Porous media combustion of lean and ultra-rich methane-air mixtures was numerically studied using the approach when the process is simulated at the pore scale with explicit consideration of the three-dimensional porous structure and interstitial flow with thermal interaction between fluid and solid phases including the detailed chemical kinetics model and solid-to-solid radiation. The geometrical model of the packed bed was generated synthetically by simulation of particles falling under gravity force. A novel workflow for a randomly packed bed meshing at the pore scale was used to avoid the point contact problem. The results demonstrate that the model predicts a thermal nonequilibrium and heat recuperation mechanism in the combustion wave in the low-velocity regime correctly. The inhomogeneous structure of the porous media leads to large spatial variation of the process parameters such as velocity and temperature. It was shown that radiation makes a significant contribution to heat transfer in the region of a large temperature gradient. Radiative heat flux is transferred through the bed via radiation layer-by-layer due to restricted mutual visibility of the opaque particles. The mixture composition has a significant impact on the heat release rate and wave velocity and direction as well as thermal flame thickness and exhaust gas composition. At the macro scale, the mode of combustion wave propagation is quasi-steady whereas at the pore scale with little time steps the unsteady effects can be observed. Different subregions of the flame front propagate with not equal velocity, stand or accelerate depending on the local flow and porous matrix inhomogeneity. For the lean mixture the oscillatory regime of propagation was detected and analyzed. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.