Page 216 - Introduction to chemical reaction engineering and kinetics

198 Chapter 8: Catalysis and Catalytic Reactions

the rate is given by

(74) = kKACACB
1 + KAcA + KCCC

Even though the reaction is bimolecular, reactant inhibition does not occur for this type
of reaction.
Variable site characteristics: Sites which have variable properties have been observed.
These have been treated in several ways, including (1) distribution ofsite types, which
can be thought of as equivalent to having a distribution of catalysts operating inde-
pendently; and (2) site properties which change with the presence of other adsorbates,
although they are all the same at a given condition. In the latter case, for example,
the rate constants for adsorption or surface reactions can depend on the amounts of
other adsorbed intermediates: k, = f(6,, 13,, . . . ). An example is the well-studied de-
pendence of the heat of adsorption of CO on various metals, which decreases as the
coverage of the surface by CO increases.

8.5 HETEROGENEOUS CATALYSIS: KINETICS IN POROUS
CATALYST PARTICLES

8.5.1 General Considerations
For a solid-catalyzed gas-phase reaction, the catalyst is commonly in the form of par-
ticles or pellets of various possible shapes and sizes, and formed in various ways. Such
particles are usually porous, and the interior surface accessible to the reacting species
is usually much greater than the gross exterior surface.
The porous nature of the catalyst particle gives rise to the possible development of
significant gradients of both concentration and temperature across the particle, because
of the resistance to diffusion of material and heat transfer, respectively. The situation
is illustrated schematically in Figure 8.9 for a spherical or cylindrical (viewed end-on)
particle of radius R. The gradients on the left represent those of CA, say, for A(g) +
. . . -+ product(s), and those on the right are for temperature T; the gradients in each
case, however, are symmetrical with respect to the centerline axis of the particle.
First, consider the gradient of CA. Since A is consumed by reaction inside the particle,
there is a spontaneous tendency for A to move from the bulk gas (CA& to the interior
of the particle, first by mass transfer to the exterior surface (c,&) across a supposed film,
and then by some mode of diffusion (Section 8.5.3) through the pore structure of the
particle. If the surface reaction is “irreversible,” all A that enters the particle is reacted
within the particle and none leaves the particle as A; instead, there is a counterdiffu-
sion of product (for simplicity, we normally assume equimolar counterdiffusion). The
concentration, cA, at any point is the gas-phase concentration at that point, and not the
surface concentration.
Next, consider the gradients of temperature. If the reaction is exothermic, the cen-
ter of the particle tends to be hotter, and conversely for an endothermic reaction. lJvo
sets of gradients are thus indicated in Figure 8.9. Heat transfer through the particle is
primarily by conduction, and between exterior particle surface (T,) and bulk gas (T,)
by combined convection-conduction across a thermal boundary layer, shown for con-
venience in Figure 8.9 to coincide with the gas film for mass transfer. (The quantities
To, ATp, ATf, and AT,, are used in Section 8.5.5.)
The kinetics of surface reactions described in Section 8.4 for the LH model refer to
reaction at a point in the particle at particular values of cA (or PA) and T. To obtain
a rate law for the particle as a whole, we must take into account the variation of CA