Fractured reservoirs are generally simulated using Warren and Root26 dual-porosity (DP) approach. The main assumption of this approach is that the geometry of fractures are uniformly distributed and interconnected in reservoirs. This may be true for many cases of naturally fractured reservoirs. However, for a large scale and disconnected fractured reservoirs, DP is often not applicable. Due to the latter case, it is necessary to have more sophisticated simulation studies which allow the fracture to be geometry explicitly represented into the static model using Discrete Fracture Network (DFN) approach. Most work on DFN grid model up to recently has been done with Delaunay tessellations. This research proposes an alternative technique to discretize the two-dimensional DFN using Voronoi diagrams, nevertheless applying the same DFN principles outlined in previous work. Through complicated procedures to generate DFN model, grid system based on Voronoi polygons has been developed. The procedure will force Voronoi edges follow the exact geometry of fractures. Furthermore, implementing the Voronoi diagrams allows the use of fewer polygons than the traditional Local Grid Refinement (LGR). And most importantly, due to the nature of the Voronoi polygons or locally orthogonal grids, the transmissibility calculations can be simplified and are more accurate than corner point formulation for non-square grid blocks. Finally, the main and most important goal of this study is to develop a black-oil Control Volume Finite Difference (CVFD) reservoir simulator that allows us to model DFN more realistically. One of the features of the developed simulator is the capability to model individual fractures with non-uniform aperture distribution, such as log-normally distributed apertures as shown using X-Ray CT scanner measurements. Prior to using the DFN simulator to model reservoirs with fractures and their apertures distribution, the simulator was validated against commercial simulators. The simulator provides results in close agreement with those of a reference finite-difference simulator in cases where direct comparisons are possible. Several simulations of synthetic DFN were presented to demonstrate the robustness of the Voronoi diagrams to represent fracture networks and its aperture distributions. In summary, the simulation of the DFN using the proposed approaches is capable to model both fractured and unfractured systems. However, the DFN model with Voronoi grids requires more efforts on building the grid model compared to other methods. Numerically, simulations of fractured systems are very challenging.

Discrete Fracture Networks (DFN) models have long been used to represent heterogeneity associated with fracture networks but all previous approaches have been either in 2D (assuming vertical fractures) or for simple models within a small domain. Realistic representation of DFN on field scale models have been impossible due to two reasons - first because the representation of extremely large number of fractures requires significant computational capability and second, because of the inability to represent fractures on a simulation grid, due to extreme aspect ratio between fracture length and aperture. This thesis presents a hierarchal approach for fracture modeling and a novel random walker simulation to upscale the fracture permeability. The modeling approach entails developing effective flow characteristics of discrete fractures at micro and macrofracture scales without explicitly representing the fractures on a grid. Separate models were made for micro scale and macro scale fracture distribution with inputs from the seismic data and field observations. A random walker simulation is used that moves walkers along implicit fractures honoring the intersection characteristics of the fracture network. The random walker simulation results are then calibrated against high-resolution flow simulation for some simple fracture representations. The calibration enables us to get an equivalent permeability for a complex fracture network knowing the statistics of the random walkers. These permeabilities are then used as base matrix permeabilities for random walker simulation of flow characteristics of the macro fractures. These are again validated with the simulator to get equivalent upscaled permeability. Several superimposed realizations of micro and macrofracture networks enable us to capture the uncertainty in the network and corresponding uncertainty in permeability field. The advantage of this methodology is that the upscaling process is extremely fast and works on the actual fractures with realistic apertures and yields both the effective permeability of the network as well as the matrix-fracture transfer characteristics. / text

Fluid flow process in fractured reservoirs is controlled primarily by the connectivity of fractures. The presence of fractures in these reservoirs significantly affects the mechanism of fluid flow. They have led to problems in the reservoir which results in early water breakthroughs, reduced tertiary recovery efficiency due to channeling of injected gas or fluids, dynamic calculations of recoverable hydrocarbons that are much less than static mass balance ones due to reservoir compartmentalization, and dramatic production changes due to changes in reservoir pressure as fractures close down as conduits. These often lead to reduced ultimate recoveries or higher production costs. Generally, modeling flow behavior and mass transport in fractured porous media is done using the dual-continuum concept in which fracture and matrix are modeled as two separate kinds of continua occupying the same control volume (element) in space. This type of numerical model cannot reproduce many commonly observed types of fractured reservoir behavior since they do not explicitly model the geometry of discrete fractures, solution features, and bedding that control flow pathway geometry. This inaccurate model of discrete feature connectivity results in inaccurate flow predictions in areas of the reservoir where there is not good well control. Discrete Fracture Networks (DFN) model has been developed to aid is solving some of these problems experienced by using the dual continuum models. The Discrete Fracture Networks (DFN) approach involves analysis and modeling which explicitly incorporates the geometry and properties of discrete features as a central component controlling flow and transport. DFN are stochastic models of fracture architecture that incorporate statistical scaling rules derived from analysis of fracture length, height, spacing, orientation, and aperture. This study is focused on developing a methodology for application of DFN to a shale gas reservoir and the practical application of DFN simulator (FracGen and NFflow) for fracture modeling of a shale gas reservoir and also studies the interaction of the different fracture properties on reservoir response. The most important results of the study are that a uniform fracture network distribution and fracture aperture produces the highest cumulative gas production for the different fracture networks and fracture/well properties considered.

