Performance Optimization of
PEM Fuel Cell by Using Modified Bruggeman Correlation Model
Thapa1, Gye Choon Park*2, Sung Gi Kwon 3, Jin Lee4
1,2,3,4 Department of Electrical Engineering, Mokpo
National University, Korea
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
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.,
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.,
And overall cell
reaction occur during the electrochemical reaction process is given by,
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;
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.
Where P and T
represent the effective pressure and temperature respectively. Activation
losses can calculated by using empirical equation 7;
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;
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.
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.
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.
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;
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,
Where, is the porosity of GDL, be the concentration and be the effective diffusivity of the reactants
to the Bruggemann correlation, the effective diffusivity in a porous structure
can be expressed as 15,
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
Where, are normalized functions.
factor for Burggeman exponents m=0.5 and saturation exponents, n=1.5. Thus
above equation 7 becomes;
function for modified Bruggeman correlation 16 with tortuosity factor (m=n=1)
is given by the following equation;
Where, be the effective conductivity and is the concentration of the liquid.
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
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
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).
S.J. Lee, ‘Numerical Simulation of Proton Exchange Membrane Fuel Cells at High
Operating Temperature’, Journal of Power Sources, Vol. 162, N°2, pp. 1182 –
A., Golkar, M.A. 2010. Control of hybrid fuel cell/energy storage distributed
generation system against voltage sag. International Journal of Electrical
Power & Energy Systems 32, 488–497
A Study of
Monitoring and Operation for PEM Water Electrolysis and PEM Fuel Cell Through
the Convergence of IoT in Smart Energy Campus MicrogridChang, Hui Il; Thapa,
Prakash; / Journal of the Korea Convergence Society , v.7, no.6, pp.13-21, 2016
J., and Li, X., 2000, “Modeling of Polymer lectrolytemembrane Fuel Cells With
Variable Degrees of Water Flooding,” J. Power Sources, 86, pp. 181–195.
M.AR.S.; Renewable Energy. 2005, 30(10), 1587-1599
S. M., Rowshanzamir S., Eikani M. H.2010. Modelling and simulation of the
steady-state and dynamic behaviour of a PEM fuel cell, Energy 35, 1633–1646.
Xue X. D.,
Cheng K. W. E, Sutanto D., 2006. Unified mathematical modelling of steady-state
and dynamic voltage–current characteristics for PEM fuel cells, Electrochimica
Acta 52, 1135–1144.
J. Golbert, D.R. Lewin, Journal of Power
Sources 135 (1–2) , 2004, pp. 135–151
D., “Berechnung verschiedener physikalischer konstanten von heterogenen
substanzen. i. dielektrizitätskonstanten und leitfähigkeiten der mischkörper
aus isotropen substanzen,” Annalen der
Physik, 416(7), 636 (1935).
M.W. Ellis, D.J. Nelson, M.R. von Spakovsky, A twodimensional computational
model of a PEMFC with liquid water transport. Journal of Power Sources; 128,
2004, pp. 173–184.
Chao-Yang Wang. A Nonisothermal, Two-Phase Model for Polymer Electrolyte Fuel
Cells. Journal of the Electrochemical Society; 153(6), 2006, pp. A1193-A1200.
Jay Tawce Pukurshpan, Modelling and control of
fuel cell systems and fuel processors, Phd Thesis of mechanical engineering,
University of Mchigan, USA, 2003.
D.A.G. Bruggeman, Calculation of various
physics constants in heterogenous substances, I. Dielectricity constants and
conductivity of mixed bodies from isotropic substances, Ann. Phys. 24 (7)
K., Vidhya S., Umamaheswari B., Rajalakshmi N., Dhathathreyan K. S. 2013.
Tuning of PEM fuel cell odel parameters for prediction of steady state and
dynamic performance under various operating conditions, international Journal
of Hydrogen Energy 38, 2370–2386.