Numerical simulation of two-phase flow and dispersion in saturated-unsaturated porous media

Abstract

A three-dimensional model describing the two-phase (air-water) fluid flow equations in an integrated saturates-unsaturated porous medium was developed. Also, a three-dimensional convective-dispersion equation describing the movement of a conservative, noninteracting tracer into a nonhomogeneous, anisotropic porous medium was developed. Finite difference forms of these two equations were derived. The two models were linked by the pore-velocity term. The computer simulator was developed to handle a variety of boundary conditions, such as, constant pressure, constant head, a no-flow boundary, a constant flux, and a time-dependent flux based on rainfall rate. The two-phase fluid flow equations were solved using an implicit scheme to solve for water or air pressures and an explicit scheme to solve for water and air saturations. The tensorial nature of the dispersion coefficient in a Cartesian coordinate system was recognized and the method of characteristics with a numerical equations.