Page 345 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Cell. Stack and System Modelling 321

strong temperature sensitivity of properties like electrolyte conductivity and
electrode kinetics may skew the reaction distribution from that expected in
isothermal operation.
Thus, even at the electrode level the interactions between electrochemical
reaction, mass transfer, ionic conduction, and heat transfer yield a very
complicated set of equations. Of course. this has given rise to many attempts to
use simplified models wherever possible. Some of these are summarised below.
Several are based on an assumption of one or more dominant rate-controlling
resistances. for instance, mass transfer or ohmic resistance or neglect of coupling
conditions that complicate the reaction distribution. Others introduce linearised
electrode kinetics and neglect mass transfer resistance. Of course, these
simplifying assumptions must be validated.
Validation by fitting empirical polarisation curves is helpful, especially if the
objective is input for full-scale performance models. But it is of limited value if
the parameter space of the fitted curves is restricted, especially when the
objective is optimisation of electrode design. Benchmarking results of simplified
models against a set of more complete model equations is also helpful but limited
by uncertainty about some important coupling conditions. The important role of
the reaction mechanism in determining kinetic rates has been recognised early
and has led to specialised electrode modelling focused on this aspect of the
electrode process. In addition, it has recently been realised that computational
studies of the electrochemical reaction steps may contribute to greater insight in
those aspects of the electrochemical rate process that are specific for the SOFC.
The following summarises a few types of simplified electrode models proposed
in the literature.

11.8.2 Electrode Models Based on a Mass Transfer Analysis
If the reaction kinetics of the electrode is assumed to be very rapid, mass transfer
and ohmic resistance are the dominant resistances. Assuming a reaction zone
that coincides with the electrode-electrolyte interface, the diffusion fluxes in
stationary operation can be expressed simply in terms of bulk gas partial
pressures and gas-phase diffusivities. This is illustrated schematically in Figure
11.8, which compares anode- and cathode-supported cell designs for the simple
case of a H2/02 fuel cell. The decrease in concentration polarisation at the
cathode, qcc. is obvious in the case of an anode-supported cell, while the model
shows that concentration polarisation at the anode, qAc, is relatively insensitive
to anode thickness. The advantage of the mass transfer-based approach is that
analytical expressions are obtained for the polarisation behaviour. These are
rather simple if activation overpotential is excluded but may still become
elaborate in the case of an internally reforming anode where a number of
reactions (discussed in Section 11.3) may occur simultaneously within the pores
of the anode.
In further development of this model, a finite reaction zone ma57 be
introduced and activation overpotential added to the polarisation [44-4 71.
Kinetic resistance is believed to be particularly important for the cathode (qc, is