Pore-scale network modeling has become an effective method for accurate prediction and upscaling of macroscopic properties, such as permeability. Networks are either mapped directly from real media or stochastic methods are used that simulate their heterogeneous pore structure. Flow is then modeled by enforcing conservation of mass in each pore and approximations to the momentum equations are solved in the connecting throats. In many cases network modeling compares favorably to experimental measurements of permeability. However, computational and imaging restrictions generally limit the network size to the order of 1 mm3 (few thousand pores). For extremely heterogeneous media these models are not large enough in capturing the petrophysical properties of the entire heterogeneous media and inaccurate results can be obtained when upscaling to the continuum scale. Moreover, the boundary conditions imposed are artificial; a pressure gradient is imposed in one dimension so the influence of flow behavior in the surrounding media is not included. In this work we upscale permeability in large, heterogeneous media using physically-representative pore-scale network models (domain ~106 pores). High-performance computing is used to obtain accurate results in these models, but a more efficient, novel domain decomposition method is introduced for upscaling the permeability of pore-scale models. The medium is decomposed into hundreds of smaller networks (sub-domains) and then coupled with the surrounding models to determine accurate boundary conditions. Finite element mortars are used as a mathematical tool to ensure interfacial pressures and fluxes are matched at the interfaces of the networks boundaries. The results compare favorably to the more computationally intensive (and impractical) approach of upscaling the media as a single model. Moreover, the results are much more accurate than traditional hierarchal upscaling methods. This upscaling technique has important implications for using pore-scale models directly in reservoir simulators in a multiscale setting. The upscaling techniques introduced here on single phase flow can also be easily extended to other flow phenomena, such as multiphase and non-Newtonian behavior. / text

Transport phenomena in heterogeneous media play a crucial role in numerous engineering applications such as hydrocarbon recovery from shales and material processing. Understanding and predicting these phenomena is critical for the success of these applications. In this dissertation, nanoscale transport phenomena in porous media are studied through physics-based simulations, and the effective solution of forward and inverse transport phenomena problems in heterogeneous media is tackled using data-driven, deep learning approaches. For nanoscale transport in porous media, the storage and recovery of gas from ultra-tight shale formations are investigated at the single-pore scale using molecular dynamics simulations. In the single-component gas recovery, a super-diffusive scaling law was found for the gas production due to the strong gas adsorption-desorption effects. For binary gas (methane/ethane) mixtures, surface adsorption contributes greatly to the storage of both gas in nanopores, with ethane enriched compared to methane. Ethane is produced from nanopores as effectively as the lighter methane despite its slower self-diffusion than the methane, and this phenomenon is traced to the strong couplings between the transport of the two species in the nanopore. The dying of solvent-loaded nanoporous filtration cakes by a purge gas flowing through them is next studied. The novelty and challenge of this problem lie in the fact that the drainage and evaporation can occur simultaneously. Using pore-network modeling, three distinct drying stages are identified. While drainage contributes less and less as drying proceeds through the first two stages, it can still contribute considerably to the net drying rate because of the strong coupling between the drainage and evaporation processes in the filtration cake. For the solution of transport phenomena problems using deep learning, first, convolutional neural networks with various architectures are trained to predict the effective diffusivity of two-dimensional (2D) porous media with complex and realistic structures from their images. Next, the inverse problem of reconstructing the structure of 2D heterogeneous composites featuring high-conductivity, circular fillers from the composites' temperature field is studied. This problem is challenging because of the high dimensionality of the temperature and conductivity fields. A deep-learning model based on convolutional neural networks with a U-shape architecture and the encoding-decoding processes is developed. The trained model can predict the distribution of fillers with good accuracy even when coarse-grained temperature data (less than 1% of the full data) are used as an input. Incorporating the temperature measurements in regions where the deep learning model has low prediction confidence can improve the model's prediction accuracy. / Doctor of Philosophy / Multiphysics transport phenomena inside structures with non-uniform pores or properties are common in engineering applications, e.g., gas recovery from shale reservoirs and drying of porous materials. Research on these transport phenomena can help improve related applications. In this dissertation, multiphysics transport in several types of structures is studied using physics-based simulations and data-driven deep learning models. In physics-based simulations, the multicomponent and multiphase transport phenomena in porous media are solved at the pore scale. The recovery of methane and methane-ethane mixtures from nanopores is studied using simulations to track motions and interactions of methane and ethane molecules inside the nanopores. The strong gas-pore wall interactions lead to significant adsorption of gas near the pore wall and contribute greatly to the gas storage in these pores. Because of strong gas adsorption and couplings between the transport of different gas species, several interesting and practically important observations have been found during the gas recovery process. For example, lighter methane and heavier ethane are recovered at similar rates. Pore-scale modeling are applied to study the drying of nanoporous filtration cakes, during which drainage and evaporation can occur concurrently. The drying is found to proceed in three distinct stages and the drainage-evaporation coupling greatly affects the drying rate. In deep learning modeling, convolutional neural networks are trained to predict the diffusivity of two-dimensional porous media by taking the image of their structures as input. The model can predict the diffusivity of the porous media accurately with computational cost orders of magnitude lower than physics-based simulations. A deep learning model is also developed to reconstruct the structure of fillers inside a two-dimensional matrix from its temperature field. The trained model can predict the structure of fillers accurately using full-scale and coarse-grained temperature input data. The predictions of the deep learning model can be improved by adding additional true temperature data in regions where the model has low prediction confidence.

