Effect of primary parameters on the performance of PEM fuel cell

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Effect of primary parameters on the performance of PEM fuel cell M. Tohidi*, S.H. Mansouri, H. Amiri Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

article info

abstract

Article history:

A one-dimensional, steady-state and isothermal model for a proton exchange membrane

Received 9 August 2009

(PEM) fuel cell has been developed to investigate the effects of various parameters such as

Received in revised form

the molar fraction of nitrogen gas, relative humidity, temperature, pressure, membrane

17 March 2010

thickness, anode and cathode stoichiometric flow ratio and the distribution of oxygen in

Accepted 25 March 2010

the cathode catalyst while water transfer in membrane is produced by diffusion, pressure

Available online 7 May 2010

gradient and electro-osmotic drag. The most critical problems to overcome in the proton exchange membrane (PEM) fuel cell technology are the water and thermal management.

Keywords:

The results show that the cell performance increases as operating pressure and temper-

Proton exchange membrane (PEM)

ature are increased. The performance of cell can decrease by decreasing the relative

Water transport

humidity of inlet gases and increasing the membrane thickness. Increasing the anode and

Mathematical model

cathode stoichiometric flow ratio can also improve the cell performance. As the oxygen

Catalyst layer

concentration becomes zero in about 8 percent depth of cathode catalyst layer, the

Parametric studies

thickness of cathode catalyst layer can be reduced 92 percent without any potential loss in output voltage. The cathode activation loss also becomes high by increasing the molar fraction of nitrogen gas. The modeling results agree very well with experimental results. ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

There is increasing interest in the use of proton exchange membrane (PEM) fuel cell for both mobile and stationary applications as an environmentally friendly power source. Emphasis is placed on high power density with adequate energy conversion efficiency for mobile applications, and on high energy efficiency with adequate power density for stationary applications. Two key issues limiting the widespread commercialization of fuel cell technology are better performance and lower cost. PEM fuel cell performance is limited by polarizations. A good understanding of the effect of design and operating conditions on the cell potential is required in order to reduce polarization. Major operating parameters include cell temperature, pressure, reactant stoichiometry, and gas stream composition. Cell structure and

materials are also of importance. Some problems particular to PEM fuel cells result from the use of an ionomer as electrolyte. The choice of membrane thickness should be decided by several factors, such as the manufacturing cost, the mechanical response of membrane and its stress failure. The solubility of a reactant gas in, and the ionic resistivity of, the electrolyte depends on the membrane moisture content and temperature. As a result, the membrane requires adequate humidification for proper performance. Humidification is often achieved via water vapor in the reactant gas streams. However, excessive water presence, especially water production at high power density from cell reaction, can lead to the flooding of the electrode pores, thereby limiting gas transport to the reaction sites. Increasing the operating temperature can decrease mass-transport limitations and increase the electrochemical reaction rates and water vapor partial pressure. Thus, both

* Corresponding author. Tel.: þ98 341 2533577. E-mail address: [email protected] (M. Tohidi). 0360-3199/$ e see front matter ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.03.112

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 9 3 3 8 e9 3 4 8

Nomenclature a c Di Di,j Er F I i0 j kp kf Ki k M n nd N P R si t T ul V xi z zi

effective catalyst surface area per unit volume, m1 concentration, mol m3 diffusion coefficient of species i, m2 s1 diffusivity of gas pair iej in a mixture, m2 s1 open-circuit potential, V Faraday constant, 96,487, C mol1 local current density, A/m2 exchange current density, A/m2 volumetric current density, A/m3 hydraulic permeability, m2 electro-kinetic permeability, m2 Henry’s law constant for species i, Pa m3 mol1 membrane ionic conductivity, A V1 m1 molecular weight, kg mol1 number of electrons electro-osmotic drag coefficient mole flux, mol m2 s1 hydraulic pressure, Pa universal gas constant, 8.3143 J mol1 K1 stoichiometric coefficient of species i thickness, m temperature, K convective velocity of the liquid water, m s1 cell potential, V molar fraction of species i distance, m charge number of species i

