Numerical simulation and homogenization of two-phase flow in heterogeneous porous media |
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Authors: | Brahim Amaziane Alain Bourgeat Joe Koebbe |
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Affiliation: | (1) Laboratoire De Mathematiques Appliquees, Universite De Pau, CNRS - U.A. 1204, Av. De L'université, 64000 Pau, France;(2) Universite De Saint-Etienne, Equipe D'analyse Numerique U.A., 740, 23 Rue Du Dr Paul Michelon, 42023 Saint-Etienne Cédex 2, France;(3) Department Of Mathematics And Statistics, Utah State University, Logan Utah, 84322-3900, USA |
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Abstract: | A mathematically rigorous method of homogenization is presented and used to analyze the equivalent behavior of transient flow of two incompressible fluids through heterogeneous media. Asymptotic expansions and H-convergence lead to the definition of a global or effective model of an equivalent homogeneous reservoir. Numerical computations to obtain the homogenized coefficients of the entire reservoir have been carried out via a finite element method. Numerical experiments involving the simulation of incompressible two-phase flow have been performed for each heterogeneous medium and for the homogenized medium as well as for other averaging methods. The results of the simulations are compared in terms of the transient saturation contours, production curves, and pressure distributions. Results obtained from the simulations with the homogenization method presented show good agreement with the heterogeneous simulations. |
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Keywords: | Heterogeneous porous media two-phase flow numerical simulation finite element method |
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