Two-Dimensional Problem of Gas Filtration in Poroelastic Medium

This article discusses a two-dimensional mathematical model of carbon dioxide (carbon dioxide, cO2) burial in the Earth’s interior. The defining system of equations consists of liquid or gas filtration equations which are a generalization of the Masket — Leverett filtration models. The assumption of the small movement speed of the solid phase, as well as the incompressibility of the gas and solid phases, makes it possible to reduce the original system of governing equations to the problem of finding the effective pressure and porosity of the medium. The filtration area is a rock layer into which gas is supplied from below through a well at a given constant speed. The upper boundary is the roof of the formation, and the lateral and lower boundaries of the formation are limited by impermeable rocks. Special cases of gas injection are considered when a nonflow condition is imposed on the roof of the formation for two phases and when the surface is permeable to gas. The release of carbon dioxide to the surface is understood to be due to an increase in porosity at the top of the formation. Numerical modeling of the resulting initial boundary value problem and analysis of the results are carried out.