MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

Effective Diffusivity
The major obstacle to rigorous description of the transition between Zone I and
Zone II is the treatment of pore diffusion through the complex pore structures of char.
According to Smith (1981), the optimum model would include a realistic representation of
the geometry of the voids (with tractable mathematics) that can be described in terms of
easily measurable physical properties of the char. These properties include the surface
area, porosity, density (true density or apparent density), and the distribution of void
volume according to size.
In general, both molecular 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 The Knudsen diffusivity can be calculated from classical kinetic theory (Smith, 1981):
DK = 9.70 ×10 3 ⎛
rp ⎝
⎜
T p
M A
1/2
⎟
⎞
⎠
where D K is in cm 2 /sec, r p is the pore radius in cm, T p is in K, and M A is the molecular
80
(6.37)
(6.38)
weight of oxygen. The bulk diffusivity can be calculated using a correlation by Mitchell
(1980):
DO2 / N2 = 1.523 ×10 − 5 1.67
Tp / P (6.39)
Pore structure models are used to convert the diffusivity to the effective
diffusivity. By using the effective diffusivity, the measurable diffusion flux can be based
on the geometric external surface area rather than the total cross-sectional area of holes on