Abstract A one-dimensional modelling approach to the reactive processes within a heated homogeneously premixed fuel–air mixture in its passage through a non-adiabatic catalytically reactive porous medium is described. The main focus of this contribution was comparison of the results obtained while using different modeling approaches that include mass diffusion to solid pores versus neglecting it; single step reaction versus detailed kinetic simulation; adiabatic versus non-adiabatic reactor operation; two different approaches accounting for radiation heat transfer. This model was tailored to our experimental results so as to obtain original kinetic data for corresponding global reactions for different types of catalysts and validate at the same time the predictive approaches. Results presented relate mainly to the fuels methane and hydrogen. It was shown that the employment of an ‘effective thermal conductivity’ to account for radiation heat transfer is adequate for producing satisfactory predictions while significantly cutting computational time. The use of multi-step reaction mechanisms produces results that are in good agreement with a much wider range of experimental data and does not require experimental data beforehand. It was also shown that a single-step reaction approach can be employed providing that corresponding kinetic data are derived from sufficient experimental data that need to be available for the same reactor and operational conditions. Then such simplified approach can be used to predict reasonably well the effect of operational parameters such as the feed inlet temperature and velocity. However, the use of such kinetic data for different operating conditions can lead to significantly erroneous results. It is shown that suitable catalytic beds can oxidize more fully and at lower temperatures very lean mixtures. Some of the results of the simulation using the model developed are shown to validate well against our own experimental results. Comparison of corresponding results obtained while employing overall single step reactions showed significant deviations from those of the more comprehensive multi-step reaction mechanism approach. The implication of applying the modelling approach to some practical applications is outlined.