Homogenization results for a coupled system modelling immiscible compressible two-phase flow in porous media by the concept of global pressure |
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Authors: | Brahim Amaziane Mladen Jurak Anja Vrbaški |
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Institution: | 1. UNIV PAU &2. PAYS ADOUR, Laboratoire de Mathématiques et de leurs Applications , CNRS-UMR 5142, Av. de l'Université, 64000 Pau , France brahim.amaziane@univ-pau.fr;4. Faculty of Science , University of Zagreb , Bijenicka 30, 10000 Zagreb , Croatia |
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Abstract: | A model for immiscible compressible two-phase flow in heterogeneous porous media is considered. Such models appear in gas migration through engineered and geological barriers for a deep repository for radioactive waste. The main feature of this model is the introduction of a new global pressure and it is fully equivalent to the original equations. The resulting equations are written in a fractional flow formulation and lead to a coupled degenerate system which consists of a nonlinear parabolic (the global pressure) equation and a nonlinear diffusion–convection one (the saturation) equation with rapidly oscillating porosity function and absolute permeability tensor. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Under some realistic assumptions on the data, we obtain a nonlinear homogenized problem with effective coefficients which are computed via a cell problem and give a rigorous mathematical derivation of the upscaled model by means of two-scale convergence. |
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Keywords: | compressible immiscible global pressure heterogeneous porous media homogenization nuclear waste two-phase flow water-hydrogen |
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