Two‐phase flow in heterogeneous porous media: 1. Model development

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Abstract
A two‐dimensional finite difference model to study the simultaneous movement of a dense, nonaqueous phase liquid and water in heterogeneous porous media is developed. A distinctive feature of the solution is that the primary variables solved for, wetting phase pressure and wetting phase saturation, are both existent throughout the solution domain regardless of whether the nonwetting phase is present. This eliminates the need to specify small, fictitious saturations of nonwetting fluid ahead of the advancing front where only wetting fluid is present, as is often required in conventional simulators. The model is therefore well suited for the simulation of ground water contamination problems involving the advance of immiscible liquids into previously uncontaminated groundwater systems. The finite difference equations are solved fully implicitly using Newton‐Raphson iteration. In order to minimize computer storage and execution time a Dupont‐Kendall‐Rachford iterative solver utilizing Orthomin acceleration has been incorporated. The numerical model is verified against an exact analytical solution which incorporates fully the effects of both relative permeability and capillary pressure. The model is validated through comparison to a parallel‐plate laboratory experiment involving the infiltration of tetrachloroethylene into a heterogeneous sand pack.