A Multiphase Approach to the Modeling of Porous Media Contamination by Organic Compounds: 2. Numerical Simulation

TLDR: In this paper, a finite difference discretization of the governing equations is proposed to handle the solution of the resultant system of nonlinear algebraic equations, a Newton-Raphson iteration scheme is employed.

Abstract: A system of equations, derived in part 1 of this paper, which describes the multiphase migration of an organic contaminant in the subsurface is presented. Although this system is not amenable to solution by analytical means, an approximate solution can be sought by a finite difference discretization of the governing equations. A one-dimensional, implicit numerical model is developed in this manner. To handle the solution of the resultant system of nonlinear algebraic equations, a Newton-Raphson iteration scheme is employed. In order to apply the finite difference model to a specific problem a number of parameters must be evaluated. These include three-phase relative permeabilities, saturation-pressure relations, partition coefficients, and mixture densities and viscosities. As a demonstration of the model's applicability, the migration of a two-component hydrocarbon mixture in a soil column is simulated. A mass balance is performed, and convergence of the iteration scheme as well as convergence of the difference scheme in space and time are examined heuristically.