Homogénéisation Numérique de Paramètres Pétrophysiques Pour des Maillages Déstructurés en Simulation de Réservoir

Abstract : NUMERICAL HOMOGENIZATION OF PETROPHYSICAL PARAMETERS USING UNSTRUCTURED GRIDS IN RESERVOIR SIMULATION : Homogenization methods that require to solve local problems subject to boundary conditions are addressed in this thesis. In the first part we study a method with linear boundary conditions which can be applied to unstructured grids. We show that using a mixed [resp. conforming] finite elements method we obtain a lower [resp. upper] numerical approximation of equivalent tensor. We prove also that the resulting equivalent permeability tensor is stable as defined relative to parabolic G-convergence. Numerical approximations of equivalent tensor computed on 2D and 3D unstructured grids are given. Moreover simulations of one-phase and two-phase flow are performed in order to validate the method. In the second part we define a new upscaling method which can take into account general boundary conditions applied to local problems. The determination of equivalent tensor is made, on unstructured grid, by minimizing the difference of dissipated energies (or averaged velocity) at local and global scale. Using optimal control techniques, we obtain an effective computing algorithm which allows us to find, with classical boundary conditions, the well-know results. Convergence results and errors estimates are presented. We show finally that this method is stable as defined relative to G-convergence and 2D numerical experiments are presented.
Document type :
Theses
Mathematics [math]. Université de Pau et des Pays de l'Adour, 2000. French


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Submitted on : Wednesday, April 3, 2002 - 9:38:04 AM
Last modification on : Wednesday, April 3, 2002 - 9:38:04 AM

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Thierry Hontans. Homogénéisation Numérique de Paramètres Pétrophysiques Pour des Maillages Déstructurés en Simulation de Réservoir. Mathematics [math]. Université de Pau et des Pays de l'Adour, 2000. French. <tel-00001294>

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