The effect of coupled thermo-poroelastic behavior on hydraulic fracture propagation is of much interest in geothermal- and petroleum-related geomechanics problems such as wellbore stability and hydraulic fracturing as pore pressure and temperature variations can significantly induce rock deformation, fracture initiation, and propagation. In this dissertation, a two-dimensional (2D) boundary element method (BEM) was developed to simulate the fully coupled thermo-poroelastic fracture propagation process. The influence of pore pressure and temperature changes on the fracture propagation length and path, as well as on stress and pore pressure distribution near wellbores and fractures, was considered in isotropic and homogeneous rock formations. The BEM used in this work consists of the displacement discontinuity (DD) method and the fictitious stress (FS) method. Also, a combined FS-DD numerical model was implemented for the hydraulically or thermally-induced fractures in the vicinity of a wellbore. The linear elastic fracture mechanics (LEFM) theory was adopted to numerically model within the framework of poroelasticity and thermo-poroelasticity theory. For high accuracy of crack tip modeling, a special displacement discontinuity tip element was developed and extended to capture the pore pressure and temperature influence at the tip. For poroelastic fracture propagation, a steadily propagating crack driven by fluid pressure was modeled to find the effect of pore pressure on crack path under the two limiting poroelastic conditions (undrained and drained). The results indicate that the pore pressure diffusion has no influence on the crack growth under the undrained condition because the crack propagation velocity is too fast for the diffusion effect to take place. On the other hand, its influence on the crack path under the drained condition with its low propagation velocity has significance because it induces a change in principal stress direction, resulting in an alteration of fracture orientation. For the thermal fracturing, when the rock around a wellbore and a main fracture is cooled by injecting cold water in a hot reservoir, the rapid decrease in temperature gives rise to thermal stress, which causes a crack to initiate and propagate into the rock matrix. The single and multiple fracture propagation caused by transient cooling in both thermoelastic and poro-thermoelastic rock were numerically modeled. The results of this study indicate that the thermal stresses induced by cooling may exceed the in-situ stress in the reservoir, creating secondary fractures perpendicular to main fracture. Furthermore, the faster cooling rate produces longer crack extension of the secondary thermal fractures. This implies that the faster cooling induces a higher tensile stress zone around the fracture, which tends to produce larger driving forces to make the secondary fractures penetrate deeper into the geothermal reservoir.

[pt] No ano 1999 as quedas de blocos rochosos já representaram cerca de 8% dos diferentes tipos de escorregamentos registrados no Rio de Janeiro. A atividade antrópica gera um aumento das áreas de risco devido às construções próximas da base de escarpas rochosas e uma aceleração destes fenômenos. Desde 1993 o número de quedas de lascas e blocos rochosos a partir de faces de pedreiras desativadas tem aumentado. As condições geológicas e estruturais da região favorecem este fenômeno ao discretizarem blocos nos taludes rochosos. Muitas destas quedas tem sido reportadas em condições climáticas particulares, em períodos relativamente secos correspondentes aos meses de junho, julho e agosto. O presente trabalho discute que, dentro dos possíveis mecanismos para a ocorrência destes fenômenos, está a variação térmica diária, a qual pode criar tensões que favorecem a propagação de fraturas existentes dentro dos maciços rochosos. Por tal motivo, simulou-se em laboratório as condições de um maciço rochoso fraturado e obtiveram-se dados das variações diárias de temperatura, mediante a disposição de blocos rochosos graníticos simulando a forma da fratura e com o auxilio de sensores térmicos em diferentes posições, como na superfície, no interior e na fresta. A partir disto elaborou-se um modelo de bloco com auxílio do software ABAQUS para se determinar a variação dos valores de concentração de tensões sob a influência térmica. / [en] In 1999, the falls of rock blocks had represented about 8% of the different types of slides registered in Rio de Janeiro. The anthropic activity generates