We derive simplified low-dimensional models for real time simulation, control and optimization of catalytic converters used in automobiles. Liapunov-Schmidt (LS) technique of bifurcation theory is used to average the convection-diffusion-reaction equation in the transverse direction. The resulting low-dimensional models are described by a system of differential algebraic equations involving multiple concentration and temperature modes. These "multi-mode models" capture all the important features involving exchange of mass and thermal energy between different phases. For the case of CO oxidation reaction carried out in a catalytic monolith, we compare the solutions obtained by the averaged model and detailed model. It is observed that there is a very good agreement between both the predictions. Further we show that low dimensional models reduce to classical two-phase models under certain assumptions. These multi-mode models retain all the parameters and essential physics of the detailed model. Since these models contain measurable quantities like cup mixing concentration, these are amenable for calculation and analysis of quantities of practical interest like exit conversion. We conclude that low dimensional models are accurate with practically acceptable error and can be used with confidence for control and design of catalytic monoliths.

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