Complex Discrete Fracture Networks Research Articles

Advanced method for estimating the volumetric intensity along tunnels using ANN

ABSTRACT Simulating realistic scenarios with numerical models often demands substantial computational resources, which can be excessively time-consuming. In complex Discrete Fracture Network (DFN) simulations where mutual influence among fracture parameters is crucial, efficient Artificial Intelligence (AI) algorithms offer a promising solution. This study focuses on the Monte Seco tunnel in Brazil, employing Artificial Neural Networks (ANN) with the Levenberg-Marquardt Algorithm (ANN-LM) to estimate Volumetric discontinuity intensity (P32). Comparative analysis with traditional DFN-based methods reveals superior predictive performance of the ANN model over Multiple Linear Regression (MLR). MATLAB was utilized for implementation, considering the interdependence of geometric parameters across fracture sets to estimate P32 values. Sensitivity analysis identified correlations between F1 parameters (density and trace length) and P32 estimates for F2, aiding in predicting potential tunnel instability. A Graphical User Interface (GUI) was developed to streamline calculations, replacing cumbersome spreadsheet methods.

Numerical modelling of CO2 leakage through fractured caprock using an extended numerical manifold method

In this study, the cohesive element-based numerical manifold method (Co-NMM) and unified pipe network method (UPM) are further developed and integrated to analyze the CO2 leakage through fractured caprock considering CO2-water two-phase flow, CO2 adsorption and deformation of both caprock matrix and fractures. First, the Co-NMM is modified to better treat complex discrete fracture networks (DFNs) problems, while the CO2 adsorption effect is introduced into the UPM governing equation of two-phase seepage. And then, a two-phase seepage-stress coupling model and an implicit sequential solution are successively adopted to combine the Co-NMM and UPM tightly to capture the interplay between the two-phase flow and fractured caprock accurately and flexibly. The extended Co-NMM formulation is verified by reproducing the CO2 plume distribution evolution process in deep brine aquifers for geological sequestration. Finally, we conduct a series of simulations where CO2 displaces water through caprock formation with different DFNs that serve as a dominant conduit for potential CO2 leakage from storage reservoirs. The effects of DFN connectivity and hydraulic characteristics on the CO2 leakage through caprock are discussed. The research results can offer a reference for the evaluation of caprock sealing efficiency and also indicate that the modified hybrid NMM-UPM method is a potentially effective tool for analyzing CO2 leakage through fractured caprock under complex DFN conditions.

A semi-theoretical method for determining the permeability tensor of fractured rock masses in three-dimensional space

The permeability tensor is a critical parameter for analyzing the hydraulic behavior of anisotropic permeability in fractured rock masses. However, determining this tensor for three-dimensional (3D) fractured rock masses has proven to be challenging and resource-intensive. Both field tests, requiring numerous costly in situ tests, and numerical experiments, hindered by complex discrete fracture networks with a high fracture density, present difficulties in obtaining accurate results. In response, this study proposes a semi-theoretical method for determining the permeability tensor of 3D fractured rock masses, significantly reducing labor and economic costs. The proposed method focuses on establishing the theoretical relationship of directional permeabilities in a 3D space, with emphasis on the properties of the permeability tensor and the influence of fractures' geometry on the flow rate. To facilitate the construction of the method, anisotropic ellipse and ellipsoid are introduced, providing a description of permeability anisotropy. With this innovative approach, engineers can calculate the permeability tensor even when only one value of permeability is available along any flow direction. The utilization of the anisotropic ellipse and ellipsoid concepts helps simplify the determination process. Through numerical experiments, the method is validated and its accuracy demonstrated, making it a valuable tool for analyzing the hydraulic behavior of 3D fractured rock masses.

