MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

Laurendeau (1978) assumed steady-state for the adsorption-desorption sequence
and obtained the simple, non-dissociative Langmuir rate equation (SNDL):
r ′ = k C(1− ) a a (5.51)
r ′ = k d d
Assuming quasi-steady state leads to:
r ′ = r ′ ′ a d
Substituting Eqs (5.51) and (5.52) into Eq. (5.53) leads to:
= KC
1 + KC
where K = k a/k d. Substituting Eq. (5.54) into Eq. (5.52) gives:
Or equivalently,
r ′ = kd KC
1+ KC = k aC 1+ KC
1 1 1
= +
r ′ kaC kd The parameters k a and k d were used exclusively by Essenhigh (1988). However, this
mechanism is in conflict with some experimental observations (see the discussion
regarding the graphite flake oxidation data and the rough sphere combustion data in
64
(5.52)
(5.53)
(5.54)
(5.55)
(5.56)
Chapter 7). Therefore, k a and k d are not used in this study. Instead, k 1 and k 0 are used in
place of k a and k d since several different mechanisms lead to expressions that can be
simplified to the same form as the SNDL. For example, Laurendeau noticed that in case
of surface migration control, the reaction rate becomes:
r ′ = kc = kc KC
1+ KC
(5.57)