L'activité chimique des catalyseurs a longuement été le coeur des travaux R&D, conduisant à une influence accrue des limitations diffusionnelles internes. Il est donc important de quantifier et modéliser ces limitations dans le but d'optimiser la conception et les performances des catalyseurs.Dans le cadre de notre projet, en s'appuyant sur une approche de Monte Carlo, des réseaux aléatoires en 2D ou 3D, constitués par des pores cylindriques interconnectés, sont générés de façon à reproduire la porosité, la surface spécifique et le volume poreux des supports d'alumine-gamma. Cet outil est capable de générer des réseaux jusqu'à 18000×18000 noeuds en 2D et 600×600×600 en 3D et contenant 2 milliards de pores. Seulement 4s sont nécessaires à la génération de réseaux 2D carré en 200x200.Un modèle 1D du transport de matière est utilisé à l'échelle du pore en supposant une diffusion fickienne. La diffusion peut être simulée dans des réseaux de taille jusqu'à 200×200. La confrontation des tortuosités simulées aux données de la littérature montre un bon accord. Cependant, la comparaison avec les valeurs expérimentales issues d'études par chromatographie inverse, montre des valeurs expérimentales plus élevées, probablement dû à la présence de deux niveaux de porosité.L'algorithme a par conséquent été modifié afin de générer des réseaux à deux niveaux de porosité et ainsi, reproduire les propriétés texturales et de transfert de matière d'une alumine. Pour un réseau 2D périodique en 100×100, concernant les propriétés texturales, des erreurs relatives inférieures à 10% ont été obtenues. De plus, des tortuosités comparables ont été estimés, 2.34 pour 2.40 expérimentalement / The chemical activity of catalysts has long been the core of R&D studies, leading to an increased influence of internal diffusion limitations. It is therefore important to model and quantify these mass transfer limitations in order to optimize catalyst design and increase performance.In the framework of our project, 2D or 3D pore networks, constituted by interconnected cylindrical pores, are randomly generated by a Monte Carlo approach to reproduce the porosity, specific surface area and pore volume of gamma-alumina supports. A highly efficient tool, capable of generating 2D networks of 18000×18000 and 600×600×600 nodes in 3D, containing up to 2 billion pores. Only 4s are required to generate 2D networks of size 200x200.Mass transfer is simulated by the 1D Fick’s diffusion model within each pore of the network. 200×200 networks, containing up to 80,000 pores, can be simulated. The confrontation of the calculated tortuosities as a function of porosity, to theoretical correlations shows a good agreement. However, when comparing with experimental values from fixed-bed tracer experiments obtained for different gamma-alumina pellets, actual aluminas exhibit higher tortuosities, probably due to the organisation of the porous structure in two levels.Hence, by modifying the developed model to generate two-level networks, we have been able to reproduce both textural and diffusion properties of one alumina. Taking a 2D periodic network of size 100×100 and concerning the textural properties, relative errors less than 10% were obtained. In addition, a good agreement was found for the tortuosity values, 2.34 against the experimental value of 2.40

Cette thèse est consacrée à l'étude des propriétés des transports diphasiques au sein des couches de diffusions (Gas Diffusion Layer = GDL) des piles à combustible PEMFC (Proton Exchange Membrane Fuel Cells). La GDL est faite d'une structure fibreuse (dont l'épaisseur est de quelques centaines de micromètres) traitée généralement avec une matière hydrophobe. Des images numériques de la GDL réelle obtenues par tomographie X sont d'abord analysées afin d'étudier des propriétés telles que la porosité, la perméabilité, ou le tenseur de diffusion. L'écrasement de la GDL est ensuite simulé en utilisant un algorithme comprimant les fibres dans un plan transversal. Les transports diphasiques (invasion quasi statique d'eau liquide) sont modélisés dans des réseaux de pores, milieux représentatifs de l'espace poreux de la GDL, en relation avec le problème de la gestion de l'eau dans les