Heterogeneous Catalysis

Abstract

The phenomenon of diffusion and reaction in catalyst pellets has engaged the attention of chemical engineers for the past thirty-five years (Thiele, 1967), though the basic problem was solved many years before and lay neglected (Jüttner 1909; see notes on the history of the subject in Ch. 1 of Aris, 1974). The calculation of effectiveness factors for various reaction kinetics, pellet geometries, and models of the diffusion-reaction process provides a number of interesting problems that may be approached using variational methods. We shall use complementary variational principles to obtain both upper and lower bounds on the effectiveness factor in a homogeneous slab of catalyst. A measure of the accuracy achieved by the variational calculation is the closeness of these bounds. Calculations will be carried out both for linear and for Langmuir-Hinshelwood kinetics. Some general results concerning pellet shape can also be obtained using variational principles, and it is shown in section 4.3 that of all catalyst pellets having a given volume the spherical pellet has the least effectiveness factor when the kinetics are of the first order.