Coupled groundwater flow and solute transport with fluid density strongly dependent upon concentration

Abstract

The governing equations are discussed for the flow of salt solution with significant density variations through a porous medium. Equations for mass conservation, salt conservation, and momentum conservation are formulated in terms of the mass fraction weighted average velocity and the mass fraction of concentrated salt solution, and the underlying approximations are considered. These equations are incorporated in the finite element groundwater code NAMMU and applied to test case 5 of level 1 of the international HYDROCOIN project. This test case proposed to model the groundwater flow over a hypothetical salt dome. The nonlinearities arising from the density variation and from a velocity‐dependent dispersion tensor made the problem very hard: we had to use special techniques including mixed interpolation finite elements and parameter stepping. Starting from a related problem involving a large diffusivity we obtained a series of solutions at successively smaller values of dispersion. Our final solution is to a physically realistic problem very similar to that specified. We draw general conclusions relevant to modeling these flows and have built confidence in our numerical code.