the effects of porosity distribution variation

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The effects of porosity distribution variationon PEM fuel cell performance

R. Roshandela,*, B. Farhanieha, E. Saievar-Iranizadb

a

School of Mechanical Engineering, Sharif University of Technology, Tehran, IranbDepartment of Physics, Faculty of Science, University of Tarbiat Modarres, Tehran, Iran

Received 2 May 2004; accepted 22 November 2004

Available online 17 March 2005

Abstract

Gas diffusion layers (GDL) are one of the important parts of the PEM fuel cell as they serve

to transport the reactant gases to the catalyst layer. Porosity of this layer has a large effect on

the PEM fuel cell performance. The spatial variation in porosity arises due to two effects: (1)

compression of the electrode on the solid landing areas and (2) water produced at the cathodeside of gas diffusion layers. Both of these factors change the porosity of gas diffusion layers

and affect the fuel cell performance. To implement this performance analysis, a mathematical

model which considers oxygen and hydrogen mass fraction in gas diffusion layer and the

electrical current density in the catalyst layer, and the fuel cell potentials are investigated. The

porosity variation in the GDL is calculated by considering the applied pressure and the amount

of the water generated in the cell. The validity of the model is approved by comparing the

computed results with experimental data. The obtained results show that the decrease in the

average porosity causes the reduction in oxygen consumption, so that a lower electrical current

density is generated. It is also shown that when the electrical current density is low, the

porosity variation in gas diffusion layer has no significant influence on the level of polarization

whereas at higher current density the influence is very significant. The porosity variation causesnon-uniformity in the mass transport which in turn reduces the current density and a lower fuel

cell performance is obtained.

q 2005 Elsevier Ltd. All rights reserved.

0960-1481/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.renene.2004.11.017

Renewable Energy 30 (2005) 15571572

www.elsevier.com/locate/renene

* Corresponding author.
http://www.elsevier.com/locate/renenehttp://www.elsevier.com/locate/renene


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Nomenclature

A electrode surface area (cm2)

C concentration (mol/cm3)C channel concentration (mol/cm3)

CHC fixed charge concentration (mol/cm3)

F faraday constant (C)

I electrical current density (A/cm2)

I0 exchange electrical current density (A/cm2)

Ilim limiting current density (A/cm2)

k membrane ionic conductivity (1/U cm)

k4 membrane electrokinetic permeability (cm2)

kp membrane hydraulic permeability (cm

2

)lm membrane thickness (cm)

MK water balance in anode (mol/s)

MC water balance in cathode (mol/s)

M1,Max water amount corresponding to complete flooding (mol/s)

P total pressure (atm)

pH2 hydrogen pressure (atm)

pO2 oxygen pressure (atm)

psatw saturation vapor pressure (atm)

R gas constant (J/mol K)

rH catalyst transfer rateT temperature (K)

U reactant velocity in GDL (cm/s)

v water velocity in membrane (cm/s)

V operational voltage (V)

VOCV open circuit voltage (V)

wel water produced in cathode (mol/cm2 s)

wtr water transport in membrane (mol/cm2 s)

whu water entering the cell due to reactant humidification (mol/cm2 s)

wout water outgoing from the cell (mol/cm2 s)

x mole fractionhact activation overpotential (V)

hohm ohmic overpotential (V)

hdif diffusion overpotential (V)

hconv convection overpotential (V)

d water density in membrane pores (kg/cm3)

4 electrical potential (V)

m viscosity (kg/m s)

r density

tR membrane resistance ratio

z stoichiometric ratiox membrane water transport ratio

R. Roshandel et al. / Renewable Energy 30 (2005) 155715721558


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1. Introduction

Fuel cells convert the chemical energy of hydrogen in the presence of oxygen into

electricity. Their high efficiency and low emissions have made them a very suitable power

system for next generation of vehicular application as well as small stationary power

plants. Fuel cells are usually classified by the nature of electrolyte they use. Polymerelectrolyte membrane (PEM) fuel cell systems are considered to be promising and

environmentally friendly power source. This is due to the attributes of high energy density

at low operating temperature, good performance in intermittent operation, zero emission,

quick start up capacity, and minimal problems from components corrosion and electrolyte

leakage [15].

