Practical Approach to Polymer Electrolyte Fuel Cell Modeling

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1 39 Researh Report Pratia Approah to Poymer Eetroyte Fue Ce odeing Haruhiko Yamada, Yu orimoto A simpe simuation method to predit the urrent distribution in a poymer eetroyte fue e is presented. This method ombines a mode for the materia transport aong the gas fo and through a membrane eetrode gas diffusion ayer assemby ith eperimentay determined IV (urrent-otage) harateristis and ater transport properties. The IV harateristis and ater transport properties ere measured under arious gas onditions using a sma e haing an eetrode area of m. The urrent distribution and the humidity profie ere Abstrat auated for a e ith an eetrode area of 3 m for different fo patterns and stoihiometri fo ratios. The resuts ere ompared ith eperimenta data obtained using a segmented e and hied-mirror hygrometers. The simuation resuts agreed e ith the eperimenta data. This method gies us a rough insight into the phenomena of an operating e and is usefu for designing the e for a membrane eetrode gas diffusion ayer assemby due to the simpiity of the simuation proedure. Keyords Poymer eetroyte fue e, Simuation, IV harateristi, Water transport properties, Current distribution, Humidity distribution, Eperimenta aidation (PEFC) 3m m R&D Reie of Toyota CRDL Vo. 39 No. 3

2 4. Introdution In a poymer eetroyte fue e (PEFC), reatantontaining gases are fon aong the gas fo hannes in the in-pane diretion, and the reatants, hydrogen and oygen, diffuse into atayst ayers through gas diffusion ayers and are onsumed in eetrohemia reations. The onentration of the reatant gases dereases donstream if the fon gas ontains an inert omponent, suh as nitrogen in the ase of air. On the other hand, ater produed by the eetrohemia reation is arried into the fon gases, and the onentration of ater usuay inreases donstream. Beause the hanges in the onentrations of gases and ater hae a signifiant effet on the reation rate and the proton ondutiity of the membrane, the urrent distribution in the e is not uniform. Therefore, in order to anayze a PEFC, it is important to obtain information on the urrent distribution and pursue further improement. The urrent distribution of the PEFC has been anayzed both eperimentay, ) 3, 4) and theoretiay in preious studies. In prinipe, the theoretia approah ith mathematia simuation is ery effetie for designing arious PEFCs beause this method an be performed ithout assembing an atua fue e. A three-dimensiona simuation 5-7) has reenty been deeoped using a omputationa fuid dynami ode. Hoeer, this simuation appears to be too ompiated, requiring too many unknon parameters, espeiay for physiohemia phenomena in a membrane eetrode gas diffusion ayer assemby (EGA) suh as eetrohemia reations, moeuar diffusion in porous media and eetro-osmosis. In addition, the physiohemia modes used in this simuation hae not yet been erified eperimentay. In the present study, e hae deeoped a simpe simuation method to predit the urrent distribution and the ater ontent profie. This method ombines a simpe mathematia mode, hih aounts for the materia transport aong the gas fo hanne and through the EGA, and empiria equations, hih desribe the IV harateristis and ater transport properties of the EGA. The aidity of this method is erified by an eperiment using a segmented e and hied-mirror hygrometers.. ode desription Our mode, hih is based on the mode by Nguyen et a., 3) is a steady-state, isotherma, quasi to-dimensiona mass-transfer and eetrohemia mode. The mode onsists of to fo hannes and the EGA (Fig. ). In this mode the EGA is treated as an interfae haing no thikness. The mode aounts for the mass transport of gases and ater aong the gas fo hannes (-diretion) and mass transport of ater through the EGA (ydiretion). The mode is desribed in further detai as foos. The onentrations of the reatants, hydrogen and oygen, in the fo hannes hange in the - diretion by onsumption due to the eetrohemia reations. The humidities hange in the -diretion by ater prodution due to the eetrohemia reation and ater transport in the y-diretion. The oa urrent density, I, is assumed to be epressed as a funtion of oygen onentration (dry gas base), C O, the aerage of the atiities of ater, a,a and a,, and the e otage, V, as: a, a + a, I f C, V I O, () here the subsripts a and indiate the anode and athode sides, respetiey. Water transport through the EGA is epressed as the sum of a term proportiona to the urrent density and a term proportiona to the differene in reatie humidity beteen the athode fo hanne and the y Fig. Anode fo hanne embrane Catayst ayers Gas diffusion ayers Cathode fo hanne H,in H O in H H,out H O out O,in N H O in H O O EGA O,out N H O out Shemati diagram of modeing region. R&D Reie of Toyota CRDL Vo. 39 No. 3