Greek letters a ratio of the water flux to the hydrogen flux

thermal and water management are critical to the performance of PEM fuel cells. In the last decade, a number of fundamental studies have been directed towards increasing our understanding of PEM fuel cells and their performance. One of the earlier studies by Bernardi [1] focused on the humidification requirements of inlet gases in order to maintain water balance in a PEM cell. Bernardi and Verbrugge continued to investigate the performance of a gas-fed porous cathode bonded to an ion-exchange membrane [2], and developed a one-dimensional isothermal cell model [3]. Springer and his colleagues developed an isothermal, one-dimensional, steady-state model of a complete PEM fuel cell [4], including variable membrane hydration. The anode catalyst layer was neglected and the cathode catalyst layer was taken to be a thin reactive plane. Rama et al. [5] developed an isothermal, one-dimensional, steady-state model and investigated the effect of carbon dioxide in inlet fuel. Marr and Li [6] investigated the catalyst utilization as well as the optimal composition and structure for the cathode catalyst layer, such as the catalyst loading, catalyst type, catalyst layer thickness, void fraction, and ionomer content. Also Rowe and Li [7] developed a one-dimensional and steady-state model and investigated the temperature distribution across the cell. Wu et al. [8] developed a two-dimensional, isothermal and transient model and investigated the

a A , aC 3 3mem w h l m d z s f r

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anodic and cathodic transfer coefficients porosity volume fraction of water in membrane over-potential, V water content of membrane viscosity, kg m1 s1 experimentally determined swelling coefficient for membrane stoichiometric flow ratio conductivity of the electronically conductive phase, A V1 m1 electrical potential, V density, kg m3

Subscripts and superscripts 0 initial value A anode a water activity C cathode Cat catalyst layer region d gas diffuser eff effective value ele electrode region g gas phase i mobile species i ij species i, j mem membrane region ref reference s solid phase sat saturated condition w water

variation of reactants concentration, activation over-potential, reaction rate and corresponding current density distribution in the catalyst layer (CL). Owejan et al. [9] investigated the flow of water from the porous gas diffusion layer (GDL) into the channel gas flows, the flow of water within the bipolar plate channels themselves and the dynamics of flow through multiple channels connected to common manifolds which maintain a uniform pressure differential across all possible flow paths. These two-phase flow effects were studied at relatively low operating temperatures under steady-state conditions and during transient air purging sequences. Liu et al. [10] investigated the effect of the assembly error of the bipolar plate on the pressure distribution and stress failure of membrane electrode assembly (MEA). In this study, a methodology based on FEA model, “least squares-support vector machine (LS-SVM)” simulation and statistical analysis is developed very well. Also, Kusoglu et al. [11] investigated the mechanical response of fuel cell proton exchange membranes subjected to a single hygro-thermal duty cycle in a fuel cell assembly. In this study, the behavior of the membrane with temperature and humidity dependent material properties is simulated under temperature and humidity loading and unloading conditions. The aim of the present work is to develop a one-dimensional and steady-state model to investigate the effects of various parameters such as the molar fraction of nitrogen gas,

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relative humidity, temperature, pressure, membrane thickness, anode and cathode stoichiometric flow ratio and the distribution of oxygen in the cathode catalyst layer. Such a study will be useful for the design and operation of practical PEMFC stacks.

where I is the local current density and F is the Faraday constant. In anode, the water flux is not constant and is obtained by the iteration method: NA3 ¼ NAH2 O ¼ aNH2 ¼ a

2.

Governing equations

In this section, we present governing equations in electrodes, catalyst layers and membrane. Fig. 1 is a schematic of a fuel cell.

2.1.