Effect of fracture characteristics on groundwater flow adjacent to high-level radioactive waste repository

In the study, a 2-D numerical model-delineating the high-level radioactive waste repository surrounded by hosting granite-rock was designed to evaluate pressure build-up, elevated temperature, and fracture flow caused by heat generation at the repository. During the early stage (0.1 years), build-up pressure at the repository induced radial groundwater flow. On the other hand, buoyancy-driven vertical flow was dominant during the late stage (2,000 years). The pressure build-up and elevated temperature varied significantly in bentonite, excavation-damaged zone and granite, resulting in different groundwater velocity. Fracture flow in both single and intersecting fractures were also influenced by the pressure and temperature, but their impact varied depending on the geometrical properties (e.g. orientation, elevation, lateral position) of the fracture. In complex discrete fracture network models, build-up pressure in the early stage mainly generated preferential fracture flow through few pathways, while in the late stage, convection-circulating flow induced by the buoyancy was distinct. In the early stage, higher density and connectivity of fracture network did not lead to an increase in average fracture flow, whereas the circulating flow in the late stage became more frequent and larger. Especially, long fractures served as both preferential flow pathways in the early stage and conduits for circulating flow in the late stage. The circulating flow was highly dependent on the spatial distribution of the long fractures, causing a significant uncertainty of average fracture flow in the late stage. The low angle of intersection between fractures resulted in low connectivity that decelerated the average fracture flow in both stages.

Reconstruct lower‐dimensional crack paths from phase‐field point cloud

AbstractBecause of the smeared representation of phase‐field fracture, reconstructing lower‐dimensional crack paths is challenging, which may impede the further applications of the phase‐field method in the modeling of fault friction and fluid flow in fracture. In the present work, we propose to capture the crack curves or surfaces from two‐dimensional or three‐dimensional phase‐field point cloud using an optimized ridge regression algorithm, and k‐nearest neighbor and principal component analysis are used to estimate the normal direction of each segment on the identified discrete crack path. The sensitivity and computational efficiency of the proposed method are investigated thoroughly. Subsequently, this method is extended to reconstruct the complex discrete fracture networks. Finally, several benchmarks for fracture, fault friction and fluid flow problems are presented to demonstrate the strength of the proposed approach.

A multiscale neural network model for the prediction on the equivalent permeability of discrete fracture network

An equivalent permeability approach can upscale the discrete fracture network (DFN) model to an equivalent DFN model and significantly reduce the gas flow simulations in a large-scale fractured gas reservoir. Current equivalent permeability prediction models are only applicable to the reservoir with a simple fracture network. However, an equivalent permeability prediction model has not been available for a reservoir with a multiscale discrete fracture network. This study proposes a multiscale convolutional neural network model (called MsNet) and introduces three mainstream structures with high performance convolutional neural network (CNN) (ResNet-18, VGG-16 and GoogLeNet) to efficiently predict the equivalent permeability of a complex multiscale fracture network. These CNN models use both the images and features of DFN as their input and the equivalent permeability as their output. This MsNet model is validated with the simulation results simulated by Lattice Boltzmann method and compared with the three mainstream CNN structures and an existing permeability prediction model (CNN-4). It is found that this MsNet model innovatively considers the multiscale characteristics of DFN by a multiscale convolution feature fusion and combines the residual connection for further performance enhancement. Both DFN dataset and MsNet model structure affect the model prediction ability. A deeper network structure of MsNet model can enhance its prediction ability, but significantly increases training time. The MsNet-8-4 (a MsNet structure with 8 multiscale connection modules and 4 sub-networks in each module) has the least convergence time and the lowest mean absolute error on the test set. It performs obviously better than other four models on the DFN dataset with higher fracture density. The MsNet model can well accelerate the simulation on the gas flow in a complex discrete fracture network.

Calibration of Complex Discrete Fracture Network Using Microseismic Events and Fracture Propagation Modelling with Seamless Reservoir Production Simulation

