Effects of inlet relative humidity (RH) on the performance of a high temperature-proton exchange membrane fuel cell (HT-PEMFC)

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Effects of inlet relative humidity (RH) on the performance of a high temperature-proton exchange membrane fuel cell (HT-PEMFC) Purushothama Chippar a, Kyungmun Kang a, Young-Don Lim b, Whan-Gi Kim b, Hyunchul Ju a,* a

School of Mechanical Engineering, Inha University, 253 Yonghyun-Dong, Nam-Gu, Incheon 402-751, Republic of Korea b Department of Applied Chemistry, Konkuk University, 322 Danwol, Chungju 380-701, Republic of Korea

article info

abstract

Article history:

A high temperature-proton exchange membrane fuel cells (HT-PEMFC) based on phos-

Received 15 December 2012

phoric acid (PA)-doped polybenzimidazole (PBI) membrane is able to operate at elevated

Received in revised form

temperature ranging from 100 to 200
C. Therefore, it is evident that the relative humidity

11 April 2013

(RH) of gases within a HT-PEMFC must be minimal owing to its high operating temperature

Accepted 22 May 2013

range. However, it has been continuously reported in the literature that a HT-PEMFC per-

Available online 21 June 2013

forms better under higher inlet RH conditions. In this study, inlet RH dependence on the performance of a HT-PEMFC is precisely studied by numerical HT-PEMFC simulations.

Keywords:

Assuming phase equilibrium between membrane and gas phases, we newly develop a

High temperature-proton exchange

membrane water transport model for HT-PEMFCs and incorporate it into a three-

membrane fuel cell

dimensional (3-D) HT-PEMFC model developed in our previous study. The water diffu-

Polybenzimidazole (PBI)

sion coefficient in the membrane is considered as an adjustable parameter to fit the

Numerical modelling

experimental water transport data. In addition, the expression of proton conductivity for

Proton conductivity

PA-doped PBI membranes given in the literature is modified to be suitable for commercial PBI membranes with high PA doping levels such as those used in Celtec
MEAs. Although the comparison between simulations and experiments shows a lack of agreement quantitatively, the model successfully captures the experimental trends, showing quantitative influence of inlet RH on membrane water flux, ohmic resistance, and cell performance during various HT-PEMFC operations. Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

A typical perfluorosulfonic acid (PFSA) membrane such as DuPont’s Nafion
has been widely used as proton conducting membranes due to its good proton conductivity, chemical stability, and mechanical strength [1]. However, PFSA

membranes require sufficient membrane hydration to ensure efficient proton conduction, which limits operating temperature range of PFSA membrane to below 100
C (typically 60e80
C). On the other hand, a PA-doped PBI membrane exhibits good proton conductivity without requiring water content in the membrane and also shows excellent chemical,

* Corresponding author. Tel.: þ82 32 860 7312; fax: þ82 32 868 1716. E-mail addresses: [email protected], [email protected] (H. Ju). 0360-3199/$ e see front matter Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2013.05.115

