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Modeling the stimulated reservoir volume during hydraulic fracturing is important to geothermal and petroleum reservoir stimulation. The interaction between a hydraulic fracture and pre-existing natural fractures exerts significant control on stimulated volume and fracture network complexity. This thesis presents a boundary element and finite difference based method for modeling this interaction during hydraulic fracturing process. In addition, an improved boundary element model is developed to more accurately calculate the total stimulated reservoir volume. The improved boundary element model incorporates a patch to calculate the tangential stresses on fracture walls accurately, and includes a special crack tip element at the fracture end to capture the correct stress singularity the tips The fracture propagation model couples fluid flow to fracture deformation, and accounts for fracture propagation including the transition of a mechanically-closed natural fractures to a hydraulic fracture. The numerical model is used to analyze a number of stimulation scenarios and to study the resulting hydraulic fracture trajectory, fracture aperture, and pressures as a function of injection time. The injection pressure, fracture aperture profiles shows the complexity of the propagation process and its impact on stimulation design and proppant placement. The injection pressure is observed to decrease initially as hydraulic fracture propagates and then it either increases or decreases depending on the factors such as distance between hydraulic fracture and natural fracture, viscosity of the injected fluid, injection rate and also other factor that are discussed in detail in below sections. Also, the influence of flaws on natural fracture in its opening is modeled. Results shows flaws that are very small in length will not propagate but are influencing the opening of natural fracture. If the flaw is located near to one end tip the other end tip will likely propagate first and vice versa. This behavior is observed due to the stress shadowing effect of flaw on the natural fracture. In addition, sequential and simultaneous injection and propagation of multiple fractures is modeled. Results show that for sequential injection, the pressure needed to initiate the later fractures increases but the geometry of the fractures is less complicated than that obtained from simultaneous injection under the same fracture spacing and injection. It is also observed that when mechanical interaction is present, the fractures in sequential fracturing have a higher width reduction as the later fractures are formed

Ce travail de thèse concerne la modélisation numérique fine des processus locaux dans le transport sédimentaire, à l'échelle d'un à plusieurs centaines de grains. Une méthode aux éléments discrets (DEM) basée sur la méthode dite des sphères molles et prenant en compte les contacts entre les grains a été développée et couplée à une méthode de frontière immergée (IBM) qui calcule l'écoulement autour d'objets solides mobiles dans un fluide Newtonien incompressible. Dans ce couplage, une force de lubrification est incluse pour représenter les interactions entre le fluide et les particules proches d'un contact. Il est montré que la méthode numérique reproduit de manière satisfaisante le coefficient de restitution effective mesuré dans des expériences de rebonds normal et oblique d'un grain sur un plan, ainsi que de rebond entre deux grains dans un fluide visqueux. Deux modèles analytiques associés au phénomène de rebond sont proposés et montrent l'importance de la rugosité de surface du grain et du nombre de Stokes sur le phénomène. La méthode numérique est ensuite utilisée pour simuler deux configurations tridimensionnelles d'écoulements granulaires pilotés par la gravité en milieu fluide : l'avalanche de grains sur un plan incliné rugueux et l'effondrement d'une colonne de grains. Dans le premier cas, les résultats permettent de caractériser les différents régimes d'écoulement granulaires (visqueux, inertiel et sec) observés dans les expériences en fonction du rapport de masse volumique grain-fluide et du nombre de Stokes. En particulier, les simulations apportent des informations originales quant aux profils de vitesse de grains et du fluide ainsi qu'aux forces prédominantes dans chacun des régimes. Dans le second cas, les résultats sont en bon accord avec les expériences et le mécanisme dit de « pore pressure feedback », qui dépend de la compacité initiale de la colonne, est pour la première fois observé dans des simulations numériques directes. / This work deals with direct numerical simulations of sediment transport at the scale of O(103) grains. A soft-sphere discrete element method (DEM) taking into account grain contacts is developed and coupled to an immersed boundary method (IBM) which computes the flow around moving solid objects in an incompressible Newtonian fluid. A lubrication force is added for representing fluid-particles interaction near contact. The numerical method is shown to adequately reproduce the effective coefficient of restitution measured in experiments of the normal and oblique rebound of a grain on a plane and the rebound between two grains in a viscous fluid. Two analytical models are proposed and highlight the importance of the grain roughness and Stokes number on the rebound phenomenon. This numerical method is then used for simulating two three-dimensional configurations of gravity-driven dense granular flow in a fluid, namely the granular avalanche on a rough inclined plane and the collapse of a granular column. In the first case, results allow to characterize the granular flow regimes (viscous, inertial and dry) observed in experiments as a function of the grain-to-fluid density ratio and the Stokes number. In particular, the simulations provide insight on the grain and fluid velocity profiles and force balance in each regime. In the second case, results agree well with experiments and in particular the pore pressure feedback, which depends on the initial volume fraction of the column, is observed for the first time in direct numerical simulations.

