Stochastic Discrete Fracture Network Research Articles

Parameter Sensitivity Analysis for Long-Term Nuclide Migration in Granite Barriers Considering a 3D Discrete Fracture–Matrix System

As a geological barrier for high-level radioactive waste (HLW) disposal in China, granite is crucial for blocking nuclide migration into the biosphere. However, the high uncertainty associated with the 3D geological system, such as the stochastic discrete fracture networks in granite, significantly impedes practical safety assessments of HLW disposal. This study proposes a Monte Carlo simulation (MCS)-based simulation framework for evaluating the long-term barrier performance of nuclide migration in fractured rocks. Statistical data on fracture geometric parameters, on-site hydrogeological conditions, and relevant migration parameters are obtained from a research site in Northwestern China. The simulation models consider the migration of three key nuclides, Cs-135, Se-79, and Zr-93, in fractured granite, with mechanisms including adsorption, advection, diffusion, dispersion, and decay considered as factors. Subsequently, sixty MCS realizations are performed to conduct a sensitivity analysis using the open-source software OpenGeoSys-5 (OGS-5). The results reveal the maximum and minimum values of the nuclide breakthrough time Tt (12,000 and 3600 years, respectively) and the maximum and minimum values of the nuclide breakthrough concentration Cmax (4.26 × 10−4 mSv/a and 2.64 × 10−5 mSv/a, respectively). These significant differences underscore the significant effect of the uncertainty in the discrete fracture network model on long-term barrier performance. After the failure of the waste tank (1000 years), nuclides are estimated to reach the outlet boundary 6480 years later. The individual effective dose in the biosphere initially increases and then decreases, reaching a peak value of Cmax = 4.26 × 10−4 mSv/a around 350,000 years, which is below the critical dose of 0.01 mSv/a. These sensitivity analysis results concerning nuclide migration in discrete fractured granite can enhance the simulation and prediction accuracy for risk evaluation of HLW disposal.

Impacts of T-type intersections on the connectivity and flow in Complex two-dimensional fracture networks

Natural fractures usually form T-type intersections, but the impacts of T-type intersections on the connectivity and flow results (such as permeability and fluid production) in complex fracture networks are rarely investigated. Here, a stochastic discrete fracture network method is implemented to construct complex two-dimensional fracture networks, denoted as original fracture networks. By implementing the rule-based fracture growth algorithm, the corresponding kinematic fracture networks are generated with a substantial proportion of T-type intersections. The connectivity and flow results of both the single-phase and two-phase flow simulations in these two types of fracture networks are systematically investigated. The results show that kinematic fracture networks tend to connect more fractures with fewer intersections and yield better connectivity than the original ones. Most kinematic fracture networks have larger permeability in the single-phase flow simulation and higher cumulative gas production in the two-phase flow simulation than original fracture networks under the same boundary conditions. The proportions of permeability and production enhancement are 68% and 77%, respectively. Flow results have strong positive correlations with the connectivity of fracture networks, but they are nonequivalent and strongly impacted by the number of inlets and outlets.

Characterization of a fractured rock mass using geological strength index: A discrete fracture network approach

Rock mass contains siginificant heterogeneity due to the presence of structural discontinuities. The failure in the rock mass may cause a serious concern to road and rail transportation. Rock mass characterization is a first step towards preliminary investigation for road or tunnel excavations. Different field-based methods have been developed to characterize the rock mass conditions. The Geological Strength Index (GSI) is a simple and commonly adopted method with wide applicability in rock engineering. Traditional approaches are limited to 2D exposures for mapping purposes, but block formation or joint intersection is a 3D parameter. The advancement in computational techniques led to significant involvement of numerical modeling techniques such as those backed with discrete fracture network (DFN). The remote sensing techniques render the data with high precession potential not accessible with conventional methods. The stochastic DFNs generated based upon the statistical distribution of the input parameters can represent the natural fracture system in 3D. The developed synthetic fracture network can be used to examine the rock mass characteristics. This work addresses the incorporation of the Discrete Fracture Network (DFN) in the estimation of the Geological Strength Index (GSI) of the rock mass. The work compares the results of DFN generated using aggregate and disaggregate approaches in block size distribution (BSD) and rock quality designation (RQD) measurements for a fractured slope. The calculated BSD and RQD using DFN and field-estimated joint condition parameter are used to estimate GSI of the rock mass. A machine learning based python GUI tool was developed to find GSI from block volume and joint condition parameters. The prediction of GSI from input parameters using machine learning has led to systematically digitizing the standard GSI chart.

