Computation of the filtration laws through porous media for a non-Newtonian fluid obeying the power law |
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| Authors: | Olivier Gipouloux Abdel-Malek Zine |
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| Institution: | 1. Equipe d’Analyse Numérique, UMR 5585, Université de Saint Etienne, 23 Rue du Docteur Michelon, F-42023, Saint Etienne Cedex, France
2. Département de Mathématiques Informatique et Systèmes, UMR 5585, Ecole Centrale de Lyon, B.P. 163, F-69131, Ecully Cedex, France
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| Abstract: | We consider a stationary flow of an incompressible non-Newtonian flow through a porous medium, induced by an injection velocity when inertial effects are negligible. At the pore scale, the governing equations are based on a nonlinear relation between the stress and the rate of deformation. In such a situation, the limit problem obtained when the pore size tends to zero, is called the homogenized problem that leads to the filtration law. This filtration law is given by a non-linear system coupling a local problem on a typical cell of the porous medium to a global problem at the scale of the whole porous medium. We propose, in this work, a numerical method to solve this homogenized problem and apply this method when the velocity dependent viscosity is given by the power law. Finally, we propose some numerical experiments to illustrate our approach. |
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