We derive averaged multi-mode models for real time simulation and accurate design of multiphase catalytic reactors. The Liapunov-Schmidt (LS) technique of bifurcation theory is used to average the convection-diffusion-reaction equation. The resulting low-dimensional models are described by a system of differential algebraic equations involving multiple concentration and temperature modes namely, cup-mixing concentration and temperature, averaged concentrations and temperature in each phase, interfacial concentration and temperature. These "multi-mode models" capture all the important features involving exchange of mass and thermal energy between different phases. For the case of first order reaction with arrhenius kinetics, we compare the predictions of averaged model with detailed convection--diffusion--reaction (C-D-R) model. It is shown that the multi-mode averaged model is as accurate as the exact solution within the range of validity. Further it is shown that we can expand the range of validity of the model to any parameter value of practical interest by modifying the dimensionless mass transfer coefficients and make the model as accurate as full C-D-R model. For fluid-solid catalytic reactors we compare these models with the classical two-phase models. We show that the multi-mode model reduces to classical two-phase model under certain assumptions. The multi-mode models retain all the parameters and essential physics of the full C-D-R equation. 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 the low dimensional models are accurate with practically acceptable error and can be used with confidence for the design of multiphase catalytic reactors.