MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

approximated by the Knudsen diffusion within 5%. In summary, the diffusivity of
oxygen in a pore with a radius r p is:
D = D O2,N2, when r p ≥ 20r p,crit
D = D K, when r p ≤ r p,crit/20
D = 1/(1/D O2,N2 + 1/D K), when r p,crit/20 ≤ r p ≤ 20r p,crit.
The values of the critical pore radius were computed and shown in Table 5.2.
Table 5.2. The Values of Critical Pore Radius (Å) at Different Temperatures and
Gas Pressures.
Tp (K)
P (atm)
1 5 10 15
1000 2874 575 287 192
1250 3731 746 373 249
1500 4618 924 462 308
1750 5531 1106 553 369
For example, at 1500 K and 1 atm, the critical pore radius is 4618 Å, the Knudsen
diffusion cannot be neglected unless the pore radius of the char is greater than 20 × 4618
= 92360 Å = 9.236 μm. Similarly, at 1500 K and 1 atm, the molecular diffusion should
not be neglected unless the pore radius is less than 4618 / 20 = 231 Å (0.023 μm). Eq.
5.20 is generally applicable and is therefore recommended.
Another way to tell whether Knudsen diffusion or molecular diffusion is
important is to compare the pore radius to the mean free path of oxygen. Note that the
critical pore radius is slightly different from the mean free path of oxygen molecules.
According to classic kinetic theory (Bird et al., 1960), the mean free path of oxygen is:
=
1
2 d 2 NC =
1
2 N
RT p
P
1
d 2 = 2.60 T p
P
56
(Å) (5.25)