La technologie la plus utilisée pour séparer les principaux composants de l'air est aujourd'hui ladistillation en colonne à garnissage structuré. Ce procédé se caractérise par un écoulement gazliquide contre-courant au sein d'une structure constituée de plaques corruguées placées parallèlement et agencées en packs. La description d'un tel procédé est rendue difficile par les très grandes dimensions du système et par la complexité des phénomènes à la petite échelle. La méthode de la prise de moyenne volumique, utilisée pour les problèmes de changement d'échelleen milieu poreux, est utilisée pour décrire le système à une échelle qui permet une résolution. Le travail est organisé en trois étapes. Dans un premier temps, pour les débits modérés, une méthode est proposée pour évaluer la perte de charge au sein de la structure en prenant en compte des rugosités de structure ou créées par des instabilités du film liquide. A ce stade, l'effet de la surface rugueuse est caractérisé par une condition limite effective. Le problème aux limites effectif pour la phase gaz est ensuite moyenné en volume pour obtenir un système d'équations à grande échelle. Le bilan de quantité de mouvement à grande échelle est une loi de Darcy généralisée aux écoulements inertiels, dans laquelle les paramètres effectifs contiennent les effets des instabilités de surfaces de la petite échelle. La seconde étape est dédiée à l'interaction entre les deux phases à plus hauts débits. On montre que des modèles qui incluent explicitement des termes croisés à grande échelle permettent de décrire l'écoulement au sein du garnissage à grands nombres de Reynolds. Plus généralement, ces modèles, peu utilisés dans la littérature sur les milieux poreux, s'avèrent adaptés pour les écoulements dans les milieux très perméables, pour lesquels des variations importantes de la perte de charge et des saturations sont observées. Enfin, on s'intéresse à la description de la distribution de la phase liquide au sein de la structurede garnissage. Une approche multiphasique, où la phase liquide est séparée en plusieurs pseudophases, est adaptée pour modéliser l'anisotropie de l'écoulement. Deux méthodes impliquant une approche à deux pseudo-phases et une approche à quatre pseudo-phases pour la phase liquide sont comparées. Cette dernière méthode est notamment utile pour décrire des régimes d'écoulement très différents, et permet de capturer à grande échelle les chemins préférentielssuivis par le film liquide au sein du garnissage. / Distillation in columns equipped with structured packings is today the most used technology for separating air in its primary components. This process is characterized by a counter-current gasliquid flow in a structure made of parallel corrugated sheets arranged in packs. The description of such system is constrained by the large dimensions of the columns and by the complexity of the local-scale phenomena. This leads to consider a strategy of upscaling, based on the volume averaging method, to describe the system at a scale at which a resolution is possible. The work is organized in three steps. As a first step, considering moderate flow rates, a methodology ofupscaling is developed to predict the pressure drop in the flow of the gas phase taking into account small scale roughnesses due to the structure itself or perturbations of the liquid film. At this stage, the effect of this rough surface is characterized by an effective boundary condition. The boundary value problem for the flow of the gas phase is volume averaged in order to derive a system of equations at large scale. The resulting momentum balance is a generalized Darcy's law for inertial flows, involving effective parameters accounting for the roughness at the microscale. The second step of this work focuses on the interaction between the two phases at higher flow rates. It is shown that models involving non-standard macroscopic cross-terms are more prone to describe the flow in packings at high Reynolds numbers than the models usually used in porousmedia sciences. More generally, these models are shown to characterize accurately processes in highly permeable media, where drastic changes of pressure drop and retention are observed. We finally study the distribution of the liquid phase in the structured packing. It is shown that a specific approach involving a multiphase model with liquid decomposition is required to capture the anisotropy generated in the flow of the liquid phase. Two methods involving two pseudo-phases and four pseudo-phases for the liquid phase are compared. This last method captures a number of very different distribution regimes in the column and offers additional flexibility to describepreferential paths of the liquid.