piles PEMFC. Deux algorithmes d'invasion, dénommés algorithmes séquentiel et cinétique, sont développés et comparés pour analyser les distributions de phases au sein des GDL. Un point clé est que l'eau rentre dans la couche poreuse par divers points d'injection indépendants, conduisant à la possibilité de multiples points de percée. Des expériences sur un système microfluidique sont conduites pour valider les algorithmes utilisés. Une étude statistique est menée pour caractériser le nombre de points de percée, les profils de saturation, l'accès au gaz, le transport diffusif, de même que l'influence du piégeage et de la mouillabilité mixte. / This thesis is devoted to the study of transport properties and two-phase flow in the Gas Diffusion Layer (GDL) of Proton Exchange Membrane Fuel Cells (PEMFC). A GDL is a thin fibrous structure (a few hundreds μm thick) treated generally with a hydrophobic agent. Numerical images obtained from X-ray computed tomography X are first exploited to study properties such as the porosity, permeability and diffusion tensors of a real GDL microstructure. The effect of GDL compression is also investigated using an algorithm mimicking the compression in GDL through plane direction. Then two phase flow (quasi-static water invasion) is studied in relation with the water management problem in PEMFC, using a structured pore network representation of the pore space. Two invasion algorithms, referred to as the sequential and the kinetic algorithm respectively, are developed and compared to study the fluid distributions within the GDL. A key point is that water enters the porous layer through multiple independent inlet injection points, leading to the possibility of many breakthrough points. Experiments are conducted on a microfluidic device to validate the algorithms. A numerical statistical study is performed to characterize the breakthrough point statistics, saturation profiles, gas access, diffusion transport as well as the influence of trapping and mixed wettability.

[pt] A formação e o acúmulo de condensado em reservatórios de gás retrógrado, especialmente na vizinhança de poços de produção, obstruem parcialmente o fluxo de gás e afetam negativamente a composição dos fluidos produzidos. Entretanto, a previsão de bloqueio por condensado é comumente imprecisa, visto que experimentos raramente reproduzem as condições extremas e composições complexas dos fluidos dos reservatórios, enquanto a maioria dos modelos em escala de poros simplificam demasiadamente os fenômenos físicos associados à transição de fases entre gás e condensado. Para corrigir essa lacuna, um modelo de rede de poros isotérmico composicional e totalmente implícito é apresentado. As redes de poros propostas consistem em estruturas tridimensionais de capilares constritos circulares. Modos de condensação e padrões de escoamento são atrubuídos aos capilares de acordo com a molhabilidade do meio, as saturações locais e a influência de forças viscosas e capilares. Nos nós da rede, pressão e conteúdo molar são determinados através da solução acoplada de equações de balanço molar e consistênc ia de volumes. Concomitantemente, um cálculo de flash à pressão e à temperatura constantes, baseado na equação de estado de Peng e Robinson, é realizado em cada nó, atualizando as saturações e composições das fases. Para a validação do modelo proposto, análises de escoamento foram executadas baseadas em experimentos de escoamento em testemunho reportados na literatura, usando composição dos fluidos e condições de escoamento correspondentes, e geometria do meio poroso aproximada. Curvas de permeabilidade relativa medidas nos experimentos e previstas pelo modelo mostraram boa concordância quantitativa, para dois valores de tensão interfacial e três valores de velocidade de escoamento de gás. Após a validação, o modelo foi usado para avaliar alteração de molhabilidade e injeção de gás como possíveis métodos de recuperação avançada para reservatórios de gás retrógrado. Os resultados exibiram tendências similares àquelas observadas em experimentos de escoamento em testemunhos, e condições ótimas para melhoramento do escoamento foram identificadas. / [en] Liquid dropout and accumulation in gas-condensate