Performance Optimization of

PEM Fuel Cell by Using Modified Bruggeman Correlation Model

Prakash

Thapa1, Gye Choon Park*2, Sung Gi Kwon 3, Jin Lee4

1,2,3,4 Department of Electrical Engineering, Mokpo

National University, Korea

[email protected], [email protected], [email protected], [email protected]

Abstract

Background/Objectives: In Proton Exchange

Membrane Fuel Cell (PEMFC), the modified Burggeman correlation is used

to estimate the effective conductivity and diffusivity of both catalyst and gas

diffusion of PEM fuel cell.

Methods/Statistical analysis: It should be

2. Proton

Exchange Membrane Fuel Cell (PEMFC)

Figure 1 shows

the geometry of a single fuel cell, which consists of a membrane, catalyst

layers, gas diffusion layers, gas channels, and two collector plates. The main

functions of these components are: collector plates with flow channels are used

for reactants and products transport, electron conduction and heat removal; gas

diffusion layers are for reactant distributions, electron conduction, and

liquid water removal; catalyst layers are used to promote electrochemical

reactions where reactants are consumed, and products and heat are generated;

and the membrane is used to conduct protons from the anode catalysts layer to

the cathode catalyst layer.

The electrochemical reaction occurring in the anode in which

hydrogen gas is consumed to produce protons and electrons 4, i.e.,

Anode:

(1)

The produced electrons

are passes through an external circuit to the cathode by providing electrical

power, while the protons transport through the membrane to the cathode. At the

cathode catalyst layer, oxygen combines with the protons and electrons to

produce water, i.e.,

Cathode:

(2)

And overall cell

reaction occur during the electrochemical reaction process is given by,

Water (3)

Above these reactions involve on border

between ionically conductive electrolyte and electrically conductive electrode.

For the better electrochemical reaction and the gases to arrive as well as

water to leave, the electrodes must be porous medium. Under steady state

conditions, the thickness of the cell is negligible compared to its other

isothermal approximation and the membrane is assumed to be fully hydrated.

Moreover, the anode reaction over potential is neglected in the present study,

because over potential due to the anode reaction to be negligible 5.

Therefore, overall cell potential is obtained by subtracting the losses from

reversible cell voltage which is given by the following expression;

(4)

Where, is the reversible cell voltage and is the activation loss, is Ohmic loss, is concentration loss and is the diffusion loss. is calculated from a modified version of the

Nernst equation, which is modified with an extra term to account for changes in

temperature from the standard reference temperature 6. Which is given by Eq.

(5).

(5)

Where P and T

represent the effective pressure and temperature respectively. Activation

losses can calculated by using empirical equation 7;

(6)

Where are empirical coefficient and I is the cell

current and T is the absolute temperature. is the undissolved oxygen concentration which

can be expressed as 8;

Ohmic Overpotential

Due to membrane

resistance (Ionic Resistance)

The voltage drop due

to the membrane resistance to the flow of ions produce the ohmic overpotential

loss in the fuel cell.

where

is the ionic resistance as a function of membrane conductivity, is the membrane height and is the ionic conductivity of membrane with

water content and temperature 9.

Where be the degree of membrane humidification and is the cell temperature.

Electronic Resistance

The potential loss due

to the electronic bipolar plates and electrodes current collectors is called

electronic resistance losses and is given by,

But the ohmic

resistance of the electronic materials is given by,

Where, is the material resistivity, l is the length

and A is the cross-sectional area of the conductor.

The ohmic

overpotential due to electronic and ionic resistance is 10 given by,

The resistance proton

is calculated by the following expression,

The resistivity of the

membrane depends on the water activity and cell temperature. Empirical formula for is express as follows 11.

J is the current

density with in the cell. The value of l can be fitted for a particular cell.

To obtain the value of l we can use the Sharifi model, which is given by 7;

Where,

3. Gas

Diffusion and Catalyst Layer

Both gas diffusion and

catalyst layers are porous media, the diffusion of oxygen gas at the cathode

terminal is given by 12;

The diffusion of

hydrogen gas at the anode terminal is given by 13;

The production of

water at the cathode terminal side is given by 14;

4. Bruggeman Correlation

According to the

Flick’s law, the gaseous diffusion in gas diffusion layer (GDL) and catalyst

layers (Cl) of PEM fuel cell is given by,

(4)

Where, is the porosity of GDL, be the concentration and be the effective diffusivity of the reactants

gaseous.

Similarly, according

to the Bruggemann correlation, the effective diffusivity in a porous structure

can be expressed as 15,

(5)

Where, is the tortuosity factor of porous medium. The

tortuosity ( is defined as the ratio of the actual flow

path length and the thickness of the porous medium along the flow direction.

When the impact of

liquid water saturation is taking into account then above Bruggeman correlation

equation become,

(6)

Where, are normalized functions.

Similarly, tortuosity

factor for Burggeman exponents m=0.5 and saturation exponents, n=1.5. Thus

above equation 7 becomes;

Then normalized

function for modified Bruggeman correlation 16 with tortuosity factor (m=n=1)

is given by the following equation;

(8)

Where, be the effective conductivity and is the concentration of the liquid.

5.

Simulation Results

The figure 2 and 3 shows the simulated

polarization curve by using different value of m and n. At higher current

density the PEMFC has significant effect of the tortuosity factor m and n.

The normalized function g(s) Vs average

porosity value and average water saturation function g(s) Vs

average saturation for

various values of m and n are shown in figure 5 and 6.When the value of m and n

are increased the normalized function’s as well as saturation function’s values

are decreased. Which indicates that the distribution of pore size of porous

medium and the water saturation has greater impact on the gas diffusion. Thus

these parameter has greater impact on the performance optimization on the PEM

fuel cell.

6.

Conclusion

The tortuosity factor for Burggeman

exponent’s m and n has significant effect on the performance of PEM fuel cell

at current density. So for the PEMFC design process the value of m and n must

be equal to 1.5. Above this value the fuel cell performance will be decreased.

The sensitivity of the fuel cell performance to the value of n in GDL and CL is

neglected as compared to that in the cathode GDL and CL but the sensitivity in

cathode CL is stronger than that in the cathode GDL. So for the performance

optimization of fuel cell, concentration of the gas should be increased and

water removal from the cathode GDL and CL during gaseous diffusion, must be

improve.

7. Acknowledgement

This work was supported by KEPCO Research

Institute grant funded by Korea Electric Power Corporation (R16DA11) and

Business for Cooperative R&D between Industry, Academy and Research

Institute funded by Korea Small and Medium Business Administration (C0442952).

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