Mathematical Modeling of Water Vapor Injection into a Saturated Porous Medium

Abstract

A mathematical model of the process of water vapor injection into a porous reservoir containing methane is proposed, taking into account vapor condensation in the porous medium. A self-similar solution of this problem is constructed and an algorithm for its numerical solution is developed. Calculations were carried out, which showed good agreement between the self-similar and numerical solutions at a sufficiently low reservoir permeabilities. It is noted that for high-permeability reservoirs, in order to obtain adequate results, it is necessary to carry out longer-term calculations using the proposed numerical algorithm. Based on the analysis of the numerical experiment results, it is shown that when vapor is injected into a reservoir containing methane, five characteristic regions can be formed, namely: region with superheated vapor; with vapor and water in state of phase equilibrium; with methane, vapor and water in state of phase equilibrium; with methane and vapor; and region that contains only methane. Also the results of numerical experiments on the effect of vapor injection pressure and temperature on a reservoir heating are presented.