(5)

where a is the ratio of the water flux to the hydrogen flux. The wet air is used as oxidant in cathode and the electrochemical reaction is represented as: O2 þ 4Hþ þ 4e 02H2 O 1 ¼ O2

Governing equations in electrodes

I 2F

2 ¼ N2

(II)

3 ¼ H2 OðgÞ

In cathode, the oxygen flux is determined as: Assumption: the gases are ideal; the condition is steady; the gas-phase viscosity is quite small (the gas transport is only by diffusion in electrodes); the water phase is vapor in electrodes; the gases emission is very low in the membrane. For the diffusion of an n-component ideal-gas through a porous medium, the StefaneMaxwell equation takes the form: Vxi ¼

n X j¼1

1

0

xi Nj  xj Ni A RT@ PDeff i;j

(1)

where Ni is the gas-phase flux of species i, xi is the molar fraction of species i, Di,jeff is an effective binary diffusivity of the pair iej in the porous medium, P is the hydraulic pressure, R is the universal gas constant and T is the absolute temperature. We relate the effective diffusion coefficient to the diffusion coefficient in a nonporous system, Di,j, by:  1:5 d Di;j Deff i;j ¼ eg

(2)

where edg is the porosity and binary diffusion coefficient can be calculated by using the equation commended by Bird et al. [12]. The wet hydrogen is used as fuel in anode and the electrochemical reaction is represented as: þ



H2 02H þ 2e 1 ¼ H2

2 ¼ CO2

As the net motion of nitrogen is zero, thus: N2 ¼ NN2 ¼ 0

I 2F

(7)

The water flux in the cathode is related to the hydrogen flux: NC3 ¼ NCH2 O ¼ ð1 þ aÞNH2

(8)

The solid-phase potential gradient is related to the cell operating current density by Ohm’s law: dfs is ¼  eff dz s

(9)

where seff is the effective conductivity of the electronically conductive phase and fs is the electrical potential in the solid phase. The fluid composition in the anode and cathode flow channels is assumed to be uniform. The anode and cathode feed streams are each assumed to be saturated with water vapor as: xsat ¼

Psat ðTÞ P

(10)

(I)

(3)

x3 ¼

In anode, the hydrogen flux is determined as: N1 ¼ NH2 ¼

(6)

where Psat(T ), xsat are the pressure and molar fraction of water in saturated conditions. Thus, the governing equations as in Ref. [7] and the boundary conditions are represented as: at z ¼ za:

3 ¼ H2 OðgÞ

N2 ¼ NCO ¼ 0

I N1 ¼ NO2 ¼  4F

  xAsat zA  a 1  xAsat xAsat  að1  xAsat Þ þ zA  1

(11)

x2 ¼ 0

(12)

x1 ¼ 1  x3

(13)

(4)

at Z ¼ Zf:

Fig. 1 e The schematic of a fuel cell.

x3 ¼

  xCsat zC þ 2ð1 þ aÞ 1  xCsat xON zC þ ð2a þ 1Þð1  xCsat ÞxON

(14)

x1 ¼

  ðzC  1Þ 1  xCsat xON zC þ ð2a þ 1Þð1  xCsat ÞxON

(15)

x2 ¼ 1  x1  x3

(16)

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where z is the stoichiometric flow ratio, xON is the molar fraction of oxygen gas in inlet dry air and Psat can be represented as [13]: Psat

5 2 7 3 ¼ 10ð2:1794þ0:02953T9:183710 T þ1:445410 T Þ

2.2.

a¼ (17)

Assumption: the pressure gradient is neglected in the catalyst layer; the oxygen solubility obeys the Henry’s law. The governing equations in catalyst layer are ButlereVolmer, NernstePlanck and the conservation equations. The ButlereVolmer equation represents the general relation between the net current density produced and the activation over-potential: ck cref k

