Multicomponent flow in a porous medium adsorption and Soret effect phenomena: Local study and upscaling process

Our aim here is to study the thermal diffusion phenomenon in a forced conve ctive ow. A system of nonlinear parabolic equations governs the evolution o f the mass fractions in multicomponent mixtures. Some existence and uniquen ess results are given under suitable conditions on state functions. Then, w e present a numerical scheme based on a "mixed finite element" method adapt ed to a finite volume scheme, of which we give numerical analysis. In a las t part, we apply an homogenization technique to the studied equations in or der to obtain an efficient modelling of Soret effect and adsorption in a po rous medium at a macroscopic scale.