Generalizamos o modelo de percolação por invasão de maneira que vários sítios possam ser simultaneamente invadidos. Propomos dois tipos de generalização: na primeira, o fluxo de fluido invasor e controlado através do perímetro do aglomerado, enquanto que na segunda modificação, o crescimento e governado pela relação de escala entre a massa e o raio de giração dos aglomerados. Estudamos cuidadosamente tanto o perfil de aceitação quanto as dimensões fractais (\'D IND.F\') dos aglomerados assim crescidos. No modelo baseado nas relações de escala, \'D IND.F\' pode ser tratado como um mero parâmetro real que pode assumir qualquer valor no intervalo (0, ?). Nos intervalos (0, \'91 SOB.48\') e (2, ?), o sistema e frustrado. Para \'D IND.F\' > 2, o modelo exibe um fenômeno interessante: em algumas etapas ocorrem explosões no crescimento da massa dos aglomerados (bursts). Na região [\'91 SOB.48\',2], os aglomerados obedecem exatamente e em qualquer escala a relação M ~ RgDF entre a massa m e o raio de giração \'RG\'. Acreditamos que estes fractais cuja estrutura completamente e estabilizada possam ser muito úteis no tratamento de problemas de diluição da mecânica estatística. / We generalize the standard site invasion percolation model to permit simultaneous invasion of several sites. We propose two kinds of generalizations: one in which the invasion flux is controlled by the perimeter size and another where the scaling properties command the growth process. The acceptance profile as well as the fractal dimension \'D IND.F\' are carefully studied. In the model based on scaling relation, \'D IND.F\' can be treated as a mere real parameter in the range (0, ?). In the intervals (0, \'91 SOB.48\') and (2, ?) the system is frustrated. For \'D IND.F\' > 2 the model exhibits also an interesting burst phenomenon that is explained in the text. In the region [\'91 SOB.48\',2], the clusters obey exactly and in any scale the relation M ~ RgDF between the mass M and gyration radius Rg. These stable random fractals may be very useful in the study of dilute systems.

