Among various reaction systems, investigation of optimal catalyst distribution in a single pellet has received the most attention. Although the general problem of an arbitrary number of reactions following arbitrary kinetics occurring in a nonisothermal pellet has been solved and will be discussed later in this chapter, it is instructive to first consider simpler cases and proceed gradually to the more complex ones. This allows one to understand the underlying physicochemical principles, without complex mathematical details. Thus, we first treat single reactions, under isothermal and nonisothermal conditions, and then analyze multiple reactions.

The Case of a Single Reaction

Isothermal Conditions

In early studies, step distributions of catalyst were analyzed for the simple case of a single reaction occurring under isothermal conditions. Researchers often treated bimolecular Langmuir–Hinshelwood kinetics, which exhibits a maximum in the reaction rate as a function of reactant concentration. Thus, there is a range of reactant concentrations where reaction rate increases as reactant concentration decreases. This feature occurs in many reactions; for example, carbon monoxide or hydrocarbon oxidation, in excess oxygen, over noble metal catalysts (cf. Voltz et al., 1973), acetylene and ethylene hydrogenation over palladium (Schbib et al., 1996), methanation of carbon monoxide over nickel (Van Herwijnen et al., 1973), and water-gas shift over iron-oxide-based catalyst (Podolski and Kim, 1974).

Wei and Becker (1975) and Becker andWei (1977a) numerically analyzed the effects of four different catalyst distributions. In three of these, the catalyst was deposited in only one-third of the pellet: inner, middle, or outer (alternatively called egg-yolk, egg-white, and eggshell, respectively). In the fourth it was uniformly distributed.