an increase of the risk areas due the building of vulnerable houses near to foot rock scarps, and an acceleration of these phenomena. Since 1993 the number of falls of rock blocks from slopes of disactivated quarries has increased. The geologic and structural conditions of the region favor this phenomenon forming blocks in rock slopes. Many of these falls have been reported in particular climatic conditions, in relatively dry periods correspondents to the months of June, July and August. This work argues that, the daily thermal variation could be one of the possible mechanisms for the occurrence of these phenomena, which can create stresses to propagate cracks already existing on the rock mass. For such reason, conditions of a broken rock mass was simulated in laboratory to obtain daily temperature variations, it was made by the disposal of granítics rock blocks simulating a fracture form, where was placed thermal sensors. From this, a model of rock block in the ABAQUS sofware was elaborated to determine the variation of stress concentration factor values under the thermal influence

O presente trabalho de pesquisa está relacionado à análise do progresso do fraturamento na zona tracionada de fundações rochosas de barragens de concreto e suas conseqüências nas avaliações de estabilidade global. Tomou-se como exemplo a barragem de Porto Primavera de propriedade da CESP (Companhia Energética de São Paulo), situada entre os estados de São Paulo e Mato Grosso do Sul, Brasil. Com a ajuda de modelos elaborados com elementos finitos e sob a ótica da mecânica da fratura não linear e da mecânica do dano, analisa-se o desenvolvimento da fratura mediante uma avaliação iterativa tensão-deformação e carga hidráulica. Devido ao carregamento progressivo de água, realiza-se a análise iterativa baseada no avanço da fratura e na aplicação de pressão hidráulica, até quando a fratura deixa de progredir. A simulação numérica proposta tem o objetivo de estudar o desenvolvimento de fraturas, determinar as deformações ocorridas sob a ação das forças de empuxo d'água, de subpressão, do peso próprio e das pressões de água na fratura do maciço rochoso fraturado. As deformações calculadas são comparadas com registros da instrumentação na fundação efetuados durante o enchimento do reservatório, o que permitirá o ajuste dos parâmetros adotados na simulação, assim como estabelecer as reais características da fundação / This study is related to the analysis of crack propagation in the tensioned zone of concrete dam foundation. The example of Porto Primavera dam owned by CESP (São Paulo State Power Company) Brazil is presented. Fracture growth is analyzed by mean iterative stress-strain and hydraulic head analysis with codes based on finite elements incorporating non-linear fracture mechanics and damage models. Due to progressive load of water, a step-by-step analysis is performed, based on the development of fracture and application of forces due of hydraulic pressure. The proposed numerical simulation has the purpose of studying the development of fracture, determining deformations due to the action of uplift pressure, self-weight and hydraulic pressure on the fracture walls. The computed deformations are compared with instrumentation data, obtained during the impoundment of the reservoir, from devices installed in the foundation, which will allow to adjust the adopted parameters in the simulation and to determine the real characteristics of the foundation

O presente trabalho de pesquisa está relacionado à análise do progresso do fraturamento na zona tracionada de fundações rochosas de barragens de concreto e suas conseqüências nas avaliações de estabilidade global. Tomou-se como exemplo a barragem de Porto Primavera de propriedade da CESP (Companhia Energética de São Paulo), situada entre os estados de São Paulo e Mato Grosso do Sul, Brasil. Com a ajuda de modelos elaborados com elementos finitos e sob a ótica da mecânica da fratura não linear e da mecânica do dano, analisa-se o desenvolvimento da fratura mediante uma avaliação iterativa tensão-deformação e carga hidráulica. Devido ao carregamento progressivo de água, realiza-se a análise iterativa baseada no avanço da fratura e na aplicação de pressão hidráulica, até quando a fratura deixa de progredir. A simulação numérica proposta tem o objetivo de estudar o desenvolvimento de fraturas, determinar as deformações ocorridas sob a ação das forças de empuxo d'água, de subpressão, do peso próprio e das pressões de água na fratura do maciço rochoso fraturado. As