Asymptotic approximation for counterflow combustion in porous media

Abstract

Air injection and in situ combustion have long been considered as potential techniques for displacement and recovery of medium and heavy oil. They utilize heavy and immobile oil components as fuel producing heat and improving the recovery of upgraded crude oil. We consider a porous rock cylinder with a homogeneously distributed solid fuel, initially filled with air that is injected at constant rate on the left end of the cylinder. We assume that combustion starts at the production end and propagates upstream toward the injection end. A bimolecular reaction is assumed to take place between the injected oxygen and the solid fuel; hence, the region of reaction behaves as a source of heat as well as a sink for the oxygen and the fuel. We neglect air compressibility and heat losses. Assuming that the combustion front has a traveling wave profile, we analyze the possible wave sequences present for the counterflow combustion. Besides the analysis of the wave sequences, we apply the asymptotic expansion technique for ordinary differential equations to approximate the traveling wave profile of the combustion front. We perform numerical simulations to validate this approximation.

Keywords:

• counterflow combustion
• traveling wave
• asymptotic expansions
• singular perturbation
• porous media

AMS Subject Classifications:

• 80A25
• 35C07
• 34D15

Acknowledgements

The authors thank Prof D. Marchesin and A. Mailybaev for fruitful discussions during the development of this work. The authors thank anonymous referee for valuable comments and suggestions.

Notes

A.J.S. was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico [grant number 551016/2011-6].