Connectivity Of Fracture Network Research Articles

The influence of subseismic-scale fracture interconnectivity on fluid flow in fracture corridors of the Brejões carbonate karst system, Brazil

The present study used a multitool approach to characterize fractures of several orders of magnitude in large fracture corridors, caves, and canyons to investigate their impact on fluid flow in carbonate units. The study area is the Brejões carbonate karst system that is located in the Neoproterozoic Salitre Formation in the Irecê Basin, São Francisco Craton, Brazil. The approach included satellite imagery, used for interpreting the regional structural context, Unmanned Aerial Vehicle (UAV) and ground-based Light Detection And Ranging (LiDAR) imagery, used for detailed structural interpretation. Regional interpretation revealed that fracture corridors, caves and canyons occur along a N–S-oriented anticline hinge. An advanced stage of karstification caused fracture enlargement and intrabed dissolution, and the formation of caves and canyons. A river captured by the highly fractured zone along the anticline hinge played an important role as an erosive agent. Detailed characterization of fracture corridors comprised structural analysis, topological studies, persistence estimations, power-law fitting of fracture trace length distributions, and identification of network backbones. Our results indicate that fracture corridors comprise four subvertical fracture sets: N–S and E-W and a conjugate pair, NNE-SSW and NW-SE. Fractures observed in the caves show the same dominant directions. Fracture directions are consistent with a common origin associated with the anticline folding. Fracture traces range from 1.0 m to 300 m, comprising both subseismic (<50 m) and seismic scale fractures (>50 m). Networks have dominance of node terminations Y and X (notably Y), CB values higher than 1.8, high P20 and P21 persistence values, and highly interconnected backbones. Fracture network connectivity is associated with power-law exponents greater than 2.5 for the fracture trace distributions, indicating large influence of subseismic-scale fractures on fluid flow. As the final result of folding and karstification, large volumes of secondary macroporosity were created, particularly in the zone of maximum fracture intensity around the hinge zone of the anticline. This scenario can be used to understand better oil reservoirs formed in similar structural controls in near-surface conditions.

The quantitative characterization of hydraulic fracture connectivity from a postmortem investigation

AbstractTwo bio-siliceous Onnagawa (ONG I and ONG II) shale samples have been hydraulically fractured under two constant differential stresses (60 and 85 MPa, respectively) to investigate the fracture network's connectivity evolution by a postmortem analysis. The pressure inside the drilled borehole in a cylindrical core sample is increased above the confining pressure (10 MPa) until failure by hydraulic fracture. The two samples failed at two different borehole pressures (ONG I: 42 MPa, ONG II: 16 MPa). Fractured samples were scanned in an industrial X-ray CT machine and the tomographic images of the fracture network were extracted for a postmortem investigation. From the fracture volume segments, obtained by thresholding the frequency distribution of the fracture network's voxel values, a quantitative estimation of fracture connectivity was carried out. The connectivity was quantified based on the relative entropy of size distribution of fractures (${H_r}$), a method adapted from information theory. Fracture connectivity estimation shows that ${H_r}$ is at a maximum value when the fractures show a significant distribution with very limited connectivity. The value of ${H_r}$ is at a minimum and close to 0 when a well-linked fracture network is formed. In both samples, this minimum was attained at the threshold of 43k indicating the highest connectivity and the best representation of the fracture network. The extracted fracture network of ONG I showed a multi-winged hydraulic fracture network while a planar conventional two-winged hydraulic fracture network had been generated in ONG II with a lower fracture volume.

Can we infer the percolation status of 3D fractured media from 2D outcrops?

Fractures and their connectivity are essential for fluid flow in low permeability formations. Geological outcrops can only provide two-dimensional (2D) information, but subsurface fractures are three-dimensional (3D). The percolation status of 3D fracture networks and their 2D cross-section maps are rarely investigated simultaneously. In this work, we construct 3D fracture networks with their geometries characterized by different stochastic distributions. Cross-section maps are taken to mimic real outcrops, and clusters are labeled to check the percolation status of 3D fracture networks and their 2D cross-section maps. The properties, reflecting the connectivity of two essential phases, are summarized and analyzed. We find that clustering effects impact local intersections significantly but have negligible impacts on fracture intensities of 3D fracture networks. The number of intersections per fracture is not a proper percolation parameter for complex 2D and 3D fracture networks. Real fracture networks in the subsurface should be geometrically well-connected and over-percolative if their outcrop maps have a spanning cluster formed. Empirical limits are provided to predict the fracture intensity and connectivity of subsurface 3D fracture networks based on their outcrop maps. If a spanning cluster is formed in the outcrop map, the corresponding 3D fracture networks should be over-percolative, and its fracture intensity can be larger than 3.5 times the intensity at percolation. However, if no spanning cluster is formed in the outcrop map, but the fracture intensity is larger than 0.43 times the intensity at percolation, the corresponding 3D fracture networks can form a spanning cluster and show good connectivity.

