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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Development of a 2-D black-oil reservoir simulator using a unique grid-block system

Chong, Emeline E 12 April 2006 (has links)
The grid orientation effect is a long-standing problem plaguing reservoir simulators that employ finite difference schemes. A rotation of the computational grids yields a substantially different solution under certain circumstances. For example, in a five-spot pattern, the predicted recovery, water cut performance and the locations of the fronts depend on the type of grid system used. A Cartesian grid with one axis parallel to the line joining an injector and producer gives a solution significantly different from a grid that has the axes oriented at 45° to this line. This study develops a unique grid-block assignment where rectangular grid blocks are interspersed with octagonal grid blocks. This grid block system is called the Hybrid Grid Block (HGB) system. The objective of this study is to evaluate the grid orientation effect of the HGB grid to see whether it is an improvement over the conventional Cartesian grid system. In HGB, flow can progress in four directions in the octagonal grid blocks and two in the square grid blocks. The increase in the number of flow directions in the octagonal grid blocks is expected to reduce the grid orientation effect in the model. Hence, this study also evaluates the grid orientation effect of the HGB and compares it with the Cartesian grid system. To test the viability of HGB, a general purpose finite difference IMPES-formulated two-dimensional black oil simulator was developed in this study, while retaining the familiar finite-difference discretization of the flow equations. Several simulation cases were conducted to compare HGB and conventional grid block systems. Comparisons with commercial simulator are also made. Despite the fact that the reservoir is isotropic and homogeneous, grid orientation effect was still observed when rectangular Cartesian grid models are run at mobility ratio, M = 1.0. Grid refinement can help to reduce the grid orientation effect in rectangular Cartesian grid models when there are favorable mobility ratios, i.e. M = 1.0 or less. However, at an unfavorable mobility ratio of M = 10.0, it is found that neither parallel nor diagonal orientation can be used reliably for the displacement problems run in this study. This is because as the number of grid blocks is increased, the performance of diagonal and parallel models actually diverges for the grid spacings investigated here. On the other hand, HGB grid is able to reduce the grid orientation effect even for unfavorable mobility ratio displacement problems (up to M = 50.0), with maximum relative difference in pore volume recovered of 6% between parallel and diagonal HGB grid models for all the cases run in this study. Comparisons between the conventional Cartesian and HGB grid show that the HGB grid is more effective in reducing the grid orientation effect than the Cartesian grid. The HGB grid performs better by consistently giving a smaller relative difference between HGB parallel grid and HGB diagonal grid in pore volume recovered (6.0, 4.5, 3.3, and 2.2%) compared to the relative difference between Cartesian parallel grid and Cartesian diagonal grid in pore volume recovered (17.0, 13.0, 9.3, 7.9%) at similar averaged area per grid block for all the four comparison cases studied.
2

Schémas volumes finis sur maillages généraux en milieux hétérogènes anisotropes pour les écoulements polyphasiques en milieux poreux / Finite volume schemes on general meshes for heterogeneous anisotropic porous media multiphase flow

Guichard, Cindy 29 November 2011 (has links)
Cette thèse est consacrée à l'étude de méthodes numériques pour la simulation des écoulements polyphasiques en milieu poreux, en vue de leur application à des problèmes d'ingénierie pétrolière ou environnementale. Nous présentons une formulation générique du modèle d'écoulements à nombre quelconque de composants présents dans un nombre quelconque de phases. Dans notre approche l'approximation des flux diffusifs (issus, par exemple, de la loi de Darcy) s'appuie sur de nouveaux schémas, appelés schémas gradient, qui ont plusieurs avantages sur les schémas industriels standard : ces derniers, qui sont des schémas volumes finis multi-points centrés aux mailles, ne sont généralement pas symétriques et convergent difficilement sur des cas à forts rapports d'anisotropie. Nous montrons en revanche que les schémas gradient conduisent naturellement à des approximations symétriques et convergentes. Parmi cette classe de schémas, nous étudions plus particulièrement le schéma "VAG" qui fait intervenir des inconnues au centre des mailles et aux sommets du maillage. Ce schéma conduit à la définition de flux entre le centre d'une maille et ses sommets, qui sont utilisés pour généraliser la méthode "VAG" au contexte polyphasique. Des tests numériques montrent alors que ce schéma est robuste, et conduit à un très bon compromis précision/coût, ce qui en fait un candidat idoine pour les applications industrielles. Nous présentons notamment un cas test, basé sur des observations de terrains, d'injection et de dissolution de CO2 dans la région proche d'un puits foré dans un aquifère salin. Nous montrons alors que le schéma numérique permet de simuler l'assèchement et la précipitation de minéral observée en pratique. Un chapitre de la thèse est enfin consacré à l'étude pratique et théorique d'une méthode numérique générique pour contrôler l'effet d'axe lors de l'utilisation de schémas industriels / This thesis is focused on numerical methods dedicated to the simulation of multiphase flow in porous media, involved in petroleum or environmental engineering. We present a generic formulation of the flow model which is able to take into account any number of components within any number of phases. In our approach the approximation of the diffusive fluxes (mainly resulting from Darcy's law) is based on new schemes, called gradient schemes, which show several advantages over the standard industrial numerical schemes : these schemes, which belong to the class of the cell-centred MultiPoint Flux Approximation finite volume schemes, are not symmetric and may lead to difficulties of convergence in the case of high anisotropy ratios. We indeed show that gradient schemes are naturally providing symmetric and convergent approximations. We particularly study the Vertex Approximate Gradient scheme (called the VAG scheme), whose discrete unknowns are the values at the cell centres and at the vertices of the mesh. This scheme implies the definition of fluxes between the centre of a given cell and its vertices, used for the extension of the scheme to multiphase flow. Numerical tests show the robustness and the accuracy of the method for a low computational cost, which enables the use of the VAG scheme in an industrial framework. A test case, based on experimental data of injection and dissolution of CO2 in the near-well region within a saline aquifer, shows the aptitude of the scheme for reproducing drying and salt precipitation, which are practically observed. Finally, a chapter of the thesis is devoted to the theoretical and practical study of a general numerical method for controlling Grid Orientation Effect in industrial simulators

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