MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

where k 1 and K are two kinetic parameters. It should be noted that 1) the product of K
and C is non-dimensional; 2) there are different possible mechanisms leading to Eq. 2.17;
3) the physical meanings of the two parameters k 1 and K depend on the mechanism
leading to Eq. 2.17. The discussion in this study is general and independent of
mechanisms. The above equation is also referred to as a "Langmuir adsorption isotherm"
(Essenhigh, 1988), a shifting order rate equation (Farrauto and Bartholomew, 1997) and
more specifically, a non-dissociative, single-adsorbed-species Langmuir rate equation
(Hill, 1977). The Langmuir rate equation can be re-written as:
1
r in′
′ = 1 1
+
k1 C k0 where k 0 is the ratio of k 1 to K. The Langmuir rate equation is the simplest form of all
14
(2.18)
Langmuir-Hinshelwood kinetic expressions capable of modeling apparent reaction order
shifting between zero and unity.
In an attempt to treat effects of pressure, Essenhigh proposed a so-called "second
effectiveness factor" (Essenhigh, 1988) to account for the internal combustion. This
method uses some approximations to achieve a simple form of the final rate expression.
The second effectiveness factor ( ) was calculated from the power index ( ) of the
normalized density-diameter relationship (Essenhigh, 1988; Essenhigh and Mescher,
1996; Essenhigh et al., 1999) in the following manner:
= 1+ /3 (2.19)
o
= d ⎛
⎝
⎜
d o
⎞
⎟ (2.20)
⎠