deformações calculadas são comparadas com registros da instrumentação na fundação efetuados durante o enchimento do reservatório, o que permitirá o ajuste dos parâmetros adotados na simulação, assim como estabelecer as reais características da fundação / This study is related to the analysis of crack propagation in the tensioned zone of concrete dam foundation. The example of Porto Primavera dam owned by CESP (São Paulo State Power Company) Brazil is presented. Fracture growth is analyzed by mean iterative stress-strain and hydraulic head analysis with codes based on finite elements incorporating non-linear fracture mechanics and damage models. Due to progressive load of water, a step-by-step analysis is performed, based on the development of fracture and application of forces due of hydraulic pressure. The proposed numerical simulation has the purpose of studying the development of fracture, determining deformations due to the action of uplift pressure, self-weight and hydraulic pressure on the fracture walls. The computed deformations are compared with instrumentation data, obtained during the impoundment of the reservoir, from devices installed in the foundation, which will allow to adjust the adopted parameters in the simulation and to determine the real characteristics of the foundation

[pt] Esta pesquisa aborda o processo de fraturamento hidráulico ou processo de propagação de fraturas em rocha através da injeção de um fluido sob pressão, o que gera fissuras no material que se propagam de acordo com a quantidade de fluido injetado. Esta técnica leva a um incremento da transmissividade hidráulica da rocha e, como consequência, ocorre um incremento da produção de óleo. Diversos trabalhos analíticos e numéricos têm sido propostos para estudar o mecanismo de fratura, geralmente baseados em meios contínuos ou através da utilização de elementos de interface em uma trajetória de propagação conhecida. Neste trabalho, a propagação de uma fratura é simulada utilizando o modelo potencial PPR[72] através da sua implementação extrínseca. Assim, os elementos coesivos de interface são inseridos na malha de elementos finitos de forma adapativa para capturar o processo de fraturamento. A pressão do fluido é simulada utilizando o modelo de lattice-Boltzmann[84]. Através de um processo interativo, os contornos da fratura, computados utilizando o método dos elementos finitos, são transferidos para o modelo de lattice-Boltzmann como uma condição de contorno. Assim, a força que o fluido exerce nestes contornos, gerada pela injeção do fluido, pode ser calculada. Estas forças são utilizadas no modelo de elementos finitos como uma força externa aplicada nas faces da fratura. A nova posição das faces da fratura é calculada e transferida novamente para o modelo de lattice-Boltzmann como condição de contorno. Este processo interativo fluido-estrutura permite modelar o processo de fraturamento hidráulico em trajetórias de propagação irregulares. / [en] This research addresses hydraulic fracturing or hydro-fracking, i.e. fracture propagation process in rocks through the injection of a fluid under pressure, which generates cracks in the rock that propagate according to the amount of fluid injected. This technique leads to an increase of the hydraulic transmissivity of the rock mass and, consequently, improves oil production. Several analytical and numerical models have been proposed to study this fracture mechanism, generally based in continuum mechanics or using interface elements through a known propagation path. In this work, the crack propagation is simulated using the PPR potential-based cohesive zone model[72] by means of an extrinsic implementation. Thus, interface cohesive elements are adaptively inserted in the mesh to capture the softening fracture process. The fluid pressure is simulated using the lattice Boltzmann model[84] through an iterative procedure. The boundaries of the crack, computed using the finite element method, are transferred to the lattice Bolztmann model as boundary conditions, where the fluid pressure (or fluid forces) applied on these boundaries, caused by the fluid injected, can be calculated. These forces are then used in the finite element model as external forces applied on the faces of the crack. The new position of the crack faces is then calculated and transferred to the lattice-Boltzmann model to update the boundary conditions. This feedback-loop for fluid-structure interaction allows modeling of hydraulic fracturing processes for irregular path propagation.

