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Découplage de la thermodynamique et hydrodynamique et solutions asymptotiques des problèmes d'écoulement compositionnel gaz-liquide en milieux poreux

Abstract : The present work deals with the problem of the compositional gas-liquid flow for the well representation in reservoir simulations. The objective is to develop analytical relationships which would be able to link the wellbore pressure, saturation and component concentrations to their mean values within each zone of the well influence. It is shown that N-2 equations describing the transport of phase concentrations can be transformed into the space- and time-independent ordinary differential equations (differentiation with respect to pressure) when examined along flow streamlines. These transformed equations represent additional thermodynamic relations reducing the thermodynamic degree of freedom. Due to this the thermodynamic variance of the limit compositional model is shown to be equal to 1 for any number of chemical components. This transformation ensure a total splitting of the limit compositional model into the new thermodynamic model and a hydrodynamic model, which may be resoved inedpendently of one another. The split thermodynamic model is totally independent on the hydrodynamic one, and describes the equilibrium behaviour of an open gas-liquid system. This model contains the classic equilibrium equations and EOS, as well as N-2 new differential equations called the "delta-law" which determine the composition variation in an open system, in which the mass of each component is not conserved. The split hydrodynamic model consists of two equations for pressure and saturation. The split hydrodynamic model was used to develop asymptotic solutions of gas-condensate flow problems. The problem was shown to be singularly perturbed with formation of a boundary layer in the vicinity of the well. In this layer the basic contrast property of gas and liquid mobilities is perturbed. A special technique is developed which enables to construct asymptotic expansions in the form of two various series, one of them is valid far from the well (the exterior expansion), while the second one in valid in the vicinity of the well (the boundary-layer or interior expansion). By applying the suggested asymptotic method, we have developed the asymptotic solutions for the problem of multi-component gas-condensate flow to a well in a bounded domain at a variable flow rate. In several cases the solution may be obtained in the analytical form, while in general case of flow the method leads to a semi-analytical solution presented as an initial problem for a differential equation. This solution, even being presented in non-analytical form, is much simpler than the original compositional model, as the equation for saturation does not depend on the local pressure, but on the boundary pressure only. In the last chapter we extended this approach to the case when the capillary pressure is not neglected. We assumed however that the capillary forces are lower than the pressure difference between the wellbore and reservoir boundary, due to which we applied the perturbation method over the small inverse capillary number. The improved asymptotic solutions are obtained which take into account the capillary effect. Numerical simulations shown that these effects are maximal in the vicinity of the well. For the practice, the obtained asymptotic solutions may be used in the following way to resolve the problem of gas-condensate well representation. The case of a long-term exploitation of the reservoir}. First of all, the traditional simulation of the reservoir behaviour can be performed with ECLIPSE by adding the Peaceman method of well representation, which is an analytical relation for the wellbore pressure via the production rate. This relation includes a condensate saturation which can be evaluated as a mean reservoir saturation. Such a simulation provides a good result for the wellbore pressure (or the production rate), and a good result for the boundary saturation, but poor data for the wellbore saturation. This value can be calculated next by using the asymptotic solutions suggested in the presented project. The case of a short-term well production (a well test). It is sufficient to simulate the reservoir behaviour in the domain of the well influence, by assuming that the boundary state remains invariable (and known a priori). In this case the asymptotic solutions suggested in the presnet work can be directly used to simulate the problem (without using ECLIPSE)
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Submitted on : Thursday, March 29, 2018 - 1:56:54 PM
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Sergey Oladyshkin. Découplage de la thermodynamique et hydrodynamique et solutions asymptotiques des problèmes d'écoulement compositionnel gaz-liquide en milieux poreux. Autre. Institut National Polytechnique de Lorraine, 2006. Français. ⟨NNT : 2006INPL059N⟩. ⟨tel-01752758⟩



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