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Détermination analytique du coefficient de thermodiffusion effectif en milieu poreux : application aux fluides de gisements. Etude locale et changement d'échelle.

Abstract : We study the equations governing a fluid submitted to thermodiffusion and adsorption effects in a porous medium. The species segregation in the fluid is governed at the local scale by a system of non linear divergential parabolic equations. We prove that this system is well posed, in the Hadamard sense. The existence of a solution of this problem has been proved with a fixed-point method, the uniqueness with the help of a duality technique. This theoretical approach has been completed by numerical simulations at a pore scale, with the help of a numerical scheme, based on a "finite volume" method, for which we present a convergence result. Determination of the macroscopic equations is done in a second time. We prove that they are similar to the microscopic ones, the upscaling introducing tensors governing fluxes and some porosity coefficients before the scalar lengths. Several techniques have been used: the demonstration of the transition from Navier-Stokes equation to linear Darcy's law has been proved using asymptotic behaviours. The macroscopic model can then be completely determined solving local problems, posed on an elementary cell, which is representative of the periodic medium. A last part is devoted to the modelling of contamination of aquiferous layers by pollutants; the upscaling of conservation equations is then proved for two extreme cases, the reversible and the irreversible ones. Two approaches are considered: the first one is based on a version of the two-scale convergence applied to the boundaries, the second one is based on a result established in the problem of chemical reactions.
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https://tel.archives-ouvertes.fr/tel-00003207
Contributor : Bruno Lacabanne <>
Submitted on : Sunday, January 18, 2004 - 8:45:22 PM
Last modification on : Tuesday, February 2, 2021 - 2:54:04 PM
Long-term archiving on: : Friday, April 2, 2010 - 8:12:41 PM

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  • HAL Id : tel-00003207, version 1

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Bruno Lacabanne. Détermination analytique du coefficient de thermodiffusion effectif en milieu poreux : application aux fluides de gisements. Etude locale et changement d'échelle.. Modélisation et simulation. Université de Pau et des Pays de l'Adour, 2001. Français. ⟨tel-00003207⟩

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