An optimum solution for coal permeability estimation from mesoscopic scale calibrated stochastic and deterministic discrete fracture network models

The efficiency of a coal bed as a reservoir of methane and CO2 sink primarily depends on its fracture permeability. Conventional techniques of permeability estimation from drilled-core plugs in the laboratory and analytical computations are often different from in-situ measurements by multiple orders. Hence, pre-drill estimation of coal bed permeability remains one of the major challenges for the operators. Researchers usually try to solve this issue by building DFN models based on the direct use of µCT images of millimeters scale coal chips. However, such small-scale DFN models also overestimate permeability by many folds. As a solution, we propose the deployment of calibrated Discrete Fracture Network (DFN) modeling technique based on mesoscale coal images. Deterministic and stochastic DFN models are simulated by replicating thirteen coal specimens collected from the Gondwana coal seams in the Raniganj coalfield of India. Different model outputs such as directional permeabilities, permeability anisotropy, connectivity, etc. are used to distinguish and calibrate these models. The derived average permeabilities from these models closely match with available field measurements. Thus, the proposed technique helps in minimizing the huge gap between the laboratory and well-test measurements. In the process, we derive the threshold sample/model size that would sufficiently address the average cleat permeability at the well-drainage scale. Additionally, sensitivity analysis of key fracture attributes is carried out to quantify their effect on coal permeability.

Complexity analysis of three-dimensional stochastic discrete fracture networks with fractal and multifractal techniques

Systematic analysis of the complexity of fracture systems, especially for three-dimensional (3D) fracture networks, is largely insufficient. In this work, we generate different fracture networks with various geometries with a stochastic discrete fracture network method. The fractal dimension (D) and the singularity variation in a multifractal spectrum (Δα) are utilized to quantify the complexity of fracture networks in different aspects (spatial filling and heterogeneity). Influential factors of complexity, including geometrical fracture properties and system size, are then systematically studied. We generalize the analysis by considering two critical (percolative and over-percolative) stages of fracture networks. At the first stage, κ (fracture orientation) is the most significant parameter for D, following a (fracture length) and L (system size). FD (fracture positions) has a weak correlation with D but a strong correlation with Δα. At the second stage, the sensitivity results of each geometrical parameter and the system size are the same as in stage one for D. For Δα, κ and FD become more significant. For both stages, there is a weak finite-size effect for D and no finite-size effect for Δα. Therefore, a large fracture system is more suitable for a stable fractal dimension estimation, but no requirement for the estimation of Δα. D and Δα are almost independent. Therefore, they can separately quantify different aspects of complexity.

Hydrothermal Numerical Simulation of Injection Operations at United Downs, Cornwall, UK

