Naturally fractured reservoirs represent significant portion of the world's oil and gas reserves. In most of the reservoirs, fractures are important contributors to fluid flow. Thus, modeling and simulation of discrete fracture network is essential to assess responses of the reservoirs under stimulation pressure, develop the best hydraulic fracture treatments, carry out feasibility studies, design optimum production methods and improve reservoir potentials. It is also a very complicated process. Natural fractures are by nature highly heterogeneous with different size, orientation and spatial distribution. The complexity is further raised, taking into account the role of matrix, the flow interaction between matrix and fractures, the effect of production-induced stress on fluid flow. Previous works fail to balance sufficient geological complexity and excessive needs of high computational resources. This thesis presents an innovative procedure to simulate stress-dependent fluid flow through discrete fracture network. Three numerical models (tensor, flow and deformation) are developed and coupled iteratively for this purpose. - A tensor model calculates grid based permeability tensor from discrete fracture network model, which includes individual fracture properties such as spatial distribution, length, location and orientation. The tensor model accounts for fluid flow from the matrix to matrix and matrix to fracture. It also includes flow through connected and disconnected fractures. - An unsteady state simulation model investigates fluid flow through the fracture system and gives pressure profile, velocity profile as output. - A dual continuum deformation model studies the reservoir rock deformation and its effects on fluid flow. The geo-mechanic solution is decomposed into matrix and fracture parts that allow calculation of dynamic porosity and permeability separately. The proposed work procedure has been validated to match nicely with analytical results. Furthermore, several case study scenarios are carried out to illustrate how it could help evaluate different aspects of reservoir performance including fracture connectivity, rock deformation, well injectivity and productivity, recovery and even distribution of fluid inside reservoir as a result of rock deformation. The case studies have proven the method to be very efficient in terms computational resources. It also eliminates most of the limitations in the previous models such as handling fracture connectivity, permeability anisotropy and change in effective stress.

Hydraulic fracturing of a naturally-fractured reservoir is a challenge for industry, as fractures can have complex growth patterns when propagating in systems of natural fractures in the reservoir. Fracture propagation near a natural fracture (NF) considering interaction between a hydraulic fracture (HF) and a pre-existing NF, has been investigated comprehensively using a two dimensional Displacement Discontinuity Method (DDM) Model in this thesis. The rock is first considered as an elastic impermeable medium (with no leakoff), and then the effects of pore pressure change as a result of leakoff of fracturing fluid are considered. A uniform pressure fluid model and a Newtonian fluid flow model are used to calculate the fluid flow, fluid pressure and width distribution along the fracture. Joint elements are implemented to describe different NF contact modes (stick, slip, and open mode). The structural criterion is used for predicting the direction and mode of fracture propagation. The numerical model was used to first examine the mechanical response of the NF to predict potential reactivation of the NF and the resultant probable location for fracture re-initiation. Results demonstrate that: 1) Before the HF reaches a NF, the possibility of fracture re-initiation across the NF and with an offset is enhanced when the NF has weaker interfaces; 2) During the stage of fluid infiltration along the NF, a maximum tensile stress peak can be generated at the end of the opening zone along the NF ahead of the fluid front; 3) Poroelastic effects, arising from fluid diffusion into the rock deformation can induce closure and compressive stress at the center of the NF ahead of the HF tip before HF arrival. Upon coalescence when fluid flows along the NF, the poroelastic effects tend to reduce the value of the HF aperture and this decreases the tension peak and the possibility of fracture re-initiation with time. Next, HF trajectories near a NF were examined prior to coalesce with the NF using different joint, rock and fluid properties. Our analysis shows that: 1) Hydraulic fracture trajectories near a NF may bend and deviate from the direction of the maximum horizontal stress when using a joint model that includes initial joint deformation; 2) Hydraulic fractures propagating with higher injection rate or fracturing fluid of higher viscosity propagate longer distance when turning to the direction of maximum horizontal stress; 3) Fracture trajectories are less dependent on injection rate or fluid viscosity when using a joint model that includes initial joint deformation; whereas, they are more dominated by injection rate and fluid viscosity when using a joint model that excludes initial joint deformation.

