Non-diffusive combustion waves in insulated porous media
Co-flow filtration combustion | Porous media | traveling wave
Air injection with in-situ combustion has long been considered as a potential technique for displacement and recovery of heavy oil. It utilizes heavy and immobile components of the crude oil as fuel for producing in-place heat necessary for the recovery of upgraded crude oil. As a laboratory model for air injection, we consider a porous rock cylinder with a homogeneously distributed solid fuel, initially filled with air that is injected at constant rate on the left end of the cylinder. We investigate a forward combustion technique, whereby the combustion starts at the injection end of the cylinder and propagates upstream towards the production end. We neglect air compressibility and heat losses. A bimolecular reaction is assumed to take place between the injected oxygen and the solid fuel, so the region of reaction behaves as a source of heat as well as a sink for the oxygen and fuel. The combustion reaction rate is given by Arrhenius law. In order to solve the corresponding Riemann problem and find the combustion wave profile some simplifications are commonly used. Many of them are related to the diffusion terms that appear in thermal and gas mass balance laws, for example, one common approximation is to consider high Lewis number. The goal of this work is to discuss the importance of the diffusion terms for the traveling wave solution in these models. There are different mathematical models describing similar physical phenomena developed in previous works. Here, we compare the solutions of our model with the solutions of earlier models.