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thermal stability and negligible electro-osmotic drag at relatively high temperatures ranging from 100 to 200
C [2e4]. Therefore, a PA-doped PBI membrane based fuel cell is able to operate at elevated temperatures (usually above 120
C) without humidification of the reactant gases, showing several advantages over a PFSA membrane based low temperature (LT) fuel cell. The beneficial features include faster electrode kinetics, simpler water and heat management, improved mass transfer and higher tolerance to CO, which renders a HT-PEMFC using a PA-doped PBI membrane well suited for most distributed energy or combined heat and power (CHP) applications. It has been reported in the literature that the proton conductivity of a PA-doped PBI membrane generally increases with acid doping level, temperature, and inlet feed gas relative humidity (RH) [5e12]. He et al. [5] measured the proton conductivity of PA-doped PBI membrane as a function of inlet RH. They showed that an increase in the RH significantly improves the proton conductivity for PA-acid doped PBI membrane under high operating temperature of 200
C. Asensio et al. [6] measured the proton conductivity of an ABPBI membrane in a wide temperature range from 50 to 200
C under different inlet RH conditions (5e30%). Their data exhibit that the proton conductivity generally increased with temperature and RH but showed exceptional behaviour at 5% RH and high operating temperatures above 180
C that they attributed to the dehydration of PA in the membrane. Ma et al. [7] experimentally showed that the proton conductivity measured at RH ¼ 0% decreases with temperature whereas the proton conductivity under humidified inlet gases (RH ¼ 5, 10, 20, and 30%) shows a significant improvement with rising temperature. They concluded that the different behaviour of the proton conductivity data under dry conditions (RH ¼ 0%) is due to the formation of H4P2O7 and the dehydration of PA at higher temperature. Lobato et al. [9] and Chen and Lai [12] measured the ionic resistance of a PA-doped PBI membrane as a function of operating temperature. Their proton conductivity data reflect Arrhenius behavior up to 130e140
C but further increasing temperature beyond 130e140
C reduces the proton conductivity. The experimental trend clearly implies that the effect of membrane dehydration becomes significant at the high temperatures, significantly deteriorating a network for proton transfer in the membrane. Note that the RH values corresponding to a high operating temperature range of HT-PEMFCs (usually 120e180
C) must be minimal and consequently the effect of RH on a PA-doped PBI fuel cell is less significant as compared with that of a PFSA fuel cell [12,13]. However, the aforementioned experimental studies clearly confirm the important role of RH on the proton conductivity of a PA-doped PBI membrane, which implies that cell performance is affected by inlet gas humidification. Simultaneously, several numerical HT-PEMFC models have been developed and presented in the literature in order to more precisely study key reaction and transport phenomena occurring in a HT-PEMFC [14e25]. Sousa et al. [18] developed a dynamic two-dimensional (2-D), nonisothermal model and investigated transient responses of HT-PEMFCs under time-dependent changes in cell voltage and external climate conditions. Shamardina et al. [19]

developed a simple 2-D, steady state, isothermal HT-PEMFC model and numerically explored the effects of gas crossover through the membrane on cell performance. Lobato et al. [20] developed a 3-D single-phase half-cell model and investigated the effects of flow channel configuration on cell performance. Boaventura et al. [22] developed a dynamic 1-D, isothermal model and mainly explored the transient behaviours of species transport in the bipolar plates, gas diffusion layers and double layers. Regarding the effects of RH on HTPEMFCs, Sousa et al. [23] considered the RH dependence of proton conductivity in their models. However, the water absorption and transport equations for a PA-doped PBI membrane and relevant simulation results were not presented in their paper. Jiao and Li [24] derived the proton conductivity expression as a function of temperature, doping level, and RH using the proton conductivity data measured by Ma et al. [7] and He et al. [26]. However, they employed the volume averaged RH of the anode and cathode CLs to estimate RH in the membrane without considering water uptake and transport between the membrane and CLs. Olapade et al. [27] numerically investigated the effects of inlet feed gas humidification on HT-PEMFC performance using a 1-D, nonisothermal HT-PEMFC model. However, they adopted the same treatment of RH calculation for the membrane done by Jiao and Li [24], i.e. flawed because it neglects water absorption and transport in the membrane. In this study, we newly develop a water transport model for a PA-doped PBI membrane via assuming the local interfacial equilibrium between the gas and membrane phases of water and subsequently incorporate it into our previous HT-PEMFC model [28]. Due to lack of experimental data for water diffusion coefficient through a PA-doped PBI membrane, we numerically estimate it based on the water flux data measured by Galbiati et al. [29]. The HT-PEMFC model coupled with the new membrane water transport model is tested against various experimental data given by Galbiati et al. [29]. A comparison between the simulation and experimental results is made and fully discussed. In addition, key multidimensional contours within HT-PEMFCs such as membrane water content, proton conductivity, current density, oxygen, and cathode overpotential distributions are presented to provide greater insight into detailed water transport processes inside a HT-PEMFC and the effects of inlet RH and membrane hydration on cell performance.

2.

