MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

The value of the roughness factor was pre-set to be 5, which seemed high
compared to the value of 2.5 used by Banin et al. (1997). Following the argument of
Banin et al. (1997), the roughness factor accounts not only for the increased surface area
due to surface roughness, but also for penetration of oxygen molecules within a pore
before the first collision with the pore wall. The latter mechanism means internal
diffusion does not play any role up to a distance equal to about the pore diameter. Figure
7.2 illustrates how this latter mechanism makes one unit of void surface area equivalent to
4 units of solid surface area.
Figure 7.2. Schematic of a pore connected to the surface of a char particle. One unit of
void area is equivalent to 4 units of solid area since internal diffusion does
not play any role up to a distance equal to about the pore diameter.
The void area of a pore mouth is πr p 2 , while the internal pore wall that is not
affected by internal diffusion and must be counted as external surface area is 2πr p •2r p =
4πr p 2 . Assuming that the surface roughness increases the surface area by a factor of 2, the
overall roughness factor can be calculated from the porosity of the particle: 2[(1- ) + 4 ]
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2r p
r p
O 2
O 2
O 2
O2