MODELING CHAR OXIDATION AS A FUNCTION OF PRESSURE ...

particle can therefore be conveniently expressed by its rate based on surface reactant
concentrations multiplied by the effectiveness factor:
r obs(C ′ s) = − dnC V dt p
= S int
V p
( + S ext
S int
= 1
V p
( Sint + Sext ) r in ′ (Cs) ) r in ′ ′ (Cs) = ( + Sext )
Sint Sint Stot 16
S tot
V p
r in ′ ′ (Cs )
= ( + Sext )
Sint Sint r in ′ ′ (Cs) (2.21)
Stot It is commonly observed that the external surface area is negligible compared to the
internal surface area. Therefore the above equation becomes:
r obs ′ (Cs ) = r ′ ′ in (C s ) (2.22)
The intrinsic char oxidation rate can be represented by an intrinsic m-th order rate
equation in the form of
r in ′ = kmC m
where k m is the kinetic coefficient in (mol C/m 3 ) 1-m sec -1 , and m is the intrinsic reaction
order. Correspondingly, the observed reaction rate becomes
m
r obs ′ = kmCs Alternatively the intrinsic char oxidation rate can be represented by the Langmuir rate
equation (Eq. 2.17), and the observed reaction rate becomes:
r obs ′ =
k 1 C s
1 + KC s
(2.23)
(2.24)
(2.25)
It has been established that the effectiveness factor can be approximately (except
that it is exact for first order reactions) predicted by (Bischoff, 1965; Thiele, 1939):