A one dimensional (1-D) numerical model to describe forward filtration combustion in a porous bed is proposed. The numerical model is based on mass and momentum conservation law (generalized Darcy's law). We assume local thermal equilibrium between gas and solid phases. The effect of carbon and calcium carbonate content on the propagation of the high temperature combustion front has been investigated. A simple carbon oxidation reaction, producing CO and CO2, describes the combustion. We found that increasing the carbon content of the bed increases the peak temperature. However, the combustion front velocity versus carbon content does not show a monotone behaviour. The front velocity increases while carbon content increases up to a certain value and then decreases. Also, we observed that higher the temperature is, stronger the calcium carbonate decomposition is. Consequently, the calcium carbonate decomposition is closely linked to the peak temperature. Moreover, increasing the calcium carbonate content of the porous bed resulted a decrease of the peak temperature. These results as well as the composition of produced gases are consistent with the previous published experimental study. Results of this paper show that using a 1-D model with a simple reaction scheme for combustion and for calcium carbonate decomposition produces satisfactory results for simulation of filtration combustion process. (C) 2011 Elsevier Ltd. All rights reserved.