!gk 

    naA F naC F exp ðhact Þ  exp  ðhact Þ RT RT (18)

where j(z) is the volumetric current density, a is the effective catalyst surface area per unit volume, iref is the reference 0 are the concentration of exchange current density, ck, cref k species k in total and reference state, gk is the function of stoichiometric coefficient of species k, n is the number of electrons, hact ¼ fs  fm is the activation over-potential and aA, ac are anodic and cathodic transfer coefficients. The flux of soluble species in the membrane is described by the NernstePlanck equation: zi F Ni ¼  Di ci Vfm  Di Vci þ ci ul RT

(19)

where the terms on the right-hand side represent migration due to the electric field, diffusion and convection. zi is the charge number of ion, Di is the diffusion coefficient species i, ci is the concentration of species i, fm is the electrical potential in the membrane phase and ul is the convective velocity of the liquid water which can be estimated by Schlogl’s equation [3]. The convection of water in the catalyst layer is determined by two processes: pressure gradient and electro-osmotic drag.  ul ¼

emem w

Nw ¼ Dw

kf kP  cHþ FVfm  VP m m



kp dp dcw im þ nd  emem cw w dz F m dz

(20)

(21)

(23)

l ¼ 0:043 þ 17:81a  39:85a2 þ 36:0a3 l ¼ 14 þ 1:4ða  1Þ cHþ ¼ cp ¼

for 0 < a  1 for 1 < a  3

e ð1 þ dlÞ

(24)

(25)

here, d is an experimentally determined swelling coefficient for the membrane and e is expressed as: dry

e¼

rm Mm

(26)

dry

with rm corresponding to the density of the dry membrane and Mm is the equivalent membrane weight. Water concentration is calculated as follows: cH2 O ¼ cw ¼

el ð1 þ dlÞ

(27)

The conservation law represents the rate of production or consumption reaction species as: si si V$Ni ¼  V$i ¼  jðzÞ nF nF

(28)

where si is the stoichiometric coefficient of species i which is expressed as: X

si Mi i ¼ ne Z

(29)

i

The flow of charged species is related to the current density by: i¼F

X

zk Nk

(30)

K

Catalyst : 1 ¼ O2 ; H2

2 ¼ Hþ

3 ¼ H2 OðlÞ

Thus, the governing equations as in Ref. [7] and the boundary conditions are represented as:at z ¼ zb, z ¼ ze: Cat ¼ Nele ¼ Nele NCat 1 1 ; im ¼ 0; N3 3 ; fm ¼ 0; lCat ¼ lele ¼ f ðx3ele ; Pele Þ;

c1 ¼ c01

where m is the viscosity, nd is the electro-osmotic drag coeffiis the volume fraction of the water in the cient, 3mem w membrane, kf is the electro-kinetic permeability and kp is the hydraulic permeability. The determination of the electro-osmotic drag coefficient, nd, follows the work of Springer et al. [4] who proposed a functional relationship between this coefficient and membrane water content for Nafion 117: 2:5l nd ¼ 22

Pw P ¼ xw Psat ðTÞ Psat ðTÞ

A fit of the relationship of l versus water activity, a, used in the model is [4]:

Governing equations in catalyst layers

jðzÞ ¼ airef 0 P

migrating Hþ ion and the possible maximum water content of membrane. Also the water activity is represented as:

(31)

at z ¼ zc, z ¼ zd: im ¼ I

(32)

where the Eq. (32) is used to find fs, and c01 is expressed as: c01 ¼ x1

P K1

(33)

where K1 is the Henry’s constant.

(22)

where l is the water content of membrane, which is defined as the number of water molecules per sulfonic acid groups present in the polymer. The numerical values 2.5 and 22 correspond to the number of water molecules dragged per

2.3.

Governing equations in membrane

Assumption: pressure gradient is linear in the membrane; the gases emission is very low in the membrane.