reservoirs, especially in the near wellbore region, hinder gas flow and affect negatively the produced fluid composition. Yet, condensate banking forecasting is commonly inaccurate, as experiments seldom reproduce reservoir extreme conditions and complex fluid composition, while most pore-scale models oversimplify the physical phenomena associated with phase transitions between gas and condensate. To address this gap, a fully implicit isothermal compositional pore-network model for gas and condensate flow is presented. The proposed pore-networks consist of 3D structures of constricted circular capillaries. Condensation modes and flow patterns are attributed to the capillaries according to the medium s wettability, local saturations and influence of viscous and capillary forces. At the network nodes, pressure and molar contents are determined via the coupled solution of molar balance and volume consistency equations. Concomitantly, a PT-flash based on the Peng-Robinson equation of state is performed for each node, updating the local phases saturations and compositions. For the proposed model validation, flow analyses were carried out based on coreflooding experiments reported in the literature, with matching fluid composition and flow conditions, and approximated pore-space geometry. Predicted and measured relative permeability curves showed good quantitative agreement, for two values of interfacial tension and three values of gas flow velocity. Following the validation, the model was used to evaluate wettability alteration and gas injection as prospect enhanced recovery methods for gas-condensate reservoirs. Results exhibited similar trends observed in coreflooding experiments and conditions for optimal flow enhancement were identified.

[pt] A produtividade de poços produtores de gás, que operam com pressões de fundo inferiores à pressão de orvalho, é afetada pelo aparecimento da saturação de líquido em seus entornos. Para entender esse fenômeno, conhecido como bloqueio por condensado, os simuladores em escala de poros são ferramentas úteis na investigação dos parâmetros que influenciam na quantidade e na distribuição da saturação de condensado, assim como seus efeitos na redução do fluxo de gás. Esse trabalho apresenta um modelo de rede de capilares composicional e isotérmico para o estudo do escoamento de gás retrógrado em meios porosos. Forças capilares e gravitacionais não foram consideradas. O escoamento monofásico é comutado para bifásico de padrão anular quando a pressão e a composição do fluido atingem um critério de estabilidade. O método de Newton é aplicado para resolver as equações de fluxo e consistência dos volumes e calcular o transporte de cada um dos componentes ao longo da rede. As propriedades do fluido e o comportamento do escoamento foram testadas contra os resultados de um simulador termodinâmico comercial e soluções analíticas, respectivamente. Após validação, o simulador foi utilizado para obter curvas de permeabilidade relativa gás-líquido através da despressurização de uma rede 2D e alguns resultados são discutidos. / [en] Gas well deliverability in retrograde gas reservoirs is affected by the appearance of liquid saturation around the wellbore when the bottom-hole pressure is below the dew point. Pore-scale simulators are used to model this phenomenon, known as condensate blockage, and to investigate parameters that ifluence the amount and the distribution of condensate saturation, as well as how it chokes the gas flow. Here, a fully-implicit isothermal compositional pore-scale network model is presented for retrograde gas flow in porous media. Capillary and gravitational forces are neglected. The model shifts from single-phase flow to annular flow regime when the pressure and the fluid composition reach a stability criteria. Newton s method is applied on flow and volume consistency equations to calculate the transport of each component through the network. Fluid properties and flow behavior were tested against a commercial thermodynamic simulator and analytical solutions respectively. After validation, the simulator was used to predict gas-liquid relative permeability from a depletion process in a 2D network and some results are discussed.