3 4 anode fo hanne. Hereafter, the former is aed the gross drag oeffiient, r, and the atter is aed the gross diffusion oeffiient, D. The parameters r and D are assumed to be funtions of the aerage atiities of ater: r D f f r a a + D,, a a + a,, (a) (b) In the gas fo hannes, ondenion and eaporation of ater are taken into onsideration. That is, hen the partia pressure of ater beomes greater than the ater uration pressure, ater apor ondenses and forms sma dropets, the oumes of hih are negigibe. Simiary, hen the partia pressure of ater is ess than the ater uration pressure, iquid ater eaporates to generate ater apor. The equations used in the mode are gien in Tabe. These equations are soed using a finite differene method. 3. Empiria epressions a The empiria epressions needed for the simuation, IV harateristis and ater transport properties, ere determined eperimentay. A sma e ith an eetrode area of m as used ith eess fo rates in order to minimize the nonuniformity of gases and ater. The EGAs ere assembed ith Nafion as the poymeri membrane, to arbon-supported Pt atayst ayers and to ELAT arbon oth diffusion ayers. The atayst oadings for the anode and the athode ere. mg-pt/m and.4 mg-pt/m, respetiey. The measurement as onduted under the gas pressure of atm abs. at 8 o C. 3. IV harateristis The IV harateristis ere measured under arious oygen onentrations and humidities. The oygen onentration as ontroed to be 5,, 5, or % (dry gas base) by hanging the miing ratio of oygen and nitrogen. For the anode, pure hydrogen as suppied. The dry gas fo rates for the anode and the athode ere 7 sm and 3 sm, respetiey. The anode and athode gases ere equay humidified ith bubbers to yied a reatie humidity of 6, 33, 66, or %. The IV harateristis ere reorded using a urrentseeping method at ma/s under 6 onditions. Tabe Goerning equations. Hydrogen Anode iquid ater Anode apor ater Oygen Nitrogen Cathode iquid ater Cathode apor ater Water ontent of membrane Net ater transfer oeffiient Water onentration at membrane surfae Water atiity Vapor pressure for ater C h - I() F, a, a() pa - p, a + H, a d, a h - - I F - I() dh d d do N, d, d, λ α, () p -, () () + O + N, d, h[ + α ] - + I r og N, h 4F a X p a p F - I a D F, a + 36.a [ C, - C, a() ] t ( p ) T T +.44 T ρ dry dry λ α m 3 p, (7) (8) (9) () () () (3) (4) (5) (6) (7) (8) R&D Reie of Toyota CRDL Vo. 39 No. 3

4 4 Figures and 3 sho eampes of the IV harateristis. As the oygen onentration or reatie humidity inrease, the otage and imiting urrent density inrease. An empiria equation as deried for eah IV data by ure-fitting using the fooing epression proposed by Kim et a. 8) : V V o - bog(i) - RI - ep(ni) (3) here V o and b represent the eetrode kineti parameters for oygen redution, R represents the e resistane, and the eponentia term haraterizes the mass transport region of the IV harateristis. In the ure-fitting, a parameters, V o, b, R, and n, ere determined using a noninear east squares method. Using the determined parameters for a sets of oygen onentration and humidity, a mathematia epression as determined as a funtion of oygen onentration or gas humidity for eah parameter. The obtained epressions are as foos: V o (mv) C O (4a) b(mv/deade) a (4b) R(Ω. m ) ep(-5.9a ).. (4) n(m /ma) C O (4d) here C O and a are the oygen onentration (dry gas base) and the atiity of ater respetiey. In Figs. and 3, the obtained ures are shon as soid ines. The ures agree e ith the eperimenta data. 3. Water transport properties The gross drag of ater as determined as foos. The -m fue e as operated at.5 A/m ith H /air humidified equay. The reatie humidities of the inet and outet gases ere measured using hied-mirror hygrometers. The gross drag oeffiient of ater as determined from the differenes beteen the inets and the outets as a funtion of the inet reatie humidity. The gross diffusion oeffiient of ater as determined simiary, eept that sighty different humidified H /air as suppied to the open-iruit e. In these measurements, the fo rate of H /air 5/5 sm as used. Figures 4 and 5 sho respetiey the gross drag oeffiient of ater, r, and the gross diffusion oeffiient of ater, D, as funtions of the ater ontent of the membrane. In these figures, the ater ontent of the membrane as deried from the gas humidity using the sorption isotherm 9) (refer to Eq. (4) in Tabe ). The negatie aue for the gross drag oeffiient may seem unusua. Hoeer, this gross drag oeffiient inudes ater diffusion from the athode to the anode drien by the ater onentration gradient due to ater generation on the athode. Therefore, the negatie aue simpy means that the ater diffusion from the athode to the anode is arger than the eetro-osmoti drag. ) The gross diffusion oeffiient has a maimum around the ater ontent of 3. This agrees e ith the oeffiient of otupay et a., ) hih as etrated from the sef-diffusion oeffiient reported in the iterature. ) This means that the gross diffusion oeffiient of the present study is neary equa to the diffusion oeffiient of ater in the.8 Symbos: eperiment Lines: using Eq. 3.8 Symbos: eperiment Lines: using Eq. 3 Ce otage / V % % 5% % O Ce otage / V % 66% 33% % RH Current density / A m Current density / A m - Fig. Effet of O onentration in the gas mitures of O /N on IV harateristis at RH a RH %. Fig. 3 Effet of reatie humidity of anode and athode on IV harateristis at % O /(O +N ). R&D Reie of Toyota CRDL Vo. 39 No. 3

