Riemann Solutions for a Model of Combustion in Two-Phase Flow in Porous Media

For very viscous oil, the injection of air in reservoirs, with subsequent burning of a small part of the hydrocarbons, is a very effective method of recovery, since it maintains pressure and reduces oil viscosity by heating. It is very desirable to understand exactly the nature of the flow in order to devise strategies for maximizing recovery at minimal cost without creating safety hazards. Also, numerical simulation is not an easy process, so simplified solutions can be used to validate simulation codes. In this paper, we describe some Riemann solutions containing a combustion front ahead of other waves.