Page 219 - Introduction to chemical reaction engineering and kinetics

8.5 Heterogeneous Catalysis: Kinetics in Porous Catalyst Particles 201
The final expression for estimating D, is

D, = D*E~/~~ (8.54d)

Equation 8.5-4d reveals the “true” units of D,, m3 (void space) m-l (particle) s-l, as
opposed to the “apparent” units in equation 8.5-4, m2 s-l.

8.54 Particle Effectiveness Factor q

8.5.4.1 Definition of r)
Since cA and T may vary from point to point within a catalyst particle (see Figure 8.9),
the rate of reaction also varies. This may be translated to say that the effectiveness of
the catalyst varies within the particle, and this must be taken into account in the rate
law.
For this purpose, we introduce the particle effectiveness factor 7, the ratio of the
observed rate of reaction for the particle as a whole to the intrinsic rate at the surface
conditions, cAs and T,. In terms of a reactant A,

77 = ,-A (observed)/rA(ch, T,) (8.54)

We consider the effects of cA and T separately, deferring the latter to Section 8.5.5. In
focusing on the particle effectiveness factor, we also ignore the effect of any difference
in concentration between bulk gas and exterior surface (cAg and c&); in Section 8.5.6,
we introduce the overall effectiveness factor to take this into account.
We then wish to discover how TJ depends on reaction and particle characteristics in
order to use equation 8.5-5 as a rate law in operational terms. To do this, we first con-
sider the relatively simple particle shape of a rectangular parallelepiped (flat plate) and
simple kinetics.

8.5.4.2 T,I for Flat-Plate Geometry

For a flat-plate porous particle of diffusion-path length L (and infinite extent in other direc-
tions), and with only one face permeable to diffusing reactant gas A, obtain an expression
for 7, the particle effectiveness factor defined by equation 8.5-5, based on the following
assumptions:

(1) The reaction A(g) -+ product(s) occurs within the particle.
(2) The surface reaction is first order.
(3) The reaction is irreversible.
(4) The particle is isothermal.
(5) The gas is of constant density.
(6) The overall process is in steady-state.
(7) The diffusion of A in the particle is characterized by the effective diffusivity D,,
which is constant.
(8) There is equimolar counterdiffusion (reactants and products).