A rock mass is characterised by the properties of the intact rock and the fractures. Considering the impact of both constituents is of vital importance for assessing the behaviour of the rock mass. In particular in the case of complex or heterogeneous rock mass compositions. A discrete approach, by using the Discrete Fracture Network (DFN) methodology, enables for the consideration of these aspects.This master’s thesis concerns the evaluation of elastic properties of the Singö deformation zone. A discrete approach has been applied by three-dimensional discrete fracture network modelling, using previously evaluated DFN parameters. The elastic properties have then been obtained by analytical means by using the methodology developed by Davy et al. (2018).The results show that in comparison to earlier evaluations of the elastic properties of the Singö zone, the respective Young’s moduli and Poisson’s ratios obtained by this thesis may indicate a weaker material. However, this study differs from the earlier evaluation by more extensive DFN modelling and the application of a state of stress which is more representative of the surroundings of the zone in Forsmark. The analysis indicates that theadequate model size is slightly larger than the maximum studied DFN model size. A suggested future improvement would be a re-evaluation and updating of the DFN parameters. As a concluding remark, the methodology of Davy et al. (2018) may prove successful in the future for the application to deformation zones. / En bergmassa karakteriseras av egenskaperna hos det intakta berget och dess sprickor. Det är därmed av vikt att båda dessa beståndsdelar beaktas vid utvärdering av bergmassans beteende, speciellt vid komplexa eller heterogena bergartssammansättningar.Detta examensarbete syftar till att utvärdera deformationsegenskaper för den så kallade Singözonen. Ett diskret angreppsätt har tillämpats genom modellering av tredimensionella diskreta spricknätverk med hjälp av tidigare utvärderade DFN-parametrar. Deformationsegenskaperna har sedan utvärderats med hjälp av metodiken som presenteras i Davy et al. (2018).Jämfört med tidigare utvärderade deformationsegenskaper hos Singözonen så indikerar resultaten av denna masteruppsats en svagare bergmassa, med hänsyn till uppskattade värden på E-moduler och tvärkontraktionstal. Däremot skiljer sig modelleringsprocessen i detta arbete mot de som utförts i de tidigare studierna. Detta med hänsyn till omfattningen av DFN-modelleringen samt tillämpandet i detta arbete av en spänningsansats som är mer representativ för Forsmarksområdet. Vidare indikerar resultaten att den representativa modellvolymen är något större än den största modellvolym som tillämpats i detta arbete. Förslagsvis kan en utvärdering och eventuell uppdatering av de använda DFN-parametrarna utgöra en möjlig utveckling eller förbättring av det arbete som utförts i detta mastersarbete. Slutligen kan det konstateras att framtida tillämpningar av den metodik som tagits fram av Davy et al. (2018) verkar lämplig att applicera på deformationszoner.

