An improved semi-analytical solution for verification of numerical models of two-phase flow in porous media

A closed-form solution for one-dimensional two-phase flow through a homogeneous porous medium is presented that is applicable to water flow in the vadose zone and flow of nonaqueous phase fluids. The solution is a significant improvement to the one originally presented by McWhorter and Sunada, allowing the analysis of wetting phase entry saturations ranging from residual to full. Our aims are to provide a detailed analysis of how the solution to the governing partial differential equation of two-phase flow can be obtained from a functional integral equation arising from the analytical treatment of the problems and to present an improved algorithm for the implementation of this solution. The integral functional equation is obtained by imposing a set of assumptions for the boundary conditions. The proposed method can be used to obtain solutions that incorporate a wide range of saturation values at the entry point. The semi-analytical solution will be useful in the verification of vadose zone flow and multi-phase flow codes designed to simulate more complex two-phase flow problems in porous media where capillary effects must be included.