Upscaling of mass and thermal transports in porous media with heterogeneous combustion reactions

The present paper aims at an upscaled description of coupled heat and mass processes during solid–fluid combustion in porous media using volume-averaging theory (VAT). The fluid flows through the pores in a porous medium where a heterogeneous chemical reaction occurs at the fluid–solid interface. The chemical model is simplified into a single reaction step with Arrhenius kinetic law, but no assumption of local thermal equilibrium is made. An array of horizontal channels is chosen for the microstructure. The corresponding effective properties are obtained by solving analytically the closure problems over a representative unit cell. For a range of Péclet and Δ numbers, the results of the upscaled model are compared with microscale computations found in the literature. The results show that, under the same circumstances, the upscaled model is capable of predicting the combustion front velocity within an acceptable discrepancy, smaller than 1% when compared to the analytical solution. Furthermore, it has been found that for the Péclet and Δ numbers considered in this study, the fluid concentration and temperature profiles that stem from the present upscaled model are in accordance with those obtained using a microscale model.