[pt] Reservatórios de shale gas/shale oil possuem elevado grau de anisotropia devido à presença de fraturas naturais (NFs) e também da orientação dos estratos. Com isso as fraturas induzidas hidraulicamente (HFs) interagem com as NFs e geram uma rede de fraturas com morfologia complexa. A existência de NFs modifica o campo de tensões no folhelho e influencia diretamente o comportamento geomecânico das HFs durante a operação de fraturamento, gerando ramificações na fratura dominante e contribuindo para a formação da rede complexa de fraturas. A construção de uma rede de fraturas aumenta significativamente a condutividade da formação, pois conecta fraturas e poros que anteriormente encontravam-se isolados, incrementando assim o índice de produtividade dos poços e proporcionando maior viabilidade econômica nos projetos em reservatórios de shale gas/oil. Este trabalho apresenta uma análise de sensibilidade da influência do espaçamento entre fraturamentos na construção da rede de fraturas complexas gerada em shales, visando entender como este parâmetro modifica o volume de reservatório estimulado e a distribuição de propante na rede de fraturas, de maneira a evitar problemas nesta fase do projeto e assim, manter a sustentação da rede economicamente viável. A revisao de literatura contempla os principais trabalhos publicados sobre este tema e os modelos não-convencionais de fraturas (UFM) usados para a modelagem da rede de fraturas complexas. A análise de sensibilidade será realizada por meio do software MShale, que usa um método estocástico de rede de fraturas discretas (DFN) e resolve numericamente as equações de equilíbrio e da poroelasticidade para shales, em termos de tensões efetivas, além das equações de conservação de massa, momento linear e energia com dissipação viscosa para escoamento lento (creeping flow). Para a análise, os demais parâmetros que influenciam na contrução da rede serão mantidos constantes e somente o espaçamento entre fraturamentos sofrerá variação. / [en] Shale gas/shale oil reservoirs have a high degree of anisotropy due to the presence of natural fractures (NFs) and also the orientation of beddings. Thus, hydraulically induced fractures (HFs) interact with NFs and generate a network of fractures with complex morphology. The existence of NFs modifies the stress field in the shale and directly influences the geomechanical behavior of the HFs during the fracturing operation, generating branches in the dominant fracture and contributing to the complex network of fractures. The construction of a network of fractures significantly increases the conductivity of the formation, as it connects previously isolated fractures and pores, thus increasing the productivity index of the wells and providing greater economic viability in the shale gas/oil reservoir designs. This work presents a sensitivity analysis of the influence of fracturing spacing in the construction of the network of complex fractures generated in shales, aiming to understand how this parameter modifies the volume of stimulated reservoir and the distribution of propant in the network of fractures, in order to avoid problems in this step of the design and thus, maintain the economical viability of the network. The literature review includes the main published works on this subject and the non-conventional fracture models (UFM) used to model the network of complex fractures. Sensitivity analysis will be performed using the MShale software, which uses a stochastic of the discrete fracture network (DFN) method and numerically solves the equilibrium equations and poroelasticity for shales in terms of effective stresses, in addition to mass conservation equations, linear momentum and energy with viscous dissipation for creeping flow. For the analysis, the other parameters that influence the construction of the network will be kept constant and only the spacing between fracturings will suffer variation.

The transport and fate of contaminants in fractured sedimentary rock aquifers depends strongly on the nature and distribution of the fracture network. The current standard practice of using only vertical coreholes to characterize bedrock aquifers can result in significantly biased data that is insufficient for fracture orientation analysis. This study involves the addition of two inclined coreholes to supplement existing data from eleven vertical coreholes at a contaminated site in Guelph, Ontario to reduce the effects of this bias. A suite of high-resolution, depth discrete data collection methods including core logging, borehole geophysics, and hydraulic testing were conducted to determine fracture orientation and spacing as well as hydraulic aperture distributions. The results of the orientation analysis demonstrate that the inclined coreholes were more effective at sampling high-angled fractures than the vertical coreholes and were necessary to identify all three of the dominant fracture sets on the site. The fracture network properties from this study can be used as input parameters for static and dynamic discrete fracture network models to assess current and future risks to municipal supply wells.

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京都大学 / 0048 / 新制・論文博士 / 博士(工学) / 乙第13304号 / 論工博第4183号 / 新制||工||1728(附属図書館) / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 小池 克明, 教授 林 為人, 准教授 奈良 禎太 / 学位規則第4条第2項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23491号 / 工博第4903号 / 新制||工||1766(附属図書館) / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 小池 克明, 教授 岸田 潔, 准教授 奈良 禎太 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Les analyses structurale et mécanique des pentes rocheuses constituent des éléments clés pour l'évaluation de leur stabilité. L'utilisation complémentaire de la photogrammétrie et des modèles numériques qui couplent les réseaux discrets de discontinuités (DFN selon son sigle en anglais) avec la méthode des éléments discrets (DEM selon son sigle en anglais), présente une méthodologie qui peut être utilisée pour évaluer le comportement mécanique des configurations tridimensionnelles de terrain pour lesquelles l'existence de discontinuités non persistantes peut être supposée. La stabilité des masses rocheuses est généralement supposée être contrôlée par la résistance au cisaillement le long des plans de discontinuité. Si les discontinuités sont non persistantes, avec leur continuité interrompue par la présence de ponts rocheux (portions de roche intacte reliant la