Topological Representative Element Volume of Fractured Rock Mass

The representative element volume (REV) of the fractured rock mass is the basis for its homogenization, and is essential for the study of groundwater seepage. In order to determine a simple method for estimating REV, we studied the topological characteristics of the fractured network. We propose the concept of topological representative element volume (TREV) for estimating the fractured rock mass. The topological structure can reflect many properties of the fractured rock mass, to which a great deal of attention has been paid. We examine the applicability of eleven topological parameters as the equivalent parameters of the TREV. According to the selected equivalent parameter, the TREV of twenty-three kinds of fractured rock mass were calculated and then compared with the permeability representative element volume (PREV). The results show that the size of TREV and PREV are essentially the same for a given rock mass. In other words, the PREV can be estimated accurately using the TREV for the rock mass with orthogonal connected fracture networks. The advantage of using TREV to estimate PREV is that there is no need for complex seepage calculations, as the calculation of TREV only needs to account for the geometric characteristics of the fracture network.

An integrated UAV photogrammetry-discrete element investigation of jointed Triassic sandstone near Sydney, Australia

Over the last decade, UAV Structure-from-Motion photogrammetry and digital rock mass mapping tools have been rapidly adopted into geotechnical engineering practice. As computing power has increased, numerical models and remote sensing methods have become more sophisticated, and much research has been applied to the development of digital rock mass classification and data collection methods. This investigation presents a case study of UAV photogrammetry mapping, discrete fracture network analysis and discrete element method modelling of jointed sandstone exposed in coastal cliffs and wave-cut platforms near Sydney, Australia. The aim of the study is to investigate a selection of digital mapping and numerical modelling approaches for rock mass geomechanical characterisation. A cohesive workflow is presented for UAV photogrammetry survey, discontinuity mapping, simulation of rock mass scale laboratory tests, and 3D DFN simulations of roof reinforcement in a large-span road tunnel.Digital discontinuity mapping is undertaken using two different software tools, and results are compared with historical conventional mapping. A novel GIS-based workflow is demonstrated to interrogate the mapping data, using a cellular grid approach to measure fracture intensity and fracture network connectivity. The discontinuity statistics are used as inputs to a series of 3D discrete element method numerical UCS, triaxial, and biaxial load tests that investigate the rock mass anisotropy and the impact of confining stress on rock mass shear strength, stiffness, and failure mechanisms. Next, the mapping data are applied to DFN simulations of a 31 m span tunnel, based on upcoming proposed road tunnels in Sydney. The tunnel simulations show how predicted displacements in the tunnel roof are proportional to fracture intensity.

Evolution of fracture networks and connectivity during fault–bend folding: Insights from the Sinon Anticline in the southwestern Hongseong–Imjingang Belt, Korea

Crustal shortening in an elastico-frictional regime is mainly accommodated by contractional fault–fold systems with fracture networks. According to recent research, fracture networks in fold–thrust belts express complex internal strain states in response to thrusting and related folding. Furthermore, their connectivity and fluid flow characteristics likely depend on the structural positions and mechanical stratigraphy that control heterogeneous deformation processes. This study provides characteristics of fold-related fracture networks in the Sinon Anticline, which was formed by fault–bend folding in the southwestern Hongseong–Imjingang Belt, Korea. The fracture networks in the metamorphosed turbidites characterized by interbedded competent metasandstone layers and relatively thin incompetent schist layers have evolved through pre-, syn-, and post-folding fracturing events. Their complexity reflects the spatiotemporal variation in the strain pattern related to early layer-parallel shortening and subsequent fault–bend folding. Based on insights from detailed mapping and topological analysis of the fracture network, we conclude that strain partitioning that occurs during flexural folding results in a superposed tangential longitudinal strain expressed by fractures with a high (hydraulic) connectivity in the hinge zones. Strain partitioning is caused by flexural interlayer slip along incompetent schist layers in the fold limbs. Bed-parallel slip localization zones probably have low porosity and permeability and may act as barriers to fluid migration across beds. We suggest that heterogeneous vertical axis rotation, which occurred as the system's hanging wall slid over the footwall ramp, increased the complexity of fracture networks within the Sinon Anticline. Our findings indicate that the evolution, connectivity, and fluid flow properties of fracture networks can be characterized through careful interpretation of folding mechanisms and related strain states during formation of fault–bend fold systems.

