Oxidation heat pulses in two-phase expansive flow in porous media

When air or oxygen is injected into a petroleum reservoir, and low temperature oxidation or combustion is induced, traveling oxidation fronts are observed to form.¶We construct a two-phase model for oxidation, involving air or oxygen and oil, that includes heat loss to the rock formation. We use Darcy's law and energy and mass balance equations. We take into account heat generation and the oil's ensuing viscosity reduction, volume and flow rate changes due to the reaction, capillary pressure, and heat diffusion. The main simplifications are (1) we neglect volume changes of gases due to pressure variations, since the latter are assumed to be small; (2) we assume that liquid water is absent; and (3) we assume that the same Arrhenius chemical reaction rate governs the oxidation of all hydrocarbons in the oil.¶Our analysis shows: (1) For small heat loss, the oxidation front is actually the lead part of a traveling pulse, while the trailing part of the pulse is a slow cooling process. The overall pulse has a triangular saw-tooth shape and may be long. (2) If the heat loss is too small, the pulse may be so long that only its lead front fits in an actual reservoir of finite length, so just this part of the pulse is observed. On the other hand, if the cooling is faster, not all oxygen is burned, a fact with deleterious consequences when the unburned oxygen reaches the producing well. (3) If the heat loss is too large, the medium does not sustain oxidation pulses. This last result is proved under the further simplifying assumption of constant effective thermal conductivity.