Dans ce travail, nous nous intéressons à la dynamique de croissance d'une poche de vapeur par vaporisation en milieu poreux, en relation avec l'analyse des transferts couplés de masse et de chaleur dans les mèches poreuses des boucles fluides diphasiques à pompage capillaire. Nous proposons un modèle pour les régimes transitoires, régimes encore très mal compris en dépit de leur grande importance pratique (phase de démarrage, variations de puissance, etc.). Une approche de type "réseau de pores" est adoptée et permet de prédire la distribution des phases à l'échelle de l'espace des pores. Dans une étape préliminaire, une étude spécifique de drainage (déplacement d'un fluide mouillant par un fluide non mouillant) par pressurisation du fluide envahisseur est abordée. Cette étape, nécessaire au développement et au test d'un algorithme de croissance de poche de gaz, permet de valider le modèle hydrodynamique quantitativement par une étude expérimentale dédiée. Il est mis en évidence le rôle des films liquides et de la compressibilité du gaz. Le modèle est ensuite complété par l'ajout des transferts thermiques et du changement de phase. Ici encore, une étude expérimentale dédiée est proposée, afin de valider l'outil numérique mis en place. Enfin, un ultime ajout au modèle permet de prendre en compte les phénomènes particuliers liés à l'imbibition (déplacement d'un fluide non mouillant par un fluide mouillant). Des résultats statistiques concernant la réponse dynamique d'une poche de vapeur à l'application d'une densité de puissance sont présentés, ainsi que certaines situations oscillantes dans la mèche poreuse. Nous finissons par discuter de l'influence du re-mouillage de la mèche poreuse, phénomène qui entraîne une hystérésis significative. / We study the dynamic of a vapour pocket growing by vaporisation in a porous medium, in relation with the analysis of coupled heat and mass transfers in the porous wick of loop heat pipes (LHP). We propose a model for transient modes, which are still poorly understood in spite of their importance (start-ups, power transitions, etc.). This work is based on a pore network approach enabling us to predict the phase distribution at the pore space scale. In a preliminary step, a study of drainage (displacement of a wetting fluid by a non wetting one) by pressurisation of the invading fluid is performed. This step is necessary for the development and the test of the vapour pocket growing algorithm. A quantitative validation of the hydro-dynamical model is obtained thanks to a dedicated experimental study. The influence of liquid films as well as gas compressibility is investigated. Our model is then improved to deal with heat transfer and phase change. Again, a dedicated experimental study is performed in order to validate the numerical tool. The model is finally improved a last time to deal with the effects due to imbibition mechanisms (displacement of a non wetting fluid by a wetting one). Statistical results concerning the dynamic response of a vapour pocket to the application of a power density are presented, andsome specific oscillating situations in the wick are identified. We finish discussing the influence of the re- etting of the porous wick, a phenomenon which induces a significant hysteresis effect.

[pt] A microtomografia computadorizada de uma amostra de rocha possibilita uma caracterização do meio poroso e pode ser utilizada para estimar propriedades da rocha em macroescala, isto é, em escala de reservatório. Métodos baseados em mapas de distâncias e em algoritmos de erosão são as principais abordagens utilizadas para extração de uma rede de poros e gargantas a partir de imagens microtomográficas de rocha. Este trabalho propõe um método híbrido para a construção da rede, de modo que, durante o processo de modelagem na escala de poros, obtemos um esqueleto do espaço poroso por meio de um algoritmo de erosão e utilizamos um mapa de distâncias para construir uma rede de poros e gargantas. A determinação dos poros e gargantas a partir do esqueleto adota uma abordagem não-determinística possibilitando a geração de múltiplas redes com configurações distintas a partir de um mesmo esqueleto. Avaliamos a variabilidade dos cenários gerados e comparamos as estimativas para as propriedades petrofísicas com as obtidas pelo método de Bolas Máximas por meio dos resultados de uma simulação de fluxo monofásica na rede. / [en] Computerized microtomography of a rock sample enables a characterization of the porous medium and can be used to estimate rock properties at the macro-scale, i.e., reservoir-scale. Methods based on distance maps and thinning algorithms are the main approaches used for extracting a pore and throats network from microtomographic rock images. This paper proposes a hybrid method for constructing the network. So that during the pore-scale modeling process, we obtain a skeleton of the pore space by using a thinning algorithm and a distance map to build a network of pores and throats. The determination of pores and throats from the skeleton assumes a non-deterministic approach enabling the generation of multiple networks with distinct configurations from the same skeleton. We evaluate the variability of the generated scenarios and compare the estimates for the petrophysical properties with those obtained by the Maximum Ball Method through the results of a single-phase flow simulation on the network.