  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.
