Two-phase two-component flow in porous medium in low solubility regime

TL;DR

This paper investigates a mathematical model of two-phase flow in porous media with low gas solubility, proving the existence of weak solutions and clarifying the low solubility assumption.

Contribution

It introduces a rigorous mathematical framework for modeling low solubility gas-liquid flow in porous media and proves existence of solutions under these conditions.

Findings

Existence of weak solutions established

Low solubility hypothesis precisely formulated

Mathematical framework for two-phase flow developed

Abstract

We study a system of equations governing liquid and gas flow in porous media. The gas phase is homogeneous while the liquid phase is composed of a liquid component and dissolved gas component. It is assumed that the gas component is weakly soluble in the liquid. We formulate a weak solution of the initial-boundary value problem and prove the existence theorem by passing to the limit in regularizations of the problem. Hypothesis of low solubility is given precise mathematical meaning.