Abstract During the unconventional reservoir development, a proper modelling of the underground fracture networks and their effects on production is crucial for reservoir development potential and realistic economic analysis. Conventionally, the complex fracture system formed by hydraulic and natural fractures is extremely difficult to capture, let alone to numerically simulate it. Most importantly, the current best solution can only rely on the knowledge of the natural fractures from the geology and geophysics team and hydraulic fractures from the engineering team. Nevertheless, this solution fails to realize the dynamic stress regime variations when fracturing jobs are done within the horizontal wellbore. In this study, a variety of data source and modelling tools is harnessed to delineate a more realistic and representative discrete fracture network (DFN). The first step is to obtain the original natural fractures already depicted from geological and geophysical information and the statistical information regarding the spatial configurations of this DFN. Next, a new set of natural fractures is generated by an in-house natural fracture generator while preserving the spatial characteristics of the original natural fractures at the same time. Then, a combined DFN of the original natural fracture and newly generated natural fractures is accomplished. This combined DFN is then intensity-calibrated by the given microseismic cloud events, especially focusing on the near-wellbore region. Then, a displacement discontinuity method- (DDM-) based in-house hydraulic fracture propagation model is used to generate hydraulic fractures with complex boundaries, honoring the fracturing job logistics from the engineering team. After this step, an ultimate and highly representative DFN can be achieved. By applying this very novel workflow, DFN characterizations of both a single-well scenario and well-pad (3 wells) scenarios have been highly successful. Statistics such as the cluster-wise hydraulic fracture half-length, height, aperture, and numbers of activated/nonactivated natural fractures can be easily presented. Through the powerful numerical method called the embedded discrete fracture model (EDFM), production simulation and stimulated reservoir volume evaluation can be seamlessly studied. Extents of 3D drainage volumes can also be plotted with ease. Overall, a holistic picture regarding the unconventional reservoir’s underground DFN can be reliably depicted, using the proposed workflow.

Improvements to the Fracture Pipe Network Model for Complex 3D Discrete Fracture Networks

AbstractFractures widely present in the subsurface and play a critical role in the fluid flow processes in porous media. The Fracture Pipe Network Model (FPNM) is an efficient method to represent and calculate fluid flow properties as a particular part of Discrete Fracture Networks (DFNs) method compared to direct numerical simulations. However, the current FPNM formulation can result in large deviations in computed fluid flow properties when applied to complex interconnected DFNs, although it can produce good results for simple DFNs. To enhance the performance and versatility of current FPNMs, four modifications to the FPNM formulation are introduced from different perspectives to improve the accuracy of pipe conductance assignment and ensure the correct topology of the fracture network. Two benchmarking examples with complex interconnected fractures and two real fractured samples are presented and the results show the modifications significantly improve the accuracy of computed fluid flow properties in complex DFNs.

Modeling and Simulation of Shale Fracture Attitude.

A large number of natural fractures are distributed in shale gas reservoirs. In-depth studying of the attitude of fractures is of great significance for the efficient development of shale gas. In previous studies, the complex three-dimensional discrete fracture networks (DFNs) and transport mechanisms were often not fully considered. In this study, the fully coupled multimechanism transport model and the complex discrete fracture networks (DFNs) model are developed to incorporate these complexities. The comprehensive transport model can couple multiple mechanisms such as slippage, diffusion, adsorption, and dissolution of shale gas. Moreover, the mechanisms of two-phase flow, reservoir deformation, real gas effect, and fracture closure are also considered. The three-dimensional DFN model can flexibly characterize the fracture attitudes, which means that the construction of the discrete fracture network is easier and faster. Under these frameworks, a series of partial differential equations (PDEs) were derived to describe transport mechanisms of shale gas in the shale fracture-matrix system. These PDEs were numerically discretized and solved by the finite element method. The proposed models are verified against gas production data from the field and validated against others’ solutions. This study numerically simulates the influence of different fracture attitudes on shale gas transport and analyzes the sensitivity of the model. The results and sensitivity analysis reveal that both fracture dip angle and strike direction will significantly affect the gas production, and the smaller the angle between the strike direction and the flow direction, the higher the shale gas production. The length, density, area, and shape of fractures also play important roles in shale gas transport. There is an ideal fracture density in the fracture network, and the suggested excessive fracturing is not economic. The shale fracture-matrix system modeling and simulation methods can improve the development of shale gas reservoirs and increase the gas production of wells.

A Three-field Based Optimization Formulation for Flow Simulations in Networks of Fractures on Nonconforming Meshes

A new numerical scheme is proposed for flow computation in complex discrete fracture networks. The method is based on a three-field domain decomposition framework in which independent variables are introduced at the interfaces generated in the process of decoupling the original problem on the whole network into a set of fracture-local problems. A PDE-constrained formulation is then used to enforce compatibility conditions at the interfaces. The combination of the three-field domain decomposition and of the optimization-based coupling strategy results in a novel method which can handle nonconforming meshes, independently built on each geometrical object of the computational domain, and ensures a local mass conservation property at fracture intersections, which is of paramount importance for hydrogeological applications. An iterative solver is devised for the method, suitable for parallel implementation on parallel computing architectures.