Numerical model

A three-dimensional, two-phase, non-isothermal, electrochemical-transport coupled HT-PEMFC model used for this study is based on previous publications [28,30]. The governing equations, relevant source terms, electrochemical kinetics parameters, and physical properties at the anode and cathode CLs are summarized in Tables 1e4, respectively. As compared with our previous papers [28,30], note that the values of the volumetric exchange current density for HOR and ORR (denoted by airef 0 in Table 3) were reduced due to the thicker anode and cathode CLs (i.e. 30 mm in Table 4) with the same Pt-loading. Readers are referred to our previous publications [28,30] for a more detailed description of the model.

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Table 1 e High-temperature PEMFC model: governing equations. Governing equations V$ðr! u Þ ¼ Sm

Mass

Species

2

p

(4) (5)



(6) (7)

T

Model assumptions

(2) (3)

Electron transport : V$ seff VFs  SF ¼ 0     V$ rc ! u T ¼ V$ keff VT þ S

Energy

transport in the CLs is through both gas and membrane phases and thus the total effective diffusivity is calculated as

The assumptions made with respect to the model include the following: 1) The flow is incompressible and laminar because of a small pressure gradient and low flow velocities. 2) The gas mixtures obey the ideal gas law because of low pressure and high-temperature operation. 3) Water exists in the gas phase because of high operating temperatures (above the boiling point of water).

2.2.

1=ε V$ðr! u! u Þ ¼ Vp þ V$s

Porous media ðDarcys equationsÞ: r! u ¼ ðK=nÞVp   V$ð! u Ci Þ ¼ V$ Deff i VCi þ Si   Proton transport : V$ keff VFe þ SF ¼ 0 

(1)



Flow channels ðNaviereStokes equationsÞ :

Charge

2.1.



Momentum

Transport properties

The water transport equation in the membrane is obtained by assuming the local interfacial equilibrium between the gas and membrane phases of water as follows, JD ¼ Dmem H2 O VCH2 O

(22)

where Dmem H2 O denotes fictitious water diffusivity and will be discussed in details in Section 3. On the other hand, the water

Deff ¼ εs DH2 O þ εsmem Dmem H2 O g

(23)

where ε and εmem are the porosity and volume fraction of membrane phase in the CL, respectively. The proton conductivity of the PA-doped PBI membrane can be interpreted using an Arrhenius equation as: s¼


 AB Ea exp T RT

(24)

where both A and B are pre-exponential factors and Ea, the activation energy. The experimental studies by Ma et al. [31] showed that the activation energy sharply decreases with low doping levels whereas no significant changes in the activation energy were observed at higher doping levels. Celtec
-P 1000 MEAs considered in this work are based on high PA doping, usually having PA content of more than 95 wt% or doping level up to 70 [32] and thus the constant value of 20.0 kJ mol1 is used in this work. The pre-exponential factor, A in Eq. (24) accounts for the effects of PA doping level on the membrane proton conductivity and is assumed to be constant

Table 2 e High-temperature PEMFC model: source/sink terms. Source terms H2

Anode CL

Cathode CL

nxover ja nxover H O SH2 ¼   2  2 2 2F dCL dCL

(8)

O2

SO2 ¼ H 2O

SH2 O ¼ 2

Mass

Sm ¼

nxover O2 dCL

X

Sk ¼ MH2

k

Charge

SF ¼ ja

Heat

ST ¼ ja h þ

(10a) ja þ 2F

  MO2 nxover  MH2 nxover O2 H2

2nxover I2 O2 þ DH H 2 keff dCL

dCL

(11a)

jc nxover 1 nxover O H2  2  2 dCL 4F dCL

jc nxover H SH2 O ¼  þ 2 2F dCL Sm ¼

X

Sk ¼ MO2

k

(12a)

S F ¼ jc

(13a)

S T ¼ jc h þ

jc jc  MH2 O þ 4F 2F

(9) (10b)   MH2 nxover  MO2 nxover H2 O2 dCL

(11b) (12b)


Ixover I2 dUo dUo H2 T  T þ j h þ c keff dT dCL dT

(13b)

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Table 3 e High-temperature PEMFC model: electrochemical properties. Description Exchange current density  ratio of the reaction surface to the CL 3 volume, airef 0 (A m ) Reference H2/O2 molar concentration (mol m3) Anodic transfer coefficient Cathodic transfer coefficient Thermodynamic equilibrium potential, U0 (V) Surface overpotential, h (V)

Anode CL 0.33  10

Cathode CL

9

0.33  10

40.88

Ref.

