The increasing concentration of CO_(2) has been linked to global warming and changes in climate. Geologic sequestration of CO_(2) in deep saline aquifers is a proposed greenhouse gas mitigation technology with potential to significantly reduce atmospheric emissions of CO_(2). Feasibility assessments of proposed sequestration sites require realistic and computationally efficient models to simulate the subsurface pressure response and monitor the injection process, and quantify the risks of leakage if there is any. This study investigates the possibility of obtaining closed form expressions for spatial distribution of CO_(2) injected in brine aquifers and gas reservoirs. Four new semi-analytical solutions for CO_(2) injection in brine aquifers and gas reservoirs are derived in this dissertation. Both infinite and closed domains are considered in the study. The first solution is an analysis of CO_(2) injection into an initially brine-filled infinite aquifer, exploiting self–similarity and matched asymptotic expansion. The second is an expanding to the first solution to account for CO_(2) injection into closed domains. The third and fourth solutions are analyzing the CO_(2) injection in infinite and closed gas reservoirs. The third and fourth solutions are derived using Laplace transform. The brine aquifer solutions accounted for both Darcyian and non-Darcyian flow, while, the gas reservoir solutions considered the gas compressibility variations with pressure changes. Existing analytical solutions assume injection under constant rate at the wellbore. This assumption is problematic because injection under constant rate is hard to maintain, especially for gases. The modeled injection processes in all aforementioned solutions are carried out under constant pressure injection at the wellbore (i.e. Dirichlet boundary condition). One major difficulty in developing an analytical or semi-analytical solution involving injection of CO_(2) under constant pressure is that the flux of CO_(2) at the wellbore is not known. The way to get around this obstacle is to solve for the pressure wave first as a function of flux, and then solve for the flux numerically, which is subsequently plugged back into the pressure formula to get a closed form solution of the pressure. While there is no simple equation for wellbore flux, our numerical solutions show that the evolution of flux is very close to a logarithmic decay with time. This is true for a large range of the reservoir and CO_(2) properties. The solution is not a formation specific, and thus is more general in nature than formation-specific empirical relationships. Additionally, the solution then can be used as the basis for designing and interpreting pressure tests to monitor the progress of CO_(2) injection process. Finally, the infinite domain solution is suitable to aquifers/reservoirs with large spatial extent and low permeability, while the closed domain solution is applicable to small aquifers/reservoirs with high permeability.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18938号 / 工博第3980号 / 新制||工||1613(附属図書館) / 31889 / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 松岡 俊文, 教授 後藤 仁志, 准教授 村田 澄彦 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

Flotation is a complex, multiphase process used to separate minerals. Four problems central to the fundamentals of the flotation process were studied. A multiphase grid turbulence experiment was conducted to verify particle collision models. The slip velocities of solid particles and bubbles were measured using Digital Particle Image Velocimetry (DPIV). The experimental results were compared with the predictions from empirical and theoretical collision models. Time-resolved DPIV was used to measure the turbulent velocity field in a Rushton turbine around the impeller region. The turbulence quantities were found by removing the periodic component from the blade passing, which is a dominant part of the measured velocities near the impeller. We provide evidence that larger, biased dissipation and turbulent kinetic energy values are estimated in the vicinity of the impeller due to the periodic component of the blade passage. The flow was found to be anisotropic close to the impeller. Vortex detection revealed that the tip vortices travel in a nearly radial direction from the impeller for small Reynolds numbers and with a wider distribution for higher Reynolds numbers. The rise of a buoyant bubble and its interaction with a free liquid surface was experimentally investigated using Time-Resolved Digital Particle Image Velocimetry as a function of bubble size, and surfactant concentration of the fluid medium. It is shown that the presence of a surfactant significantly affected the characteristics of the velocity field during the rise and interaction with the free surface. This difference is attributed to the adsorption coverage of the surfactant at the bubble-fluid interface. Wake profiles were compared. The presence of large vortices were observed and found to play a significant role. Finally, Numerical and experimental results of stable and unstable foams are presented by comparing liquid fractions and bubble sizes. There was good agreement between the experiments and numerical modeling in free drainage and forced drainage experiments. In addition, foam coarsening was measured and characterized experimentally. Each of the problems investigated have added to the understanding in the underlying physics of the flotation process and can lead to more accurate modeling. The ultimate goal of this work is to contribute to the design of more effective and efficient flotation machines. / Ph. D.

