Page 226 - Introduction to chemical reaction engineering and kinetics

208 Chapter 8: Catalysis and Catalytic Reactions

surface reactions may follow other kinetics, such as Langmuir-Hinshelwood kinetics,
there is a need to define a general Thiele modulus (&) applicable to all forms of kinetics
as well as shape.
The form of & developed by Petersen (1965) in terms of reactant A, and for constant
D,, is:

I I
Le( - rA~intlck, (8.5-22)
” = [2D, jiAs( -‘A)in

where (-r&t is the intrinsic rate given by the rate law, and (-rA)i&, is the rate
evaluated at the concentration at the exterior surface of the particle, cAs. All forms of
Thiele modulus given previously may be obtained from this general expression.

8.5.4.6 Identifying the Presence of Diffusion Resistance
The presence (or absence) of pore-diffusion resistance in catalyst particles can be read-
ily determined by evaluation of the Thiele modulus and subsequently the effectiveness
factor, if the intrinsic kinetics of the surface reaction are known. When the intrinsic rate
law is not known completely, so that the Thiele modulus cannot be calculated, there are
two methods available. One method is based upon measurement of the rate for differ-
ing particle sizes and does not require any knowledge of the kinetics. The other method
requires only a single measurement of rate for a particle size of interest, but requires
knowledge of the order of reaction. We describe these in turn.

8.5.4.6.1 Effect of particle size. If the rate of reaction, (-rA)&, is measured for two
or more particle sizes (values of L,), while other conditions are kept constant, two ex-
tremes of behavior may be observed.

(1) The rate is independent of particle size. This is an indication of negligible pore-
diffusion resistance, as might be expected for either very porous particles or suffi-
ciently small particles such that the diffusional path-length is very small. In either
case, 11 -+ 1, and (-r.Jobs = (-IA)& for the surface reaction.
(2) The rate is inversely proportional to particle size. This is an indication of strong
pore-diffusion resistance, in which 7-t + l/&’ as 4” + large. Since 4” m L, for
fixed other conditions (surface kinetics, D,, and c~), if we compare measured
rates for two particle sizes (denoted by subscripts 1 and 2) for strong pore-
diffusion resistance,

(-rA)obs,l 71 _ 4; _ J5e2 - (8.5-23)
-
-
-
(-rA)obs,2 = ii +;’ Lel
8.5.4.6.2 Weisz-Prater criterion. The relative significance of pore-diffusion resistance
can be assessed by a criterion, known as the Weisz-Prater (1954) criterion, which re-
quires only a single measurement of the rate, together with knowledge of D,, L,, cAs
and the order of the surface reaction (but not of the rate constant).
For an nth-order surface reaction of species A, the rate and Thiele modulus, respec-
tively are
(8.5-24)
(-rA)obs = vkAck