masse rocheuse au massif), leur résistance apparente augmente considérablement. Dans ce cas, la contribution des ponts rocheux localisés entre ces discontinuités doit être prise en compte dans l'analyse de stabilité. La déstabilisation progressive des massifs rocheux dans lesquels des discontinuités non persistantes sont présentes, peut être étudiée par des simulations numériques réalisées à l'aide de l'approche DEM. La roche intacte est représentée comme un assemblage de particules (ou éléments discrets) liées entre elles par des contacts dont les lois de comportement spécifiques peuvent être calibrées pour représenter correctement le comportement de la roche. L'intérêt de la méthode est qu'elle permet de simuler l'initiation de la rupture et sa propagation à l'intérieur de la matrice rocheuse du fait de la rupture des contacts cohésifs entre les particules. De plus, les discontinuités préexistantes peuvent être prises en compte explicitement dans le modèle en utilisant une loi de contact ad hoc qui assure un comportement mécanique représentatif des plans de discontinuité. Des analyses de stabilité ont été effectuées et ont mis en évidence le rôle des ponts rocheux dans la génération de nouvelles surfaces de rupture qui peuvent se développer à travers des mécanismes de rupture mixte en traction et en cisaillement. On peut considérer la formulation de Jennings comme l'une des premières méthodes d'analyse de la stabilité des pentes rocheuses qui évaluent la résistance au glissement comme une combinaison pondérée des résistances mécaniques des ponts rocheux et des plans de discontinuité. Sa validité a été discutée et systématiquement comparée aux résultats obtenus à partir de simulations numériques. Il a pu être montré que la formulation de Jennings perd sa validité dès que la rupture des ponts rocheux intervient majoritairement par des mécanismes de traction. Une formulation complémentaire a alors été proposée. En ce qui concerne l'étude de la stabilité des massifs rocheux sur site, il a été montré que l'association entre les données issues de la photogrammétrie en haute résolution et l'approche DFN-DEM peut être utilisée pour identifier des scénarios de rupture. L'analyse en retour de cas réels a montré que les surfaces de rupture peuvent être simulées comme le résultat de mécanismes combinant la fracturation des ponts rocheux et le glissement le long des discontinuités préexistantes. La rupture d'un dièdre qui a eu lieu dans une mine de charbon australienne, a été utilisée pour valider cette méthodologie. Des simulations numériques ont été réalisées pour déterminer les scénarios pour lesquels les surfaces de rupture simulées et celles repérées sur le terrain, peuvent être utilisés pour calibrer les paramètres de résistance du modèle numérique. Le travail présenté ici répond à un besoin plus général visant à améliorer la gestion des risques naturels et miniers liés aux masses rocheuses instables. La méthodologie proposée constitue une alternative robuste dédiée à renforcer la fiabilité des analyses de stabilité pour les pentes rocheuses fracturées à structure complexe. / Structural and mechanical analyses of rock mass are key components for rock slope stability assessment. The complementary use of photogrammetric techniques and numerical models coupling discrete fracture networks (DFN) with the discrete element method (DEM) provides a methodology that can be applied to assess the mechanical behaviour of realistic three-dimensional (3D) configurations for which fracture persistence cannot be assumed. The stability of the rock mass is generally assumed to be controlled by the shear strength along discontinuity planes present within the slope. If the discontinuities are non–persistent with their continuity being interrupted by the presence of intact rock bridges, their apparent strength increases considerably. In this case, the contribution of the rock bridges located in-between these discontinuities have to be accounted for in the stability analysis. The progressive failure of rock slope involving non–persistent discontinuities can be numerically investigated based upon simulations performed using a DEM approach. The intact material is represented as an assembly of bonded particles interacting through dedicated contact laws that can be calibrated to properly represent the behaviour of the rock material. The advantage of the method is that it enables to simulate fracture initiation and propagation inside the rock matrix as a result of inter-particle bond breakage. In addition, pre–existing discontinuities can be explicitly included in the model by using a modified contact logic that ensures an explicit and constitutive mechanical behaviour of the discontinuity planes. Stability analyses were carried out with emphasis on the contribution of rock bridges failure through a mixed shear-tensile failure process, leading to the generation of new failure surfaces. Jennings' formulation being considered to be one of the first rock slope stability analysis that evaluates the resistance to sliding as a weighted combination of both, intact rock bridges and discontinuity planes strengths, its validity was discussed and systematically compared to results obtained from numerical simulations. We demonstrate that the validity of Jennings' formulation is limited as soon as tensile failure becomes predominant and an alternative formulation is proposed to assess the resulting equivalent strength. Regarding field slope stability, we show that the combination of high resolution photogrammetric data and DFN-DEM modelling can be used to identify valid model scenarios of unstable wedges and blocks daylighting at the surface of both natural and engineered rock slopes. Back analysis of a real case study confirmed that failure surfaces can be simulated as a result of both fracture propagation across rock bridges and sliding along pre-existing discontinuities. An identified wedge failure that occurred in an Australian coal mine was used to validate the methodology. Numerical simulations were undertaken to determine in what scenarios the measured and predicted failure surfaces can be used to calibrate strength parameters in the model. The work presented here is part of a more global need to improve natural and mining hazards management related to unstable rock masses. We believe that the proposed methodology can strengthen the basis for a more comprehensive stability analysis of complex fractured rock slopes.