A simplified model for analyzing catalytic reactions in short monoliths

We present a new simplified model for analyzing catalytic reactions in shor t monoliths. The model is described by a two-point boundary value problem i n the radial co-ordinate with the reaction terms appearing in the boundary conditions. For the case of linear kinetics, we compare the predictions of the new short monolith (SM) model with the more general two-dimensional mod el as well as other literature models such as the widely used one-dimension al two-phase model and the two-dimensional convection model (plug flow or p arabolic velocity profile but without axial diffusion or conduction). For t he case of monotone kinetics, we show that the steady-state behavior of the general model is bounded by the two limiting models, namely the SM model a nd the convection model (this is analogous to the homogeneous CSTR and PFR models bounding the behavior of the more general axial dispersion model). M ore importantly, for the case of an exothermic reaction, the SM model retai ns all the qualitative bifurcation features of the general two-dimensional model. We use the SM model to analyze and classify the steady-state bifurca tion behavior of the catalytic monolith for the case of a single exothermic surface reaction and derive explicit analytical expressions for the igniti on, extinction and hysteresis loci in terms of the system parameters. We sh ow that there exist four qualitatively different types of bifurcation diagr ams of exit temperature (or conversion) versus residence time when the flui d Lewis number is less than unity (Le(f) < 1). Some of the diagrams contain isolated high-temperature branches and solution profiles on these branches show a local maximum in the surface temperature. We also show that in the practically important mass transfer controlled regime, the predictions of t he SM model are close to the more general two-dimensional model. Finally, w e discuss the practical implications of the results presented in this work. (C) 2000 Published by Elsevier Science Ltd. All rights reserved.