The properties of the diffusion layer effects the optimum performance of the catalyst

and electrode [6]. These layers are porous to allow for distribution of the gases to

unexposed areas of the flow channel and for complete utilization of the electrode area. The

electrical conductivity of these layers could affect the transport of electrons to the current

collector from the electrode.The development of a theoretical model of the PEM fuel cell as well as corresponding

analyses, are crucial to gain a good understanding of the effect of the operating conditions

on the cell potential. Most of the studies in this area has assumed for simplicity constant

porosity of the GDL [716]. This, however, cannot reflect the importance of GDL porosity

on fuel cell performance. The hydrophobicity of the diffusion layers may interact with the

amount of water available for hydration at the membrane. The thickness and porosity of

the gas diffusion layers can also change due to the applied compression. These layers can

be porous carbon cloths or paper coated with polytetrafluoroethylene (PTFE). Although it

has been recognized that the performance of the fuel cell can be significantly influenceddue to the porosity variation [1721], systematical studies are still rarely reported in the

open literature.

Gurau et al. [22] considered the non-uniformity of the porosity of the gas diffusion

layers by developing a one-dimensional half-cell model in which the concept of the

effective porosity was employed to account for the fact that the pores may be partially

filled with liquid water. Chu et al. [23] investigated the effects of non-uniform porosity on

fuel cell performance in terms of physical parameters such as oxygen consumption,

current density, power density, etc. The non-uniformity of the porosity was accounted for

by four different continuous functions of position, each of which had a different averaged

value of porosity and a different type of distribution across the diffusion layers. Lee et al.[24] experimentally studied the effects of porosity change on the performance of the fuel

cell due to the compression applied onto the GDL.

3mw membrane water porosity

30 initial porosity

3com

porosity corresponding to compression pressure3hum porosity corresponding to humidification condition

R. Roshandel et al. / Renewable Energy 30 (2005) 15571572 1559


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In the present study, fuel cell performance is investigated by considering the effects of

porosity variation distribution in gas diffusion layers. The effect of compression of the

electrodes on the solid landing areas and the water generated at cathode side of GDL are

both considered in expressing the variation of porosity distribution.

2. Mathematical model

The operation principle of a PEM fuel cell is presented in Fig. 1. Humidified air enters

the cathode channel and hydrogen diffuse through the anode diffusion layer towards the

catalyst, where each hydrogen molecule splits up into two hydrogen protons and two

electrons according to:

2H2/4HCC4eK (1)

The protons migrate through the membrane and the electrons travel through the

conductive diffusion layer and an external circuit where they produced electric work.

On the cathode side the oxygen diffuses through the diffusion layer, splits up at the

catalyst layer surface and reacts with the protons and electrons to form water:

O2C4eKC4HC/2H2O (2)

From above, it can be seen that the overall reaction in a PEM fuel cell can be written as:

2H2CO2/2H2O (3)

Fig. 1. Operating scheme of a PEM fuel cell.



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2.1. Gas diffusion layer modeling

Gas diffusion layer does much more than diffuse the gas. It forms an electrical

connection between the catalyst layer and the bipolar plate, or other current collectors. Inaddition, it carries the product water away from the electrolyte surface, and also forms a

protective layer over the very thin layer of catalyst [4]. They are usually made of a porous

carbon paper or carbon cloth, typically 100300 mm thick.

The gas diffusion layer also assists in water management during the operation of the

fuel cell. Too little or too much water can cause the cell to cease operation. The correct

backing material allows the right amount of water vapor to reach the membrane and keep it

humidified. This layer also allows the liquid water produced at the cathode to leave the

cell, so it does not flood[3]. Therefore, it is important to investigate and analyze the effect

of reactant distribution in this layer on the fuel cell performance. A cross-sectional view

through a GDL is depicted in Fig. 2.The upper boundary (I, II) represents the interface between the GDL and either the solid

graphite plate or an open Gas-filled flow channel. The lower boundary (IV) corresponds to

the catalyst layer separating the GDL and the polymer electrolyte membrane.

Single-phase flow in porous media is typically modeled using Darcys law [26]

~UZKK

mVP (4)

In this equation, the averaged velocity is related to pressure gradient.

