Reactive miscible displacement of light oil in porous media

We develop a theory for the problem of high pressure air injection into deep reservoirs containing light oil. Under these conditions, the injected fluid (oxygen + inert components) is completely miscible with the oil in the reservoir. Moreover, exothermic reactions between dissolved oxygen and oil are possible. We use Koval's model to account for the miscibility of the components, such that the fractional-flow functions resemble the ones from Buckley-Leverett flow. This allows to decompose the solution of this problem into a series of waves. We then proceed to obtain full analytical solutions in each wave. Of particular interest {is the case where} the combustion wave presents a singularity in its internal wave profile. Evaluation of the variables of the problem at the singular point determines the macroscopic parameters of the wave, i.e., combustion temperature, wave speed and downstream oil fraction. The waves structure was observed previously for reactive immiscible displacement and we describe it here for the first time for reactive miscible displacement of oil. We validate the developed theory using numerical simulations.