Hydraulic fracturing is essential for producing gas and oil at an economic rate from low permeability sands. Most fracturing treatments use water and polymers with a gelling agent as a fracturing fluid. The water is held in the small pore spaces by capillary pressure and is not recovered when drawdown pressures are low. The un-recovered water leaves a water saturated zone around the fracture face that stops the flow of gas into the fracture. This is a particularly acute problem in low permeability formations where capillary pressures are high. Depletion (lower reservoir pressures) causes a limitation on the drawdown pressure that can be applied. A hydraulic fracturing process can be energized by the addition of a compressible, sometimes soluble, gas phase into the treatment fluid. When the well is produced, the energized fluid expands and gas comes out of solution. Energizing the fluid creates high gas saturation in the invaded zone, thereby facilitating gas flowback. A new compositional hydraulic fracturing model has been created (EFRAC). This is the first model to include changes in composition, temperature, and phase behavior of the fluid inside the fracture. An equation of state is used to evaluate the phase behavior of the fluid. These compositional effects are coupled with the fluid rheology, proppant transport, and mechanics of fracture growth to create a general model for fracture creation when energized fluids are used. In addition to the fracture propagation model, we have also introduced another new model for hydraulically fractured well productivity. This is the first and only model that takes into account both finite fracture conductivity and damage in the invaded zone in a simple analytical way. EFRAC was successfully used to simulate several fracture treatments in a gas field in South Texas. Based on production estimates, energized fluids may be required when drawdown pressures are smaller than the capillary forces in the formation. For this field, the minimum CO2 gas quality (volume % of gas) recommended is 30% for moderate differences between fracture and reservoir pressures (2900 psi reservoir, 5300 psi fracture). The minimum quality is reduced to 20% when the difference between pressures is larger, resulting in additional gas expansion in the invaded zone. Inlet fluid temperature, flowrate, and base viscosity did not have a large impact on fracture production. Finally, every stage of the fracturing treatment should be energized with a gas component to ensure high gas saturation in the invaded zone. A second, more general, sensitivity study was conducted. Simulations show that CO2 outperforms N2 as a fluid component because it has higher solubility in water at fracturing temperatures and pressures. In fact, all gas components with higher solubility in water will increase the fluid’s ability to reduce damage in the invaded zone. Adding methanol to the fracturing solution can increase the solubility of CO2. N2 should only be used if the gas leaks-off either during the creation of the fracture or during closure, resulting in gas going into the invaded zone. Experimental data is needed to determine if the gas phase leaks-off during the creation of the fracture. Simulations show that the bubbles in a fluid traveling across the face of a porous medium are not likely to attach to the surface of the rock, the filter cake, or penetrate far into the porous medium. In summary, this research has created the first compositional fracturing simulator, a useful tool to aid in energized fracture design. We have made several important and original conclusions about the best practices when using energized fluids in tight gas sands. The models and tools presented here may be used in the future to predict behavior of any multi-phase or multi-component fracturing fluid system. / text

[pt] O processo de fraturamento de materiais quase-frágeis requer atenção especial para a predição da direção de propagação de fraturas. A simulação do fraturamento com o método dos elementos finitos (MEF) tem como desvantagem a dependência da trajetória da fratura com respeito à malha adotada. Além disso, há certa dificuldade para os modelos numéricos representarem a fratura em modo misto por conta dos parametros envolvidos. O Método dos Elementos Finitos Estendido (XFEM) é uma técnica que combina o MEF com funções de enriquecimento para representar descontinuidades no campo de deslocamentos. Neste contexto, discutem-se nesta dissertação os critérios para a nucleação e propagação de fraturas e sua implementação no contexto do XFEM. As implementações foram feitas no framework GeMA, um software desenvolvido no Tecgraf / PUC-Rio. Os critérios de propagação de fraturas implementados baseiamse na abordagem das tensões e permitem controlar diferentes geometrias e tamanhos da área de avaliação na ponta da trinca. Um estudo paramétrico é apresentado para modelar uma viga de concreto sob carregamento não proporcional com fratura em modo misto. Foram consideradas diferentes questões como: discretização da malha, zona de avaliação, iniciação e propagação de fraturas e técnicas de controle de solução. Além disso, outros modelos com diferentes condições de contorno foram analisados para validar os critérios em situações complexas. As constatações paramétricas obtidas através do estudo da viga se monstraram válidas para os demais modelos avaliados. As implementações dos critérios de propagação de fraturas no XFEM, demonstraram excelentes concordâncias nas simulações das trajetórias de fraturamento, comparado com os dados experimentais. / [en] The fracture process of quasi-brittle materials requires special attention for the prediction of the direction of fracture propagation. The fracture simulation with the finite element method (FEM) has as its disadvantage the dependence of the fracture trajectory with respect to the mesh adopted. Besides, there is some difficulty for numerical models to represent the fracture in mixed mode because of the parameters involved. The Extended Finite Element Method (XFEM) is a technique which combines the FEM with enrichment functions to represent discontinuities in the displacement field. In this context, this dissertation discusses the criteria for nucleation and propagation of fractures and their implementation in the context of XFEM. The implementations were made in the GeMA framework, a software developed at Tecgraf / PUC-Rio. The implemented crack growth criteria is based on the stress approach and allows to control different geometries and sizes of the evaluation area in the crack tip. A parametric study is presented for modeling a concrete beam under nonproportional loading with mixed-mode fracture. Different situations were taken into account such as mesh refinement, geometry and size of the evaluation region, crack initiation and propagation and solution control techniques. Also, several models with different loading and boundary conditions were made to validate the criteria under complex situations. The parametric findings obtained through the study of the beam proved to be valid for the other models. The implementations of the fracture propagation criteria in the XFEM demonstrated excellent agreement in the simulations of the fracture trajectories compared to the experimental data.

