MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

the surface rate coefficient may produce “apparent” kinetics, just as absorbing the effects
of internal combustion into the global n-th order rate coefficient k s (see Eq. 2.16) does.
In contrast to the approach of Sun and Hurt (1999), Charpenay et al. (1992)
neglected the molecular diffusion mechanism and used only the Knudsen diffusivity to
calculate the effective diffusivity:
D e = D K / (5.19)
Although both groups used the tortuosity factor to convert the diffusivity into effective
diffusivity, the selections of diffusion mechanism seemed somewhat arbitrary. In this
study the relative importances of these two diffusion mechanisms were compared, and
the situations where one of these mechanism may be neglected were explored.
In general, both bulk diffusion (also called molecular diffusion) and Knudsen
diffusion may contribute to the mass transport rate within the porous structure of the
char. The combined effects of these two diffusion mechanisms can be described by the
combined diffusivity D (Smith, 1981):
1
D =
1/ DAB + 1/ DK 54
(5.20)
The combined diffusivity can be controlled by molecular diffusion, Knudsen diffusion or
both of them, depending on the ratio of the size of pore to the mean free path (Knudsen,
1950). The Knudsen diffusivity can be calculated from classical kinetic theory (Smith,
1981):
DK = 9.70 ×10 3 ⎛
rp ⎝
⎜
T p
M A
1/2
⎟
⎞
⎠
(5.21)