The sustained propagation of combustion fronts in porous media is a necessary condition for the success of an in-situ combustion project for oil recovery. Compared to other recovery methods, in-situ combustion involves the added complexity of exothermic chemical reactions and temperature-dependent chemical kinetics. This gives rise to reaction zones of a spatially narrow width, within which heat release rates, temperatures and species concentrations vary significantly. This sharp variation makes difficult the simulation of combustion processes using coarse grids and the implementation of upscaling methods.
In this paper, we propose a method for solving this problem by treating the reaction region as a place of discontinuities in the appropriate variables, which include, for example, fluxes of heat and mass. Using a rigorous perturbation approach, similar to that used in the propagation of flames , and smoldering combustion , we derive appropriate jump conditions that relate the change in these variables across the front. These conditions account for the kinetics of the reaction between the oxidant and the fuel, the changes in the morphology of the pore space and the heat and mass transfer in the reaction zone. Then, the modeling of the problem reduces to the modeling of the dynamics of a combustion front, on the regions of either side of which transport of momentum (fluids), heat and mass, but not chemical reactions, must be considered. Properties of the two regions are coupled using the derived jump conditions. This methodology allows to explicitly incorporate permeability heterogeneity effects in the process description, without the undue complexity of the coupled chemical reactions.
The propagation of combustion fronts in porous media is a subject of interest to a variety of applications, ranging from the in-situ combustion for the recovery of oil , to filtration combustion  and to smoldering combustion . While these problems may differ in application and context, they share a common characteristic, namely that the main combustion reaction involves the burning of a stationary solid fuel, which in the first two applications is part of the initial state of the system, while in the second it is created by a preceding Low-Temperature-Oxidation (LTO) process. In-situ combustion for oil recovery has been studied quite extensively since the mid 1950s. The two texts by Prats  and Boberg  summarize the relevant literature on the subject until the late 1980s. A large number of experimental, analytical and numerical studies have been reported on a variety of in-situ combustion topics.
Of interest to this paper is a particular but important issue of in-situ combustion, specifically the dynamics of combustion fronts. They are influenced by a number of factors, including fluid flow of injection and produced gases, mass transfer of the injected oxidant, heat transfer in the porous medium and the surroundings, the rate of reaction(s), the heterogeneity of the medium and possibly the evolution of the pore morphology due to the combustion reaction.