This dissertation presents the development of a method for quantitative integration of seismic (elastic) anisotropy attributes with reservoir performance data as an aid in characterization of systems of natural fractures in hydrocarbon reservoirs. This new method incorporates stochastic Discrete Feature Network (DFN) fracture modeling techniques, DFN model based fracture system hydraulic property and elastic anisotropy modeling, and non-linear inversion techniques, to achieve numerical integration of production data and seismic attributes for iterative refinement of initial trend and fracture intensity estimates. Although DFN modeling, flow simulation, and elastic anisotropy modeling are in themselves not new technologies, this dissertation represents the first known attempt to integrate advanced models for production performance and elastic anisotropy in fractured reservoirs using a rigorous mathematical inversion. The following new developments are presented: . • Forward modeling and sensitivity analysis of the upscaled hydraulic properties of realistic DFN fracture models through use of effective permeability modeling techniques. . • Forward modeling and sensitivity analysis of azimuthally variant seismic attributes based on the same DFN models. . • Development of a combined production and seismic data objective function and computation of sensitivity coefficients. . • Iterative model-based non-linear inversion of DFN fracture model trend and intensity through minimization of the combined objective function. This new technique is demonstrated on synthetic models with single and multiple fracture sets as well as differing background (host) reservoir hydraulic and elastic properties. Results on these synthetic control models show that, given a well conditioned initial DFN model and good quality field production and seismic observations, the integration procedure results in convergence of both fracture trend and intensity in models with both single and multiple fracture sets. Tests show that for a single fracture set convergence is accelerated when the combined objective function is used as compared to a similar technique using only production data in the objective function. Tests performed on multiple fracture sets show that, without the addition of seismic anisotropy, the model fails to converge. These tests validate the importance of the new process for use in more realistic reservoir models.

Horizontal wells have been used to increase reservoir recovery, especially in unconventional reservoirs, and hydraulic fracturing has been applied to further extend the contact with the reservoir to increase the efficiency of development. In the past, many models, analytical or numerical, were developed to describe the flow behavior in horizontal wells with fractures. Source solution is one of the analytical/semi-analytical approaches. To solve fractured well problems, source methods were advanced from point sources to volumetric source, and pressure change inside fractures was considered in the volumetric source method. This study aims at developing a method that can predict horizontal well performance and the model can also be applied to horizontal wells with multiple fractures in complex natural fracture networks. The method solves the problem by superposing a series of slab sources under transient or pseudosteady-state flow conditions. The principle of the method comprises the calculation of semi-analytical response of a rectilinear reservoir with closed outer boundaries. A statistically assigned fracture network is used in the study to represent natural fractures based on the spacing between fractures and fracture geometry. The multiple dominating hydraulic fractures are then added to the natural fracture system to build the physical model of the problem. Each of the hydraulic fractures is connected to the horizontal wellbore, and the natural fractures are connected to the hydraulic fractures through the network description. Each fracture, natural or hydraulically induced, is treated as a series of slab sources. The analytical solution of superposed slab sources provides the base of the approach, and the overall flow from each fracture and the effect between the fractures are modeled by applying superposition principle to all of the fractures. It is assumed that hydraulic fractures are the main fractures that connect with the wellbore and the natural fractures are branching fractures which only connect with the main fractures. The fluid inside of the branch fractures flows into the main fractures, and the fluid of the main fracture from both the reservoir and the branch fractures flows to the wellbore. Predicting well performance in a complex fracture network system is extremely challenged. The statistical nature of natural fracture networks changes the flow characteristic from that of a single linear fracture. Simply using the single fracture model for individual fracture, and then adding the flow from each fracture for the network could introduce significant error. This study provides a semi-analytical approach to estimate well performance in a complex fracture network system.

