Asymptotic approximation of long-time solution for low-temperature filtration combustion

Abstract

There is a renewed interest in using combustion for the recovery of medium viscosity oil. We consider the combustion process when air is injected into the porous medium containing some fuel and inert gas. Commonly the reaction rate is negligible at low temperatures, hence the possibility of oxygen breakthrough. In this case, the oxygen gets in contact with the fuel in the downstream zone leading to slow reaction. We focus on the case when the reaction is active for all temperatures, but heat losses are negligible. For a combustion model that includes heat and mass balance equations, we develop a method for calculating the wave profile in the form of an asymptotic expansion and derive its zero-and first-order approximations. This wave profile appears to be different from wave profiles analyzed in other papers, where only the reaction at the highest temperatures was taken into account. The combustion wave has a long decaying tail. This tail is hard to observe in the laboratory because heat losses must be very small for the long tail to form. Numerical simulations were performed in order to validate our asymptotic formulae.

Oxidation wave structure and oxygen breakthrough for air injection into light oil reservoirs

“…Otherwise, if Y unb o is significant, the oxygen propagates to the region of lower temperatures. When the lowtemperature reaction is not negligible, a long reaction tail may appear [10]. This is typically the case in our study, due to relatively low activation energy of the light oil oxidation combined with elevated reservoir temperatures [13].…”

Numerical Simulation of In Situ Combustion of Oil Shale

“…In this study, the temperatures of oil shale and gas are equal (local thermal equilibrium) [20]. Heat losses are neglected.…”

Numerical Validation of Analytical Estimates for Propagation of Thermal Waves Generated by Gas-Solid Combustion

“…Due to these reasons, a good model for this technique generally consists of many equations, which hinders its analytical and numerical study. That is why a number of works simplify ISC process to one of its main components, gas-solid combustion; see [3][4][5][6][7] and references therein.…”

“…Other works use this method to obtain estimates on the combustion wave speed, temperature, and oxygen concentration; see [3][4][5]9] and references therein. (2) The second method considers that the reaction is active for all temperatures but heat losses are negligible; see [7] and references therein. The last method also allows obtaining physically consistent process parameters such as combustion wave speed and combustion front temperature.…”

“…2 Geofluids None of these is directly applicable to two-dimensional models, nor to models containing the pressure equation. The main goal of this work is to verify whether the analytical estimates proposed in [7] can be applied to more general two-dimensional nonhomogeneous models.…”