Using a pore-network simulator we study pattern formation in reverse filtration combustion in porous media. The two-dimensional pore network includes all relevant pore-level mechanisms, including heat transfer through the pore space and the solid matrix, fluid and mass transfer through the pore space, and reaction kinetics of a solid fuel embedded in the pores. Both adiabatic and nonadiabatic cases are considered, the latter modeled with the inclusion of heat losses from the pore network to the ambient. The simulation results show the development of unstable, fingered patterns of the burned fuel, similar to previously reported in the literature in the related problem of reverse combustion in a Hele-Shaw cell. We study the sensitivity of the patterns obtained on a number of parameters, including the Peclet number. The results on finger spacing and finger width are analyzed in terms of a selection principle, similar to that used in the theory for unstable Laplacian growth.