Modeling of 2D density-dependent flow and transport in porous media using finite volume method

Abstract

A two-dimensional finite volume unstructured mesh method (FVUM) based on a triangular mesh is developed for modeling density-dependent flow and transport through saturated–unsaturated porous media. The combined flow and transport model can handle a wide range of real-word problems, including the simulation of flow alone, contaminant transport alone, and combined flow and transport. Saltwater intrusion problems and instability caused by denser water on the top were investigated in this paper. Because the fundamental mechanism causing saltwater intrusion most likely is caused by density-induced convection and dispersion, the developed model is used to assess the interplay between density-driven flow and subsurface media through which the saltwater intrusion occurs. The mathematical formulation of the model is comprised of fluid flow and solute transport equations, coupled by fluid density. In the specific case of saltwater intrusion and unstable brine transport problems, this set of governing equation is non-linear and requires iterative methods to solve them simultaneously. Three case studies, which include a wide range of physical conditions, are used for verification of presented model and comparison with previously published solutions from other researchers presents encouraging agreements.