Factors controlling the formation of complex fracture networks in naturally fractured geothermal reservoirs

Economic and efficient energy production from enhanced geothermal systems in naturally fractured rocks depends on the stimulation of natural fractures by hydraulic fractures to generate complex connected fracture networks. This fracture network provides pathways for maintaining high fluid injection and production rates which lead to high heat extraction rates. However, little work has been conducted to describe the formation of these complex fracture networks formed by the interaction of multiple hydraulic fractures with natural fractures. This paper presents a dynamic (time dependent), fully coupled hydraulic fracturing model that is capable of capturing fracture propagation, fracture deflection, the interaction between propagating hydraulic fractures and pre-existing natural fractures and fluid flow inside the fractures. The proposed model is validated against an analytical model for a penny-shaped hydraulic fracture. This model is then applied to conduct a detailed parametric study to investigate the effect of pre-existing natural fracture networks on the connectivity and propagation of hydraulic fractures. The orientation, length distribution, width distribution and connectivity of the created fracture network is studied. Simulation results indicate that: (1) the hydraulic fracture network is oriented in the direction of the dominant natural fracture network when the length of the natural fractures is large, and this leads to a large connected fracture area; (2) If the hydraulic fracture propagates at a large angle to the natural fractures, it results in a smaller connected fracture area and a complicated hydraulic fracture network that is dominated by shear failure events; (3) Natural fracture density plays a dominant role in the propagation direction of hydraulic fractures and the resulting connected fracture area; (4) Increasing the injection rate increases the connected fracture area and width while creating more complex hydraulic fracture networks and leads to more fracture dilation and less shear opening of cracks. The detailed parametric study helps us better understand the creation of fracture networks and can serve to guide us in hydraulic fracture design and optimization in naturally fractured geothermal reservoirs.

Controlling Factors on the Development and Connectivity of Fracture Network: An Example from the Baekildo Fault in the Goheung Area

Controlling Factors on the Development and Connectivity of Fracture Network: An Example from the Baekildo Fault in the Goheung Area

بررسی تاثیر شبکه شکاف گسسته بر رفتار فشارگذرای محیط متخلخل شکافدار

The most famous theory for analyzing the pressure data of NFRs is the dual-porosity model presented by Warren and Root. Recent studies have shown that the dual-porosity model because of restricting assumptions may not be appropriate for interpreting well test from all NFRs. In this study, the pressure transient response of naturally fractured reservoirs was investigated using numerical simulation without considering analytical and semi-analytical methods. To this end, a set of models, including connected and disconnected fracture networks, was simulated in Eclipse software. The Warren and Root's well-testing signature was observed in all simulations but is was highly obvious for a well is located in the matrix and was negligible for a well is intersected by fractures. Because this phenomenon happens quickly for a well is intersected by fractures, and it's virtually impossible to record such an event in reality. The results of the simulation for a well is intersected by fractures showed a bilinear flow regime with a slope of 1/4. The period of this flow regime increased in the unconnected fracture network and changed to the linear flow regime with a slope of 1/2 in two cases 1: increasing fracture permeability in the connected fracture network 2- small-unconnected fractures. Moreover, the sensitivity analysis was performed on the well location in a connected fracture network. Results showed that by decreasing the well distance to the fracture network, the transition period becomes deeper and appears earlier.

