MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

2 [ (i +1) − (i − 1)] i
b = −9M1 2 1+ KCs i
31
, (4.11d)
and N + 1 is the number of grid points in the radial coordinate in this model (therefore the
spherical particle is divided into N layers). The boundary conditions are:
n+1
1 = 2
=1, (4.12a)
. (4.12b)
For m-th order rate equations, the discretization equations are the same as Eq. (4.10) and
Eq. (4.11) except that Eq. (4.8) and (4.11d) are replaced by:
M 1 = r s
3
m −1
kmCs De 2 [ (i +1) − (i − 1)]
b = −9M1 2
, (4.13)
m
i . (4.14)
As mentioned previously, in Zone II the effectiveness factor is approximately 1/M T.
Therefore as M T gets large, only a small fraction (can be roughly estimated as 1/M T) of the
radial particle layers are accessible to oxygen. To maintain the accuracy of the model, the
number of layers into which the particle is divided must be increased linearly with M T.
However, when the number of layers is too large, the computation is very slow and the
round-off errors may prevent further improvement of accuracy through grid refinement.
The number of layers N in the radial coordinate was chosen to be:
N = max( 150,150 MT ) . (4.15)
Non-uniform gridding was used, where each layer was given the same volume (V p/N), in
order to reduce numerical errors.