Homogenization of Immiscible Compressible Two-Phase Flow in Porous Media: Application to Gas Migration in a Nuclear Waste Repository
This paper is devoted to the homogenization of a coupled system of diffusion- convection equations in a domain with periodic microstructure, modeling the flow and transport of immiscible compressible, such as water-gas, fluids through porous media. The problem is formulated in terms of a nonlinear p...
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Veröffentlicht in: | Multiscale modeling & simulation 2010-01, Vol.8 (5), p.2023-2047 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | This paper is devoted to the homogenization of a coupled system of diffusion- convection equations in a domain with periodic microstructure, modeling the flow and transport of immiscible compressible, such as water-gas, fluids through porous media. The problem is formulated in terms of a nonlinear parabolic equation for the nonwetting phase pressure and a nonlinear degenerate parabolic diffusion-convection equation for the wetting saturation phase with rapidly oscillating porosity function and absolute permeability tensor. We obtain a nonlinear homogenized problem with effective coefficients which are computed via a cell problem. We rigorously justify this homogenization process for the problem by using two-scale convergence. In order to pass to the limit in nonlinear terms, we also obtain compactness results which are nontrivial due to the degeneracy of the system. [PUBLICATION ABSTRACT] |
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ISSN: | 1540-3459 1540-3467 |
DOI: | 10.1137/100790215 |