Behaviour of Infiltration Plume in Porous Media

Abstract

The proposed numerical code simulates the movement of a fluid as well as the transport of a non-reactive pollutant into a saturated porous media (2D configuration). The model uses a combination of the mixed hybrid finite element method and the discontinuous finite element method. Coupling between flow and transport is carried out by an equation of state. In the mixing zone, the density is assumed to vary as a function of concentration. In a saturated media, the transport of an incompressible fluid is described by a set of initial and boundary conditions and by a system of equations constituted by Darcy’s law, the continuity equation, Fick’s law and the advection-dispersion equation. Precision in estimating the velocity field, which determines pollutant propagation, is essential. Results obtained by classical numerical methods (conforming finite element method or classical finite difference methods) are often not very satisfactory due to the diffusive character of these methods. In order to compensate for these disadvantages, a combination between the mixed hybrid finite element technique and the discontinuous finite element technique has been implemented. When applied to the problem under consideration, this technique makes it possible to simultaneously estimate the pressure field and the velocity field (hydrodynamic module) as well as the dispersive flux and concentration field (mass transport module). Furthermore, application of these methods makes it possible to preserve the mass balance at the scale of each element and to ensure the continuity of the normal components of the velocity and dispersive flux from one element to another. In order to analyse the infiltration of a salt solute punctually injected into a porous medium, a comparison between a simplified theory and numerical simulations is presented. The density contrast between the two miscible fluids, as also the injection flow rate, play an important role. Studies carried out on 2D physical models have shown the existence of a steady-state regime located in the middle of the mixing zone. With such observations, the equations describing the transport phenomenon can be modified in order to lead to a simplified analytic solution. This result experimentally established is bounded by numerical verifications.