MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

1996) that there is a need for more careful direct investigation on the simple Langmuir rate
equation and other rate expressions that are available in the literature (i.e., Temkin,
Elovich, Freundlich, and dissociative Langmuir rate expressions; Essenhigh, 1981). This
study does not try to theoretically prove or disprove the correctness or applicability of
the simple Langmuir equation to the carbon-oxygen reaction rate. Rather, it is assumed in
this study that the simple Langmuir rate equation is sufficient for describing the carbon-
oxygen reaction rate, and the subsequent theoretical implications are derived.
The Observed Reaction Orders in Zone I and Zone II
rate equation:
It is a common practice to describe the carbon-oxygen reaction with an m-th order
r in ′ = kmC m
where C is the local oxygen concentration at a specific carbon surface. At low
46
(5.1a)
temperatures, pore diffusion is fast compared to kinetics, and the oxygen concentration is
uniform in the particle (i.e., C ≡ C s). The intrinsic reaction rate can be related to C s (the
oxygen concentration at the external surface of the particle):
m
r in ′ = kmCs in Zone I (5.1b)
Eq. (5.1b) can be re-written as
ln( r in ′ ′ ) = ln(km ) + m ln(Cs ) (5.2)
From the above equation, it can be seen that a plot of ln(r in''') vs. ln(C s) will yield a
straight line, and the slope of this line is the reaction order m. In fact, this is how the