With the recent comeback of three-dimensional (3D) movies to the cinemas, there have been increasing efforts to spread the commercial success of 3D to new markets. The possibility of a 3D experience at home, such as three-dimensional television (3DTV), has generated a great deal of interest within the research and standardization community. A central issue for 3DTV is the creation and representation of 3D content. Scene depth information plays a crucial role in all parts of the distribution chain from content capture via transmission to the actual 3D display. This depth information is transmitted in the form of depth maps and is accompanied by corresponding video frames, i.e. for Depth Image Based Rendering (DIBR) view synthesis. Nonetheless, scenarios do exist for which the original spatial resolutions of depth maps and video frames do not match, e.g. sensor driven depth capture or asymmetric 3D video coding. This resolution discrepancy is a problem, since DIBR requires accordance between the video frame and depth map. A considerable amount of research has been conducted into ways to match low-resolution depth maps to high resolution video frames. Many proposed solutions utilize corresponding texture information in the upscaling process, however they mostly fail to review this information for validity. In the strive for better 3DTV quality, this thesis presents the Edge-Weighted Optimization Concept (EWOC), a novel texture-guided depth upscaling application that addresses the lack of information validation. EWOC uses edge information from video frames as guidance in the depth upscaling process and, additionally, confirms this information based on the original low resolution depth. Over the course of four publications, EWOC is applied in 3D content creation and distribution. Various guidance sources, such as different color spaces or texture pre-processing, are investigated. An alternative depth compression scheme, based on depth map upscaling, is proposed and extensions for increased visual quality and computational performance are presented in this thesis. EWOC was evaluated and compared with competing approaches, with the main focus was consistently on the visual quality of rendered 3D views. The results show an increase in both objective and subjective visual quality to state-of-the-art depth map upscaling methods. This quality gain motivates the choice of EWOC in applications affected by low resolution depth. In the end, EWOC can improve 3D content generation and distribution, enhancing the 3D experience to boost the commercial success of 3DTV.

>Magister Scientiae - MSc / This study is aimed at illustrating the reservoir heterogeneity in the BCII - BCI interval of the Ga-field, offshore South Africa. This was achieved by generating a conceptual static model as a predictive tool for the BCII - BCI interval. The reservoir zones between BCII - BCI were sub divided into two major zones, viz: zone A and zone B. Petrophysical analysis was conducted on the three wells Ga-A3, Ga-Q1 and Ga-Q2. The application of the sequential gaussian algorithm ensured that all of the available data was honoured to the highest extent in generating the realisations to display the heterogeneity of the BCII – BCI sandstone reservoir. Sampling values from the well logs were extrapolated into the 3D grid. Each reservoir contained a percentage of shale or clay of about 45% -50%. Small scaled reservoir heterogeneity has been construed to the influence of the sedimentary structures. Large scaled reservoir heterogeneity has been identified, due to the lateral extent of the claystones which is widely distributed throughout the study area

The subsurface flow is usually subject to uncertain porous media structures. However, in most cases we only have partial knowledge about the porous media properties. A common approach is to model the uncertain parameters as random fields, then the expectation of Quantity of Interest(QoI) can be evaluated by the Monte Carlo method. In this study, we develop a full multigrid-multilevel Monte Carlo (FMG-MLMC) method to speed up the evaluation of random parameters effects on single-phase porous flows. In general, MLMC method applies a series of discretization with increasing resolution and computes the QoI on each of them, the success of which lies in the effective variance reduction. We exploit the similar hierarchies of MLMC and multigrid methods, and obtain the solution on coarse mesh Qcl as a byproduct of the multigrid solution on fine mesh Qfl on each level l. In the cases considered in this thesis, the computational saving is 20% theoretically. In addition, a comparison of Monte Carlo and Quasi-Monte Carlo (QMC) methods reveals a smaller estimator variance and faster convergence rate of the latter method in this study.

