Modélisation du transport des polluants dans un réservoir d’eau avec deux sources de contamination placées aux frontières.

Abstract

In this thesis we propose two models of pollutants transport with two conta- minants sources localized at the boundaries of the domain. The first model concerns the transport in groundwater with distance variable coefficients and the second, pollu- tant transport in groundwater with spatio-temporal dependent coefficients. In the first model, derives an analytical solution of a one-dimensional (1-D) Advection-Dispersion Equation (ADE) for solute transport with two contaminant sources incorporating the source term is derived. Groundwater velocity is considered as a linear function of space while the dispersion as a n power of velocity and analytical solutions are obtained for n = 1, 1.5 and 2. The solution is derived using the Generalized Integral Transform Technique (GITT) with a new regular Sturm-Liouville Problem (SLP). In the second model, we present a new approach to solve the one-dimensional solute transport equation with distance variable coefficients and two input sources in a finite porous media. The porous medium is divided into m-layers porous media with constant coefficients in each solute transport problem. The transport equations in layer i-1 and i are coupled by imposing the continuity of solute concentration and the dispersive flux at the interfaces of the layers. Unknown functions representing the dispersive flux at the interfaces between adjacent layers are introduced allowing the multilayer problem to be solved separately on each layer in the Laplace domain before being numerical inverted back to the time domain. This approach is all the more innovative in that it circumvents the difficulties encountered when using conventional approaches and also overcomes their limitations. The obtained solutions for the two models are compared with numerical solutions obtained in MATLAB pedpe solver and/or with analytical solutions for transport problem in porous media with variable coefficients. Both solutions are found to be in good agreement for each of problem studied. The effects of some parameters on solute distribution are demonstrated graphically for the set of input data based on similar data available in the literature. As illustration, the second model was applied to two real problems of contamination, the first one considers an advective-dispersive transport problem with a sinusoidal time-dependent emitting rate at the boundary was study in order to illustrate the effect of sinusoidal frequency on solute concentration. The second problem concerns practical implementation of the solution to an actual field, single-well push-pull test example designed to obtain the concentration distribution of reactant consumed during the injection phase and after. Finally, as another illustration, the predictions of the two models are used to estimate the time histories of the radiological doses of uranium at different distances from the sources boundary in order to understand the potential radiological impact on the general public for such problem.