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The most critical problems to overcome in the proton exchange membrane (PEM) fuel cell technology are the water and thermal management. The flux of convective water transport in the membrane is determined by two processes: pressure gradient and electro-osmotic drag, Eqs. (20) and (21). Hence, the flux of water and proton in the membrane are obtained by the NernstePlanck equation. The membrane ionic conductivity is a function of the water content of membrane as:

where: hact ¼

( !gk ) cref RT 1 j k sin h1 ck naF 2 airef o

(42)

I hmem ¼ tmem k hohmic ¼

(43)

I tele seff

(44)

and the power density is expressed as:

   1 1  k ¼ ð0:005139l  0:00326Þexp 1268 303 T

(34)

P ¼ IV ¼ IðEr ðT; Pi Þ  hact  hmem  hohmic Þ

(45)

also, the water diffusion coefficient in the membrane [4] is expressed as:

2.5.

Dw ¼ Dl

As the above equations are Stiff, Gear method is used [15]. Thus, in the first step, we guess the value of a, then we decouple the equations of anode and cathode electrode, anode and cathode catalyst and membrane. On the interface between the membrane and cathode catalyst, if the hydration index obtained by the membrane equations becomes equal to the hydration index obtained by the cathode catalyst equations, the iteration process will stop.

8 1 > > < 1 þ 2ðl  2Þ ¼ DT 3  1:38ðl  3Þ > > : 2:563  0:33l þ 0:0264l2  0:000671l3

for for for for

l2 24 (35)

where DT is expressed as:    1 1 DT ¼ 106 exp 2416  303 T

(36)

Thus, the governing equations as in Ref. [7] and the boundary conditions are represented as:at z ¼ zc: ljACat ¼ ljmem

(37)

fjACat ¼ fjmem

(38)

Nw jmem ¼ cte ¼ Nw jACat

(39)

where the Eq. (39) is used to find the water flux in the membrane.

2.4.

Solution technique

Cell potential

The thermodynamic open-circuit potential is estimated with the following relationship (Nernst equation): Er ðT; Pi Þ ¼ 1:229  0:9  103 ðT  298Þ þ

 RT  2 ln PH2 PO2 4F

(40)

3.

Results and discussion

A mathematical model of PEM fuel cell is a very useful and effective tool to optimize cell design and its operating conditions. In this section, the above model will be used to evaluate various real operating conditions based on Refs. [2e4] and investigate the effects of membrane and catalyst thickness on the performance of a PEM fuel cell. Table 1 [3] lists the important parameters used for the base-case.

3.1. Comparison of the calculated and experimental results Fig. 2 compares the calculated fuel cell potential as a function of current density with experimental data and Bernardi and Verbrugge model [3,16] for the base-case conditions. Due to the potential losses in fuel cell, the output voltage is lower than open-circuit potential. The results of the present model are in agreement with experimental data and B & V model.

Due to the potential losses in fuel cell (h), the output voltage is lower than open-circuit potential [14]:

3.2.

V ¼ Er ðT; Pi Þ  hact  hmem  hohmic

Due to the three mechanisms of irreversible losses: activation and membrane and ohmic, the actual cell potential is smaller

(41)

Effect of molar fraction of nitrogen gas

Table 1 e Operating parameters for a cell with hydrogen fuel, air oxidant and Nafion 117 membrane at base-case conditions [3]. Parameter tele tcat tmem PC PA xON

Value 4

2.6  10 m 1  105 m 2.3  104 m 5  105 Pa 3  105 Pa 0.21

Parameter

Value

Parameter

Value

Parameter

Value

T zA zC edg 3mem w d

353 K 1.3 3 0.4 0:35l=16:8 0.0126

Anode: aA, aC Cathode: aA, aC seff kp kf Mm

0.5 2 53 Um1 1.8  1018 m2 7.18  1020 m2 1.1  103 kg mol1

mw rw E0r KH2 KO2 dry rm

3.56  104 kg ms1 5.4  104 mol m3 1.229 4.5  103 Pa m3 mol1 2  104 Pa m3 mol1 1.98  103 kg m3

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Fig. 2 e Comparison of predicted performance curve with experimental data and B & V model at base-case conditions with hydrogen fuel and air oxidant [3,16].