The United Downs Deep Geothermal Project (UDDGP) is designed to utilize a presumably permeable steep dipping fault damage zone (constituting the hydrothermal reservoir in a very low permeability granitic host rock) for fluid circulation and heat extraction between an injection well at 2.2 km depth (UD−2) and a production well at 5 km depth (UD−1). Soft hydraulic stimulation was performed to increase the permeability of the reservoir. Numerical simulations are performed to analyze the hydraulic stimulation results and evaluate the increase in permeability of the reservoir. Experimental and field data are used to characterize the initial reservoir static model. The reservoir is highly fractured, and two distinct fracture networks constitute the equivalent porous matrix and fault zone, respectively. Based on experimental and field data, stochastic discrete fracture networks (DFN) are developed to mimic the reservoir permeability behavior. Due to the large number of fractures involved in the stochastic model, equivalent permeability fields are calculated to create a model which is computationally feasible. Hydraulic test and stimulation data from UD−1 are used to modify the equivalent permeability field based on the observed difference between the real fractured reservoir and the stochastic DFN model. Additional hydraulic test and stimulation data from UD−2 are used to validate this modified permeability. Results reveal that the equivalent permeability field model derived from observations made in UD−1 is a good representation of the actual overall reservoir permeability, and it is useful for future studies. The numerical simulation results show the amount of permeability changes due to the soft hydraulic stimulation operation. Based on the validated permeability field, different flow rate scenarios of the petrothermal doublet and their respective pressure evolution are examined. Higher flow rates have a strong impact on the pressure evolution. Simulations are performed in the acidized enhanced permeability region to make a connection between the ongoing laboratory works on the acid injection and field response to the possible acidizing stimulation.

Impacts of fracture properties on the formation and development of stimulated reservoir volume: A global sensitivity analysis

Stimulated reservoir volume (SRV), the highly permeable fracture network created by hydraulic fracturing, is essential for fluid production from low-permeable reservoirs. However, the configuration of SRV and its impacting factors are largely unknown. In this work, we adopt the stochastic discrete fracture network method to mimic natural fractures in subsurface formations and conduct a global sensitivity analysis with the Sobol method. The sensitivity of different fracture properties, including geometrical properties (fracture lengths, orientations, and center positions), mechanical properties (fracture roughness and fracture strength), fracture sealing properties (probabilities of open fractures and segment lengths), and the fracture intensity, are investigated in two and three-dimensional fracture networks. JRC-JCS model is adopted to identify critically stressed fractures. We find that critically stressed fractures compose the backbone of SRV, while partially open fractures can significantly enlarge the size of SRV by connecting more critically orientated fractures. The fracture roughness is the most influential factor for the total length (area) of critically stressed fractures. For the relative increase of SRV (RI) in 2D/3D fracture networks, the probability of open fractures is the most significant factor. The fracture lengths and center positions are essential factors for RI in 2D fracture networks but insignificant in 3D fracture networks. This work provides a realistic scenario of the subsurface structure and systematically investigates the influential factors of SRV, which is useful for estimating the size of SRV and predicting shale gas reservoirs’ production in an accurate and physically meaningful way.

On the Influence of Sampling Scale on the In Situ Block Size Distribution

The modelling of discontinuities in rock mass is undertaken with different measurement techniques and used to determine the in situ block size distribution (IBSD). Two monitoring techniques are employed: televiewer logging of boreholes and photogrammetry of highwall faces in a quarry bench; televiewer performs at the borehole diameter scale, while photogrammetry surveys at the entire bench scale. Ground sampling distances were, respectively, about 1 and 8.5 mm. The discontinuities are modelled as a stochastic discrete fracture network (DFN), with the number of discontinuities used in the simulation calibrated by the intensity per unit length (P10) on the televiewer data, or by the fracture density (P21) on the photogrammetry data, leading to different fracture networks. From the discontinuity network models, the IBSDs are calculated and discussed as function of the sampling scale (i.e. televiewer or photogrammetry data source) and of the fracture density. The goal is to compare the results from both techniques for rock mass structural characterization, to assess their limitations and shortcomings, and to show their potential complementarity at different sampling scales. The televiewer data provides smaller block sizes than the photogrammetry, following the higher number of fractures observed in the former. All volumetric distributions obtained are extremely well represented by Gamma with a power law tail distribution. Despite different location parameters, it is particularly remarkable that all distributions present very similar Gamma shape parameters. The constant log–log slopes of the tails provide evidence of multi-scale validity and a scaling invariant structure (more than two orders of magnitude) of discontinuities of the rock mass. The IBSDs and the scale effect are discussed in the light of the fragment size distributions from blasts carried out in the area characterized.