Although many fracture models are based on two-dimensional plane strain approximations, accurately predicting fracture propagation geometry requires accounting for the three-dimensional aspects of fractures. In this study, we implemented 3-D displacement discontinuity (DD) boundary element modeling to investigate the following intrinsically 3-D natural or hydraulic fracture propagation problems: the effect of fracture height on lateral propagation of vertical natural fractures, joint development in the vicinity of normal faults, and hydraulic fracture height growth and non-planar propagation paths. Fracture propagation is controlled by stress intensity factor (SIF) and its determination plays a central role in LEFM. The DD modeling is used to evaluate SIF in Mode I, II and III at the tip of an arbitrarily-shaped embedded crack by using crack-tip element displacement discontinuity. We examine the accuracy of SIF calculation is for rectangular, penny-shaped, and elliptical planar cracks. Using the aforementioned model for lateral propagation of overlapping fractures shows that the curving path of overlapping fractures is strongly influenced by the spacing-to-height ratio of fractures, as well as the differential stress magnitude. We show that the angle of intersection between two non-coincident but parallel en-echelon fractures depends strongly on the fracture height-to-spacing ratio, with intersection angles being asymptotic for "tall" fractures (large height-to-spacing ratios) and nearly orthogonal for "short" fractures. Stress perturbation around normal faults is three-dimensionally heterogeneous. That perturbation can result in joint development at the vicinity of normal faults. We examine the geometrical relationship between genetically related normal faults and joints in various geologic environments by considering a published case study of fault-related joints in the Arches National Park region, Utah. The results show that joint orientation is dependent on vertical position with respect to the normal fault, the spacing-to-height ratio of sub-parallel normal faults, and Poisson's ratio of the media. Our calculations represent a more physically reasonable match to measured field data than previously published, and we also identify a new mechanism to explain the driving stress for opening mode fracture propagation upon burial of quasi-elastic rocks. Hydraulic fractures may not necessarily start perpendicular to the minimum horizontal remote stress. We use the developed fracture propagation model to explain abnormality in the geometry of fracturing from misaligned horizontal wellbores. Results show that the misalignment causes non-planar lateral propagation and restriction in fracture height and fracture width in wellbore part. / text

The thesis considers three-dimensional analyses of fractures and wellbores in low-permeability petroleum/geothermal reservoirs, with a special emphasis on the role of coupled thermo-hydro-mechanical processes. Thermoporoelastic displacement discontinuity and stress discontinuity methods are elaborated for infinite media. Furthermore, injection/production-induced mass and heat transport inside fractures are studied by coupling the displacement discontinuity method with the finite element method. The resulting method is then used to simulate problems of interest in wellbores and fractures for related to drilling and stimulation. In the examination of fracture deformation, the nonlinear behavior of discontinuities and the change in status from joint (hydraulically open, mechanically closed) to hydraulic fracture (hydraulically open, mechanically open) are taken into account. Examples are presented to highlight the versatility of the method and the role of thermal and hydraulic effects, three-dimensionality, hydraulic/natural fracture deformation, and induced micro earthquakes. Specifically, injection/extraction operations in enhanced geothermal reservoirs and hydraulic/thermal stimulation of fractured reservoirs are studied and analyzed with reference to induced seismicity. In addition, the fictitious stress method is used to study three-dimensional wellbore stresses in the presence of a weakness plane. It is shown that the coupling of hydro-thermo-mechanical processes plays a very important role in low-permeability reservoirs and should be considered when predicting the behavior of fractures and wellbores.

Aujourd’hui, l’un des principaux défis dans l’industrie pétrolière, et particulièrement dans le domaine de l’exploration, est l’exploitation des nouvelles ressources dans des zones structuralement complexes.Nous savons que la géométrie et le glissement le long des failles actives modifie la distribution locale des contraintes. La connaissance du champ de contrainte perturbé actuel est importante pour l’étude des tremblements de Terre, pour la planification de forages ainsi que pour la prédiction de la fracturation induite par l’hydro-fracturation et la prédiction de la réactivation des fractures. Les contraintes perturbées passées, quant à elles sont responsables du développement des fractures naturelles (préexistantes). La détection et la modélisation de celles-ci sont essentielles tant dans le domaine pétrolier (migration et piégeage des fluides) pour une exploitation efficace et à moindre coût des réserves naturelles.Comprendre et quantifier le développement spatial et temporel de ces contraintes a un impact économique non négligeable. L'analyse des paléo-contraintes a été introduite dans un premier temps par Anderson (1905 & 1942) de manière intuitive, puis dans le milieu du siècle dernier, Wallace (1951) et Bott ( 1959) proposèrent les simples postulats que le champ de contrainte est homogène et que la direction du rejet est parallèle à la traction projetée sur le plan de faille. Beaucoup de méthodes d’inversion de contraintes reposent aujourd’hui sur ce principe.Afin d’étudier la validité de l’hypothèse Wallace et Bott, une comparaison avec les vecteurs de glissement