Numerical Study Of Boundary Conditions For Solute Transport Through A Porous Medium

A transition region may be defined as a region of rapid change in medium properties about the interface between two porous media or at the interface between a porous medium and a reservoir. Modelling the transition region between different porous media can assist in the selection of the most appropriate boundary conditions for the standard advection-dispersion equation (ADE). An advantage of modelling the transition region is that it removes the need for explicitly defining boundary conditions, though boundary conditions may be recovered as limiting cases. As the width of a transition region is reduced, the solution of the transition region model (TR model) becomes equivalent to the solution of the standard ADE model with correct boundary conditions. In this paper numerical simulations using the TR model are employed to select the most appropriate boundary conditions for the standard ADE under a variety of configurations and conditions. It is shown that at the inlet boundary between a reservoir and porous medium, continuity of solute mass flux should be used as the boundary condition. At the boundary interface between two porous media both continuity of solute concentration and solute mass flux should be used. Finally, in a finite porous medium where the solute is allowed to advect freely from the exit point, both continuity of solute concentration and solute mass flux should be used as the outlet boundary condition. The findings made here are discussed with reference to a detailed review of previous relevant theoretical and experimental observations.