Numerical modeling of fluid flow in tight oil reservoirs considering complex fracturing networks and Pre-Darcy flow

Multistage hydraulic fracturing for horizontal wells is extensively applied in the exploitation of tight oil reservoirs. Complex fracture networks with different scales are created and hydrocarbon flowing in the matrix demonstrates a Pre-Darcy characteristic due to a strong interaction of rock and fluids in nanoscale pores. The modeling of complex fracture networks and a Pre-Darcy effect is required in numerical simulation of tight oil reservoirs. In this paper, stochastic fracture networks are employed to mimic actual fracturing networks according to the corresponding probability density functions (PDFs), and microseismic events are used to constrain the locations of fractures. The numerical simulation for tight oil reservoirs is developed by considering complex fracture networks and the Pre-Darcy effect based on an embedded discrete fracture model (EDFM) framework. Finally, the influences of fracture network properties including isolated fractures, connected fracture networks and the Pre-Darcy effect on well production are investigated via integrating the developed fracture network generation and tight oil numerical simulator. The results indicate that for isolated fractures with no direct connection with a wellbore, there is little influence on well performance. The influence becomes more obvious when isolated fractures connect to a wellbore, and an increase in fracture length and conductivity can enhance well performance especially when fractures lie off streamline lines. Similarly, for a connected fracture network, an increase in fracture network properties (number, length and conductivity) can promote well performance and fractures perpendicular to a horizontal wellbore can generate a maximal flow rate compared with other fracture orientations. The fracture network connectivity plays an important role in the fluid flow, and there are good relationships between well production and two proposed parameters, which can be treated as candidates to characterize the flow characteristics in fractured reservoirs.

Impact of Fracture Geometry and Topology on the Connectivity and Flow Properties of Stochastic Fracture Networks

AbstractIn a low permeability formation, connectivity of natural and induced fractures determines overall hydraulic diffusivity in fluid flow through this formation and defines effective rock permeability. Efficient evaluation of fracture connectivity is a nontrivial task. Here, we utilize a topological concept of global efficiency to evaluate this connectivity. We address the impact of key geometrical properties of stochastic fracture networks (fracture lengths, orientations, apertures, and positions of fracture centers) on the macro‐scale flow properties of a shale‐like formation. Six thousand different realizations have been generated to characterize these properties for each fracture network. We find that a reduced graph of a fracture network, which consists of the shortest paths from the inlet nodes (fractures) to all outlet nodes, contributes most to fluid flow. Three‐dimensional (3D) fracture networks usually have higher global efficiency than two‐dimensional (2D) ones, because they have better connectivity. All geometrical properties of fractures influence quality of their connectivity. Aperture distribution impacts strongly global efficiency of a fracture network and its influence is more significant when the system is dominated by large fractures. Fracture clustering lowers global efficiency in both 2D and 3D fracture networks. Global efficiency of 2D and 3D fracture networks also decreases with the increasing exponent of the power‐law distribution of fracture lengths, which means that the connectivity of the system decreases with an increasing number of small fractures. Realistic fracture networks, composed of several sets of fractures with constrained preferred orientations, share all the characteristics of the stochastic fracture networks we have investigated.

Transport and Localization of Elastic Waves in Two‐Dimensional Fractured Media: Consequences on Scattering Attenuation

AbstractWe present numerical simulations of elastic wave transport in two‐dimensional fractured media. Natural fracture systems, following a power‐law length scaling, are modeled by the discrete fracture network approach for geometrically representing fracture distributions and the displacement discontinuity method for mechanically computing fracture‐wave interactions. The model is validated against analytical solutions for wave reflection, transmission, and scattering by single fractures, and then applied to solve the wavefield evolution in synthetic fracture networks. We find that the dimensionless angular frequency ῶ = ωZ/κ plays a crucial role in governing wave transport, where ω, Z, and κ are the angular frequency, seismic impedance, and fracture stiffness, respectively. When ῶ is smaller than the critical frequency ῶc (≈5), waves are in the extended mode, either propagating (for small ῶ) or diffusing by multiple scattering (for intermediate ῶ); as ῶ exceeds ῶc, waves become trapped, entering either the Anderson localization regime (kl* ≈ 1) in well‐connected fracture systems or the weak localization regime (kl* &gt; 1) in poorly‐connected fracture systems, where k is the incident wavenumber and l* is the mean free path length. Consequently, the inverse quality factor Q−1 scales with ῶ obeying a two‐branch power‐law dependence, showing significant frequency dependence when ῶ &lt; ῶc and almost frequency independence when ῶ &gt; ῶc. Furthermore, when ῶ &lt; ῶc, the wavefield exhibits a weak dependence on fracture network geometry, whereas when ῶ &gt; ῶc, the fracture network connectivity has an important impact on the wavefield such that strong attenuation occurs in well‐connected fracture systems.

