Multicomponent flow in a porous medium. Adsorption and Soret effect phenomena: local study and upscaling process (Q2781499)

The authors give a report about a remarkably broad research effort on the study of the evolution of several components in a porous medium in the presence of a stationary temperature field, the practical aim being prediction of contamination (in space and time) of aquifer layers by hydrocarbons. Taking into account (stationary) heat conduction, thermodiffusion, convection (using a given stationary divergence-free velocity field) and adsorption, they establish existence and unicity of a solution (using the Schauder-Tikhonov fixed point theorem), as well as nonnegativity (under special assumptions), further, they obtain local Lipschitzian dependence of the mass fractions on their initial values, on Soret coefficients and temperature gradients. NEWLINENEWLINENEWLINENext, a numerical scheme (based on a mixed finite volume method) of implicit Euler type is investigated and results on existence, unicity, stability and first order convergence of the numerical solution are found (where a condition of the type \(\Delta t\leq h^2\) appears). Further, to better model the thermodiffusion and adsorption phenomena in a porous medium, a homogenization procedure is investigated assuming that the porous structure is periodic with period \(\varepsilon\to 0\). NEWLINENEWLINENEWLINEFinally, for a rectangular capillary and a quasilinear thermal field, using the Langmuir isotherm, numerical results are shown, including concentration profiles and the computation of macroscopic heat conduction and thermodiffusion tensors.