Multi-scale coarse-grained continuum models for bifurcation and transient analysis of coupled homogeneous-catalytic reactions in monoliths

Abstract

We use the Lyapunov-Schmidt (L-S) reduction technique of bifurcation theory to develop reduced order models for monolith reactors with catalytic reactions in the washcoat layer and homogeneous reactions in the flow channel, and with thermal effects. The L-S technique eliminates the two transverse coordinates and converts the detailed models expressed in terms of three spatial coordinates and time to multi-mode models in axial coordinate and time. The reduced order models are expressed in terms of phase averaged multiple concentration (temperature) modes and interfacial fluxes which are related through various transfer coefficients that are local scale, flow and property dependent. Accurate expressions are provided for estimating the local transfer coefficient matrices for multi-component systems. Various limiting cases of the multi-mode reduced order models are discussed and compared to other models in the literature. The usefulness of the reduced order models is illustrated by two examples: the first is the oxidative coupling of methane in a laboratory scale monolith reactor, the second is the determination of the ignition-extinction behavior of catalytically assisted combustion of propane. Other possible applications and extensions are also discussed.