générés à partir de modèles numériques (BEM) est effectuée. En testant l’influence de multiples paramètres (géométrie, contraintes au limites du modèle, friction, coefficient de poisson, demi-espace, pression de fluide dans la faille), il est montré que les failles à géométries complexes soumises à certaines contraintes aux limites peuvent engendrer des vecteurs glissements présentant des écarts important avec les la plus grande contraintes cisaillantes résolue sur le plan de faille. A l’inverse, la présence d’une forte friction de glissement permet, dans certaines conditions, de valider l’hypothèse de Wallace et Bott. On s’attache ensuite à comparer les résultats des inversions de contraintes basées sur l’hypothèse de Wallace et Bott (appelé méthode d’inversion classique de contraintes) avec une méthode géomécanique. Pour cela, une faille à géométrie complexe est utilisée dans une étude de sensibilité (contraintes aux limites, friction, échantillonnage) permettant d’analyser l’incertitude des résultats des deux méthodes d’inversion. Cette analyse est ensuite confrontée à l’étude d’un cas de terrain, montrant les avantages et inconvénients des méthodes d’inversions classiques de contraintes.Un des principaux défis de l’industrie pétrolière est l’exploitation des ressources des zones structuralement complexes telles que les réservoirs naturellement fracturés. Connaitre l’état de contraintes hétérogène passé permet d’optimiser la modélisation de ces fractures naturelles. Etant donné que les glissements sur les failles sont difficiles à observer dans les réservoirs pétroliers, les données de d’orientation de fractures (joints, failles, stylolites) sont naturellement prises en compte lors de l’inversion des contraintes. On montre, en utilisant divers exemples de terrain et d’industrie, que dans de tels cas, l’utilisation d’inversions basée sur la mécanique est beaucoup plus appropriée. Cependant, il est parfois difficile de déterminer le type cinématique de fracture observée le long des puits, et très souvent, les zones étudiées ont subi une tectonique polyphasée. La dernière partie vise donc à résoudre le problème des données de types cinématiques non identifiables (joints, failles, stylolites…) et étend parallèlement l’inversion mécanique des contraintes à la séparation de phases tectoniques. / Today, one of the main challenges in the oil industry, especially during the exploration phase, is the exploitation of new resources in structurally complex areas such as naturally fractured reservoirs, salt diapirs, mountain ranges, and unconventional reservoirs.We know that the geometry and sliding along active faults modifies the local stress distribution. Knowing the present day perturbed stress field is important for the study of earthquakes, for the planning of the borehole drilling and stability as well as for the prediction of fractures induced by hydro-fracturing and reactivation of natural fractures. In the other side, perturbed paleostress are responsible for the development of (pre-existing) natural fractures. The detection and modeling of the latter, are essential both in the oil industry (migration and trapping of fluids) for a cost efficient recovery of natural reserves.Understanding and quantifying the spatial and temporal development of the stress distribution has a significant economic and environmental impact. The analysis of paleo-constraints was intuitively introduced first by Anderson (1905 & 1942), then in the middle of the last century, Wallace (1951) and Bott (1959) proposed the simple hypothesis that (i) The stress field is homogeneous in space and constant in time, and that (ii) the slip direction is parallel to the traction projected on the fault plane which gives the direction of the shear stress. Many stress inversion methods are based on this hypothesis while recent studies raise doubts as to their compatibility with rock mechanics.In order to investigate the validity of the Wallace and Bott hypothesis, a comparison with vectors of slip generated with numerical models (BEM) is performed. By testing the influence of multiple parameters (geometry, boundary conditions, friction, Poisson’s coefficient , half-space, fault fluid pressure), it is shown that the complex geometry faults subject to specific boundary conditions can yield slip vectors with significant discrepancies with the maximum shear stress resolved on the fault plane. Conversely, the presence of a high sliding friction, allows under certain conditions, to validate the hypothesis of Wallace and Bott.We then focus on the task to compare the results of stress inversions based on the assumption of Wallace and Bott (called classical stress inversion methods) to a geomechanical method. For this, a complex fault geometry is used in a sensitivity analysis (boundary conditions, friction, sampling) to evaluate the uncertainty of the results of the two inversion methods. This analysis is then compared to a case study, Chimney Rock (Utah, USA), showing the advantages and disadvantages of the classical stress inversion methods.One of the main challenges of the oil industry is the exploitation of resource in structurally complex oil fields such as naturally fractured reservoirs. Knowing the heterogeneous paleostress allows to optimize the modeling of these natural fractures. Since slip on faults is hardly observed in petroleum reservoirs, fracture orientation data (joints, faults, stylolites) are naturally taken into account during the inversion of stresses. It is shown, using various field and industry examples, that in such cases the use of mechanical stress inversions is much more appropriate.However, it is sometimes difficult to determine the fracture kinematics observed along wellbores, and very often the studied regions underwent multiple tectonic phases. The final section aims to address the problem of data with unknown kinematic (joints, faults, stylolites ...) and expends the mechanical stress inversion to the separation of tectonic phases.

