MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

correction. The values of functions g(M T) and f c(M T, m s) are listed in Table 4.4. The
correction function is also illustrated in Figure 4.3.
Table 4.3. The Pattern of Error Associated with the General Asymptotic Solution
for both Types of Reaction Rate Equations
General Moduli MT = L
Patterns of Errors
for Predicting the
Effectiveness
Factor
m-th Order Rate Equations Langmuir Rate Equation
(m + 1)
2
okmC m −1
s
De 37
M T = r s
3
ok 1
KC s
2De 1 + KCs 1
−
2
[KC − ln(1+ KC )] s s
0% to -17% 0% to -17%
Very small error at m = 1 Very small error at KCs = 0
(Ideally error should be zero) (Ideally error should be zero)
Error increases as m decreases Error increases as KCs approaches
to zero at a constant MT infinity at a constant MT Error decreases toward zero Error decreases toward zero as MT as MT departs from 0.707 in departs from 0.707 in both
both directions at a constant
m
directions at a constant KCs Maximum error occurs at Maximum error occurs at zeroth
zeroth order limit at MT =
0.707
order limit at MT = 0.707
Table 4.4. Values of g(M T) and f c(M T, m s)
M T g(M T) f c(M T, 1) f c (M T, 0.75) f c (M T, 0.5) f c (M T, 0.25) f c (M T, 0)
0.125 32.0 1 1.001 1.003 1.006 1.011
0.250 8.13 1 1.003 1.010 1.024 1.043
0.354 4.25 1 1.005 1.019 1.044 1.079
0.500 2.50 1 1.008 1.032 1.073 1.133
0.707 2.00 1 1.010 1.039 1.089 1.163
1.000 2.50 1 1.008 1.032 1.073 1.133
1.414 4.25 1 1.005 1.019 1.044 1.080
2.000 8.13 1 1.003 1.010 1.024 1.043
4.000 32.0 1 1.001 1.003 1.006 1.011