How can we model global phenomenon based on local interactions? Agent-Based (AB) models are local rule-based discrete method that can be used to simulate complex interactions of many agents. Unfortunately, the relative ease of implementing the computational model is often counter-balanced by the difficulty of performing rigorous analysis to determine emergent behaviors. Calculating existence of fixed points and their stability is not tractable from an analytical perspective and can become computationally expensive, involving potentially millions of simulations. To construct meaningful analysis, we need to create a framework to approximate the emergent, global behavior. Our research has been devoted to developing a framework for approximating AB models that move via random walks and undergo state transitions. First, we developed a general method to estimate the density of agents in each state for AB models whose state transitions are caused by neighborhood interactions between agents. Second, we extended previous random walk models of instantaneous state changes by adding a cumulative memory effect. In this way, our research seeks to answer how memory properties can also be incorporated into continuum models, especially when the memory properties effect state changes on the agents. The state transitions in this type of AB model is primarily from the agents’ interaction with their environment. These modeling frameworks will be generally applicable to many areas and can be easily extended.

The task of upscaling pictures is very ill-posed since it requires the creation of novel data. Any algorithm or model trying to perform this task will have to interpolate and guess the missing pixels in the pictures. Classical algorithms usually result in blurred or pixelated interpolations, especially visible around sharp edges. The reason it could be considered a good idea to use neural networks to upscale pictures is because they can infer context when upsampling different parts of an image. In this report, a special deep learning structure called U-Net is trained on reconstructing high-resolution images from the Div2k dataset. Multiple loss functions are tested and a combination of a GAN-based loss function, simple pixel loss and also a Sobel-based edge loss was used to get the best results. The proposed model scored a PSNR score of 33.11dB compared to Lanczos 30.23dB, one of the best classical algorithms, on the validation dataset.

This study aims to examine how simulation models can be performance optimized in Python. Optimized in the sense of executing faster and enabling upscaling with more data. To meet this aim, two models simulating the Greenland ice sheet are studied. The simulation of ice sheets is an important part of glaciology and climate change research. By following an iterative spiral model of software development and evolution with focus on the bottlenecks, it is possible to optimize the most time-consuming code sections. Several iterations of implementing tools and techniques suitable for Python code are performed, such as implementing libraries, changing data structures, and improving code hygiene. Once the models are optimized, the upscaling with a new dataset, called CARRA, created from observations and modelled outcomes combined, is studied. The results indicate that the most effective approach of performance optimizing is to implement the Numba library to compile critical code sections to machine code and to parallelize the simulations using Joblib. Depending on the data used and the size and granularity of the simulations, simulations between 1.5 and 3.2 times the speed are gained. When simulating CARRA data, the optimized code still results in faster simulations. However, the outcome demonstrates that differences exist between the ice sheets simulated by the dataset initially used and CARRA data. Even though the CARRA dataset yields a different glaciological result, the overall changes in the ice sheet are similar to the changes shown in the initial dataset simulations. The CARRA dataset could possibly be used for getting an overview of what is happening to the ice sheet, but not for making detailed analyses, where exact numbers are needed.

