MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

Boundary Layer Diffusion
The molar flux of oxygen, N O2, in the bulk phase can be related to the surface mole
fraction (Bird et al., 1960):
N O2 − x s (N O2 + N CO + N CO 2 ) = k xm (x ∞ − x s ) (2.6)
where N denotes the molar flux of a substance, x is the oxygen mole fraction in the bulk
stream, x s is the oxygen mole fraction at the external surface of the particle, and k xm is the
mass transfer coefficient and can be obtained from the Sherwood number correlation for
spheres in a convective flow (Bird et al., 1960; Field et al., 1967; Mulcahy and Smith,
1969)
k xm d p
C f D ABf
= Sh = 2.0 + 0.60Re 1/2 Sc 1/3
where Sh is the Sherwood number, C f is the total gas concentration at the film
10
(2.7)
temperature, D ABf is the molecular diffusivity at the film temperature, Re is the Reynolds
number, and Sc is the Schmidt number. Note that in Eq. 2.6, the positive flux direction is
designated as the direction from the bulk phase to the particle. As a result, N CO and N CO2
take negative values. Using the stoichiometric relations in Eq. (2.3), N CO and N CO2 in Eq.
(2.4) can be expressed in terms of N O2. Eq. 2.6 can be re-written as
where =
NO2 − x s NO 2 = C f DABf Sh
(x∞ − x s ) (2.8)
d p
− 1
+ 1
The oxygen molar flux can be converted to carbon consumption rate q diff
(gC/cm 2 /sec) by multiplying the molecular weight of carbon and the reciprocal of the
stoichiometric coefficient of oxygen
(2.9)