Modelling scale-dependent radial two-phase flow of liquid and gas in unsaturated porous media

Abstract

In this paper we investigate scale-dependent radial two-phase flow of liquid and gas in unsaturated porous media. First we present an equation of two-phase flow of liquid and gas in porous media in radial coordinates (ETPR) based on McWhorter’s equation in Cartesian coordinates. Then we present three analytical solutions for the ETPR: [1] an exact solution of ETPR in three dimensions for radial two-phase flow into a spherical domain subject to an instantaneous point source input; [2] an exact solution of ETPR in two dimensions for two-phase outflow from a well subject to an instantaneous line source input; and [3] an equation of the two-phase wetting front movement in three dimensions is presented based on a coordinate transform, yielding a moving boundary problem in two-phase flow in porous media, and an analytical solution is given which can be used to infer a fractal parameter of the porous media, . These analytical solutions can aid in the verification of numerical solutions, and explicitly illustrate the functional relationships between the variables and parameters affecting two-phase flow in unsaturated porous media.