Quantitative characterization of irregular microfracture network and its effect on the permeability of porous media

Based on the comprehensive understanding on microfractures and matrix pores in reservoir rocks, numerical algorithms are used to construct fractured porous media and fracture-pore media models. Connectivity coefficient and strike factor are introduced into the models to quantitatively characterize the connectivity and strike of fracture network, respectively. The influences of fracture aperture, fracture strike and fracture connectivity on the permeability of porous media are studied by using multi-relaxation-time lattice Boltzmann model to simulate fluid flow in them. The greater the strike factor and the smaller the tortuosity of the fractured porous media, the greater the permeability of the fractured porous media. The greater the connectivity coefficient of the fracture network is, the greater the permeability of the fracture-pore media is, and the more likely dominant channel effect occurs. The fracture network connectivity has stronger influence on seepage ability of fracture-pore media than fracture aperture and fracture strike. The tortuosity and strike factor of fracture network in fractured porous media are in polynomial relation, while the permeability and fracture network connectivity coefficient of the fracture-pore media meet an exponential relation.

3D Multi-scale Reconstruction of Fractured Shale and Influence of Fracture Morphology on Shale Gas Flow

Quantitative characterization of shale gas flow in fractured shale is a key problem in shale gas extraction. In this study, 3D multi-scale structures in fractured shale were reconstructed, firstly, by X-ray micro-computerized tomography (CT), high-resolution scanning electron microscope (SEM), and fractal function. Then, a REV (representative elementary volume)-scale lattice Boltzmann (LB) model, considering Klinkenberg’s effect and gas absorption, was built, and the effects of fracture complexity and gas pressure on shale gas flow and shale permeability were analyzed and studied quantitatively. The simulation results indicate that the gas flow behaviors in the fractured shale are related strongly to fracture morphology and gas pressure. The decreased fracture fractal dimension or increased complexity of the fracture network leads to increase in permeability of the fractured shale. The gas velocity in the shale matrix decreases with increasing fracture roughness. Increased fracture network connectivity contributes to the formation of local high-intensity velocity fields and the improvement of gas flow in the shale matrix. The gas rarefaction effect has a significant influence on gas flow in the fractured shale, and permeability of the fractured shale must be regarded as a dynamic shale reservoir parameter. The gas flow behavior in the fractured shale is more sensitive at low-pressure condition whereas the gas rarefaction effect is more sensitive to the fractured shale with highly rough fracture or low fracture connectivity.

How wide is a fault damage zone? Using network topology to examine how fault-damage zones overprint regional fracture networks

Topological analysis of networks of linear features has recently gained popularity in structural geology, as it provides a robust system of fracture network characterisation with consistent terminology. This approach has mainly been applied by using discontinuous sample areas to characterise topology of a region, or geological feature (e.g. Procter and Sanderson, 2018). We apply network topology to investigate spatial variation of a natural fracture network in the damage zone of the Castle Cove Fault, Otway Basin, Victoria. The Castle Cove Fault's associated fracture network occurs in the hanging-wall Eumeralla Formation, a fine-to medium-grained volcanogenic sandstone or Early Cretaceous age. Topological characterisation of the Castle Cove Fault damage-zone identified an increase in the two-dimensional intensity of fracturing in the hanging-wall at a distance 70 m from the fault, reaching a maximum ~40 m from the fault, indicating the extent of the fault-damage zone is between 40 and 70 m from the main fault. Maximum fracture intensity values decay with a power law relationship with respect to distance from the fault plane, averaging ~0.06 adjacent to the fault, and ~0.02 within what is interpreted as the regional fracture network, 70 m + outboard of the fault. Fracture orientations in the damage zone are synthetic and antithetic with respect to the ~60° dip to the NW of the of the Castle Cove Fault, with these fault-related fractures overprinting an existing regional fracture network, creating high fracture network connectivity within the fault-damage zone. Our results show that network topology is a powerful tool for quantifying and visualising the properties of fracture networks associated with crustal-scale faults.

