Optimizing proppant pack conductivity and proppant-transport and -deposition patterns in a hydraulic fracture is of critical importance to sustain effective and economical production of petroleum hydrocarbons. In this research, a numerical modeling approach, combining the discrete element method (DEM) with the lattice Boltzmann (LB) simulation, was developed to provide fundamental insights into the factors regulating the interactions between reservoir depletion, proppant-particle compaction and movement, single-/multiphase flows and non-Darcy flows in a hydraulic fracture, and fracture conductivity evolution from a partial-monolayer proppant concentration to a multilayer proppant concentration. The potential effects of mixed proppants of different sizes and types on the fracture conductivity were also investigated. The simulation results demonstrate that a proppant pack with a smaller diameter coefficient of variation (COV), defined as the ratio of standard deviation of diameter to mean diameter, provides better support to the fracture; the relative permeability of oil was more sensitive to changes in geometry and stress; when effective stress increased continuously, oil relative permeability increased nonmonotonically; the combination of high diameter COV and high effective stress leads to a larger pressure drop and consequently a stronger non-Darcy flow effect. The study of proppant mixtures shows that mixing of similar proppant sizes (mesh-size-20/40) has less influence on the overall fracture conductivity than mixing a very fine mesh size (mesh-size-100); selection of proppant type is more important than proppant size selection when a proppant mixture is used. Increasing larger-size proppant composition in the proppant mixture helps maintain fracture conductivity when the mixture contains lower-strength proppants. These findings have important implications to the optimization of proppant placement, completion design, and well production. In the hydraulic-mechanical rock-proppant system, a fundamental understanding of multiphase flow in the formation rock is critical in achieving sustainable long-term productivity within a reservoir. Specifically, the interactions between the critical dimensionless numbers associated with multiphase flow, including contact angle, viscosity ratio, and capillary number (Ca), were investigated using X-ray micro computed tomography (micro-CT) scanning and LB modeling. The primary novel finding of this study is that the viscosity ratio affects the rate of change of the relative permeability curves for both phases when the contact angle changes continuously. Simulation results also indicate that the change in non-wetting fluid relative permeability was larger when the flow direction was switched from vertical to horizontal, which indicated that there was stronger anisotropy in larger pore networks that were primarily occupied by the non-wetting fluid. This study advances the fundamental understanding of the multiphysics processes associated with multiphase flow in geologic materials and provides insight into upscaling methodologies that account for the influence of pore-scale processes in core- and larger-scale modeling frameworks. During reservoir depletion processes, reservoir formation damage is an issue that will affect the reservoir productivity and various phases in fluid recovery. Invasion of formation fine particles into the proppant pack can affect the proppant pack permeability, leading to potential conductivity loss. The combined DEM-LB numerical framework was used to evaluate the role of proppant particle size heterogeneity (variation in proppant particle diameter) and effective stress on the migration of detached fine particles in a proppant supported fracture. Simulation results demonstrate that a critical fine particle size exists: when a particle diameter is larger or smaller than this size, the deposition rate increases; the transport of smaller fines is dominated by Brownian motion, whereas the migration of larger fines is dominated by interception and gravitational settling; this study also indicates that proppant packs with a more heterogeneous particle-diameter distribution provide better fines control. The findings of this study shed lights on the relationship between changing pore geometries, fluid flow, and fine particle migration through a propped hydraulic fracture during the reservoir depletion process. / Doctor of Philosophy / Hydraulic fracturing stimulation design is required for unconventional hydrocarbon energy (e.g., shale oil and gas) extraction due to the low permeability and complex petrophysical properties of unconventional reservoirs. During hydrocarbon production, fractures close after pumping due to the reduced fluid pressure and increased effective stress in rock formations. In the oil and gas industry, proppant particles, which are granular materials, typically sand, treated sand, or man-made ceramic materials, are pumped along with fracturing fluids to prevent hydraulic fractures from closing during hydrocarbon extraction. In order to relate the geomechanical (effective stress), geometric (pore structure and connectivity), and transport (absolute permeability, relative permeability, and conductivity) properties of a proppant assembly sandwiched in a rock fracture, a geomechanics-fluid mechanics framework using both experiment and simulation methods, was developed to study the interaction and coupling between them. The outcome of this research will advance the fundamental understanding of the coupled, multiphysics processes with respect to hydraulic fracturing and benefit the optimization of proppant placement, completion design, and well production.

[pt] O escoamento de fluidos imiscíveis em tubos ocorre em diferentes processos industriais, como a extração de óleo em meios porosos, a cimentação de poços de petróleo e o revestimento de superfícies internas de tubos. Para uma boa compreensão e otimização destes processos, é extremamente relevante o estudo da influência da capilaridade, da inércia e da razão de viscosidades no padrão de escoamento. Além disso, os materiais envolvidos são frequentemente polímeros de moléculas flexéveis, portanto, o estudo dos efeitos dos parâmetros reológicos faz-se igualmente importante. Os diferentes padrões de escoamento são caracterizados pela fração de massa depositada na parede do tubo, pelo perfil da frente da interface e pela presen¸ca de recirculações. Analisa-se o problema através de uma abordagem experimental e outra numérica. A comparação dos resultados obtidos pelas duas abordagens mostra uma boa concordância para o caso com fluidos Newtonianos e qualitativamente boa para o caso não Newtoniano. / [en] There are many important processes in industry that use liquid displacement of imiscible fluids in tubes. Some practical applications include enhanced oil recovery, ce- mentation of drilling wells and coating of internal surfaces of the tubes. For a good understanding of these problems, it is extremely important to study the effect of cap-illarity,inertia and viscosity ratio in these flows. Furthermore, the materials used are frequently flexible polymer molecules. Hence, the study of rheological properties is very important as well. The focus of the thesis is to analyze the fractional mass deposited on the tube wall and the configuration of the interface. The analysis followed two approaches: theoretical and experimental study. The comparison of the two approaches shows a good agreement for Newtonian fluids and a qualitatively good agreement for Non-Newtonian.