4

[24,30]

40.88

aa ¼ 0:5

[33] ac ¼ 0:65

[34,35] [30]

0 3

fs  fe  U0 ðwith fs ¼ 0Þ

Transfer current density, j (A cm3)

ja ¼ airef 0;a

CH2 CH2;ref

(15)

!1=2
 aa þ ac Fh (17) Ru T

1:1669  0:24  10 ðT  373:15Þ

(14)

fs  fe  U0 ðwith fs ¼ Vcell Þ

(16)

jc ¼ airef 0;c

CO2 CO2;ref

!3=4


exp



ac Fh Ru T

 þ

Ixover H2 dCL

(18)

8 < Mi ¼ chemical formula of species i X z  Electrochemical reactions si Mi ¼ ne ; where s ¼ stoichiometry coefficient : i k n ¼ number of electrons transferred

(19)

Hydrogen oxidation reaction ðHORÞ at the anode side : H2  2Hþ ¼ 2e

(20)

Oxygen reduction reaction ðORRÞ at the cathode side : 2H2 O  O2  4Hþ ¼ 4e

(21)

(3.0  106 S$K m1). On the other hand, for the RH dependent term, B, the correlation given by Jiao and Li [24], i.e. based on the experimental measurements of Ma et al. [7] and He et al. [26] is chosen. That is: 8 < 1 þ ð0:01704T  4:767ÞRH if 373:15 K  T  413:15 K B ¼ 1 þ ð0:1432T  56:89ÞRH if 413:15 K  T  453:15 K : 1 þ ð0:7T  309:2ÞRH if 453:15 K  T  473:15 K (25) The effective proton conductivity in the CLs is obtained by combining the effects of the volume fraction of the membrane phase and tortuosity of the porous medium by using Bruggemann’s correlation:

keff ¼ ε1:5 mc k

(26)

2.3. Numerical implementation, computational domain, and boundary conditions The HT-PEMFC model described in Section 2 is numerically implemented in a commercial computational fluid dynamics (CFD) program, FLUENT, basing on its user-defined functions (UDF). The convergence criteria for all species and energy calculation residuals are set to 108. Fig. 1 shows the mesh configuration of the simple single-straight channel HT-PEMFC geometry. The cell dimensions and operating conditions are given in Table 5. As described in Fig. 1, the isothermal

Table 4 e Physical properties. Description Porosity of GDL, CL Volume fraction of ionomers in CL Permeability of GDL, CL Water diffusivity in the membrane Electronic conductivity in the GDL, CL, BP Specific heat capacities of GDL, CL, membrane, BP Specific heat capacities of species e H2, O2, N2, H2O Thermal conductivities of GDL, CL, membrane, BP Thermal conductivities of species e H2, O2, N2, H2O

Value

Ref.

0.6, 0.3 0.4 1  1012, 1.0  1013 m2 1  107 m2 s1 250, 300, 14,000 S m1 568, 3300, 1650, 2930 J kg1 K1 14,430, 929, 1042, 1968 J kg1 K1 1.2, 1.5, 0.95, 20 W m1 K1 0.2040, 0.0296, 0.0293, 0.02378 W m1 K1

[24] [24] [28] [28] [24] [36] [37] [36]

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Fig. 1 e Computational domain and mesh configuration of a single-channel HT-PEMFC geometry [30].

boundary condition is applied to the anode and cathode side walls of the computational cell for temperature calculations whereas the symmetric boundary condition is assumed on the top and bottom surfaces. In addition, the no-flux condition is applied to the outer faces for flow and species transport equations except for the channel inlets and outlets. The inlet velocities in the anode and cathode gas channels can be expressed as functions of the anode and cathode stoichiometric ratios, the operating current density, the crosssectional areas of the anode and cathode GCs, and the concentrations of hydrogen and oxygen, which are functions of the anode/cathode inlet pressure and temperature: uin;a ¼