The Investigation of Fracture Networks on Heat Extraction Performance for an Enhanced Geothermal System

Hydraulic fracturing is usually employed to create a complex fracture network to enhance heat extraction in the development of an enhanced geothermal system. The heat extraction depends on the heat conduction from the rock matrix to the flowing fractures and the heat convection through a complex fracture network. Therefore, the geometries of the fracture network have important influences on the thermal breakthrough. In this paper, a hydro-thermal coupling mathematical model considering a complex fracture network is established. The embedded discrete fracture model is adopted to explicitly model the individual fracture on the mass flow and heat transfer. The model is validated by analytical solutions. Fracture network parameters are changed systematically to investigate the effects of fracture network distribution including regular and complex shape on the thermal production performance. The results show that the increase of producing pressure differential, fracture number, and conductivity will cause an early thermal breakthrough. The strong variation in fracture conductivity, as well as spacing and orientation, will cause thermal flow channeling and decrease the efficiency of heat extraction. A modified connectivity field is proposed to characterize the spatial variation of fracture network connectivity, which can be used to infer the thermal flow path.

Estimating effective permeability using connectivity and branch length distribution of fracture network

In this study, a new approach to estimate the effective permeability of the fracture network is proposed. New functional expressions are derived considering laminar fluid flow through fracture networks. Effective permeability of the fracture network is expressed as a function of topological connectivity, statistical branch segment length distributions, maximum, and minimum branch segment lengths. It is observed that the statistical cumulative branch segment length distribution of fracture networks can follow both fractal and multi-fractal patterns. Hence, analytical expressions of effective permeability are proposed considering both fractal and multi-fractal distribution of branch segment lengths. Obtained expressions are validated using numerical simulation results from past studies. It is observed from derived expressions that, effective permeability of fracture networks increases non-linearly with increasing topological connectivity and fractal dimensions of statistical branch segment length distributions. However, the non-linearity in the relationship is mainly governed by the scaling exponent and scaling coefficient of the fracture network. With increasing scaling exponent and scaling coefficient, non-linearity in the relation between effective permeability and topological connectivity increases. It is observed from the derived relation that, effective permeability of a fracture network is more sensitive to longer branch segments compared to the shorter branch segments. Effective permeability of fracture networks increases rapidly with increase in length of the branch segments. Hence it is interpreted, longer branch segments in fracture networks play a critical role in determining the effective permeability of the fractured reservoir.

Modelling fluid injection-induced fracture activation, damage growth, seismicity occurrence and connectivity change in naturally fractured rocks

We develop a fully-coupled hydro-mechanical model to simulate fluid injection-induced activation of pre-existing fractures, propagation of new damages, development of seismic activities, and alteration of network connectivity in naturally fractured rocks. The natural fracture system is represented by a discrete fracture network. The stress and strain fields of the fractured porous media are solved in the framework of a finite element model, which mimics the damage evolution in rock matrix based on an elasto-brittle failure criterion and simulates the normal/shear displacement of natural discontinuities based on a non-linear constitutive law. The coupled geomechanics and fluid flow processes in the fractured rock are computed honouring essential coupling mechanisms such as pore pressure-induced shear slip of pre-existing fractures, poro-elastic response of rock matrix, and stress-dependent permeability/storativity of both fractures and rocks. We use the numerical model developed to investigate the hydro-mechanical behaviour of two cases of deeply buried fractured rock in response to high-pressure fluid injection, one case with fracture density just below the percolation threshold and the other above the threshold. We observe a strong control of natural fracture network connectivity on the damage emergence, seismicity occurrence and connectivity change in the rock mass subject to hydraulic stimulation. We also highlight the strong poro-elastic effect that tends to drive heterogeneous connectivity evolution of fracture systems during fluid injection. The results of our research and insights obtained have important implications for injection-related geoengineering activities such as the development of enhanced geothermal systems and extraction of hydrocarbon resources.