than the reversible cell potential. The activation polarization arises from the slow rate of electrochemical reactions, the membrane loss depends on the water content of membrane and ionic resistance to the flow of ions in the electrolyte, and the ohmic loss due to electronic resistance to the flow of electrons in the electrode. Fig. 3 shows components of the overall cell polarization at the molar fraction of 0% nitrogen gas for the base-case. We observe that at the low current densities (less than 1000 A/m2), the activation over-potential of the oxygen reduction reaction is almost entirely responsible for the potential losses of the cell. For current densities greater than 2000 A/m2, the membrane and ohmic losses become more significant, and the cathode activation over-potential reaches a relatively constant value. In the last, the anode activation

Fig. 3 e The potential losses at the molar fraction of 0% nitrogen gas for base-case conditions (Table 1).

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Fig. 4 e Polarization curve at several molar fractions of nitrogen gas for base-case conditions (Table 1).

over-potential is zero at the low operating current densities and it makes only a minor contribution to the total cell overpotential even at the high operating current densities. Thus, by increasing the molar fraction of nitrogen gas, the oxygen concentration decreases and the cathode activation loss increases which also leads to the potential loss in output voltage, Fig. 4. By increasing the molar fraction of nitrogen gas, the loss in output voltage also leads to the loss of power density, Fig. 5.

3.3.

Effect of thickness of cathode catalyst layer

Fig. 6 shows that the oxygen gas diffuses into the cathode catalyst layer up to about 8 percent at the current densities more than 1000 A/m2and the diffusion of oxygen gas

Fig. 5 e Power density curve at several molar fractions of nitrogen gas for base-case conditions (Table 1).

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Fig. 6 e The distribution of oxygen concentration in the cathode catalyst layer for four current densities at basecase conditions (Table 1).

catalyst layer thickness has not been used, we can decrease the thickness of cathode catalyst layer from 1  105 m to 8  107 m which the oxygen concentration becomes zero at low current densities, 1000 A/m2, without any loss in output voltage, Fig. 7. Fig. 8 shows that the effect of decreasing the thickness of cathode catalyst layer on the mass transfer. By decreasing the thickness of cathode catalyst layer from 1  105 m to 8  107 m at current density 4000 A/m2, the oxygen flux does not change in catalyst layer. Thus, the mass transfer remains constant. Bernardi and Verbrugge [2] also used a very thin catalyst layer thickness around 1  107 m in their one-dimensional model of the cathode side of a PEM fuel cell which the oxygen concentration did not become zero at current densities lower than 3000 A/m2and the oxygen gas could inter into the membrane. If the thickness of catalyst layer becomes lower than 8 percent of its original value, we will have losses in the output voltage. Fig. 9 shows that by decreasing the thickness

decreases by increasing the current density. At higher current densities, 8000 A/m2, only 0.7% utilization of the cathode catalyst is predicted. This result is in agreement with the predictions of the oxygen electrode/membrane model, which showed that at higher current densities, such as 8800 A/m2, only 0.4% of the cathode catalyst is used [3]. By increasing the current density, the oxygen concentration also becomes negligible in the catalyst layer. The catalyst layer is made of platinum which costs high. In order to decrease the cost of material, we should decrease the thickness of catalyst layer without affecting the cell performance. As the oxygen gas has diffused only into the catalyst layer up to about 8 percent, and the remaining 92 percent of the

Fig. 7 e The effect of decreasing the thickness of cathode catalyst layer on the polarization curve (T [ 353 K, PC [ 5 3 105 Pa, PA [ 3 3 105 Pa, zA [ 1.3, zC [ 3).

Fig. 8 e The effect of decreasing the thickness of cathode catalyst layer on the mass transfer (a) in total scale, (b) in small scale (I [ 4000 A/m2, T [ 353 K, PC [ 5 3 105 Pa, PA [ 3 3 105 Pa, zA [ 1.3, zC [ 3).

