Multi-mode low-dimensional models for non-isothermal homogeneous and catalytic reactors

Abstract

A systematic procedure based on the Liapunov–Schmidt method of bifurcation theory is used to derive low-dimensional models for different types of non-isothermal homogeneous, catalytic and coupled homogeneous–heterogeneous reactors. These low-dimensional models are described by multiple concentration and temperature modes (variables), each of which is representative of a physical scale of the system. These “multi-mode models” capture mass and thermal micromixing as exchange of material and energy, respectively, between the modes (scales). The multi-mode models retain all the parameters and most of the qualitative features of the full convection–diffusion–reaction equations. While in the limit of vanishingly small local heat and mass diffusion times, they reduce to the classical ideal pseudo-homogeneous reactor models, they are also capable of capturing the mixing or mass (and/or heat) transfer-limited asymptotes for the case of fast reactions. We illustrate the usefulness of the multi-mode models in predicting mixing and selectivity effects on reactor performance and the influence of local transport effects on reactor runaway and bifurcation behavior for the case of non-isothermal homogeneous and catalytic reactors.