A pore-network model is developed, based on a dual lattice, to study the dynamics of forward filtration combustion (FC) in porous media at the pore-network scale. A novel moving coordinate method is also implemented that allows for the long-term profiles to be obtained in a straightforward manner. The model is used to reproduce recent analytical work, including the multiplicity of steady states for the nonadiabatic case, and to study a number of other effects. Particular emphasis is placed on the effect of the heterogeneity in the microstructure, introduced by the randomness in the pore radius. It is found that the local disorder leads to less oxidant consumption, as compared to the homogeneous case. This underprediction increases with an increase in the disorder, a decrease in the thermal conductivity, and a decrease in the spatial correlation. Temporary local extinction can result for sufficiently large injection rates. As a result of the heterogeneity, the spatially averaged reaction rate is generally different from the rate calculated based on the rnicroscale Arrhenius expression, using the averaged variables, with discrepancies of a factor of 2 or higher not uncommon. Although this effect depends on the parameter values, it can be a cause of concern when the fronts at the small scale are sufficiently distorted. Coupling of fronts occurs in a layered system, when there is sufficient oxidant supply. These results show that the microscale geometry can have a strong influence on the overall macroscopic behavior of the process. (c) 2005 American Institute of Chemical Engineers