Spherical K-Means and Elbow Method Optimizations With Fisher Statistics for 3D Stochastic DFN From Virtual Outcrop Models

Fracture modeling plays a valuable role to understand the fluid flow in carbonate reservoirs. For this, the fracture characterization to generate Discrete Fracture Networks (DFNs) can take advantage of analogue outcrops through Virtual Outcrop Models (VOMs), acquired by Unmanned Aerial Vehicles (UAV) and digital photogrammetry. The stochastic DFN generation is an important step in reservoir modeling as it brings more representative data to the process and has long been studied. However, optimizations concerning automatizing some of the steps necessary to its generation like data clustering are still open to advancements. In this sense, this work aims the fracture data clustering and the definition of the number of clusters when gathering data for the stochastic process, developing an Elbow method for spherical data and a balanced K-means, both based on Fisher statistics. For this, we interpreted fracture planes in a VOM that recreates a carbonate reservoir analogue from the Jandaíra Formation, in the Northeast, Brazil. As result, we show a workflow for immersive fracture interpretation alongside a 3D stochastic DFN model with fracture intensity of 22.57m^-1 for cell sizes of 1m³. Regarding the clustering balance, our method achieved a lower standard deviation between sets while maintaining the Fisher values greater to obtain fracture sets with lower dispersion. Additionally, the Elbow method implementation proved a beneficial step to the workflow as it reduced the interpretation bias of family clusters. These results alongside the proposed workflow bring a better understanding of the outcrop geometry while offering data scalability for reservoir modeling.

Using effective medium theory to calculate permeability of rock with complex fractures

Dewatering in surface and underground mining is highly dependent on the permeability of fractured rocks, which is usually investigated by analytical and numerical methods. Analytical methods are used for simple, regular joint systems, while for complicated discrete fracture networks, numerical methods are more suitable. However, such numerical simulations demand considerable computation resources and are time-consuming for large-scale models. An attractive approach is to perform a rough mapping of the fractures into a lattice to apply effective medium theory. A computational code based on effective medium theory for calculating the overall permeability of fracture networks was developed. Several stochastic discrete fracture network models were generated with the fracture aperture distributed uniformly, correlated and uncorrelated with fracture trace length. The results showed that when the aperture was correlated or uncorrelated with trace length, the calculated mean permeability values by the effective medium theory method agreed well with numerical modelling. Also, approximated representative elementary volume was well fitted by numerical methods in the constant fracture aperture case. However, the calculated representative elementary volume by the effective medium theory method was smaller than the numerical estimation in the other two cases.

Assessment of the high-temperature aquifer thermal energy storage (HT-ATES) potential in naturally fractured geothermal reservoirs with a stochastic discrete fracture network model

High-temperature aquifer thermal energy storage (HT-ATES) is a cost-effective and suitable technology to store large amounts of energy. HT-ATES has been demonstrated to be an efficient and stable tool to buffer seasonal imbalances and significantly reduce greenhouse gas emissions. Fractured reservoirs are widespread in sedimentary basins worldwide. However, naturally fractured reservoirs have received little attention as potential formations for HT-ATES. The main concern regarding thermal energy storage in naturally fractured formations is the high fracture permeability, which may result in fast fluid flow and an increase in thermal losses. Therefore, quantification of the effects of fracture flow is essential to HT-ATES site verification.An HT-ATES system in a generic fractured reservoir is simulated with a 3D stochastically generated discrete fracture network (DFN) model combined with a fluid flow and heat transport model. The pressure and temperature evolutions at the well are analyzed, and the total extracted energy and thermal recovery efficiency are evaluated. The results confirm that the presence of the DFNs enhances thermal loss and thereby results in a lower thermal recovery efficiency compared with those of an unfractured reservoir. Such a decrease can reach 20%. However, simulations show that naturally fractured reservoirs might be potential candidates for HT-ATES due to a larger injectivity. A further discussion is conducted to characterize the relative importance of the hydrogeological properties of the fractures and fracture network structure on the thermal behavior of the HT-ATES system.This study provides preliminary insights into the impacts of complex natural DFN on the thermal performance of HT-ATES in fractured reservoirs.