In geschichteten Reservoiren mit geringer Matrix-Permeabilität kontrollieren überwiegend Bruchsysteme den Fluidtransport. In Kalk-Mergel-Wechselfolgen sind allerdings die vertikale Kluftausbreitung sowie die Vernetzung der Kluftsysteme zwischen den unterschiedlichen Schichten sehr variabel, was schließlich die Permeabilität in diesen bruchkontrollierten Reservoiren erheblich beeinflusst. Innerhalb einer Schichtfolge führen diverse sedimentologische Merkmale (z.B. sedimentäre Schichtung und diagenetische Bankung) zu kontrastreichen Gesteinseigenschaften und wirken somit als Spannungsbarrieren. Spannungsbarrieren, wie beispielsweise lithologische Kontakte oder mächtige Mergellagen, können die Kluftausbreitung in geschichteten Gesteinen ebenfalls verhindern und erschweren zusätzlich die Vorhersage potentieller Fluidwege. Aufgrund dessen ist es entscheidend Schichten, die sich mechanisch einheitlich verhalten („mechanische Einheit“) zu finden. Das Ziel dieser Doktorarbeit ist, den Einfluss von sedimentologischen und diagenetischen Merkmalen und petrophysikalischen Eigenschaften vertikaler Kluftausbreitung in Kalk-Mergel-Wechselfolgen der Jurassischen Blue Lias Formation (Bristol Channel Becken, Großbritannien) abzuschätzen, um verschiedenartige Spannungsbarrieren und mechanische Einheiten zu definieren. Zu diesem Zweck wurden sechs Profile untersucht, welche sich durch unterschiedliche morphologische Variationen auszeichnen (d.h. von kalkdominiert zu mergeldominiert). Die Untersuchungen umfassen Kombinationen aus sedimentologischer (z.B. Geländeuntersuchungen, Dünnschliffpetrografie, Rasterelektronenmikroskopie, CaCO3- and Corg-Messungen), quantitativ strukturgeologischer (z.B. Charakterisierung von Kluftsystemen) sowie petrophysikalischer Daten (z.B. Spaltzug- und Druckfestigkeits-, Rückprallhärte- und Porositäts-Messungen). Im Rahmen der quantitativen strukturgeologischen Untersuchungen wurden unter Verwendung einer modifizierten Scanline Methode (Durchführung einer flächengestützten Kluftanalyse) über 4000 schichtübergreifende Klüfte betrachtet. Generell wird angenommen, dass der Kluftabstand mit zunehmender Bankmächtigkeit zunimmt und die Kluftdichte dementsprechend abnimmt. Diese Studie zeigt jedoch, dass dieser Zusammenhang nur eingeschränkt auf Kalkbänke dieser Abfolgen anwendbar ist und nur auf Schichten mit lateral planaren Oberflächen (wohlgebankte Kalkbänke) übertragen werden kann. Bei Bänken gleicher Mächtigkeit mit allerdings irregulären Oberflächen (semiknollige Kalkbänke) variieren die Kluftabstände innerhalb dieser Bänke beträchtlich. Das bedeutet, die Kluftabstände sind in semiknolligen Kalkbänken eher unregelmäßig wohingegen die Abstände in wohlgebankten Bänken eher regelmäßig sind. Des Weiteren sind in wohlgebankten Kalken ein höherer prozentualer Anteil von schichtgebundenen Klüften (57 %) ausgebildet. Dagegen sind in semiknolligen Kalken ein