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Fig. 9 e The effect of decreasing the thickness of cathode catalyst layer on the polarization curve (T [ 353 K, PC [ 5 3 105 Pa, PA [ 3 3 105 Pa, zA [ 1.3, zC [ 3).

Fig. 11 e The effect of membrane thickness on the polarization curve (T [ 353 K, PC [ 5 3 105 Pa, PA [ 3 3 105 Pa, zA [ 1.3, zC [ 3).

of cathode catalyst layer from 8  107 m to 1  107 m, the peak of voltage loss will be 3.2% at current densities of lower than 2500 A/m2. If we neglect the loss of voltage, we can decrease the thickness of cathode catalyst layer to 1  107 m. Also, our predictions will compare with Ref. [17] as a bench mark solution. Therefore, many computations indicate that the bulk of the electrochemical reactions occur within a very thin layer close to the gas diffusion layer boundary, because the oxygen dissolved in the ionomer penetrates only a small distance into the catalyst layer. This result suggests that the catalyst maybe under-utilized at normal operating cell current densities. Therefore, future efforts in catalyst layer design

should be focused on thinner layers which will only improves platinum utilization but also reduces ohmic losses, Ref. [18].

Fig. 10 e The effect of membrane thickness on the water content of membrane (I [ 9000 A/m2, T [ 353 K, PC [ 5 3 105 Pa, PA [ 3 3 105 Pa, zA [ 1.3, zC [ 3).

3.4.

Effect of membrane thickness

In this section, we compare three thicknesses of Nafion membrane. Fig. 10 shows that by increasing the membrane thickness at current density 9000 A/m2, proton transfers hardly through the membrane due to the longer distance of proton traveled across the membrane and lower water content of the membrane. Therefore increases the membrane loss and also

Fig. 12 e The effect of cell temperature on the membrane ionic conductivity when Nafion 117 membrane is used (I [ 9000 A/m2, PC [ 5 3 105 Pa, PA [ 3 3 105 Pa, zA [ 1.3, zC [ 3).

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Fig. 13 e The effect of cell temperature on the polarization curve when Nafion 117 membrane is used (PC [ 5 3 105 Pa, PA [ 3 3 105 Pa, zA [ 1.3, zC [ 3).

Fig. 15 e The effect of operating pressure on the polarization curve when Nafion 117 membrane is used (T [ 353 K, PA [ 3 3 105 Pa, zA [ 1.3, zC [ 3).

ionic resistance to the flow of ions (particular at higher current densities) which leads to the loss of output voltage (Fig. 11). It seems that the thinner membrane (Nafion 112 membrane) to be chosen as electrolyte, the better the cell performance. However, the difficulty of preparing membrane electrode assemble using thin membrane would be a challenge.

membrane. Fig. 12 shows that the membrane ionic conductivity increases by increasing the cell temperature at current density 9000 A/m2. Thus, proton transfer through the membrane is simple and the membrane resistance decreases due to increasing the cell output voltage, Fig. 13. However, the cell temperature should not be higher than 373 K because the reactant gases are diluted by water vapor and lifetime of Nafion membrane decreases at high temperature.

3.5.

Effect of cell temperature

The membrane ionic conductivity is a function of the water content of membrane and the cell temperature. If the cell temperature is held constant, the membrane ionic conductivity has linear relationship with the water content of

3.6.

Fig. 14 e The effect of operating pressure on the water content of membrane when Nafion 117 membrane is used (I [ 9000 A/m2, T [ 353 K, PA [ 3 3 105 Pa, zA [ 1.3, zC [ 3).

Fig. 16 e The effect of operating pressure and temperature on the polarization curve when Nafion 117 membrane is used (PA [ 3 3 105 Pa, zA [ 1.3, zC [ 3).

