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Non stationnarité dans les modèles de type booléen : application à la simulation d'unités sédimentaires

Abstract : Given the important economic stakes involved in the oil industry, there is a real need for a description of the geological structure of oil reservoirs and of the petrophysical properties of the constituting rocks. Reservoir modelling consists in making up numerical models representing the heterogeneities of the reservoir at different scales. The Boolean model is frequently used to design a lithological model of the reservoir internal architecture both at the scale of the genetic unit and at the granulometric scale inside the reservoir. However, Boolean models present a major problem when applied to the modelling of reservoirs having a non stationary distribution of their constituting lithofacies. Lithofacies proportions give information about the spatial distribution of these lithofacies. They are an efficient tool for detecting a non stationarity. They also make it possible to quantify the geological information of the deposits. They are therefore an important constraint to respect in order to obtain simulations that are geologically realistic. In this work, we have integrated into the Boolean model the information contained in the proportions. The problem to be solved is the inference of the model parameters. Two aspects have been considered. First, we have defined the inference problem from a theoretical point of view by establishing the relationship between experimental information and the model parameters. Secondly, we have implemented a computing tool to automatically pass from the proportion data to the model parameters. To do that, we propose a method of inference based on a deconvolution process. This method enables us to introduce the information of the proportions in the Boolean model. As a result, simulations can reproduce a non stationary distribution of the heterogeneities in the sedimentary unit. By construction, these simulations then respect the lateral and vertical distribution of the proportions into the unit as well as the global mean value of the proportion over the studied volume. As this global value is related to petrophysical parameters, it is important to recover it in simulations.
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Submitted on : Friday, August 6, 2010 - 2:06:21 PM
Last modification on : Thursday, September 24, 2020 - 4:00:34 PM
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  • HAL Id : pastel-00001187, version 1

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Marta Benito Garcia-Morales. Non stationnarité dans les modèles de type booléen : application à la simulation d'unités sédimentaires. Mathématiques [math]. École Nationale Supérieure des Mines de Paris, 2003. Français. ⟨NNT : 2003ENMP1180⟩. ⟨pastel-00001187⟩

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