A Coupled Flow–Geomechanical Modeling of Out-of-Sequence Fracturing Using a Dual-Lattice Implementation of Synthetic-Rock-Mass Approach

Summary In out-of-sequence (OOS) pinpoint fracturing, Stage 1 is fractured, followed by Stage 3, after which Stage 2 (center fracture) is placed between Stages 1 and 3 (outside fractures). The center fracture can exploit the reduced stress anisotropy to activate planes of weakness (e.g., fissures) and create branch fractures that can connect hydraulic fractures to stress-relief fractures, ultimately enhancing fracture connectivity and complexity. It has been trialed in western Siberia (2014) and western Canada (2017 to 2019) with overall operational and production performance success. Previous fracture-modeling works calibrated by OOS fracturing trials have either used shear-decoupled planar-fracture models (in which slippage along the shear planes restricts the displacement to a limited area because of displacement damping)—which are unable to reproduce out-of-plane fracture complexity, and to dynamically track the change in stress anisotropy and orientation—or discrete-fracture-network (DFN) models, which often exaggerate the fracture-network connectivity, and reproduce unrealistically high fracture-network-extension pressures in the stimulated reservoir volume (SRV). This work attempts to resolve the issues in planar-fracture and DFN models by more realistically addressing the dominant mechanisms of OOS fracturing, dynamic changes in the stress anisotropy and orientation, activation of pre-existing planes of weaknesses, and poroelasticity using an iteratively coupled flow–geomechanical model that uses the dual-lattice implementation of the synthetic-rock-mass (SRM) model with a robust, fully coupled, iterative flow/stress solution to capture the following: Nonlinear deformations caused by induced tensile- and shear-fracture-complexity propagation Induced stress shadowing in and around the SRV Sliding of opened, pre-existing joints, fractures, and fissures using the smooth-joint model (SJM) Propagation of the hydraulic fracture as an aggregate of intact matrix fracturing and opening and slip of pre-existing fluid-filled planes of weakness (e.g., joints, fractures, fissures) Permeability enhancement in the main tensile and complex fractures following the updated deformation aperture from the coupled solution The results (fracture geometries and treatment pressures) of the three models (planar-fracture, DFN, and SRM with lattice models) are compared after using each model for treatment-pressure history matching of an OOS-fracturing trial. The calibrated, coupled SRM with lattice model more reasonably reproduces the measured fracture-extension pressures and end-of-job pressures from OOS pinpoint fracturing treatments, and it reveals the following: The dynamic change in the stress-field orientation and magnitude during OOS fracturing leads to a reduction in stress anisotropy and complex out-of-plane fracturing in the SRV for center fractures. Center fractures tend to be narrower and shorter if sufficient out-of-zone growth is attained in the absence of strong vertical containment, making OOS fracturing an option for penetrating multistacked zones in one treatment. Where center fractures are shorter or near-well fracture complexity is generated, OOS fracturing can be considered in treating the child wells to reduce fracture hits. Compared with planar-fracture and DFN models, this coupling technique achieves the following: Accounts for dominant mechanisms of complex shear and tensile fracturing Renders fast computation in simulating large 3D models with dual-lattice implementation of SRM with SJM Reproduces fracture surface area and SRV permeability more realistically Leads to a more reasonable history match of the measured OOS-fracturing pressures

A Method to Represent a Well in a Three-Dimensional Discrete Fracture Network Model.

In discrete fracture network (DFN) modeling, fractures are randomly generated and placed in the model domain. The rock matrix is considered impermeable. Small fractures and isolated fractures are often ignored to reduce computational expense. As a result, the rock matrix between fractures could be large and intersections may not be found between a well introduced in the model and the hydraulically connected fracture networks (fracture backbones). To overcome this issue, this study developed a method to conceptualize a well in a three-dimensional (3D) DFN using two orthogonal rectangular fractures oriented along the well's axis. Six parameters were introduced to parameterize the well screen and skin zone, and to control the connectivity between the well and the fracture backbones. The two orthogonal fractures were discretized using a high-resolution mesh to improve the quality of flow and transport simulations around and along the well. The method was successfully implemented within dfnWorks 2.0 (Hyman et al. 2015) to incorporate a well in a 3D DFN and to track particles leaving an injection well and migrating to a pumping well. Verification of the method against MODFLOW/MODPATH found a perfect match in simulated hydraulic head and particle tracking. Using three examples, the study showed that the method ensured the connectivity between wells and fracture backbones, and honored the physical processes of flow and transport along and around wells in DFNs. Recommendations are given for estimating the values of the six introduced well parameters in a real-world case study.