Journal of Applied Electrochemistry

, Volume 37, Issue 11, pp 1245–1259

Modelling and experimental validation of a high temperature polymer electrolyte fuel cell

Original Paper

Abstract

A steady-state, isothermal, one dimensional model of a proton exchange membrane fuel cell (PEMFC), with a polybenzimidazole (PBI) membrane, was developed. The electrode kinetics were represented by the Butler–Volmer equation, mass transport was described by the multi-component Stefan–Maxwell equations and Darcy’s law and the ionic and electronic resistances described by Ohm’s law. The model incorporated the effects of temperature and pressure on the open circuit potential, the exchange current density and diffusion coefficients, together with the effect of water transport across the membrane on the conductivity of the PBI membrane. The polarisation curves predicted by the model were validated against experimental data for a PEMFC operating in the temperature range of 125–200 °C. There was good agreement between experimental and model data of the effect of temperature and oxygen/air pressure on cell performance. The model was used to simulate the effect of catalyst loading and the Pt/carbon ratio on cell performance and, in the latter case, a 40 wt.% Pt/C ratio gave the highest peak power density.

Keywords

Polymer electrolyte fuel cell Polybenzimidazole PBI Membrane Modelling 

Notations

Aact

Active area of catalyst particles (m2)

AD

Anode diffusion region (No units)

AM

Anode microporous region (No units)

AR

Anode reaction region (No units)

AF

Anode flow region (No units)

a

Height of catalyst (m)

b

Width of catalyst (m)

ci

Molar density/concentration of component i (mol m−3)

CD

Cathode diffusion region (No units)

CR

Cathode reaction/catalyst region (No units)

c

Depth of catalyst (No units)

Dij

Stefan–Maxwell diffusivities (m2 s−1)

\(D_{ij}^{eff}\)

Effective Stefan–Maxwell diffusivities (m2 s−1)

\(\tilde{D}_{ij}\)

Symmetric diffusivities (m2 s−1)

E

Potential (V)

\(E_0^0\)

Standard state reference potential (V)

F

Faraday constant (A s mol−1)

G

Gibbs free energy (J mol−1)

H

Enthalpy (J mol−1)

I

Cell current density (A m−2)

je

Electronic current (A m−2)

ji

Ionic/proton current (A m−2)

jo

Exchange current density (A m−2)

\(j_{o\_\beta}\)

Exchange current density at electrode β (A m−2)

\(j_{o\_a}\)

Exchange current density in anode (A m−2)

\(j_V^\beta\)

Current density source term in cathode (A m−3)

\(j_V^a\)

Current density source term in anode (A m−3)

\(j_V^c\)

Current density source term in cathode (A m−3)

Ji

Diffusion flux (kg m−2 s−1)

k

Permeability of the porous media (m2)

L

Catalyst loading (g m−2)

M

Membrane region (No units)

Mcat

Mass of the catalyst (g)

Mi

Mass of species i (kg mol−1)

n

Number of electrons (No units)

Ni

Total flux of species i (kg m−2 s−1)

p

Total pressure (m−1 kg s−2)

pi

Partial pressure of species i (bar)

Q

Constant in Stefan–Maxell diffusion (No units)

u

Velocity vector (m s−1)

R

Gas constant (J K−1 mol−1)

\(\bar{R}\)

Source terms (kg m−3 s−1)

RP

Surface area of platinum (m2 g−1)

SA

Ratio of real catalyst and (m2 m−3), geometric volumes (m−1)

S

Entropy (J mol−1 K−1)

So

Entropy at standard reference temperature (J mol−1 K−1)

T

Temperature (K)

Ucell

Cell potential (V)

vi

Molecular diffusion volumes of species i (m2)

Vn

Volume of composition n

xi

Mole fraction of species i (No units)

wi

Mass fraction of species i (No units)

Greek

ɛ

Porosity fraction (No units)

αa

Anode transfer coefficient at the relevant electrode (No units)

αc

Cathode transfer coefficient at the relevant electrode (No units)

γi

Kinetic exponent of the species i in the Butler–Volmer equation (No units)

κ

Ionic conductivity (S m−1)

μβ

Pore-fluid viscosity in electrode β (m−1 kg s−1)

ρ

Density (kg m−3)

σ

Electronic conductivity (S m−1)

ϕ

Electric potential of protons (V)

ϕs

Electric potential of the electrons (V)

η

Overpotential (V)

β

Electrode (anode or cathode) (No units)

Superscripts and subscripts

A

Area

a

Anode

act

Activation region

an

Anodic

β

Electrode (anode or cathode)

c

Cathode

cb

Carbon

cat

Catalyst

ct

Cathodic

D

Diffusion region

eff

Effective in that region

F

Flow channel

h2

Hydrogen

i

Ion phase or species i

ox

Oxidation

M

Microporous region

n

Composition n

pbi

PBI membrane

pt

Platinum

s

Solid phase (electrons)

R

Reaction/catalyst

red

Reduction

v

Volume

0

Reference state

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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.School of Chemical Engineering and Advanced MaterialsUniversity of Newcastle upon TyneNewcastle-upon-TyneUK

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