Constraints upon fault zone properties by combined structural analysis of virtual outcrop models and discrete fracture network modelling

The permeability structure of a fault zone is strongly dependent on the occurrence of meso-scale fracture patterns within the damage zone. Here, structural analyses of Virtual Outcrop Models (VOM) integrated with Discrete Fracture Network (DFN) modelling are used to constrain the relationship between meso-scale fracture patterns and the bulk permeability of a regional-scale fault zone. The Goddo Fault Zone (GFZ, Bømlo – Norway) is a long-lived extensional fault zone cutting across a granodioritic body developed during the long-lasting rifting of the North Sea. Fracture geometrical characteristics and the spatial variation of fracture intensity derived from VOM structural analysis were adopted as input for stochastic DFN models representing selected portions of the GFZ to constrain the variability of the structural permeability tensor K related to the mesoscopic fracture pattern. The intensity of fault-related fracture set(s), and the associated structural permeability computed with DFN models, likely exhibits a decreasing power-law trend within the damage zone with increasing distance from the fault cores. The orientation of the maximum K tensor component is controlled by the intersection direction of the dominant fracture sets. These results highlight the fundamental role of mesoscopic fracture patterns in controlling the bulk petrophysical properties of large fault zones.

Matrix permeability and flow-derived DFN constrain reactivated natural fracture rupture area and stress drop — Marcellus Shale microseismic example

Microseismic events associated with shale reservoir hydraulic fracturing stimulation (HFS) are interpreted to be reactivations of ubiquitous natural fractures (NFs). Despite adoption of discrete fracture network (DFN) models, accounting for NFs in fluid flow within shale reservoirs has remained a challenge. For an explicit account of NFs, this study introduced the use of seismology-based relations linking seismic moment, moment magnitude, fault rupture area, and stress drop. Microseismic data from HFS monitoring of Marcellus Shale horizontal wells had been used to derive planar hydraulic fracture geometry and source properties. The former was integrated with associated well production data found to exhibit transient linear flow. Analytical solutions led to linear flow parameters (LFPs) and system permeability for scenarios depicting flow through infinite and finite conductivity hydraulic fractures. Published core plug permeability was stress-corrected for in-situ conditions to estimate average matrix permeability. For comparison, the burial and thermal history for the study area was used in 1D Darcy-based modeling of steady and episodic expulsion of petroleum to account for geologic timescale persistence of abnormal pore pressure. Both evaluations resulted in matrix permeability in the same picodarcy (pD) range. Coupled with LFPs, reactivated NF surface area for stochastic DFNs was estimated. Subsequently, the aforementioned seismology-based relations were used for determining average stress drops needed to estimate NF rupture area matching flow-based DFN surface areas. Stress drops, comparable to values for tectonic events, were excluded. One of the determined values matched stress drops for HFS operations in past and recent seismological studies. In addition, calculated changes in pore pressure matched estimates in the aforementioned studies. This study unlocked the full potential of microseismic data beyond extraction of planar geometry attributes and stimulated reservoir volume (SRV). Here, microseismic events were explicitly used in the quantitative account of NFs in fluid flow within shale reservoirs.