Simulação de fluidos tem sido um dos focos principais de pesquisa em computação gráfica nos últimos anos. O interesse por tal assunto é motivado pelas aplicações na indústria cinematográfica, jogos e sistemas voltados para simulação de fenômenos físicos realísticos em tempo real. Neste trabalho atacamos um problema ainda pouco explorado pela comunidade de computação gráfica, a simulação de fluidos em imagens digitais. Adotamos uma abordagem relacionando fluidos multifásicos, onde propriedades da imagem são incorporadas às equações de Navier-Stokes a fim de permitir que objetos contidos nas imagens \"escoem\" interagindo a forças que agem no sistema / In the last years, fluid simulation has been one of the main focus in Computer Graphics. Such a reason is related to applications to film industry, games and frameworks for realtime physical problem simulations. In this work we aim at accessing a problem which is not so much explored in Computer Graphics: fluid simulation in digital images. We adopt a approach related to multiphase fluids, where properties of the image are set to the Navier-Stokes equations in order to allow that objects into the images \"flow\"in accordance to the forces in the system

Simulação de fluidos tem sido um dos focos principais de pesquisa em computação gráfica nos últimos anos. O interesse por tal assunto é motivado pelas aplicações na indústria cinematográfica, jogos e sistemas voltados para simulação de fenômenos físicos realísticos em tempo real. Neste trabalho atacamos um problema ainda pouco explorado pela comunidade de computação gráfica, a simulação de fluidos em imagens digitais. Adotamos uma abordagem relacionando fluidos multifásicos, onde propriedades da imagem são incorporadas às equações de Navier-Stokes a fim de permitir que objetos contidos nas imagens \"escoem\" interagindo a forças que agem no sistema / In the last years, fluid simulation has been one of the main focus in Computer Graphics. Such a reason is related to applications to film industry, games and frameworks for realtime physical problem simulations. In this work we aim at accessing a problem which is not so much explored in Computer Graphics: fluid simulation in digital images. We adopt a approach related to multiphase fluids, where properties of the image are set to the Navier-Stokes equations in order to allow that objects into the images \"flow\"in accordance to the forces in the system

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Au cours de cette thèse, un modèle LBM MPMC avec échanges thermiques est développé. Des tests d'assimilation de données et des mesures par flot optique sont réalisés en vue d'une validation. Le cadre d'application de cette thèse est celui du mélange d'un fluide cryogénique avec l'eau. Dans une première partie, un travail bibliographique rappelant l'équation de Boltzmann, ses diverses hypothèses et simplifications, ainsi que l'aspect algorithmique de la LBM sont exposés. Une comparaison entre opérateur de collision SRT et MRT est réalisée, et une simulation de phénomènes turbulents à différents nombres de Reynolds est étudiée, notamment avec le benchmark de l'instabilité de Von Karman. Dans une seconde partie, le modèle MPMC de Shan & Cehn est rappelé puis étendu au cas où les échanges thermiques entre composants sont présents. Des validations quantitatives sont faites, notamment avec le benchmark du fluide de Couette à deux phases ou à deux composants, du test de cohérence vis-à-vis de la loi de Laplace, ou encore par rapport à un benchmark faisant intervenir la conduction thermique. Des tests qualitatifs de condensation en milieu multicomposants sont proposés pour valider l'aspect des échanges thermiques entre composants en présence d'une transition de phase. Dans la troisième partie de cette thèse, une méthode de validation par assimilation de données est introduite, avec le filtrage de Kalman d'ensemble. Un test d'estimation d'état d'un fluide di-phasique est réalisé, et la compatibilité du filtrage de Kalman d'ensemble par rapport au modèle LBMMPMC est évaluée. Pour la validation du comportement du modèle d'un point de vue de la présence de deux composants, un fluide de substitution (non-cryogénique) au GNL, le butane, a été choisi pour permettre des observations dans des conditions expérimentales accessibles. Puis, une plateforme expérimentale d'injection de butane liquide dans une colonne d'eau sous pression est présentée. Des images d'ombroscopie issues d'expériences de remontée de butane liquide dans de l'eau sont exposées et un algorithme de calcul de flot optique est appliqué à ces images. Une évaluation qualitative des champs de vitesses obtenus par application de cet algorithme est réalisée. / In this thesis, a LBM MPMC model with heat exchange is developed. Data assimilation tests and optical flow measurements are made in order to validate the model. The application context of this thesis is the mixture of a cryogenic fluid with water. In the first part, a bibliographical work reminding the Boltzmann equation and its various assumptions and simplifications, as well as the algorithmic aspect of the LBM are exposed. A comparison between SRT and MRT collision operator is performed, and a simulation of turbulent phenomena at different Reynolds numbers is studied, especially with the benchmark of the instability from Von Karman. In the second part, the MPMC model from Shan & Chen is reminded and extended to the case of the inter-component heat exchanges. Quantitative validations are made, especially with the benchmark of a two-phase or two-component Couette fluid. Consistency is tested against Laplace's law rule, or against a benchmark involving heat conduction. Qualitative testing of condensations in a multi-component medium are proposed to validate the heat exchange between components in the presence of a phase transition. In the third part of this thesis, a validation method for data assimilation is introduced, with the ensemble Kalman filter. A state estimation test of a bi-phase fluid is realized, and compatibility of the ensemble Kalman filtering to the LBM MPMC model is assessed. For validation of the behavior of the model for a two-component case, a substitution fluid (non-cryogenic) for LNG, butane, was selected to permit observations in experimental conditions which are accessible. Then, an experimental platform of injection of liquid butane in a pressurised water column is presented. Shadowgraph images from liquid butane experiments in water are exposed and an optical flow calculation algorithm is applied to these images. A qualitative assessment of the velocity field obtaines by application of this algorithm is performed.

