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Deux modèles mathématiques de l'évolution d'un bassin sédimentaire. Phénomènes d'érosion-sédimentation-transport en géologie. Application en prospection pétrolière

Abstract : In this thesis, we study two models describing the evolution of a sedimentary basin under an erosion rate constraint. These models are obtained by applying a mass conservation law on the flow of matter, which leads to Darcy's equation or to the equation of Darcy-Barenblatt whichever flow chosen among two possible expressions according to geologists. The equation of Darcy-Barenblatt is obtained from that of Darcy by adding a diffusion term. In addition, the maximum erosion constraint is implicit in the model formulation of Darcy-Barenblatt, but not in that of Darcy in dimension 2. After the presentation of these models in the introduction of the thesis, the first part is devoted to Darcy-Barenblatt's model. We obtained an existence result for a solution through a Schauder- Tikhonov fixed point method. Then, we have showed a regularity result by using the results of Meyers and Necas on elliptic equations with Hölder coefficients, this regularity result is specific to a dimension inferior or equal to 2. The first part concludes by demonstrating a result of uniqueness of the solution. The Darcy model is considered in the second part of the thesis. We obtained a solution of the problem discretized in time ; however in 2-dimensional space, passing to a continuous formulation imposes to study the product of two weak convergences. It raises theoretical difficulties and open problems. In dimension 1, we have solved a Bernoulli evolution problem to obtain a continuous solution in the case of the marine sedimentation.
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https://tel.archives-ouvertes.fr/tel-00437343
Contributor : Mohamed-Salem Louly <>
Submitted on : Monday, November 30, 2009 - 1:18:23 PM
Last modification on : Friday, January 15, 2021 - 9:24:29 AM
Long-term archiving on: : Tuesday, October 16, 2012 - 3:05:54 PM

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  • HAL Id : tel-00437343, version 1

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Mohamed-Salem Louly. Deux modèles mathématiques de l'évolution d'un bassin sédimentaire. Phénomènes d'érosion-sédimentation-transport en géologie. Application en prospection pétrolière. Mathématiques [math]. Université de Pau et des Pays de l'Adour, 2009. Français. ⟨tel-00437343⟩

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