5 43 membrane. From these data, empiria equations desribing the ater transport properties ere deried as foos: r.8ep(-.48λ) (5) D (λ<3) ep(.63λ) (6a) D (λ>3) [ep(-.78λ) ] (6b) here λ is the ater ontent of the membrane. 4. Vaidation 4. Eperimenta The urrent distribution as measured using a segmented e ) and the gas humidity as measured at the outets using hied-mirror hygrometers. Figure 6 is a shemati diagram of the - segmented e. The e has an atie area of 3 m and a doube-pass serpentine fo fied. The same EGA materias as the -m e ere used. The e as operated under an H /air pressure of atm abs. at 8 o C. In the eperiment, the gas fo pattern and the gas stoihiometri fo ratio ere aried. 4. Resuts Figure 7 shos a omparison of the eperimenta and simuation resuts for the urrent density distribution for different gas fo patterns. Figures 8 and 9 sho omparisons of the eperimenta and simuation resuts for the humidity profie. The simuation resuts agree e ith the eperimenta resuts. The simuation resuts of the humidity profie aount e for the urrent distribution: the Fig. 4 Gross drag oeffiient,, H HO/H Eperimenta data Using Eq. 5 ) Zaodzinski et a Water ontent of membrane,, H O/SO 3-3- Gross drag oeffiient of ater in Nafion membrane as a funtion of ater ontent of membrane. Fig. 6 36mm Channe and rib idth : mm Channe depth : mm mm Shemati diagram of the segmented e Fig. 5 Gross diffusion oeffiient, / 6 m / m s - s Eperimenta data Using Eq Water ontent of membrane,, H O/SO 3-3- ) otupay et a. ) Gross diffusion oeffiient of ater in Nafion membrane as a funtion of ater ontent of membrane. Fig. 7 Current density / A m H, HHair (o-fo) Air Air (ounter-fo) (ounter- H fo) H Co-fo, eperiment Counter-fo, eperiment Co-fo, simuation Counter-fo, simuation Comparison of urrent distribution beteen eperiment and simuation for different fo patterns at.6a/m. The stoihiometri fo ratio is 3.3 and the inet humidity is 33%. R&D Reie of Toyota CRDL Vo. 39 No. 3

6 44 high humidity makes the membrane resistane o and the urrent density high. In this highstoihiometri-fo ondition, oygen onentration does not hae a signifiant infuene on the urrent density. Figure shos the IV harateristi of the simuation ompared to that of the eperiment. The simuation resuts agree e ith the eperimenta data. Figure shos a omparison beteen simuation and eperimenta resuts for the urrent distribution for different gas stoihiometri fo ratios. In the o-stoihiometri-fo ondition, the urrent density shos the effet of o oygen onentration donstream. In this ase, again, the simuation resuts agree e ith the eperimenta data. 5. Conusions We hae proposed a simuation method to predit the urrent distribution in a rea PEFC. Rather than using theoretia equations, the proposed method empoys oera empiria equations determined by sma-e eperiments for physiohemia phenomena suh as eetrohemia reations, moeuar diffusion in a poymer or porous media and eetro-osmosis. Therefore, unertainties on Fig. 8 Reatie humidity / % HH, H, air Anode outet, eperiment Cathode outet, eperiment Anode, simuation Cathode, simuation Cauated humidity profie and measured humidity at outet at.6a/m for o-fo. The stoihiometri fo ratio is 3.3 and the inet humidity is 33%. Ce otage / V Co-fo, eperiment Counter-fo, eperiment Co-fo, simuation Counter-fo, simuation.5.5 Current density / A m - Fig. Comparison of IV harateristi beteen simuation and eperiment for both gas fo. The stoihiometri fo ratio is at A/m and the inet humidity is 33%. Fig. 9 Reatie humidity / % AirAir Anode outet, eperiment Cathode outet, eperiment Anode, simuation Cathode, simuation H Cauated humidity profie and measured humidity at outet at.6a/m for ounter-fo. The stoihiometri fo ratio is 3.3 and the inet humidity is 33%. Current density / A m H, H, air air Stoi. ratio.5, eperiment Stoi. ratio 3.3, eperiment Stoi. ratio.5, simuation Stoi. ratio 3.3, simuation Fig. Comparison of urrent distribution beteen simuation and eperiment for different stoihiometri fo ratios. The stoihiometri fo ratio is 3.3 and the inet humidity is 33%. The inet humidity is 33% and the fo pattern is o-fo. R&D Reie of Toyota CRDL Vo. 39 No. 3

