MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

q diff (1 − x s ) = M C
It is convenient to define a new parameter k D as
o
o
c f DABf Sh
(x∞ − xs ) (2.10)
d p
k D = M c C f DABf Sh 1
P = MC d p
Eq. 2.10 can thus be written as
o
D ABf Sh
d p
11
1
RT f
(2.11)
qdiff (1 − Ps P ) = kD (P ∞ − Ps ) (2.12)
The net mass diffusion rate (N O2 + N CO + N CO2) is often neglected (equivalent to assuming
equil-molar counter diffusion), and the above equation is further simplified to
q diff = k D (P ∞ − P s ) (2.13)
Despite the widespread use of this simplified equation (Smith, 1982; Essenhigh, 1988),
the more accurate form (Eq. 2.12) is recommended.
At high temperatures, surface reaction is so fast that the surface oxygen partial
pressure approaches zero, and the overall reaction rate approaches the maximum value
allowed by boundary layer diffusion:
q max = q diff Ps = 0 = k D P ∞
(2.14)
In this case the overall reaction rate is solely controlled by boundary layer diffusion. This
situation is also called Zone III combustion.
In the char combustion literature, the factor is often used to determine the
importance of boundary layer diffusion effects. The factor is defined as the observed
reaction rate (g/sec/cm 2 ) over the maximum reaction rate allowed by boundary layer
diffusion (g/sec/cm 2 ):