Les aquifères fissurés de type karst contiennent d'importantes ressources en eau. Ces aquifères sont complexes et hétérogènes sur une gamme d'échelles importantes. Leur gestion nécessite l'utilisation d'outils et de méthodologies adaptés. Dans le cadre de cette étude, différents outils et méthodologies numériques d'étude ont été développés pour la modélisation des aquifères karstiques, et plus généralement, des milieux poreux très fissurés 2D et 3D - en mettant l'accent sur la morphologie et sur le comportement hydrodynamique du milieu à travers la notion de changement d'échelle ("second changement d'échelle", reposant sur un modèle d'écoulement local de type Darcy et/ou Poiseuille avec quelques généralisations). Plusieurs axes sont explorés concernant la morphologie du milieu poreux fissuré (milieux aléatoires, milieux booléens avec réseaux statistiques de fissures, mais aussi, modèles morphogénétiques). L'étude du changement d'échelle hydrodynamique tourne autour du concept de macro perméabilité. Dans un premier temps, l'étude porte sur un modèle de perte de charge linéaire darcien. Les perméabilités effectives sont calculées numériquement en termes des fractions volumiques de fissures et du contraste de perméabilité matrice/fissures. Elles sont analysées et comparées à des modèles théoriques (analytiques). Une étude particulière des effets de quasi-percolation pour les grands contrastes aboutit à la définition de trois fractions critiques liées à des seuils de percolation. Pour tenir compte des effets inertiels dans les fissures, l'étude est étendue au cas d'une loi locale comprenant un terme quadratique en vitesse (Darcy/Ward-Forchheimer). Une perméabilité macroscopique équivalente non linéaire est définie et analysée à l'aide d'un modèle inertiel généralisé (linéaire/puissance). Enfin, l'anisotropie hydraulique à grande échelle du milieu fissuré est étudiée, en termes de perméabilités directionnelles, à l'aide d'une méthode numérique d'immersion. / Karstic aquifers contain large subsurface water resources. These aquifers are complex and heterogeneous on a large range of scales. Their management requires appropriate numerical tools and approaches. Various tools and numerical methodologies have been developed to characterize andmodel the geometry and hydraulic properties of karstic aquifers, more generally, of highly fissured 2D and 3D porous media. In this study, we emphasize morphological characterization, and we analyze hydrodynamic behavior through the concept of upscaling ("second upscaling"). Concerning the morphology of fissured porous media, several axes are explored : random media, composite random Boolean media with statistical properties, and morphogenetic models. Hydrodynamic upscaling is developed using the macro-permeability concept. This upscaling method is based on either Darcy's linear law, or on a linear/quadratic combination of Darcy's and Ward-Forchheimer's quadratic law (inertial effects). First, the study focuses on Darcy's linear head loss law, and Darcian effective permeabilities are calculated numerically in terms of volume fractions of fissures and "fissure/matrix" permeability contrasts. The results are analysed and compared with analytical results and bounds. A special study of percolation and quasi-percolation effects, for high contrasts, leads to defined three critical fractions. These critical fractions are "connected" to percolation thresholds. Secondly, in order to consider inertial effect in fissures, the study is extended to a local law with a quadratic velocity term (Darcy/Ward-Forchheimer). Then, an equivalent nonlinear macroscopic permeability is defined and analysed using a generalized inertial model (linear/power). Finally, the large scale hydraulic anisotropy of fissured medium is studied, in terms of directional permeabilities, using an "immersion" numerical method.

