Page 329 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Cell, Stack and System IModelling 305

determine the kinetic rate. This requires specialised electrochemical models, as
discussed in Section 11.8.
Chemical reactions, too, may be characterised in a similar manner, following a
strategy of effective kinetic parameters. When detailed knowledge of the reaction
mechanism is lacking, the effective rate constants and other reaction-kinetic
parameters can be determined by fitting a simplified kinetic model to the
experimental data. For example, the steam-reforming conversion rate of CH4
(reaction (1 5c)) may be expressed by the following empirical equation [6]:

Different materials and designs will have different values for the parameters in
Eq. (1 6). Depending on cell materials, the manufacturing process, and even the
operating temperature, different values of ml and m2 are possible [16-181. Other
rate expressions based on various kinetic models have also been proposed [19].
For realistic modelling, parameters that fit well with the desired systems should
be used. Equation (16) represents the mass sink term for CH4 in the CH4 mass
balance as given, in general form, by Eq. (1).
As Eq. (16) suggests, the effective rate constant strategy is particularly useful
in the case of the anode fuelled by CH4 because five or more gaseous species must
be accounted for. Hydrogen is generated by steam reforming of CH4 and by the
forward process of the shift reaction CO + H20 --+ GO2 + H2. The backward
process of the shift reaction and anodic hydrogen oxidation both consume
hydrogen. The total rate of the mole change of H2 is then
d%*/dt = 3dr~~4/dt + drf/dt - drb/dt - dr~~/dt(oxidation) (1 74
Here,

dlb/dt = kl&hiftPCO2&2 (174
where kl is a constant with dimensions of [kmol H2 m-3 s-l bar2]. From
thermodynamics, the equilibrium constant of the shift reaction is given by

Kshift = ~XP(-AG&/RT) (18)

where AGfhift is the standard Gibbs free-energy change of the shift reaction
at temperature T and can be calculated from the standard Gibbs free-energy
change at 298 IC (AG!98K) and the standard enthalpy change at 298 I< (AH!98K)
with the help of heat capacities of reactant and product expressed as functions
of temperature.
The rate of anodic hydrogen oxidation is proportional to the current density of
hydrogen oxidation (iH2). As discussed in Section 11.3, this current density
according to the electrochemical model follows a Butler-Volmer-type equation
(Eqs. (loa) and (lob)) with a concentration-dependent exchange current