Singularity of a combustion wave profile: a clue to the multicomponent theory for liquid-gas filtration combustion

TL;DR

This paper analyzes a nonlinear wave in a complex multicomponent liquid-gas flow model for porous media, revealing a special singularity that determines wave parameters and offers insights into combustion wave behavior.

Contribution

It introduces an analytic solution for a complex multicomponent combustion wave, highlighting a unique folding singularity that determines wave parameters.

Findings

Identifies a special folding singularity in the wave profile.

Provides an analytic solution for a complex multicomponent system.

Suggests broader mathematical implications for singularities in balance laws.

Abstract

We study a nonlinear wave for a system of balance laws in one space dimension, which describes combustion for two-phase (gas and liquid) flow in porous medium. The problem is formulated for a general $N$-component liquid for modeling the strong multicomponent effects reported recently for an application to light oil recovery by air injection. Despite the immense complexity of the model, the problem allows analytic solution. The clue to this solution is a special form of a folding singularity, which occurs at an internal point of the wave profile. Analysis of this singularity provides a missing determining relation for wave parameters. This result is not only interesting for the application under consideration, but also motivates a deeper mathematical study of such singularities for general systems of balance laws.