höherer Anteil nicht-schichtgebundener Klüfte ausgebildet (67 %). Entscheidend für die Kluftausbreitung in geschichteten Gesteinen ist nicht nur die Kluftverteilung der einzelnen Bänke, sondern auch verschiedenartige Spannungsbarrieren, wie beispielsweise lithologische Kontakte, Mächtigkeiten und Heterogenitäten von Mergeln hemmen die Kluftausbreitung. Anhand der vertikalen Kluftstoppung an lithologischen Kontakten und vertikale Kluftausbreitung durch Schichten wurden Spannungsbarrieren identifiziert (schichtgebundene vs. nicht-schichtgebundene Klüfte). Da nicht alle lithologische Kontakte die Ausbreitung von Klüften in geschichteten Gesteinen verhindern, wurde in dieser Studie der Terminus für 50 % Kluftstoppung an diesen Kontakten verwendet („mechanische Grenzflächen“). Zusätzlich wurden bestimmte Mergellagen, die >0.20 m mächtig sind, durch mechanische Grenzflächen begrenzt sind und weniger als 50 % nicht-schichtgebundene Klüfte beinhalten, als „mechanische Puffer“ definiert. Die Charakterisierung des Kluftsystems wird neben der vorherrschenden stark heterogenen Kluftverteilung in der Blue Lias Formation, auch durch eine signifikante Variation des Diagenese-Einflusses von Abschnitt zu Abschnitt erschwert. Beispielsweise wurden in Wales drei Teilprofile genauestens untersucht, welche trotz ihrer räumlich nahen Lage und relativ zeitgleichen Entstehung unterschiedliche sedimentologische und diagenetische Merkmale in Meter- bis Mikrometer-Skalen aufweisen (von früh lithifiziert bis physikalisch kompaktierte Abfolgen). Darüber hinaus sind diese durch unterschiedliche Muster der Kluftstoppung an Kontakten und Kluftausbreitung innerhalb der Bänke charakterisiert. Lithologische Kontakte in diagenetisch beeinflussten Abfolgen sind tendenziell eher graduell und somit keine mechanischen Grenzflächen. Wenn zusätzlich der Unterschied zwischen den CaCO3-Konzentrationen zwischen Kalken und Mergeln niedrig ist, kann die Abfolge als eine mechanische Einheit definiert werden, welches die Kluftausbreitung begünstigen würde. Die Vorhersage der Konnektivität von Kluftnetzwerken ist in lithologisch heterogenen Kalk-Mergel-Wechselfolgen, wie die in der Blue Lias Formation, aufgrund unterschiedlicher Kluftverteilung innerhalb einzelner Bänke, unterschiedliche diagenetische Einfluss und verschiedenartiger Spannungsbarrieren schwierig. Das ist insbesondere für die Charakterisierung der Kluftnetzwerke und ihre Nutzung in Aufschluss-Analogstudien problematisch, welche für die Einschätzung des Fluidtransports in solchen Systemen verwendet wird. Die Ergebnisse dieser Studie sind zur Optimierung der Quantifizierung von Kluftverteilung und -ausbreitung in heterogenen Gesteinsabfolgen entscheidend und präzisieren die Definition mechanischer Einheiten. Diese Definition ist eine wichtige Voraussetzung für die Vorhersage von Kluftpermeabilitäten und folglich entscheidend für Fluidtransportmodelle.