Dans cette thèse, nous nous intéressons à la modélisation et l'analyse mathématique de certains problèmes liés aux écoulements en suspension.Le premier chapitre concerne la justification du modèle de type transport-Stokes pour la sédimentation de particules sphériques dans un fluide de Stokes où l'inertie des particules est négligée et leur rotation est prise en compte. Ce travail est une extension des résultats antérieurs pour un ensemble plus général de configurations de particules.Le deuxième chapitre concerne la sédimentation d'une distribution d'amas de paires de particules dans un fluide de Stokes. Le modèle dérivé est une équation de transport-Stokes décrivant l'évolution de la position et l'orientation des amas. Nous nous intéressons par la suite au cas où l'orientation des amas est initialement corrélée aux positions. Un résultat d'existence locale et d'unicité pour le modèle dérivé est présenté.Dans le troisième chapitre, nous nous intéressons à la dérivation d'un modèle de type fluide-cinétique pour l'évolution d'un aérosol dans les voies respiratoires. Ce modèle prend en compte la variation du rayon des particules et leur température due à l'échange d'humidité entre l'aérosol et l'air ambiant. Les équations décrivant le mouvement de l'aérosol est une équation de type Vlasov-Navier Stokes couplée avec des équations d'advection diffusion pour l'évolution de la température et la vapeur d'eau dans l'air ambiant.Le dernier chapitre traite de l'analyse mathématique de l'équation de transport-Stokes dérivée au premier chapitre. Nous présentons un résultat d'existence et d'unicité globale pour des densités initiales de type $L^1 cap L^infty$ ayant un moment d'ordre un fini. Nous nous intéressons ensuite à des densités initiales de type fonction caractéristique d'une gouttelette et montrons un résultat d'existence locale et d'unicité d'une paramétrisation régulière de la surface de la gouttelette. Enfin nous présentons des simulations numériques montrant l'aspect instable de la gouttelette. / This thesis is devoted to the modelling and mathematical analysis of some aspects of suspension flows.The first chapter concerns the justification of the transport-Stokes equation describing the sedimentation of spherical rigid particles in a Stokes flow where particles rotation is taken into account and inertia is neglected. This work is an extension of former results for a more general set of particles configurations.The second chapter is dedicated to the sedimentation of clusters of particle pairs in a Stokes flow. The derived model is a transport-Stokes equation describing the time evolution of the position and orientation of the cluster. We also investigate the case where the orientation of the cluster is initially correlated to its position. A local existence and uniqueness result for the limit model is provided.In the third chapter, we propose a coupled fluid-kinetic model taking into accountthe radius growth of aerosol particles due to humidity in the respiratorysystem. We aim to numerically investigate the impact of hygroscopic effects onthe particle behaviour. The air flow is described by the incompressibleNavier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term.The last chapter is dedicated to the analysis of the transport-Stokes equation derived in the first chapter. First we present a global existence and uniqueness result for $L^1cap L^infty$ initial densities with finite first moment. Secondly, we consider the case where the initial data is the characteristic function of a droplet. We present a local existence and uniqueness result for a regular parametrization of the droplet surface. Finally, we provide some numerical computations that show the regularity breakup of the droplet.