MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

where r p1 and r p2 are the average macro-pore and the average micro-pore radii,
respectively. The random pore model has four parameters: (porosity), M (macro-
porosity), r p1 and r p2. The porosity of a char can be determined by its apparent density
and true density (see Eq. A.1 in Appendix).
Notice that the random pore model can also be applied to mono-disperse systems.
For chars containing only macropores, = M, and Eq. (6.41) becomes:
2
De = DM M
Similarly, for chars containing only micropores, the effective diffusivity is
D e = D 2
Comparison of these last two equations with Eq. (6.40) leads to:
= 1
The random pore model does not require the empirical tortuosity factor, and
accommodates the parallel pore model when the pore structure is assumed to be mono-
82
(6.46)
(6.47)
(6.48)
disperse. Due to these advantages, the random pore model was selected in this study as
the working model for calculating effective diffusivity in char oxidation modeling.
Estimating S
ext /S
int Using Pore Structure Model
The ratio of the external surface area to the internal surface area (S ext/S int) is an
important parameter in modeling rough sphere combustion. The in situ value of S int is
often unknown, thus making it necessary to estimate or assume a value for S ext/S int (Banin
et al., 1997). However, an arbitrarily assumed value of S ext/S int would affect the kinetic
parameters reduced from experimental data. It is therefore desirable to eliminate this