3.

xa ðI=2FÞAmem x ðI=4FÞAmem and uin;c ¼ c CH2 Aa;chan CO2 Ac;chan

(27)

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Fig. 2 e Comparison of calculated and measured water molar flux for different operating current densities for the cases of dry reactants and cathode humidification (Tsat [ 50
C).

the water diffusion coefficient in this study was assumed to be constant regardless of inlet RHs and operating current densities. Fig. 2 compares the measured and calculated water molar flux from the cathode to anode at different operating current densities in which the diffusivity value of 1.0  107 m2 s1 was taken for the simulations. Even though the simulated water flux in both dry reactant and cathode humidification cases overpredicts the experimental data, it is seen that general membrane water transport characteristics observed in the experimental data were reasonably captured by the model. Both simulated and measured water crossover fluxes from the cathode to anode increase with current density because the water production rate in the cathode side becomes higher with increasing current density. In addition,

Results and discussion

The first step for model validation is to estimate the effective water diffusion coefficient in the membrane based on the water flux data given by Galbiati et al. [29]. As the first attempt,

Table 5 e Cell dimensions and operating conditions. Description Cell length Anode/cathode channel/rib width Anode/cathode channel height Thickness of the anode GDLs Thickness of the cathode GDLs Thickness of the anode/cathode CLs Thickness of the membrane Anode/cathode inlet pressure Anode stoichiometry Cathode stoichiometry Anode/cathode inlet temperature

Value 0.1 m 0.8  103 m 0.7  103 m 345  106 m 370  106 m 30  106 m 100  106 m 1.0 atm 1.2 (pure H2) 2.0 (air) 433.15 K

Fig. 3 e Comparison of calculated and measured ohmic cell resistances at different operating current densities for the cases of dry reactants and cathode humidification (Tsat [ 50
C).

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Fig. 4 e Comparison of calculated polarization curves with the experimental data for the cases of dry reactants and cathode humidification (Tsat [ 50
C).

as expected, the higher water transport to anode is predicted with the cathode humidification. These trends confirm that water transport across the PBI membrane is mainly determined by the gradient of water concentration between the anode and cathode. Fig. 3 shows a comparison of calculated and measured ohmic cell resistances for different operating current densities and reactant humidification rates. In both numerical simulations and experimental measurements, ohmic cell resistance is reduced with the cathode air humidification. As the external water vapour pressure increases, it is expected that the water uptake of PBI membrane is increased. Therefore, the trend clearly indicates that conductivity network for proton transfer in PA-doped PBI membranes is better

established with higher water content in the membrane, which is consistent with the discussion of Ma et al. [7]. In the low current density region, a relatively good match between the simulation results and experimental data can be seen. However, agreement in the high current density region remains unsatisfactory: while the calculated ohmic cell resistances continue to decrease with increasing current density, measured ohmic resistances were almost kept as constant. The discrepancy at the high current densities underlines that there must be negative influence of RH on PBI membrane proton conductivity and resultant cell ohmic resistance. One of possible reasons may be due to increasing PA leaching with reactant humidification, which is not considered in the current version of a HT-PEMFC model. Fig. 4 compares the calculated polarization curves with the experimental data for the cases of dry reactants and cathode humidification. First, it is observed in the experimental data that the cathode humidification leads to slightly lower cell performance, which was successfully captured by the model. The trend implies that as the cathode humidification is applied to the cell, the effect of decreasing oxygen partial pressure (negative effect) dominates over the effect of proton transfer enhancement in the membrane (positive effect). In a comparison of the simulation results and experimental data, good agreement is achieved in the low current density region. However, it is appears that cell voltages in the high current density region were overpredicted by the model. The discrepancy between the simulations and experiments can be attributed to the behavior of cell ohmic resistance as a function of current density, i.e. discussed in Fig. 3. Fig. 5 displays the oxygen and overpotential distributions in the cathode CL for the cases of dry reactants and cathode humidification at 0.5 A cm2. When the air in the cathode inlet is humidified, more severe oxygen depletion is observed near the cathode outlet (see Fig. 5a), which clearly shows the

Fig. 5 e (a) Oxygen and (b) Overpotential distributions in the cathode CL for the cases of dry reactants and cathode humidification with Tsat [ 50
C at 0.5 A cmL2.

