MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

Table 4.6. The Relative Error* (%) in the Corrected General Asymptotic Solution
for the Langmuir Rate Equation
1/(1+KC s)
M T 1.00 0.75 0.50 0.25 0.00
0.125 0.019 -0.030 0.163 0.485 1.133
0.25 0.016 -0.158 0.375 1.354 0.001
0.5 -0.013 -0.729 -0.113 1.208 1.394
0.707 -0.076 -1.161 -0.849 0.128 -1.246
1 -0.215 -1.387 -1.197 0.076 1.374
2 -0.491 -1.178 -1.136 -0.324 0.545
4 -0.679 -1.068 -1.256 -1.243 -1.144
8 -0.933 -1.153 -1.337 -1.494 -1.743
*Relative error = ( asymp - numerical)/ numerical
** asym = exact when 1/(1+KC s) = 1.0
Simplified General Moduli for the Langmuir Rate Equation
The standard general modulus in Eq. (4.3) is complex in form, and encounters
division by zero at KC s = 0. However, the value of M T in Eq. (4.3) exists in the limit at
KC s = 0:
M T = L
ok1 De . (4.23)
which is the Thiele modulus for first order reactions (Thiele, 1939). Two moduli that
have simpler forms were found to closely approximate the standard general modulus in
Eq. (4.3). The first one was transformed from a modulus used by Levenspiel (1993):
M T = L
O k 0 K / D e
2KC s + 1
= L
Ok1 / De . (4.24)
2KCs +1
The second modulus was constructed to better approximate the standard general modulus
in Eq. (4.3) in this study:
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