Etude de schémas multi-échelles pour la simulation de réservoir

Abstract : In reservoir simulation, rock properties are given by a geological model defined on a grid made of hundreds of thousands of cells. Performing polyphasic flows directly on this grid may require long computation times. Therefore, reservoir engineers usually build upscaled rock properties on a coarser grid and fluid flow simulations are run with this grid. However, with this approach, the influence of the heterogeneities on the flow may be partially lost. Several multiscale methods have been introduced over the past years to improve the balance between accuracy and computation time. Most of them are dedicated to the resolution of a pressure equation. This equation is first solved on a coarse grid and a reconstruction of both fluxes and the pressures is then made at the fine scale. However, the resolution of the transport equations is still done by means of classical numerical techniques on the fine grid. The first part of this PhD work is devoted to the efficient implementation of the mixed multiscale finite element method in a parallel environment and discusses numerical tests. Many papers have been published on this topic, but, to our knowledge, its efficiency has never been completely studied in parallel in an industrial framework. The main contribution of this work is to propose, in a second part, a new multiscale method for the transport of a tracer in a porous medium. This new scheme is built using rigorous results of periodic homogenization. In particular, an explicit rate of convergence of this homogenization method is established. An error estimate is also proved for the corresponding multiscale method. Numerical results are then presented.
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https://pastel.archives-ouvertes.fr/pastel-00922783
Contributor : Franck Ouaki <>
Submitted on : Monday, December 30, 2013 - 3:38:55 PM
Last modification on : Wednesday, March 27, 2019 - 4:08:30 PM
Long-term archiving on : Sunday, March 30, 2014 - 10:20:12 PM

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Franck Ouaki. Etude de schémas multi-échelles pour la simulation de réservoir. Analyse numérique [math.NA]. Ecole Polytechnique X, 2013. Français. ⟨pastel-00922783⟩

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