Effects of lateral-well geometries on multilateral-well EGS performance based on a thermal-hydraulic-mechanical coupling model

Our previous study (Song et al., 2018) presented a novel enhanced geothermal system (EGS) with multilateral wells to exploit geothermal energy, and illustrated that the multilateral-well EGS had a better heat extraction performance than conventional double-well EGS. However, to further improve the heat extraction performance of the multilateral-well EGS, the effects of lateral-well geometries on multilateral-well performance should be studied and the geometrical parameters should be optimized. In this paper, we use a thermal-hydraulic-mechanical (THM) coupling model with a complex discrete fracture network (DFN) to investigate the influences of lateral-well geometrical parameters on the multilateral-well EGS performance. The lateral-well geometrical parameters include the lateral-well length, number, spacing and diameter. The results indicate that the longer lateral well and larger well spacing are beneficial for enhancing the multilateral-well EGS performance. In terms of better heat extraction performance and lower pressure impedance, the 400 m well spacing is the optimizing value under the fracture density of 0.067 m−1. The lateral-well number has a complicated effect on the heat extraction process. A large number of lateral wells can improve swept volume and reduce pressure impedance, but simultaneously connect more fractures and accelerate thermal breakthrough. Therefore, the lateral-well number should be optimized according to the specific DFN and under the DFN in this paper, 6 lateral wells are the best for the multilateral-well EGS performance. When there is a rotation angle between injection and production lateral wells, it can postpone the thermal breakthrough and be beneficial for heat extraction. The influence of the lateral-well diameter on the EGS performance can be ignored. The results of this study provide good guidance for the lateral-well design of the multilateral-well EGS.

Particle-Based Workflow for Modeling Uncertainty of Reactive Transport in 3D Discrete Fracture Networks

Fractures are major flow paths for solute transport in fractured rocks. Conducting numerical simulations of reactive transport in fractured rocks is a challenging task because of complex fracture connections and the associated nonuniform flows and chemical reactions. The study presents a computational workflow that can approximately simulate flow and reactive transport in complex fractured media. The workflow involves a series of computational processes. Specifically, the workflow employs a simple particle tracking (PT) algorithm to track flow paths in complex 3D discrete fracture networks (DFNs). The PHREEQC chemical reaction model is then used to simulate the reactive transport along particle traces. The study illustrates the developed workflow with three numerical examples, including a case with a simple fracture connection and two cases with a complex fracture network system. Results show that the integration processes in the workflow successfully model the tetrachloroethylene (PCE) and trichloroethylene (TCE) degradation and transport along particle traces in complex DFNs. The statistics of concentration along particle traces enables the estimations of uncertainty induced by the fracture structures in DFNs. The types of source contaminants can lead to slight variations of particle traces and influence the long term reactive transport. The concentration uncertainty can propagate from parent to daughter compounds and accumulate along with the transport processes.

Lattice modelling of gravity and stress-driven failures of rock tunnels

In this paper, an investigation is performed regarding the applicability of the Rigid Body Spring Network method (RBSN) to the analysis of hard rock tunnels in massive and fractured rock masses. For this objective, the method is enhanced with a new meshing scheme and a Cohesive Zone Model (CZM) formulation based on an exponential softening law. While the new meshing scheme provides for models containing complex Discrete Fracture Networks, the CZM affords realistic representations of fracturing phenomena. In order to demonstrate the robustness of the contributions, a verification model and three study cases are presented. The verification concerns the analysis of an elastic jointed medium with a circular hole, from which stresses and displacements are calculated and checked against Finite Element solution. The study cases are based on the real Monte-Seco and Mine-By tunnels and on a hypothetical tunnel. Simulations are performed, and the results are compared to either observed in situ behavior or Finite Element analyses. In the end, the cases show that the enhanced RBSN can realistically represent both gravity and stress-driven types of failures that are encountered in hard rock tunneling. Additional results highlight the method’s simple material calibration procedure and the practicality of the new meshing scheme.

