Page 343 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

Cell, Stuck and System Modelling 319

In principle, one could make a large set of measurements of cathode and anode
polarisations in a small-size cell with a reference electrode (three-electrode cell)
and express the total polarisation as a function of local bulk gas composition,
pressure, temperature, and current density. The essential condition is that the
small-size cells (‘button cells’) use very little fuel gas and oxidant gas, so that the
measured polarisation is representative for the bulk gas composition, pressure,
and temperature at a given current level. The cell then functions as a differential
reactor that provides data for the cell- and stack-level (integral reactor)
modelling. Although small-size cell data are obviously useful and many such
measurements are made. the effort implied in a full ‘polarisation mapping’ of this
kind for each electrode is usually prohibitive. Moreover, the results are valid only
€or the range over which the operating parameters are varied and for the
electrode-electrolyte assembly microstructure and configuration used in the
small-size cell.
In lieu of an experimental ‘map’ of polarisation, it is often desirable to have an
electrode model that provides reliable predictions of polarisation of either
electrode over a wide range of operating and structural variables. This is the first
purpose of the electrode model. But, conversely, to be a good predictor the model
should be capable of interpreting available polarisation data for welI-defined
conditions, that is, for small cells at low utilisation of fuel or oxidant. Thus, the
second purpose of an electrode model is to enable a more efficient process of
collecting, correlating, and interpreting polarisation data. The electrode model
is capable of extracting the kinetic and mass transfer (diffusion) resistance
information by fitting small-size cell polarisation data. It provides these
resistance characteristics in a form suitable as input to full-scale cell and
stack models.
An electrode model is especially advantageous if it can be used to relate the
kinetic and mass transfer resistance to electrode geometry and microstructure:
for instance, to thickness, porosity, pore or particle size, contact areas of phases,
and/or grain size of electrode and electrolyte materials. A well-tested and
validated electrode model, therefore. may serve to assist in the design of
optimised electrode structures or electrode/electrolyte interfaces to minimise
polarisation loss.

17.8.1 Fundamentals and Strategy of Electrode-Level Models
The objective of an electrode model is to analyse the point-to-point distribution of
the reaction in an SOFC electrode, leading to current, potential, and species
concentration distributions. The result of the analysis is a prediction of the
polarisation of the electrode due to (i) kinetic resistance, (ii) mass transfer
resistance, and (iii) ohmic resistance.
The analysis includes a whole set of material properties and structural
parameters. In principle it is based on the same fundamental laws used in full-
scale cell analysis. Thus, mass transfer is subject to mass balances (Eqs. (1). (2)),
heat flow to energy balances (Eqs. (5). (6)), and fluid flow to Eqs. (3), (4), but it
is usually negligible in the pores of the electrodes. In addition, current flow is