MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

Figure 4.1. The error in reaction rate may be amplified when the reaction rate calculation
is coupled with the energy balance. It is therefore necessary to improve the accuracy of
the analytical solution of the effectiveness factor.
One may argue that presently the effective diffusivity, D e, in the M T expression
cannot be determined very accurately, and thus attempts to reduce the errors associated
with the general asymptotic solution are unnecessary. However, the inability to
accurately determine the effective diffusivity is a separate problem. This study shows
how to reduce systematic errors associated with the general asymptotic solution.
Effectiveness Factor, η
2
1
8
6
4
2
0.1
8
6
4
6 8
0.1
Zeroth order, two asymptotic lines
first order
2 4 6 8
1
General Thiele Modulus, MT 28
2 4 6 8
10
Figure 4.1. The effectiveness factor curves for first order and zeroth order reactions in
Cartesian Coordinates. For reactions between zeroth order and first order
limits (0 < m < 1 or 0 < KC s < ∞), the curves lie in the narrow band
bounded by the first order and the zeroth order curves.
2