ETUDE EXPERIMENTALE ET MODELISATION NUMÉRIQUE DES TRANSFERTS HYDRIQUES ET DE SOLUTE DANS UN MILIEU POREUX NON SATURE-SATURE

Abstract

In this work, a mathematical modeling tool was developped to simulate in a simple and fast way, and with an acceptable precision, the water and solute transfers in unsaturated-saturated porous medium. The resolution of this problem in unstationary mode, is based on the use of an mathematical formulation which consists in considering as a single continuum the saturated and the unsaturated zones. The modeling tool is based on two numerical methods: the alternate directions implicit method (ADI) and the finite elements method (finite elements code Freefem++). This code was adapted to the equations used in this study, namely: Richards’ equation to study the water flow in the unsaturated zone, the diffusivity equation expressed in a linear and nonlinear form for the groundwater flow and the transport equation of advection-dispersion type to study the solute transfer. The advantage of the Freefem++ code is that it generates selfadapting grids. This is interesting to analyse the transfers at singular zones, in particular at the capillary fringe. Experiments were carried out on a laboratory physical model, consisting in a sand filled tank of 160 cm length and 50 cm in height. This experimental model enabled to follow the spacetime evolution of the water-table and the propagation of a tracer (Fluorescein) from the infiltration strip to the discharge system of the model. The modeling tool was validated using experimental data measured on the small-scale physical model and some results taken from the literature. It allowed to predict with an excellent precision the water-table position and the propagation of the non-reactive solute in both unsaturated and saturated compartments. A comparative study between the two numerical methods was carried out and showed that even if the finite differences method provides satisfactory results, the use of the finite elements Freefem++ code presents a light advantage and provides slightly more accurate results