Stochastic discrete fracture network modeling in shale reservoirs via integration of seismic attributes and petrophysical data

The prediction of natural fracture networks and their geomechanical properties remains a challenge for unconventional reservoir characterization. Because natural fractures are highly heterogeneous and of subseismic scale, integrating petrophysical data (i.e., cores and well logs) with seismic data is important for building a reliable natural fracture model. Therefore, I have developed an integrated and stochastic approach for discrete fracture network modeling with field data experimentation. In the method, I first perform a seismic attribute analysis to highlight the discontinuity in the seismic data. Then, I extrapolate the well-log data that include localized but high-confidence information. By using the fracture intensity model including seismic and well logs, I build the final natural fracture model that can be used as a background model for the subsequent geomechanical analysis such as simulation of hydraulic fractures propagation. As a result, our workflow combining multiscale data in a stochastic approach constructs a reliable natural fracture model. I validate the constructed fracture distribution by its good agreement with the well-log data.

In-Situ Block Characterization of Jointed Rock Exposures Based on a 3D Point Cloud Model

The importance of in-situ rock block characterization has been realized for decades in rock mechanics and engineering, yet how to reliably measure and characterize the geometrical properties of blocks in varied forms of exposures and patterns of jointing is still a challenging task. Using a point cloud model (PCM) of rock exposures generated from remote sensing techniques, we developed a consistent and comprehensive method for rock block characterization that is composed of two different procedures and a block indicator system. A semi-automatic procedure towards the robust extraction of in-situ rock blocks created by the deterministic discontinuity network on rock exposures (PCM-DDN) was developed. A 3D stochastic discrete fracture network (DFN) simulation (PCM-SDS) procedure was built based on the statistically valid representation of the discontinuity network geometry. A multi-dimensional block indicator system, i.e., the block size, shape, orientation, and spatial distribution pattern for systematic and objective block characterization, was then established. The developed method was applied to a synthetic model of cardboard boxes and three different rock engineering scenarios, including a road cut slope from Spain and two open-pit mining slopes from China. Compared with existing empirical methods, the proposed procedures and the block indicator system are dependable and practically feasible, which can help enhance our understanding of block geometry characteristics in related applications.

Static and dynamic analysis on slope stability using a DFN-DEM approach on the right abutment of the Karun 4 dam

Uncertainty in input fracture geometric parameters during analysis of the stability of jointed rock slopes is inevitable and therefore the stochastic discrete fracture network (DFN) — distinct element method (DEM) is an efficient modeling tool. In this research, potentially unstable conditions are detected in the right abutment of the Karun 4 dam and downstream of the dam body as a case study. Two extreme states with small and relatively large block sizes are selected and a series of numerical DEM models are generated using a number of validated DFN models. Stability of the rock slope is assessed in both static and dynamic loading states. Based on the design basis earthquake (DBE) and maximum credible earthquake (MCE) expected in the dam site, histories of seismic waves are applied to analyze the stability of the slope in dynamic earthquake conditions. The results indicate that a MCE is likely to trigger sliding of rock blocks on the rock slope major joint. Furthermore, the dynamic analysis also shows a local block failure by the DBE, which can consequently lead to slope instability over the long term. According to the seismic behavior of the two models, larger blocks are prone to greater instability and are less safe against earthquakes.

Towards real-time forecasting of natural gas production by harnessing graph theory for stochastic discrete fracture networks

In this work, we compare hydrocarbon production curves obtained from a graph-based reduced-order model with the high-fidelity Discrete Fracture Network (DFN) predictions for a fracture network created using data from a real shale site. We observe that the bounds for the high fidelity DFN model lie within the bounds for the reduced order model, implying that the reduced-order model provides a conservative estimate. Moreover, we found that except for first-passage times and late arriving mass, the production curves from the reduced-order model predict transport accurately. However, it is to be noted that the results are inspite of trading a three-dimensional geometry for a reduced system in the form of a graph, one that is 500–1000 times faster in terms of computational efficiency (for this particular application). In addition, we also compare the production curves for large drawdown and small drawdown using our graph approach. The reduced-order model is successful in showing that the long term productivity is higher in case of small drawdown although the initial productivity is higher for large drawdown. Thus, this reduced-order model offers great potential in uncertainty quantification for production, as well as in providing operators with information to make real-time decisions for optimal production.