A teoria da percolação tem se revelado muito útil no tratamento de inúmeros fenômenos da natureza. Devido a sua grande versatilidade, esta teoria é objeto de intensa pesquisa. Aqui, propomos novas formas de percolação e as estudamos através de simulações numéricas. Na primeira parte de nosso trabalho, investigamos a estrutura dos aglomerados gerados pelo modelo de percolação por invasão múltipla. Estimamos os valores das dimensões fractais do esqueleto, do esqueleto elástico, dos pontos de estrangulamento e dos menores caminhos, como função dos parâmetros do modelo. Por ter uma estrutura geométrica bastante estabilizada, o modelo otimizado pode vir a ser muito útil no tratamento de problemas com diluição da mecânica estatística. O modelo de percolação atenuada foi concebido para permitir que, durante o processo de invasão, os poros grandes possam também ser ocupados. Esta ocupação ocorre com uma probabilidade que diminui quando o tamanho do poro aumenta.Estimamos cuidadosamente os limiares de percolação e construímos os diagramas de fase correspondentes. Verificamos que os limiares de percolação de nosso modelo não satisfazem a conjectura de Galam e Mauger. Estudamos o efeito da inércia em fluidos escoando através de meios porosos incorporando uma caminhada de N passos ao modelo de percolação por invasão. A magnitude da inércia é proporcional ao parâmetro N, que representa o número de poros seqüencialmente invadidos após a ruptura do perímetro, em cada etapa do processo. Investigamos este modelo em duas e três dimensões. Verificamos que no caso bidimensional, as caminhadas de N passos são facilmente bloqueadas o que leva ao surgimento de um limite superior para o número de passos efetivamente realizados. Nossas estimativas das dimensões fractais dos aglomerados (como função do parâmetro N), indicam que este modelo pertence a uma classe de universalidade diferente daquela da percolação por invasão ordinária. Propomos um modelo de percolação para tratar um processo de solidificação de dois fluidos imiscíveis na presença de impurezas móveis. O movimento das impurezas ocorre devido a uma interação repulsiva de curto alcance observada experimentalmente por Ulhmann, Chalmers e Jackson (UCJ). Dependendo das concentrações de fluidos e impurezas, pode haver a formação de uma fase sólida que percola todo o sistema. Construímos o diagrama de fases deste modelo no espaço das concentrações e calculamos seus expoentes críticos. Nossos resultados indicam que o modelo pertence à mesma classe de universalidade que a percolação ordinária. Finalmente, estudamos um processo de percolação por invasão na presença de impurezas que se movem segundo o mecanismo UCJ. Encontramos um valor crítico para a concentração de impurezas, acima do qual não mais existe percolação. O perfil de aceitação aproxima-se de uma função de Heavyside, com o ponto de descontinuidade dependendo da concentração de impurezas. / Percolation theory provides a quantitative and conceptual model for the understanding of many natural phenomena. Here, we present new kinds of percolation and study them using Monte Carlo simulation techniques. We start studying the cluster, the backbone and the elastic backbone structures of the multiple invasion percolation for both the perimeter and the optimized versions. The behavior of the mass, the number of cutting sites and loops are investigated and their corresponding scaling exponents are estimated. By construction, the mass of the optimized model scales exactly with the gyration radius of the cluster - we verify that this also happens with the backbone. Our simulation shows that the red sites almost disappear, indicating that the cluster has achieved a high degree of connectivity. We propose a new kind of invasion percolation, which permits that, besides small pores, large pores being also occupied. In our model, the occupation probability of a pore diminishes with the pore\'s size. We estimate their corresponding percolation thresholds and show that they do not satisfy the Galam and Mauger conjecture. In order to take into account the inertia of the invader fluid, a new kind of invasion percolation is introduced. In this model, which we named N-steps invasion percolation, the inertia forces are controlled by the number N of pores (or steps) invaded after the perimeter rupture. The new model belongs to a different class of universality and has its fractal dimension depending on N. A blocking phenomenon takes place in two dimensions. It imposes an upper bound value on N. For pores sizes larger than the critical threshold, the acceptance profile exhibits a permanent tail. We also introduce a model for the solidification process of two immiscible fluids interacting repulsively with mobile impurities on a two dimensional square lattice. In the space of the fluids and impurities concentrations the phase diagram exhibits a critical curve separating a percolating from a non-percolating phase. Estimated values for the fractal dimension and the exponent ? of the order parameter, reveal that the critical exponents do not vary along this curve, i.e., they are independent of the impurities concentration. The universality class we find is that of the ordinary percolation. Finally, based on the main ideas of the dynamic epidemic and invasion percolation models, we propose a model to describe the cleaning process of a dirty porous medium by fluid injection. An analysis of the acceptance profiles strongly indicates that this model is a kind of self-organized system.

