Geometric singular perturbation analysis of oxidation heat pulses for two-phase flow in porous media

Abstract

When air or oxygen is injected into a petroleum reservoir, and oxidation or combustion is induced, a combustion front forms if heat loss to the surrounding rock formation is negligible. Here, we employ a simple model for combustion, which takes into account oil viscosity reduction, but neglects gas density dependence on temperature and uses a simplified oxidation reaction. We show that for small heat loss, this combustion front is actually the lead part of a pulse, while the trailing part of the pulse is a slow cooling process. If the heat loss is too large, we show that such a pulse does not exist. The proofs use geometric singular perturbation theory and center manifold reduction.