Page 330 - High Temperature Solid Oxide Fuel Cells Fundamentals, Design and Applications

306 High Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications

density, io, which is specific for hydrogen oxidation. For gas-phase reaction
calculations it is convenient to simplify Eq. (lob) in the form of an effective rate
expression having an empirical rate constant, k~2, reaction order, m3, and
activation energy, EH2:

drHz/dt(oxidution) = k~~pgi exp(-EH,/RT) (19)

Similarly, the rate of anodic oxidation of CO may be expressed by means of
effective rate parameters:
drco/dt(oxidation) = kcop;; exp( -Eco/RT) (20a)

The change in the CO concentration can then be written as
drco/dt = dr~~4/dt + d&/dt - drf/dt - drco/dt(oxidation) (20b)

Consequently, the rate of change of H20 concentration is
dr~zo/dt = dr~z/dt(oxidation) + dn,/dt - drf/dt - dr~~4/dt (204

At the cathode, too, effective rate expressions for oxygen reduction, if
available, may be convenient, but the gas-phase mass balances are basically
simpler than those at the anode. When current density is known, the rate of 02
loss is

dro,/dt = i/4F (21)

Assuming the current vector is everywhere transverse to gas flow direction,
that is, perpendicular to the PEN element, Eq. (21) can be used to determine the
variation of O2 in an air channel. Similarly, if there is no current component
parallel to the PEN element

dm2/dt(oxidation) + drco/dt(oxidation) = i/2F (22)

Because numerical error is inherent in modelling software, for exact mass
balance, i/2F - drH2(CO)/dt (oxidation) can determine drCO(H2)/dt (oxidation), or
drH2/dt (oxidation) + drco/dt (oxidation) can determine i/2F. However, when a
shift equilibrium reaction (1 5d) is achieved or assumed, the chemical
equilibrium condition and Eq. (22) uniquely determine the sum of the rates of
hydrogen and CO consumption. Therefore, separate rate parameter
measurements for CO and hydrogen are not necessary. In fact, experience
suggests that in most SOFCs the dominant anodic process is hydrogen oxidation,
while CO is consumed by the shift equilibrium [lo].
Similarly, if CH4 is present and steam reforming is at equilibrium, chemical
equilibrium conditions determine the rates of consumption of each fuel
component uniquely for a given current production.