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Étude de nouveaux schémas numériques pour la simulation des écoulements à rapport de mobilités défavorable dans un contexte EOR

Abstract : In dynamic reservoir simulation, one of the most troublesome artifacts for the prediction of production is the grid orientation effect. Although this normally arises from any numerical scheme, it happens to be amplified by the instability of the physical model, which occurs when the mobility contrast between the water (pushing fluid, used in the processes of secondary recovery) and the oil (pushed fluid, containing the hydrocarbons) exceeds a some critical threshold. We then speak of flows with adverse mobility ratio. This GOE issue has received a lot of attention from the engineers. Numerous works dating back to the 1980s have resulted in the so-called nine-point scheme. Currently implemented in the IFPEN software PumaFlow, this scheme performs relatively well in square meshes and depends on a scalar parameter whose value varies from one author to another, on the grounds of heuristic considerations. In this thesis, we propose a new methodological approach in order not only to optimally adjust this free parameter, but also to extend the scheme to rectangular meshes. The strategy that we advocate is based on an error analysis of the problem, from which it is possible to define a notion of angular error and to guarantee that the behavior of the obtained scheme is the "least anisotropic" possible through a minimization of its deviation from some ideal behavior. This minimization procedure is then applied to two other families of numerical schemes: (1) a multidimensional scheme proposed by Kozdon, in which the free parameter is a function; (2) another nine-point scheme involving two scalar parameters. The latter provides the best results regarding GOE reduction when the ratio of the mesh steps is far away from 1. Finally, an extension of the method to more sophisticated physical models is envisaged.
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Submitted on : Friday, December 13, 2019 - 4:16:08 PM
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Karine Laurent. Étude de nouveaux schémas numériques pour la simulation des écoulements à rapport de mobilités défavorable dans un contexte EOR. Génie des procédés. Université Paris-Saclay, 2019. Français. ⟨NNT : 2019SACLC081⟩. ⟨tel-02358752v2⟩

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