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Fig. 6 e (a) Water concentration, (b) Proton conductivity and (c) Current density distributions in the membrane for the cases of dry reactants and cathode humidification at 0.5 A cmL2.

influence of a negative decrease of oxygen partial pressure by the cathode air humidification. Consequently, as seen in Fig. 5b, the higher cathode overpotential is predicted with the cathode humidification and the overall difference between the cases of dry reactants and cathode humidification is around 11.6 mV. The water concentration (i.e. fictitious one calculated by Eq. (22)), proton conductivity, and current density distributions in the membrane for the same cases are plotted in Fig. 6. As shown in Fig. 6a, the water concentration in the PBI membrane for both cases increases towards the cathode outlet due to water production by ORR. In addition, it is clear that the cathode humidification results in the higher water concentration in the membrane. The proton conductivity distributions in Fig. 6b exhibit the same trends as the water concentration profiles in Fig. 6a because the proton conductivity was assumed to be an increasing function with the external RH (see Eq. (25)). Finally, the current density distributions in the membrane in Fig. 6c show increasing trend

towards the cathode downstream, which indicates that cell performance is mainly controlled by oxygen transport rather than proton transfer in the PBI membrane.

4.

Conclusions

In this study, a water transport model for a PA-doped PBI membrane was developed by assuming the local interfacial equilibrium between the gas phase and the membrane phase of water and subsequently incorporated it into a comprehensive HT-PEMFC model developed in the previous publication [28]. Due to the lack of experimental data regarding water crossover diffusivity through the PBI membrane, we first estimated a constant fitting diffusivity of 1.0  107 m2 s1 based on the water crossover flux data experimentally measured by Galbiati et al. [29]. Using the water crossover diffusivity value, the 3-D simulations were carried out in order to validate the HT-PEMFC model against several types of

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experimental data given by Galbiati et al. [29], i.e. the water crossover flux, cell ohmic resistance, and cell performance data. In general, the simulation results matched well with the experimental data at low current densities but showed lack of agreement in the high current density region. The discrepancy at the high current densities can be attributed to the different trends of simulated and measured ohmic resistances as the cell current density varies: the calculated cell ohmic resistance continues to decrease with current density whereas the measured ohmic resistance is roughly a constant at the high current densities. Therefore, there must be negative effect of increasing RH on the proton conductivity of PBI membranes such as increasing PA leaching with reactant humidification. In both simulations and experiments, the overall cell performance was slightly lowered with the cathode humidification, which is clearly indicative of more dominant effect of decreasing oxygen partial pressure over improvement in the proton conductivity with increasing RH. The multidimensional contours obtained from the simulations confirm the fact, showing clear decreasing trend of membrane current density towards the cathode downstream.

Greek symbols a transfer coefficient ε porosity d thickness εmc volume fraction of the ionomer phase in the CL 4 phase potential, V h overpotential, V m viscosity, kg m1 s1 y kinematic viscosity, m2 s1 s electronic conductivity, S m1 r density, kg m3 s viscous shear stress, N m2 k ionic conductivity, S m1 x stoichiometry flow ratio

Acknowledgement

Subscripts a anode c cathode CL catalyst layer GC gas channel GDL gas diffusion layer hydrogen H2 i species index in channel inlet m mass equation e electrolyte s solid mem membrane oxygen O2 u momentum equation sat saturation value chan channel water H2O F potential equation 0 standard condition, viz., 298.15 K and 101.3 kPa (1 atm)

This work was supported by the New & Renewable Energy R&D program (grant no. 2010T100200501) of the Ministry of Knowledge Economy of the government of the Republic of Korea. The authors also would like to thank TAE-SUNG S&E, INC. for providing technical supports to use ANSYS-FLUENT for fuel cell simulation.