7 45 physiohemia modes and their parameters an be aoided, and the effets of engineering and designing, suh as fo patterns and operation onditions, an be arified. For this reason, e beiee that this approah i be highy usefu in pratia appiation. A drabak of this approah is that the effets of materia properties and mirostrutures annot be separatey reognized beause these effets are ombined in the empiria equations. Therefore, it is diffiut to obtain hints for improing the materias and mirostrutures. Hoeer, suh improements require that the physiohemia phenomena in PEFCs be fuy understood and that their modes be erified eperimentay using a sma e hie aoiding engineering and designing effets. List of Symbos a : atiity of ater b : tafe sope/mv deade - Co : oygen moar fration in dry O /N gas mitures C : onentration of ater/mo m -3 D : gross diffusion oeffiient of ater/m s - F : Faraday onstant/c mo - h : EGA idth/m I : oa urrent density/a m - : moar fo rate/mo s - dry : equiaent eight of a dry membrane/g mo - n : mass transport parameter p : pressure/atm R : e resistane/ω m r : gross drag oeffiient of ater T : temperature/ o C t m : membrane thikness/m V : e otage/v V : open iruit otage/v X : moar fration : diretion aong the gas hanne ength/m Greek α : net ater transfer oeffiient per proton ρ dry : density of a dry membrane/g m -3 λ : ater ontent of membrane Subsripts and supersripts a : anode : athode H : hydrogen : iquid N : nitrogen O : oygen : uration : apor : ater : initia ondition Referenes ) orimoto, Y., Suzuki, T. and Yamada, H. : The Eetrohem. So. eet. Abstr., A- (), No. 86, ECS ) enh,.., Wang, C. Y. and Ishikaa,. : J. Eetrohem. So., 5(), A5 3) Nguyen, T. V. and White, R. E. : J. Eetrohem. So., 4(993), 78 4) Gurau, V., Liu, H. and Kaka, S. : AIChE J., 44(998), 4 5) Um, S. and Wang, C. Y. : J. Poer Soures, 5(4), 4 6) Berning, T., Lu, D.. and Djiai, N. : J. Poer Soures, 6(), 84 7) Dutta, S., Shimpaee, S. and Van Zee, J. W. : J. App. Eetrohem., 3(), 35 8) Kim, J., Lee, S.. and Sriniasan, S. : J. Eetrohem. So., 4(995), 67 9) Springer, T. E., Zaodzinski, T. A. and Gottesfed, S. : J. Eetrohem. So., 38(99), 334 ) Zaodzinski, T. A., Daey, J., Vaerio, J. and Gottesfed, S. : Eetrohim. Ata, 4(995), 97 ) otupay, S., Beker, A. J. and Weidner, J. W. : J. Eetrohem. So., 47(), 37 ) Zaodzinski, T. A., Neeman,., Sierud, L. O. and Gottesfed, S. : J. Phys. Chem., 95(99), 64 (Report reeied on Ju. 9, 4) Haruhiko Yamada Year of birth : 959 Diision : Fue Ce System Lab. Researh fieds : Eetrohemistry, Fue e Aademi soiety : Eetrohem. So. Jpn. Yu orimoto Year of birth : 957 Diision : Fue Ce System Lab. Researh fieds : Eetrohemistry, Fue e Aademi degree : Ph. D. Aademi soiety : Eetrohem. So., Eetrohem. So. Jpn. R&D Reie of Toyota CRDL Vo. 39 No. 3