Page 227 - Introduction to chemical reaction engineering and kinetics

8.5 Heterogeneous Catalysis: Kinetics in Porous Catalyst Particles 209

(8.5-20b)

Eliminating kA from these two equations, and grouping measurable quantities together
on the left side, we have

I I
(n + 1) b-dobs~: = 17(#y = cp (8.5-25)
2 D&AS

where @ is referred to as the observable modulus and is evaluated by the dimensionless
group on the left.
For negligible pore-diffusion resistance, 7) + 1 and 4” + small, say < 0.5. Thus,

@ < 0.25, say (negligible diffusion resistance) (8.5-26)

For strong pore-diffusion resistance, 77 4 l/q3”, and 4” 4 large, say > 5. Thus,

@ > 5, say (strong diffusion resistance) (8.5-27)

8.5.4.7 Strong Pore-Diffusion Resistance: Some Consequences
Here, we consider the consequences of being in the region of strong pore-diffusion re-
sistance (77 + l/$” as 4” -+ large) for the apparent order of reaction and the apparent
activation energy; 4” is given by equation 8.5-20b.
Consider an nth-order surface reaction, represented by A(g) + product(s), occur-
ring in a catalyst particle, with negligible external resistance to mass transfer so that
c,& = c&. Then the observed rate of reaction is

where

k o b s = ie (&I” (k,D,)1’2 (8.5-29)
-

According to equation 8.5-28, the nth-order surface reaction becomes a reaction for
which the observed order is (a + 1)/2. Thus, a zero-order surface reaction becomes one
of order 1/2, a first-order reaction remains first-order, and second-order becomes order
312. This is the result if D, is independent of concentration, as would be the case if Knud-
sen diffusion predominated. If molecular diffusion predominates, for pure A, D, m c&
and the observed order becomes n/2, with corresponding results for particular orders
of surface reaction (e.g., a first-order surface reaction is observed to have order 1/2).
Consider next the apparent EA. From equation 8.5-29,

(8.5-30)