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Modèles et schémas numériques pour la simulation de genèse de bassins sédimentaires

Abstract : This work presents some results concerning the modelling and the simulation
of sedimentary basins.
We first describe the mathematical models and the numerical schemes used in
the Institut Français du Pétrole within the framework of the Temis
project. This first part is illustrated by numerical tests dealing with 1D/2D basins.
We then study an upwind scheme commonly used for the resolution of Darcy's equations and we establish new mathematical results for a Dead-Oil model.
We also show how to design a scheme with a variable Péclet number in presence of capillary pressure. Again, we complete a mathematical study and we prove the convergence of the scheme for a simplified case. Numerical tests achieved on a model problem show that the use of a variable Péclet number improves the precision
of the calculations.
Finally, in a last part, we consider a flow problem where the rock changes and the changes of capillary pressure curves are coupled.
We precise the physical condition that the solutions in saturation must satisfy on the interfaces where the type of rock changes and we deduce from this condition an original weak problem. The existence of a solution to this problem is obtained by proving the convergence of a finite volume scheme. Numerical examples show
the effects of the interface condition on the capillary trapping.
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https://tel.archives-ouvertes.fr/tel-00007371
Contributor : Guillaume Enchéry <>
Submitted on : Wednesday, November 10, 2004 - 2:14:32 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM
Long-term archiving on: : Friday, April 2, 2010 - 8:56:47 PM

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  • HAL Id : tel-00007371, version 1

Citation

Guillaume Enchéry. Modèles et schémas numériques pour la simulation de genèse de bassins sédimentaires. Mathématiques [math]. Université de Marne la Vallée, 2004. Français. ⟨tel-00007371⟩

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