Nomenclature

A Cp C Di F i0 I J j K M p n nxover k H R S T ! u U0 Vcell

area, m2 specific heat, J kg1 K1 molar concentration, mol m3 mass diffusivity of species i, m2 s1 faraday constant, 96,487 C mol1 exchange current density, A m2 operating current density, A m2 molar flux, mol m2 s1 transfer current density, A m3 hydraulic permeability, m2 molecular weight, kg mol1 partial pressure, Pa number of electrons in the electrochemical reaction crossover molar flux, mol m2 s1 thermal conductivity, W m K1 thermal conductivity, W m K1 universal gas constant, 8.314 J mol1 K1 source term in the conservation equation temperature, K fluid velocity and superficial velocity in a porous medium, m s1 thermodynamic equilibrium potential, V cell potential, V

Superscripts eff effective value in the porous region g gas ref reference value mem membrane xover crossover

references

[1] Kerres JA. Development of ionomer membranes for fuel cells. J Membr Sci 2001;185:3e27. [2] Wainright JS, Wang JT, Weng D, Savinell RF, Litt MH. Aciddoped polybenzimidazoles: a new polymer electrolyte. J Electrochem Soc 1995;142(7):L121e3. [3] Samms SR, Wasmus S, Savinell RF. Thermal stability of proton conducting acid doped polybenzimidazole in simulated fuel cell environments. J Electrochem Soc 1996;143(4):1225e32. [4] Weng D, Wainright JS, Landau U, Savinell RF. Electro-osmotic drag coefficient of water and methanol in polymer

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[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15] [16] [17]

[18]

[19]

[20]

[21]

electrolytes at elevated temperatures. J Electrochem Soc 1996;143(4):1260e3. He R, Li Q, Xiao G, Bjerrum NJ. Proton conductivity of phosphoric acid doped polybenzimidazole and its composites with inorganic proton conductors. J Membr Sci 2003;226:169e84. Asensio JA, Borros S, Gomez-Romero P. Polymer electrolyte fuel cells based on phosphoric acid-impregnated poly(2, 5benzimidazole) membranes. J Electrochem Soc 2004;151(2):304e10. Ma YL, Wainright JS, Litt MH, Savinell RF. Conductivity of PBI membranes for high-temperature polymer electrolyte fuel cells. J Electrochem Soc 2004;151(1):A8e16. Pu H, Meyer WH, Wegner G. Proton transport in polybenzimidazole blended with H3PO4 or H2SO4. J Polym Sci Part B 2002;40(7):663e9. Lobato J, Ca˜nizares P, Rodrigo MA, Linares JJ. PBI-based polymer electrolyte membranes fuel cells: temperature effects on cell performance and catalyst stability. Electrochim Acta 2007;52:3910e20. Xing B, Savadogo O. The effect of acid doping on the conductivity of polybenzimidazole (PBI). J New Mat Electrochem Syst 1999;2:95e101. Li Q, Hjuler HA, Bjerrum NJ. Phosphoric acid doped polybenzimidazole membranes: physiochemical characterization and fuel cell applications. J Appl Electrochem 2001;31:773e9. Chen CY, Lai WH. Effects of temperature and humidity on the cell performance and resistance of a phosphoric acid doped polybenzimidazole fuel cell. J Power Sources 2010;195:7152e9. Li Q, He R, Jensen JO, Bjerrum NJ. PBI-based polymer membranes for high temperature fuel cells e preparation, characterization and fuel cell demonstration. Fuel Cells 2004;4(3):147e59. Cheddie D, Munroe N. Mathematical model of a PEMFC using a PBI membrane. Energy Convers Manage 2006;47:1490e504. Cheddie D, Munroe N. A two phase model of an intermediate temperature PEM fuel cell. Int J Hydrogen Energy 2007;32:832e41. Cheddie D, Munroe N. Three dimensional modeling of high temperature PEM fuel cells. J Power Sources 2006;160:215e23. Scott K, Pilditch S, Mamlouk M. Modeling and experimental validation of a high temperature polymer electrolyte fuel cell. J Appl Electrochem 2007;37:1245e59. Sousa T, Mamlouk M, Scott K. A dynamic non-isothermal model of a laboratory intermediate temperature fuel cell using PBI doped phosphoric acid membranes. Int J Hydrogen Energy 2010;35:I2065e80. Shamardina O, Chertovich A, Kulikovsky AA, Khokhlov AR. A simple model of a high temperature PEM fuel cell. Int J Hydrogen Energy 2010;35:9954e62. Lobato J, Canizares P, Rodrigo MA, Pinar FJ, Mena E, Ubeda D. Three-dimensional model of a 50 cm2 high temperature PEM fuel cell. Study of the flow channel geometry influence. Int J Hydrogen Energy 2010;35:5510e20. Lobato J, Canizares P, Rodrigo MA, Piuleac CG, Curteanu S, Linares JJ. Direct and inverse neural networks modelling applied to study the influence of the gas diffusion layer

