To understand the fluid temperature and pressure during the Ouachita orogeny, we used isotopic analysis of syntectonic veins and adjacent host material, quartz-calcite oxygen isotope thermometry and fluid inclusion analysis. The veins were at or near isotopic equilibrium with their host rocks; neither the host nor veins has been isotopically reset. The average isotopic variation in (delta18)O between vein and host is 2.4 plus/minus 1.7% and 0.7 plus/minus 1.7% for quartz and calcite, respectively. The temperature of vein formation from quartz-calcite oxygen isotope thermometry is about 210-430 degrees C. Although this is a large range, the temperature does not vary systematically in the exposed Ordovician through Mississippian rocks. The lack of isotopic difference between host and vein suggests that the host oxygen determined that of the veins. This in turn suggests that the fluid in the rocks did not change regionally. The vitrinite reflectance/temperature of the host rocks increases with restored stratigraphic depth more than that calculated with the quartz-calcite thermometer in veins. Fluid inclusion analysis in vein quartz constrains homogenization temperatures to be from 106-285 degrees C. Isochores from fluid inclusion analyses were constrained using quartz-calcite thermometry and vitrinite reflectance temperatures to calculate vein formation pressures of 0.3?4.7 kbars. These pressures correspond to vein formation depths up to 19 km, assuming an unduplicated stratigraphic section. Using burial curves and a reasonable range of geothermal gradients, vein formation ages are between 300 to 315 Ma, i.e., Early to Middle Pennsylvanian.

This thesis investigates normal faulting and its influence on fluid flow over a wide range of spatial and temporal scales using tunnel engineering geological logs, outcrop, surface fault traces, earthquakes, gravity, and volcanic ages. These data have been used to investigate the impact of faults on fluid flow (chapter 2), the geometry and kinematics of the Taupo Rift (chapter 3), the hydration and dehydration of the subducting Pacific plate and its influence on the Taupo Volcanic Zone (chapter 4), the migration of arc volcanism across the North Island over the 16 Myr and the associated changes in slab geometry (chapter 5) and the Pacific-Australia relative plate motion vectors since 38 Ma and their implications for arc volcanism and deformation along the Hikurangi margin (chapter 6). The results for each of these five chapters are presented in the five paragraphs below. Tunnels excavated along the margins of the southern Taupo Rift at depths < 500 m provide data on the spatial relationships between faulting and ground water flow. The geometry and hydraulic properties of fault-zones for Mesozoic basement and Miocene strata vary by several orders of magnitude approximating power-law distributions with the dimensions of these zones dependent on many factors including displacement, hostrock type and fault geometries. Despite fault-zones accounting for a small proportion of the total sample length (≤ 15%), localised flow of ground water into the tunnels occurs almost exclusively (≥ 91%) within, and immediately adjacent to, these zones. The spatial distribution and rate of flow from fault-zones are highly variable with typically ≤ 50% of fault-zones in any given orientation flowing. The entire basement dataset shows that 81% of the flow-rate occurs from fault-zones ≥ 10 m wide, with a third of the total flow-rate originating from a single fault-zone (i.e. the golden fracture). The higher flow rates for the largest faults are interpreted to arise because these structures are the most connected to other faults and to the ground surface. The structural geometry and kinematics of rifting is constrained by earthquake focal mechanisms and by geological slip and fault mapping. Comparison of present day geometry and kinematics of normal faulting in the Taupo Rift (α=76-84°) with intra-arc rifting in the Taranaki Basin and southern Havre Trough show, that for at least the last 4 Myr, the slab and the associated changes in its geometry have exerted a first-order control on the location, geometry, and extension direction of intra-arc rifting in the North Island. Second-order features of rifting in the central North Island include a clockwise ~20° northwards change in the strike of normal faults and trend of the extension direction. In the southern rift normal faults are parallel to, and potentially reactivate, Mesozoic basement fabric (e.g., faults and bedding). By contrast, in the northern rift faults diverge from basement fabric by up to 55° where focal mechanisms indicate that extension is achieved by oblique to right-lateral strike-slip along basement fabric and dip-slip on rift faults. Hydration and dehydration of the subducting Pacific plate is elucidated by earthquake densities and focal mechanisms within the slab. The hydration of the subducting plate varies spatially and is an important determinant for the location of arc volcanism in the overriding plate. The location and high volcanic productivity of the TVZ can be linked to the subduction water cycle, where hydration and subsequent dehydration of the subducting oceanic lithosphere is primarily accomplished by normal-faulting earthquakes. The anomalously high heat flow and volcanic productivity of the TVZ is spatially associated with high rates of seismicity in the underlying slab mantle at depths of 130-210 km which can be tracked back to high rates of deeply penetrating shallow intraplate seismicity at the trench in proximity to oceanic fluids. Dehydration of the slab mantle correlates with the location and productivity of active North Island volcanic centres, indicating this volcanism is controlled by fluids fluxing from the subducting plate. The ages and locations of arc volcanoes provide constraints on the migration of volcanism across the North Island over the last 20 Myr. Arc-front volcanoes have migrated southeast by 150 km in the last 8 Ma (185 km since 16 Ma) sub-parallel to the present active arc. Migration of the arc is interpreted to mainly reflect slab steepening and rollback. The strike of the Pacific plate beneath the North Island, imaged by Benioff zone seismicity (50-200 km) and positive mantle velocity anomalies (200-600 km) is parallel to the northeast trend of arc-front volcanism. Arc parallelism since 16 Ma is consistent with the view that the subducting plate beneath the North Island has not rotated clockwise about vertical axes which is in contrast to overriding plate vertical-axis rotations of ≥ 30º. Acceleration of arc-front migration rates (~4 mm/yr to ~18 mm/yr), eruption of high Mg# andesites, increasing eruption frequency and size, and uplift of the over-riding plate indicate an increase in the hydration, temperature, and size of the mantle wedge beneath the central North Island from ~7 Ma. Seafloor spreading data in conjunction with GPlates have been used to generate relative plate motion vectors across the Hikurangi margin since 38 Ma. Tracking the southern and down-dip limits of the seismically imaged Pacific slab beneath the New Zealand indicates arc volcanism in Northland from ~23 Ma and the Taranaki Basin between ~20 and 11 Ma requires Pacific plate subduction from at (or beyond) the northern North Island continental margin from at least 38 Ma to the present. Pacific plate motion in a west dipping subduction model shows a minimum horizontal transport distance of 285 km preceding the initiation of arc volcanism along the Northland-arc normal to the motion vector, a distance more than sufficient for self-sustaining subduction to occur. Arc-normal convergence rates along the Hikurangi margin doubled from 11 to 23 mm/yr between 20 and 16 Ma, increasing again by approximately a third between 8 and 6 Ma. This latest increase in arc-normal rates coincided with changes in relative plate motions along the entire SW Pacific plate boundary and steepening/rollback of the Pacific plate.

No description available.

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.

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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.

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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.