Upscaling for Adiabatic Solid–Fluid Reactions in Porous Medium Using a Volume Averaging Theory

In this paper, an upscaling study of solid–fluid combustion in porous medium with homogeneous and heterogeneous heat sources is carried out using a volume averaging theory. For the sake of simplicity, the reaction rate is assumed to be of first-order Arrhenius type and convection is not taken into account. Local thermal non-equilibrium is considered between the solid and fluid phases. During the resolution of closure problems, periodic boundary condition is utilized in order to determine the effective coefficients in the upscaled model.The obtained macroscale theory is validated against direct numerical simulation results for two typical porous medium geometries made of simple unit cells, namely unconsolidated and consolidated porous media. The comparisons between the present upscaled and microscale results are conducted for various Damköhler numbers for both homogeneous and heterogeneous reaction cases. It has been found that, for the low Damköhler number cases, the temperature profiles generated from the derived upscaled model are in accordance with that of the microscale model. For the high Damköhler number cases, however, the macroscale model fails to predict the combustion front and temperature profile, which evidently suggests that the effects of neglected terms during the upscaling process should be re-examined carefully in further investigations.