[22]

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36]

[37]

2775

properties on PBI-based PEM fuel cells. Int J Hydrogen Energy 2010;35:7889e97. Boaventura M, Sousa JM, Mendes A. A dynamic model for high temperature polymer electrolyte membrane fuel cells. Int J Hydrogen Energy 2011;36:9842e54. Sousa T, Mamlouk M, Scott K. An isothermal model of a laboratory intermediate temperature fuel cell using PBI doped phosphoric acid membranes. Chem Eng Sci 2010;65:2513e30. Jiao K, Li X. A three-dimensional non-isothermal model of high temperature proton exchange membrane fuel cells with phosphoric acid doped polybenzimidazole membranes. Fuel Cells 2010;10(3):351e62. Siegel C, Bandlamudi G, Heinzel A. Systematic characterization of a PBI/H3PO4 sol-gel membrane-modeling and simulation. J Power Sources 2011;196:2735e49. He RH, Qingfeng L, Bach A, Jensen JO, Bjerrum NJ. Physiochemical properties of phosphoric acid doped polybenzimidazole membranes for fuel cells. J Membr Sci 2006;277:38e45. Olapade PO, Meyeres JP, Borup RL, Mukundan R. Parametric study of the morphological properties of HT-PEMFC components for effective membrane hydration. J Electrochem Soc 2011;158(6):B639e49. Chippar P, Ju H. Three-dimensional non-isothermal modeling of a phosphoric acid-doped polybenzimidazole (PBI) membrane fuel cells. Solid State Ionics 2012;225:30e9. Galbiati S, Baricci A, Casalegno A, Maechesi R. Experimental study of water transport in a polybenzimidazole-based high temperature PEMFC. Int J Hydrogen Energy 2012;37(3):2462e9. Chippar P, Ju H. Numerical modeling and investigation of gas crossover effects in high temperature proton exchange membrane (PEM) fuel cells. Intl J Hydrogen Energy 2013;38(18):7704e14. Ma Y. The fundamental studies of polybenzimidazole/ phosphoric acid polymer electrolyte for fuel cells. Department of Chemical Engineering, Case Western Reserve University; 2004. Schmidt TJ, Baurmeister J. Properties of high temperature PEFC Celtec
-P1000 MEAs in start/stop operation mode. J Power Sources 2008;176:428e34. Vogel W, Lundquist L, Ross P, Stonehart. Reaction pathways and poisons - II: the rate controlling step for electrochemical oxidation of hydrogen on Pt in acid and poisoning of the reaction by CO. Electrochim Acta 1975;20:79e93. Appleby A. Oxygen reduction on oxide-free platinum in 85% orthophosphoric acid: temperature and impurity dependence. J Electrochem Soc 1970;117:328e35. Sugishima N, Hinatsu JT, Roulkes FR. Phosphorous acid impurities in phosphoric acid fuel cell electrolytes. J Electrochem Soc 1994;141:3332e5. Incropera FP, Dewitt DP, Bergman TL, Lavine AS. Fundamentals of heat and mass transfer. 6th ed. John Wiley & Sons; 2007. Ju H. Investigation of the effects of the anisotropy of gas diffusion layers on heat and water transport in polymer electrolyte fuel cells. J Power Sources 2009;191:259e68.