[pt] Campos de petróleo com gás não associado do tipo gás condensado possuem destaque pelo maior valor econômico agregado associado a seu recurso energético: a expressiva quantidade de condensado produzida, além do próprio gás. Porém, tais reservatórios possuem um comportamento termodinâmico particular, induzindo mudanças de composição e, consequentemente, fase ao longo do processo de produção por depleção. Nas condições de reservatório, por exemplo, pode ocorrer o fenômeno chamado de condensate blockage, em que bancos de condensado se formam, geralmente em regiões próximas aos poços, dificultando assim o escoamento e afetando a produção de gás. A fim de definirmos a melhor estratégia de gerenciamento de um projeto a ser implementado ao longo da explotação desse tipo de reservatório, uma ferramenta importante utilizada pelos engenheiros é a simulação numérica. Especialmente relacionadas à representação do fenômeno físico-químico citado, nas simulações se utilizam as curvas de permeabilidade relativa. Na realidade, porém, existe uma certa limitação de representatividade do fenômeno nos ensaios laboratoriais praticados pela indústria e os melhores insumos poderiam ser fornecidos por simulações em rede de poros, com modelos que representem a sua alteração com função das mudanças na tensão interfacial e na velocidade de escoamento ao longo do reservatório. A reprodução de uma simulação de escoamento em rede de poros para a escala mais próxima possível em uma simulação de simulador comercial de diferenças finitas é validada. Da simulação em rede de poros até a escala de campo praticada nas simulações de reservatórios, uma metodologia de scale-up é proposta, utilizando um processo de otimização, procurando ser fiel à curva de permeabilidade relativa original, em escala de microporo, obtida simulando fenomenologicamente o processo de condensação no reservatório, através de um modelo que reproduza sua dependência com a velocidade desenvolvida pelas fases em meio poroso. A comparação de produtividades na escala de campo e na evolução da saturação de condensado em regiões próximas aos poços foi apresentada para as três curvas de permeabilidade relativa utilizadas. Os resultados mostram que a metodologia proposta consegue ser mais fiel à influência da condensação no reservatório sobre a produtividade dos poços quando comparada ao insumo de curva de permeabilidade relativa de ensaio laboratorial que apresenta o condensado mais móvel. / [en] Oil fields with non-associated gas like gas condensate type stand out due to the higher added economic value associated with their energy resource: the significant amount of condensate produced, in addition to the gas itself. However, such reservoirs have a particular thermodynamic behavior, inducing changes in composition and, consequently, phase throughout the depletion production process. Under reservoir conditions, for example, the phenomenon called condensate blockage may occur, in which bridges of condensate are formed, usually in regions close to the wells, thus hindering flow and affecting gas production. In order to define the best management strategy for a project to be implemented throughout the exploitation of this type of reservoir, an important tool used by engineers is numerical simulation. The relative permeability curves are used in the simulations, especially related to the representation of the mentioned physical phenomenon. In reality, however, there is a specific limitation of representativeness of the phenomenon in the laboratory tests carried out by the industry, and the best inputs could be provided by simulations in a pore network, with models that represent its alteration as a function of changes in interfacial tension and flow velocity along the reservoir. The reproduction of a pore network flow simulation to the closest possible scale in a commercial finite difference simulation is validated. From the pore network simulation to the field scale practiced in reservoir simulations, a scale-up methodology is proposed, using an optimization process, seeking to be faithful to the original relative permeability curve, on a microporous scale, obtained by simulating phenomenologically the condensation process in the reservoir, using a model that reproduces its dependence on the velocity flow developed by the phases in a porous medium. The three relative permeability curves used were presented by comparing productivities at the field scale and the evolution of condensate saturation in regions close to the wells. The results show that the proposed methodology proves to be more faithful to the influence of condensation in the reservoir on the productivity of the wells when compared to the relative permeability curve input from the laboratory test, which presents the condensate with more mobility.

L’étude des écoulements souterrains et l’ingénierie réservoir partagent le même intérêt pour la simulation d’écoulement multiphasique dans des sols aux propriétés intrinsèquement hétérogènes. Elles rencontrent également les mêmes défis pour construire un modèle à l’échelle réservoir en partant de données micrométriques tout en contrôlant la perte d’informations. Ce procédé d’upscaling est utile pour rendre les simulations faisables et répétables dans un cadre stochastique. Deux processus de mise à l’échelle sont définis: l’un depuis l’échelle micrométrique jusqu’à l’échelle de Darcy, et, un autre depuis l’échelle de Darcy vers l’échelle du réservoir. Dans cette thèse, un nouvel algorithme traitant du second upscaling Finite Volume Mixed Hybrid Multiscale Method (FV-MHMM) est étudié. L’extension au diphasique est faite au moyen d’un couplage séquentiel faible entre saturation et pression grâce à une méthode de type IMPES. / The groundwater specialists and the reservoir engineers share the same interest in simulating multiphase flow in soil with heterogeneous intrinsic properties. They also both face the challenge of going from a well-modeled micrometer scale to the reservoir scale with a controlled loss of information. This upscaling process is indeed worthy to make simulation over an entire reservoir manageable and stochastically repeatable. Two upscaling steps can be defined: one from the micrometer scale to the Darcy scale, and another from the Darcy scale to the reservoir scale. In this thesis, a new second upscaling multiscale algorithm Finite Volume Mixed Hybrid Multiscale Methods (Fv-MHMM) is investigated. Extension to a two-phase flow system is done by weakly and sequentially coupling saturation and pressure via IMPES-like method.