La connaissance des réseaux de fractures est essentielle pour comprendre la circulation des fluides dans un réservoir. Cette thèse s’appuie sur la reconnaissance du réseau de fractures naturelles qui chenalisent les circulations à l’échelle des deux forages profonds GRT-1 et GRT-2 de Rittershoffen (Alsace, France) qui ont recoupé les sédiments gréseux triasiques et le socle granitique altéré dans le cadre d’un projet industriel de géothermie. L’étude structurale de ce réseau de fractures a été réalisée à partir d’imageries de paroi acoustiques corrélées à des diagraphies géophysiques standard tandis que l’étude pétro-minéralogique se base sur les échantillons de cuttings. Les zones de fractures perméables des puits de Rittershoffen montrent une organisation asymétrique de la perméabilité. Des fractures ouvertes à l’échelle du puits semblent agir comme des drains perméables entourés de halos d’altération hydrothermale. Ces zones de fractures sont associées à des perturbations locales du profil de température dans le puits. La présence de minéraux illitiques hétérogènes pourrait être un indicateur pour prospecter les zones de circulations actuelles et passées à l’échelle des puits. Cette étude géologique permet d’évoluer vers un modèle de forage hydrothermal possédant des connexions favorables avec le réservoir sans avoir recours à des opérations de stimulation. / The knowledge of the fracture network is a key challenge to understand the fluid circulation through a reservoir. The aim of this PhD project is to investigate the natural fracture network that channelized the hydrothermal circulations into two deep wells GRT-1 and GRT-2 at Rittershoffen (Alsace, France) that intersect Triassic sandstones and altered granitic basement in the framework of an industrial geothermal project. The structural study of the fracture network was based on acoustic image logs correlated with standard geophysical logs, whereas the mineralogical study was based on cutting samples. Permeable fracture zones of wells at Rittershoffen present an asymmetrical organization of permeability. Open fractures at the borehole scale act as fluid pathways surrounded by halos of hydrothermal alteration. These fracture zones are associated with local thermal anomalies in the temperature profiles at the borehole scale. Occurrences of heterogeneous illitic minerals could be a good indicator to prospect zones of actual and past circulations at the borehole scale.

[pt] Um elevado número de reservatórios de hidrocarbonetos é naturalmente fraturado. Quando sujeitos a estimulação hidráulica, as fraturas naturais podem influenciar a propagação da fratura hidráulica, que pode tomar uma forma geométrica complexa, criando redes de fraturas no reservatório. De forma a melhor entender e simular tais fenômenos, um elemento baseado no Método dos Elementos Finitos Estendidos (XFEM) é proposto. A formulação do elemento inclui interseção e cruzamento entre fraturas, atrito entre as faces das fraturas, comportamento acoplado entre deslocamentos, poro-pressões e pressões do fluido da fratura, absorção de fluído da fratura para o meio poroso (leak-off) e a eventual perda de pressão nas faces da fratura (filter cake). Os fundamentos teóricos e os aspectos relevantes da implementação são apresentados. Um conjunto de análises é realizado de forma a validar em separado as diferentes funcionalidades do elemento implementado. Finalmente, os resultados de quatro aplicações práticas são analisados e discutidos: dois conjuntos de ensaios de laboratório de interseção de fratura, propagação de fratura hidráulica num modelo sintético multi-fraturado e percolação na fundação fraturada de uma barragem. Conclui-se que o código implementado fornece previsões muito boas do comportamento acoplado do meio fraturado e tem capacidade de simular corretamente a interação entre fraturas hidráulicas e naturais. Pode também verificar-se que o comportamento hidráulico dos modelos e a propagação e interseção de fraturas são muito influenciados por parâmetros tais como o diferencial de tensões in-situ, ângulo entre fraturas, a abertura hidráulica das fraturas e a condutividade transversal das faces da fratura. / [en] A large number of hydrocarbon reservoirs are naturally fractured. When subjected to hydraulic fracturing treatments, the natural fractures may influence the propagation of the hydraulic fracture, which can grow in a complicated manner creating complex fracture networks in the reservoir. In order to better understand and simulate such phenomena an element based on the