Appearance of the instability from the inhomogeneity in two-phase flow with gas-producing reaction in fractured porous medium

Abstract

A homogenized model of incompressible two-phase flow accompanied by a gas-producing reaction in a double porosity medium with a chemically active skeleton is derived. The equations of the homogenized model contain non-local in time source terms corresponding to the contribution of the gas-producing chemical reaction in the matrix blocks. The time non-locality, which manifests itself as the appearance of a time delay between the change in reactant concentrations and the reaction rate, is shown to stimulate the instability of the one-dimensional two-phase flow initiated by injection of the acid solution into the double porosity medium with chemically active matrix blocks. The instability results in the development of the self-oscillating mode of the reaction wave propagation.