Effect of operating pressure

In this section, we study the effect of operating pressure. Fig. 14 shows that the membrane water content increases by

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Fig. 17 e The effect of relative humidity of reactant gases on the polarization curve when Nafion 117 membrane is used (T [ 353 K, PC [ 5 3 105 Pa, PA [ 3 3 105 Pa, zA [ 1.3, zC [ 3).

increasing the pressure of cathode side at current density 9000 A/m2. Thus, the membrane ionic resistance decreases due to increasing the cell output voltage, Fig. 15. Also, Fig. 16 shows that the cell performance increases by increasing the operating pressure and temperature.

3.7.

Effect of relative humidity of reactant gases

Fig. 17 shows that the cell performance increases as the relative humidity of inlet reactant gases increases from 0 to 75%, due to the higher water content of the membrane at

Fig. 19 e The effect of cathode stoichiometric flow ratio on the polarization curve when Nafion 117 membrane is used (T [ 353 K, PC [ 5 3 105 Pa, PA [ 3 3 105 Pa, zA [ 1.3).

higher relative humidity of inlet gases and lower membrane resistance. While the relative humidity of inlet reactant gases is higher than 75%, the performance of fuel cell almost remains constant. The reason is as membrane resistance decreases, it is compensated by an increase of cathode overpotential due to the liquid water. To reduce liquid water in the cathode, relative humidity of inlet reactant gases should not be higher than 100%.

3.8.

Effect of stoichiometric flow ratio

The stoichiometric flow ratio is the ratio of the amount of oxygen or hydrogen added in the reactant feed to the amount that is required by the electrochemical reaction. Fig. 18 shows that the cell performance increases by increasing the anode stoichiometric flow ratio up to 3. It can be concluded that the amount of inlet fuel is sufficient for flow with a ratio more than 3, therefore the cell performance becomes rather flat and recovery increases. Fig. 19 shows that the cell performance increases by increasing the cathode stoichiometric flow ratio but it has no appreciable effect on the PEMFC performance.

4.

Fig. 18 e The effect of anode stoichiometric flow ratio on the polarization curve when Nafion 117 membrane is used (T [ 353 K, PC [ 5 3 105 Pa, PA [ 3 3 105 Pa, zC [ 3).

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Conclusions

A one-dimensional isothermal model for a proton exchange membrane fuel cell was developed in which water transport in the membrane by electro-osmotic drag; back diffusion and pressure differential is included, because the most critical problems to overcome in the proton exchange membrane (PEM) fuel cell technology are the water and thermal management. The model is used to investigate the effects of the molar fraction of nitrogen gas, relative humidity, temperature, pressure, membrane thickness, and anode and cathode stoichiometric flow ratio on the PEM fuel cell performance.

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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 9 3 3 8 e9 3 4 8

The results show that the membrane ionic conductivity and the cell performance increase by increasing the cell temperature. By increasing the relative humidity of inlet gases, the water content of membrane increases and membrane resistance decreases due to increasing the output voltage. By increasing the membrane thickness, the water content of membrane decreases and membrane resistance increases due to decreasing the cell performance. However, the choice of membrane thickness should be decided by several factors, such as the manufacturing cost, the mechanical response of membrane and its stress failure. Also, the water content of membrane and the cell performance increase by increasing the pressure of cathode side. By increasing the anode and cathode stoichiometric flow ratio up to 3, the cell performance can also improve and as the oxygen concentration becomes zero in about 8 percent of cathode catalyst layer, we can decrease the thickness of cathode catalyst layer from 1  105 m to 1  107 m. Therefore, many computations indicate that the bulk of the electrochemical reactions occurs within a very thin layer close to the gas diffusion layer boundary, because the oxygen dissolved in the ionomer penetrates only a small distance into the catalyst layer. This result suggests that the catalyst maybe underutilized at normal operating cell current densities. Therefore, future efforts in catalyst layer design should be focused on thinner layers which will only improves platinum utilization but also reduces ohmic losses. The cathode activation loss also becomes high by increasing the molar fraction of nitrogen gas due to the loss of output voltage. These studies will be useful for the design and operation of practical PEM fuel cell stacks.

references

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