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Paramétrisation et optimisation sans dérivées pour le problème de calage d’historique

Abstract : We worked in this thesis on a classical inverse problem in the petroleum industry, historymatching. We proposed a new geostatistical parameterization technique as well as a new derivativefree optimization algorithm adapted to the problem specificities. The parameterization method is based on two approaches found in the literature, the local gradual deformation method and the domain deformation method. Similarly to the local gradual deformation method, our method combines two or more model realizations inside previouslydefined zones. Moreover, our method adds the possibility to dynamically update the shape ofthe zones during the optimization process. This property substantially improves its robustnesswith regard to the initial choice of the zones. Thus, the greater flexibility brought by our methodallowed us to develop an initialization methodology which garantees a good initial point for theoptimization. To reduce the number of evaluations needed to minimize the objective function, we madethe assumption that a local parameter does not influence the production data of a distantwell. With this hypothesis, the objective function is then considered partially separable. Theoptimization algorithm we developped, called DFO-PSOF, is a trust region algorithm basedon quadratic interpolation models which exploits this partial separability property. Numericalresults obtained on some reservoir test cases validate both the hypothesis and the quality of ouralgorithm for the history matching problem. Moreover, a theoretical convergence result towardsa first order critical point, is proved for this new optimization method
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Benjamin Marteau. Paramétrisation et optimisation sans dérivées pour le problème de calage d’historique. Optimisation et contrôle [math.OC]. Université de Versailles-Saint Quentin en Yvelines, 2015. Français. ⟨NNT : 2015VERS014V⟩. ⟨tel-01168480⟩

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