The equation of continuum for the reactant gas is:

V$r ~UZ0 (5)

where ~U is a mass-averaged velocity. The conservation law for the reactant concentration

takes the form

V$C~UCDVCZ0 (6)

The diffusive flux is given by Ficks law, which states that the flux of one component

relative to the molar average velocity is proportional to the gradient in mole fraction via

~JZKDVC (7)

where D is the coefficient of diffusion and it is related to the fluid properties and the

porosity of gas diffusion layer. In isotropic porous media, the dependence of the diffusion

Fig. 2. Cross-section of the gas diffusion layer and gas flow channels.



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coefficient on porosity is often approximated using the empirical formula [27]:

DeffZD3

1:5 (8)

This relates the effective diffusivity in the porous medium to that of a free gas. In anideal gas mixture, the pressure depends linearly on the mixture concentration (and hence

also the density) via the ideal gas law:

PZCRTZrRT

M(9)

Thus, the Darcy equation for gas reactant becomes:

~UZKKRT

3mVC (10)

The boundary consists of four distinct components, labeled IIV in Fig. 2.The boundary conditions on each of the four sections are obtained as follows [24]:

(I) The permeable boundary, where the mixture concentration immediately inside the

GDL is taken to be identical to that in the channel

CZ C (11)

That is, the pressure is assumed to be uniform throughout the depth of the channel.

Further it is assumed that diffusive flux of the component across the channel/GDL

interface is proportional to the difference in the concentration on either side

JZ r0 CKC (12)

(II) The impermeable boundary between the graphite palate and the GDL where no-flow

condition on the vertical component of fluxes is imposed

JZ0;vC

vyZ0 (13)

(III) The open side boundaries, where a periodic solution in x-direction is assumed.

(IV) The boundary conditions at the permeable boundary between the catalyst and GDL

are:

JZ rHC (14)

vC

vyZK

rH

DC (15)

The mass transfer coefficient rH models the reactions and electrochemistry taking place

in the catalyst region.

2.2. Porosity variation due to compression

Most of the models have assumed for simplicity that the porosity of the GDL is

constant. This, however, may not reflect the importance of GDL porosity on fuel cell



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performance. Any change in the composition or the morphology of the GDL can lead to a

substantial influence on fuel cell performance owing to a porosity change [25].

In order to seal the fuel cell against any gas leakages, gas diffusion layer and bipolar

plate are bolted together under significant pressure. Compressing the GDL reduces the

porosity over the landing area, which in turn decreases the overall flux of reactant to the

catalyst layer, particularly above the landing area (Fig. 3).

The effect of compression on the porosity variation is considered by allowing the

porosity to vary as a function of x.

Using a composition of function of the form sin2nx which is appropriately scaled and

translated, a function for the variation of porosity across gas diffusion layer is expressed as

3compxZ 30

Xn

An sin2n

x

!(16)

where 30 is initial porosity and 3comp is the porosity of the gas diffusion layer after

compression process.

2.3. Porosity variation due to water generation

It is clear from the description of the proton exchange membrane that there must be

sufficient water content in the polymer electrolyte, otherwise the conductivity

decreases. However, there must not be so much water that the electrodes which

bounded to electrolyte, flood, blocking the pores in the gas diffusion layer [4]. Thus,

the presence of water generated in the GDL during fuel cell operation can change the

effective porosity [25].

To consider the non-uniformity of the porosity of the GDL caused by presence of water,

all flow rates related to the different phenomena should be determined. Then the effectiveporosity can be specified by considering the presence of additional water amount in the

fuel cell. Fig. 4 outlines the water flows inside the cell.

Fig. 3. Effect of compression of gas diffusion layer porosity.



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2.3.1. Water inputWater entering the cell due to the fuel and oxidant humidification:

whumK Z

I

2Fz

xhumKw

1KxhumKw(17)

whumC Z

I

4FzC

xhumCw

1KxhumCw1C

x0N2x0O2

!(18)

The mole fraction of water corresponding to humidification condition (xhumK , xhumC ) canbe determined by considering the humidification temperature.

2.3.2. Water production

Water produced in the cell (on the cathode side) from the electrochemical reaction:

welZI

2F(19)

2.3.3. Water transportWater transport in the membrane depends on the electro-osmotic transport associated

with the flow of the HC protons, and the convective transport due to a pressure gradient in

Fig. 4. Schematic of water flows in a PEM fuel cell.