Equivalent discrete fracture network method for numerical estimation of deformability in complexly fractured rock masses

Equivalent continuum models estimating the deformability of complexly fractured rock masses may incur significant discrepancies. This paper proposes an equivalent discrete fracture network (E-DFN) method to proficiently capture the non-continuous characteristics of rock masses while significantly reducing computational cost compared with traditional discrete fracture network (DFN) models. A significance index of individual fractures is defined to quantitatively evaluate their impact on the elastic modulus. Accumulative significance indices are then generated to define E-DFNs containing representative quantities of fractures. Numerical simulations are conducted with E-DFN models using UDEC (universal distinct element code). The relationship between elastic moduli of complexly fractured rocks and models with E-DFNs is established by an extrapolation function obtained through regression analyses based on an assumption of the marginal diminishing effect of modulus reduction. The proposed method is validated by stochastic DFNs with different geometric configurations. The results show that reasonable estimation with small errors is achieved by the extrapolation of density-reduced E-DFN models. The E-DFN method strikes a balance between result reliability and computational intensity.

Permeability of Three‐Dimensional Numerically Grown Geomechanical Discrete Fracture Networks With Evolving Geometry and Mechanical Apertures

AbstractFracture networks significantly alter the mechanical and hydraulic properties of subsurface rocks. The mechanics of fracture propagation and interaction control network development. However, mechanical processes are not routinely incorporated into discrete fracture network (DFN) models. A finite element, linear elastic fracture mechanics‐based method is applied to the generation of three‐dimensional geomechanical discrete fracture networks (GDFNs). These networks grow quasi‐statically from a set of initial flaws in response to a remote uniaxial tensile stress. Fracture growth is handled using a stress intensity factor‐based approach, where extension is determined by the local variations in the three stress intensity factor modes along fracture tips. Mechanical interaction between fractures modifies growth patterns, resulting in nonuniform and nonplanar growth in dense networks. When fractures are close, stress concentration results in the reactivation of fractures that were initially inactive. Therefore, GDFNs provide realistic representations of subsurface networks that honor the physical process of concurrent fracture growth. Hydraulic properties of the grown networks are quantified by computing their equivalent permeability tensors at each growth step. Compared to two sets of stochastic DFNs, GDFNs with uniform fracture apertures are strongly anisotropic and have relatively higher permeabilities at high fracture intensities. In GDFN models, where fracture apertures are based on mechanical principles, fluid flow becomes strongly channeled along distinct flow paths. Fracture orientations and interactions significantly modify apertures, and in turn, the hydraulic properties of the network. GDFNs provide a new way of understanding subsurface networks, where fracture mechanics is the primary influence on their geometric and hydraulic properties.

A Discrete Fracture Network Model With Stress-Driven Nucleation: Impact on Clustering, Connectivity, and Topology

The realism of Discrete Fracture Network (DFN) models relies on the spatial organization of fractures, which is not issued by purely stochastic DFN models. In this study, we introduce correlations between fractures by enhancing the genetic model (UFM) of Davy et al. [1] based on simplified concepts of nucleation, growth and arrest with hierarchical rules. To do so, the nucleation of new fractures is correlated with the elastic strain energy of distortion stored in the matrix, which is a function of preexisting fractures. Discrete Fracture Networks so generated show multi-scale clustering effects with fractal dimensions below the topological dimension over a broad range of scales. The fractal dimension depends on the way one correlates the nucleation occurrence to the strain energy. Fracture clustering entails a spatial variability of the fracture density, which increases with the intensity of the coupling between stress and nucleation. The analysis of connected clusters density and of fracture intersections also highlights the differences between the UFM models and its equivalent Poisson model. We show that our stress-dependent nucleation model introduces some new fracture size-positions correlations, with small fractures tending to connect to the largest ones.