eXtended Finite Element Method is proposed. The element formulation comprises fracture intersection and crossing, fracture frictional behaviour, fully coupled behaviour between displacements, pore and fracture fluid pressure, leak-off from the fracture to the surrounding medium and the eventual loss of pressure due to filter cake. The theoretical background and implementation aspects are presented. A set of analyses is performed in order to validate different features of the implemented element. Finally, the results of four practical applications are analysed and discussed: two laboratory hydraulic fracture tests, hydraulic fracture propagation in a multifractured synthetic model and percolation through a dam fractured foundation. It is concluded that the implemented code provides very good predictions of the coupled fluid-rock fracture behaviour and is capable of correctly simulating the interaction between hydraulic and natural fractures. Moreover, it is shown that the hydraulic behaviour of the models and the intersection between fractures are very sensible to parameters such as differential in-situ stresses, angle between fractures, initial hydraulic aperture and fracture face transversal conductivity.

[pt] O presente estudo propõe modelos numéricos robustos para simular os fenômenos presentes nos problemas de propagação de fraturas e migração de fluidos em formações fraturadas. Uma técnica de fragmentação de malha com uma abordagem de zona poro-coesiva é desenvolvida para simular a propagação não planar de fraturas em formações fraturadas. O modelo proposto permite estudar os efeitos dos parâmetros primários sobre a interação de fraturas hidráulicas e naturais. O trabalho desenvolve uma nova formulação hidromecânica 3D do dupla porosidade e dupla permeabilidade aprimorada para a representação mais realista do médio fraturado em simulações de reservatório. O modelo permite estudar o impacto de fraturas naturais de múltiplas escalas e orientações no desempenho do reservatório. Finalmente, o trabalho propõe uma nova metodologia que integra os modelos robustos de propagação de fratura e simulação de reservatório, para aprimorando a avaliação do desempenho da produção. Foram simulados múltiplos cenários de fraturamento hidráulico para avaliar a produção dos reservatórios. Também foram integrados modelos de fratura discreta e dupla porosidade-dupla permeabilidade para estudar os efeitos de fraturas de múltiplas escalas no reservatório estimulado hidraulicamente. Os modelos desenvolvidos foram comparados com testes experimentais, soluções analíticas e numéricas. Os resultados mostram excelente concordância e validam as formulações hidromecânicas. A partir dos resultados numéricos, se identificaram os parâmetros dominantes que influenciam o resultado do fraturamento hidráulico e a produção dos depósitos hidraulicamente estimulados. / [en] The presented study proposes robust numerical models to simulate the phenomena present in fracture propagation and fluid migration problems in fractured media. An innovative mesh fragmentation technique with an intrinsic pore-cohesive zone approach is developed to simulate unrestricted hydraulic fracture propagation in fractured media. The proposed method allows studying the effect of some primary parameters on hydraulic and natural fracture interaction. A new 3D hydromechanical formulation for an enhanced dual-porosity/dual-permeability model is proposed to represent a fractured porous formation more realistically in reservoir simulations. The new model allows the study of the impacts of natural fractures with different orientations at multiple scales on the hydromechanical behavior of the reservoir. Finally, this research work proposes a new methodology that integrates a robust fracture propagation model and reservoir simulation, improving the evaluation of production performance. We simulate several hydraulic fracturing scenarios for the assessment of the cumulative production of the reservoir. Moreover, we combined discrete fracture and enhanced dual porosity-dual permeability models to study the effects of fractures of multiple lengths on the hydraulically stimulated reservoir. The developed models are compared against experimental tests, analytical and numerical solutions. The comparative results show excellent agreement and validate the fully coupled hydromechanical formulations. From the numerical results, it was possible to identify the dominant parameters that influence hydraulic fracturing and the production performance of the hydraulically stimulated deposits.