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the membrane

vZ 3mw

k4

m

ZfCfFVfKkp

m

Vp (20)The membrane water transport ratio can be calculated from:

xZ 3mw F

d

Iv (21)

The water transport in the membrane pores can be determined using the following

expression:

wtrZI

Fx (22)

2.3.4. Water outlet

Water outlet from the fuel cell is calculated using

woutK Z

I

2FzK1

xsatKw

1KxsatKw(23)

woutC Z

I

4FzC 1C

x0N2x0O2

!K1

" #xsatCw

1KxsatCw(24)

The water balance is expressed by the following relationships:

MKZwhumK CwtrKw

outK (25)

MCZwhumC CwelKwtrKw

outC (26)

Finally, the gas porosity in the cathode diffusion layer is determined using the

expression below

3humZ 3

0 1KMCj j

M1;Max ; if MCO0 (27)

where Mmax is the amount of water corresponding to a complete flooding.

2.4. The effect of porosity on fuel cell performance

The performance of a PEM fuel cell can be illustrated by a voltage vs. current density

plot, or polarization curve. The polarization curve can be divided into four regions

characterized by activation overpotentials, ohmic overpotentials, concentration over-

potentials and convection or internal current over potentials. So, the operational fuel cell

voltage can be written as:

VZVOCVKhactKhohmKhdifKhconv (28)



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2.4.1. Activation overpotential

In the activation overpotential region, the dominate source of losses is due to resistance

to electrochemical reaction. These losses also are referred to as activation losses, occurring

when slow electrochemical reactions are driven from equilibrium in order to produceelectric current [26]. The activation overpotential can be calculated from:

hactZRT

Fln

I

I0

(29)

2.4.2. Ohmic overpotential

The ohmic overpotential losses from electronic and ionic resistance in the cell is the

most significant source of performance degradation. Ohmic overpotential is determined by

the following equation:

hohmZIRcell (30)

2.4.3. Concentration (diffusion) overpotential

In the concentration overpotential region, losses due to mass transport limitation are

dominant. Concentration overpotential occurs when the chemical reaction is limited by the

rate of which reactants can be supplied. This lack of reactant shows the electrochemical

reaction, resulting in a lower cell potential. This amount can be calculated by:

hdifZuTI lnIlim

IlimKI (31)

where Ilim is the limiting current density that is affected by additional water amount and

effective porosity of the gas diffusion layer in a PEM fuel cell

IlimZK2FDO2KN2 3

dg

1:5 T273

0:823VmldC

ln1KxO2 (32)

2.4.4. Convection overpotential (internal current)

The electrolyte should only transport ions through the cell, but a certain amount of fuel

diffusion and electron flow is always possible. The fuel looses and its effect is usually not

very important. The convection overpotential can be determined using the following

equation:

hconvZFCHCvlm

k(33)

2.5. Grid size effects and numerical accuracy

Accuracy tests were performed on the numerical procedure, particularly to study the

effect of the grid fineness on the solution. The important parameters used in this analysisare shown in Table 1. Comparison of the mole fraction distribution under various grid

sizes were made and presented in Fig. 5. The results show that by increasing the fineness of



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the grid no significant changes appear in the mole fraction distribution. The final

computations were performed with 40!40 grid points to maintain relatively moderate

computing times in the final calculations. It is reasonable to assume that the accuracy in

the presented mole fraction distribution is less than 1%.

To further assess the accuracy of the mathematical model, the comparison of the

computedpolarizationcurveforairandoxygenwiththeexperimentaldataofMaggioetal [4]

Table 1

Modeling parameters

Parameter values

H 0.005

L 1

LC 0.25

LS 0.25

K 10K8

30 0.74

R 8.31!107

T 346.15

CHC 1.2!10K3

k 0.151

kp 1.8!10K14

k4 7.18!10K16

lm 0.023

dw 0.0543

3mw 0.3

t 0.77

Anode Cathode

m 2.1!10K4 1.2!10K4

D 0.089 0.123

r0 10 10

rH 0.8 0.2

T 358 353

p 3 5z 1.2 3

Fig. 5. Comparison of the mole fraction distribution under various grid sizes.



