d t ( 6 )

with rl is the themodlnamic efficiency of the stack, P is ihe net power prcduced by ihe stack,lry is the heating valu€ of the fuel and m is the mass ofrhe fuel used to produce the

2.5 PROPERTIES

Pressure and humidiry plofiles are computed using the design of the bipolar plates, output from the at flow, the ideal gas equation and psychometric relationship The bipolar plate desigrl output fiom xhe air flow and the ideal gas equation are used to calculate ihe densit and velocity of the gases in the flow channei; both of which are required to calculate the pressure drop.

2.6 CONTROL SYSTEM

The pueose of control system is io regulales the enxire stack system lt determines the amounl of process gas required to meet paticular load as well as calculales the amount of eneryy used to deliver the gas to the tuei cells. It is also calculates the amounl ofcooling flow required by the stack to maintain the desired iemperaturc. If the stack is pressurized, th€ energy requted to pressurize the syslem wili be calculated. The amount ofthe process gas requircd and the amount ol the water produced by the tuel cell stack is calculated using the electrochemical equalions

3 RESULT

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Proceedings of the lSth Svmposium olMalavsian Chemical En_qneds

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4 CONCLUSION

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".11 rnodel will prove to be verv usetul BIBLIOGR-A.PHY

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Proceedings ol the 18th Symposium of Malaysjan Chemical Eryiree6

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