In this thesis we investigate the accuracy of high-order Extended Finite Element Methods (XFEMs) for the solution of discontinuous problems, with a view to computing high-order solutions to a two-phase flow problem. We start by demonstrating optimal exponential rates of convergence for a spectral/hp element method applied to a smooth problem. We then consider an immersed method on a fixed background mesh that uses level sets to capture the location of a discontinuity and the XFEM to characterise this discontinuity on element interiors. We present an improvement to the modified XFEM of [Moes et. al., 2003] and then use it to solve both a Poisson problem and a linear elasticity problem with discontinuities modelled independently of the mesh. Very close to optimal rates of convergence are recovered for the Poisson problem with both straight and quadratically curved interfaces for approximations up to order p=4. These rates are better than those published in the literature for the XFEM with a curved weak discontinuity, and they are also the first optimally convergent results achieved using the modified XFEM for any problem with approximations of order p>1. Almost optimal rates of convergence are then also recovered for an elastic problem with a circular discontinuity for approximations up to order p=4.The use of the XFEM for time-dependent problems is investigated, and a novel level set update method that retains the signed distance property without need for reinitialisation is also presented. Finally we apply these methods to the time-dependent simulation of a two-phase flow problem. We validate the method against both an analytic dispersion relation for relaxation under small interface perturbations and an existing implementation for large interface perturbations. We then present a proof-of-concept implementation of a high-order immersed method for an oscillating tank flow problem and demonstrate the ability of our implementation to simulate problems with large amplitude interface deformations.

Computational fluid dynamics (CFD) is the analytical process of predicting fluid flow, mass transfer, chemical reactions, and other related phenomena during the design or manufacturing process. Aggressive use of CFD provides drastic reductions in wind tunnel time and lowers the number of experimental rig tests. CFD saves hundreds of millions of dollars for industries, governments, and national laboratories, offering the potential to deliver superior understanding and insight into the critical physical phenomena limiting component performance. Thus, CFD opens new frontiers in many fields, especially vehicle design. One key strength of CFD is its ability to produce simulations useful in inverse design and optimization problems. However, a simulation in a conventional solver is considerably time-consuming to converge. To enable more efficient and scalable CFD simulations, we leverage the universal approximation property of machine learning using deep neural networks (DNNs) to estimate a surrogate solution to the CFD simulation. We present an implementation of this idea in two different models, one representing the eulerian model for compressible viscous flows and another representing the compressible Navier–Stokes equations. Lastly, we discuss the compressible Navier–Stokes network’s performance by implementing an inverse design problem to know if a gradient descent step of the model w.r.t the shape would grant the optimal solution. After training, predictions from these networks are faster than conventional solvers. The network predicts the flow fields hundreds of times faster than current conventional CFD solvers while maintaining good accuracy. Using the network’s predicted solutions to initialize a CFD solver sufficiently speeds up the simulation.

Metamorphic hydrous, CO2-bearing fluids play a critical role in the global carbon cycle. However, how big this influence is on the global carbon cycle and therefore on global climatic processes, is unknown. The actual amount of CO2 which is released into the atmosphere due to metamorphic processes is still debated. For this purpose, fluid-driven reactions in metamorphic rocks must be studied by tracking fluid-rock interactions along pathways of ancient fluids. In the study presented in this thesis, we study fluid-rock interaction in the southeastern part of the Greek island Syros in the Cycladic Archipelago (Aegean). On Syros fluid-rock interaction is recorded by the preservation of blueschist facies assemblages at greenschist facies conditions along a normal shear zone. Blueschist preservation is caused by a combination of metasomatic addition of SiO2 and Na2O and elevated XCO2 which is maintained by high fluxes of a CO2-bearing, hydrous fluid along the shear zone. This research aims to provide a better understanding of the role of mountain building in the carbon cycle. Flux estimates for climate-forcing fluid components (e.g. carbon) require that their concentration in the fluid, fluid volumes and velocities are known. This will be the focus of future work. Further, whole rock chemistry and the availability of specific minerals will be studied to achieve knowledge about which kind of parameters influence and enhance the propagation of fluids through rocks.