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is presented in Fig. 6. As seen from this figure, the results of the present computations agree

well with experimental data.

3. Results and discussion

To investigate the effect of porosity on gas reactant distribution in anode and cathode

gas diffusion layer the porosity distribution in the first step is considered to be constant. In

Fig. 7, the reactant mole fraction is presented. The mole fraction plot shows that gas

Fig. 6. Comparison of polarization curve with experimental and numerical data.

Fig. 7. Reactant mole fraction in gas diffusion layer with constant porosity distribution.



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concentration decreases from channel to membrane as the reactant is consumed. However,

the reactant concentration in the GDL/membrane interface as well as the electrical current

density are both uniform. The average of electrical current density is 0.61 A/cm2.

Fig. 8 presents the reactant distribution in GDL when porosity is considered as a

function of compression pressure. In this case, due to the compression the porosity

decreases specially under the landing area. This causes decrease in overall reactant flux to

the catalyst layer particularly under the landing areas and thus creating a more non-

uniformity in the gas diffusion layer. Therefore, the variation of produced electrical

current increases across the electrodes. It means that some of the catalyst particles,especially under the landing area remain unused and the average electrical current density

reduces to 0.47 A/cm2 (w23% less!)

Another source of variation in the GDLs porosity is presence of water in the layers. If

too much water is present, flooding may occur resulting in the pores of the gas diffuser

filled by liquid water, which blocks the transport of reactant to the reaction site in the

cathode side. It is shown in Fig. 9 that the water decreases the effective porosity of GDL

Fig. 8. Reactant mole fraction in gas diffusion layer with consideration of compression effect on porosity of GDL.

Fig. 9. Reactant mole fraction in gas diffusion layer with consideration of compression effect and presence of

water droplet on porosity of GDL.



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and therefore, casing the reduction in the oxygen concentration in GDL/Membrane

interfaces. In fact the gas porosity in the diffusion layer decreases from the initial 74% to

55% considering the blockage of the pores by water.

Fig. 10 shows the electrical current density in electrodes corresponding to reactant

concentrations. It can be observed that compression pressure affects the electrical current

distribution along the electrodes and makes peaks in the electrode current densities.

Fig. 10. Electrical current density distribution in cathode and anode side of a PEM fuel cell.

63%

25%

11%1%

Activition

Ohmic

DiffusionalConvection

58%

24%

17%1%

Activition

Ohmic


49%

20%

30%1%

ActivitionOhmic


Fig. 11. Percentage of overpotential contribution corresponding to (a) constant porosity along GDL, (b) spatial

variation of porosity due to compression pressure and (c) porosity as a function of water amount in GDL at

0.85 A/cm2.



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As already mentioned, porosity variation changes the limiting current density and so

the diffusion overpotential increases. However, the potential drop related to the diffusion

overpotential appears to be too sharp compared with other overpoentials.

Fig. 11 presents the contributions of the relative share of the calculated overpotentialcorresponding to different porosity distributions. It can be observed that diffusion

overpotential increases from 11% to 30% when effective porosity deceases due to the

compression pressure and presence of liquid water in gas diffusion layers.

4. Conclusion

The gas diffusion layer is an essential component of the proton exchange membrane

fuel cell, and limitations due to mass transport in the GDL are known to be significant. Theproperties of the diffusion layer will impact the optimum performance of the catalyst and

the electrodes. These layers are porous to allow for distribution of the gases to unexposed

areas of the flow channel and this distribution allows for complete utilization of the

electrode area. Many of simulation, have assume for simplicity that the porosity of GDL is

constant, but in practice, the compression pressure corresponding to assembly process and

presence of water in these layers may change the porosity distribution and affect gas

diffusion coefficient in GDLs. Any change in porosity or diffusion coefficient can lead to a

substantial influence on fuel cell performance owing to a diffusion overpotential change.

The results in the present work demonstrate that the compression pressure can lead to

32% decrease in porosity and so reduce the reactant transport in GDL upto 10%. In

addition, water management simulation shows that the water droplet can block the pores in

GDL especially in high current density. In fact The average porosity of gas diffusion layer

decreases 23% at 0.85 A/cm2.

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