In-situ combustion in porous media find applications in a variety of problems. Existing models to date are based on a continuum description, in which effective porous media are used. In this paper, we consider the use of dual pore networks (pores and solid sites) for modeling the effect of the microstructure on combustion processes in porous media. The model accounts for flow and transport of the gas phase in the porespace, where convection predominates, and for heat transfer by conduction in the solid phase. Gas phase flow in the pores and throats is governed by Darcy's law. Heterogeneous combustion with one-step finite kinetics is assumed at the pore walls. The time-dependent problem is solved numerically using a fully implicit scheme. The validity of the model is tested against existing 1-D solutions, in which three types of combustion patterns arise, depending on the value of a dimensionless parameter related to the ratio of heat capacities. Then, we report on 2-D simulations for forward combustion. The development of sustained front propagation is studied as a function of various parameters, which include heat losses, instabilities, a correlated porespace and the distribution of fuel. Implications of the findings for continuum models are discussed.