[pt] O processo de fraturamento hidráulico tem sido amplamente usado para aumentar o volume de petróleo e gás extraído na indústria petroleira. Durante a injeção de fluido, uma região determinada do reservatório é fraturada com a finalidade de aumentar a permeabilidade do meio poroso, de tal forma que o fluxo do fluido desde o reservatório para o poço seja favorecido notoriamente. Porém, este processo pode ocasionar danos ambientais tais como contaminação de aguas subterrâneas, vazamentos de gás, fraturas indesejadas nas camadas capeadoras pela injeção de agua e atividade sísmica fazendo primordial um estudo rigoroso do fraturamento hidráulico com a finalidade de reduzir os riscos potenciais associados a esta operação. Umas das metodologias usadas para projetar o fraturamento hidráulico é a simulação computacional. É possível determinar o volume injetado e a potência da bomba de injeção necessária para obter a geometria de fratura (comprimento, abertura e altura) desejada. A modelagem numérica através de elementos coesivos acoplados do processo de fraturamento hidráulico pode ser efetuada considerando o processo transiente ou permanente, tendo geometrias da fratura e curvas de injeção diferentes. Neste trabalho foi simulado numericamente o modelo KGD nos regimes de fluxo transiente e permanente para dois casos de estudo, (1) injeção numa única camada e (2) injeção em três camadas com contraste de tensões e poropressões entre elas. O estudo numérico foi desenvolvido usando o método dos elementos finitos com modelo de zona coesiva no software Abaqus o qual foi comparado com as soluções analíticas do KGD no regime dominado pela rigidez (Vértice-K) para uma camada e de Simonson e Fung para três camadas. / [en] The hydraulic fracturing process has been widely used to improve oil and gas recovery in the petroleum industry. During the fluid injection, the desired section of rock formation is fractured in order to increase the permeability of the medium that can facilitate the flow of oil to a producing well. However, this process can lead to potential environmental risks such as seismic activity, unwanted fractures in cap layers by water injection, water contamination and gas leakage making primordial to develop a rigorous study in order to reduce this environmental risks associated to hydraulic fracturing. One of the studies developed to design the hydraulic fracturing is computational simulation to determine the fluid volume and hydraulic horsepower required in order to produce the wanted fracture geometry (length, opening and height). The numerical modelling of fracturing process by using fully coupled cohesive element hydraulic can be carried out considering either a steady state or a transient analysis, which modify the fracture geometry and injection pressure. In this work, the KGD model is simulated in transient and steady analysis for two cases: (1) injection in a single layer formation and (2) injection in tri-layered formation with stress and porepressure contrast between them. The numerical simulation of a hydraulic fracturing is carried out using the finite element method with the zone cohesive model in Abaqus whose results are compared with analytical solutions of toughness-dominated propagation regime for the one layer formation model and Simonson and Fung analytical solutions for tri-layered formations model.

Both joint sets and fault-related fractures serve as important conduits for fluid flow. In the former case, they can strongly influence both permeability and permeability anisotropy, with implications for production of water, hydrocarbons and contaminant transport. The latter can affect issues of fluid flow, such as whether a given fault seals or leaks, and fault mechanics. These fractures are commonly interpreted as Natural Hydraulic Fractures (NHFs), i.e., mode 1 fractures produced when pore fluid pressure exceeds the tensile strength of the rock. Various mathematical models have been a rich source of hypotheses to explain the formation and propagation of NHFs, but have provided only limited information and nothing about processes of fracture initiation in originally intact rock. Recent laboratory experiments of French et al. (2012) have advanced our understanding of mechanical controls on fracture initiation and spacing. Here, detailed analysis of both through-going fracture surfaces, non-through-going fractures, in experimentally deformed samples provide a deeper understanding of NHF processes and resulting geometric features in porous siliciclastic sedimentary rocks. Observations indicate that both fracture planarity and microcrack damage (which has not previously been reported for opening mode fractures) vary significantly depending on the degree of mechanical heterogeneity and anisotropy of the host rock. Variations reflect mechanical controls on fracture initiation and propagation, suggesting that fracture spacing may in part reflect the distribution of mechanical heterogeneities. These data indicate that the more homogeneous the rock, the greater the microcrack damage surrounding a given NHF, increasing expected fracture-associated permeability for a given fracture aperture.