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.

This thesis reviews algorithms that have been developed for classifying lidar data and identifies a progressive morphological filter for evaluation and improvement. Two potential weaknesses evaluated include the row-column order bias and grid orientation bias. Four different row-column orderings were developed to test for bias associated with the order choice. Moreover, a method rotating the filter grid to a series of angles was developed for testing bias associated with grid orientation. Measures of success of the improvements include Type I and II errors, where results are compared with a hand-produced "truth" dataset. Two datasets, one urban, the other rural, were selected for testing the modified filters. The results are presented and discussed for each algorithm. It was found that the four row-column orders all classified the dataset exactly the same. After the erosion and dilation functions were completed, the same surface profiles and elevations were produced regardless of row-column ordering. The filter windows used by the algorithm were found to create a rectangular area where the minimum and maximum values within that area were always selected. Therefore, it was found that the row-column orders did not create a bias in the classification. However, grid orientation was found to greatly affect results. Misclassification problems occurred at ridgelines, mounds, and along roads with ditches and steep slopes running along them. Grid angles running parallel to these objects were found to avoid these errors. Buildings also created errors, but were minimized with grid angles crossing them at 45 degrees. The selected angle directions significantly affect the classification results in all cases. Therefore, the grid orientation bias was verified. Two new methods of combining the results from the various angles have been developed. The first method used the best two classifying angles to combine the results. Best results were found in datasets with terrain objects positioned in similar directions for this method. The Multiple Angle method used all of the angle classifications to combine the results. This method performed best on datasets with terrain objects oriented in numerous directions. More accurate terrain models and better overall classification results have been generated using these methods.

The use of geosynthetics in landfill construction introduces potential planes of weakness. As a result, there is a requirement to assess the stability along the soil/geosynthetic and geosynthetic/geosynthetic interfaces. Stability is governed by the shear strength along the weakest interface in the system. Repeatability interface shear strength testing of a geomembrane/geotextile interface at low normal stresses suitable for capping systems showed considerable variability of measured geosynthetic interface shear strengths, suggesting that minor factors can have a significant influence on the measured shear strength. This study demonstrates that more than one test per normal stress is necessary if a more accurate and reliable interface shear strength value is to be obtained. Carefully controlled inter-laboratory geosynthetic interface shear strength comparison tests undertaken on large direct shear devices that differ in the kinematic degrees of freedom of the top box, showed the fixed top box design to consistently over estimate the available interface shear strength compared to the vertically movable top box design. Results obtained from measurement of the normal stress on the interface during shear with use of load cells in the lower box of the fixed top box design, raise key questions on the accuracy, reliability and proper interpretation of the interface shear strength data used in landfill design calculations. Tests on the geocomposite/sand interface have shown the interface friction angle to vary with the orientation of the geocomposite's main core, in relation to the direction of shearing. Close attention needs to be paid to the onsite geocomposite placement in confined spaces and capping slope corners, as grid orientation on the slope becomes particularly important when sliding is initiated. Attempts to measure the pore water pressure during staged consolidation and shear along a clay/geomembrane interface in the large direct shear device suggest that this interface is a partial drainage path.

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