This study area provides a unique opportunity to study the intersection of the Elsinore and West Salton detachment faults in southern California, effusing warm springs, and alteration products in the midst of the fault intersection. Structural mapping and compiling previous maps supply an interpretation of the fault zone geometries within the Tierra Blanca Mountains. Geochemical analysis of the crystalline basement and altered protolith help determine the effects of faulting and fluid flow in the study area. In the Tierra Blanca Mountains, the Elsinore strike-slip fault system transitions from the double-stranded Julian segment and Earthquake Valley fault in the northwest, to the single-stranded Coyote Mountain segment in the southeast. A network of cross faults striking northeast connects the fault segments. The Coyote Mountain segment encounters the inactive West Salton detachment fault in the study area. The detachment fault is a barrier to fluid flow and exhibits primarily brittle deformation, while the Coyote Mountain segment is a conduit for fluid flow along the northeastern flank of the Tierra Blanca Mountains. The damage zone of the Coyote Mountain segment reaches widths up to 500 m and contains intense fracturing and subsidiary faults striking parallel to the main trace. The tonalite protolith is bleached, stained, and altered from water-rock interactions. The most intense bleaching is at a county park, where the protolith is altered to clays and zeolites while the mineralogy of the stained regions contains iron oxides and clinochlore in addition to quartz, Ca-rich albite, and biotite preserved from the protolith. The water chemistry at Agua Caliente hot springs shows the fluid is partially equilibrated. Groundwater temperatures likely reached 75-85°C at depths up to 2.14 km before rising to the surface. Frequent seismicity in the study region is related to the spring characteristics including water level, conductivity, and temperatures. Spring temperature and conductivity displayed three behaviors during the summer 2011 logging period, attributed to seasonal changes and most likely local seismicity as well. Conductivity seems to be the property most influenced by earthquake activity in the area. Changes in fluid chemistry between sampling periods may indicate mixture with other fluid sources.

We examined small-displacement faults in the Jurassic Entrada Sandstone adjacent to the Iron Wash Fault, central Utah east of the San Rafael Swell, in order to describe the nature and timing of past fluid movement and deformation in the Entrada Sandstone. Using field studies, microscopy, and X-ray diffraction analysis, we identified mineralized fractures and cementation features in association with deformation bands and fractures at the interface of the Earthy and Slick Rock Members of the Entrada Sandstone. Where the faults cross the Earthy-Slick Rock Member interface, deformation band faults in the Slick Rock Member become opening-mode fractures in the Earthy Member. These fractures are frequently mineralized with calcite, and goethite pseudomorphs after pyrite, providing evidence of at least two phases of fluid flow from the Entrada reservoir into the caprock in connection with deformation bands. We also observe mineralized fractures, poikilotopic cementation, and spherical to elongate concretions on and within deformation band fins in the Slick Rock Member. These features indicate the presence and movement of fluids parallel to and between deformation band fins. At some sites, deformation band faults and fractures cross and offset the interface; at others, they are present in both units, but deformation band faults do not cross the interface and fractures are not directly connected to any bands. Mineralized fractures are only found at breached-interface sites; evidence for fluid flow in the Slick Rock Member is only found in deformation band fins. Interface crossing and fracture formation is not related to proximity to the Iron Wash Fault. We propose that mesoscale faults can act as seal bypass systems and allow fluid leakage from reservoir rock into overlying less permeable rocks. Deformation bands act as both conduits for and barriers to flow, seen most clearly in deformation band fins where iron staining and mineralization is constrained between sets of bands within the fin. In CO2 or wastewater injection scenarios, interface deformation may prevent successful fluid trapping and cause re-emission of injected fluids.