Reliable a posteriori mesh adaptivity in Discrete Fracture Network flow simulations

A new approach for the flow simulation in very complex Discrete Fracture Networks (DFNs) based on PDE-constrained optimization has been recently proposed in Berrone et al. (2013, 2014) with the aim of improving robustness with respect to geometrical complexities. In Berrone et al. (2016) a rigorous derivation of “a posteriori” error estimates has been performed, proving an equivalence relation between the discretization error and suitable quantities that are computable from the discrete solution and the problem data.In this paper, the previous results are applied to several fracture networks in order to investigate mesh adaptivity applied to complex realistic fracture networks.

A Coupling Model of Distinct Lattice Spring Model and Lattice Boltzmann Method for Hydraulic Fracturing

In this work, the distinct lattice spring model (DLSM) and the lattice Boltzmann method (LBM) are coupled together to simulate hydraulic fracturing problems. As the DLSM and LBM are both lattice modelling methods, the lattice meshes in these two systems are simply overlapped, which results in the same resolution in both the DLSM and LBM. The momentum exchange bounce-back algorithm is used to evaluate the forces exerted on the solid particles. Moreover, the calculation step in the LBM and DLSM is synchronised for prompt updates of fluid–solid interactions. The coupled model is further validated through a series of benchmarks. Finally, the coupled model shows its ability to simulate hydraulic fracturing in formations with complex discrete fracture networks.

Numerical analysis of heat mining and geological carbon sequestration in supercritical CO2 circulating enhanced geothermal systems inlayed with complex discrete fracture networks

Enhanced geothermal systems using supercritical CO2 (scCO2-EGS) as working fluid in place of water provides better heat extraction rate and sequestrates CO2 in the formations for reducing atmospheric CO2 content and the greenhouse effect. This paper proposed a numerical three-dimensional fully coupled thermo-hydro-mechanical (THM) model to simulate and evaluate the performances of heat mining and geological carbon sequestration in scCO2-EGS embedded in complex discrete fracture networks. The variable thermophysical properties of supercritical CO2 in response to pressure and temperature are taken into account during the reservoir development. Verification, sensitivity analysis, and convergence for the model are accomplished. The three-spot layout of the practical EGS project at Soultz-sous-Forêts is then simulated using a stochastic DNF model under different operation pressures. The efficiencies and quantities of heat mining, carbon sequestration, and production of electric power for a period of 30 years have been studied and discussed. By verification against analytical solutions, the results demonstrate that the current nuermical model is effective to investigate the details of the multi-physical interactions in scCO2-EGS.

Fast and robust flow simulations in discrete fracture networks with GPGPUs

A new approach for flow simulation in very complex discrete fracture networks based on PDE-constrained optimization has been recently proposed in Berrone et al. (SIAM J Sci Comput 35(2):B487–B510, 2013b; J Comput Phys 256:838–853, 2014) with the aim of improving robustness with respect to geometrical complexities. This is an essential issue, in particular for applications requiring simulations on geometries automatically generated like the ones used for uncertainty quantification analyses and hydro-mechanical simulations. In this paper, implementation of this approach in order to exploit Nvidia Compute Unified Device Architecture is discussed with the main focus to speed up the linear algebra operations required by the approach, being this task the most computational demanding part of the approach. Furthermore, two different approaches for linear algebra operations and two storage formats for sparse matrices are compared in terms of computational efficiency and memory constraints.

A mesh mapping method for simulating stress-dependent permeability of three-dimensional discrete fracture networks in rocks

A mesh mapping method is proposed to incorporate stress effect into the hydraulic analysis for highly fractured rock masses. Mechanical and hydraulic mesh are introduced for the hydraulic and mechanical simulations, respectively. The mechanical mesh contains strong discontinuities for capturing the fracture opening, closure and shearing, while the hydraulic mesh only consists of merged triangles on fractures. Using finite element method and unified pipe network method, stress effects on the equivalent permeability of complex discrete fracture networks (DFNs) are studied. The numerical result demonstrates that the mesh mapping method is effective to the stress-dependent analysis of 3D complicated DFNs.

Evolution and Evaluation of SRV in Shale Gas Reservoirs: An Application in the Horn River Shale of Canada

Summary A hybrid-hydraulic-fracture (HHF) model composed of (1) complex discrete fracture networks (DFNs) and (2) planar fractures is proposed for modeling the stimulated reservoir volume (SRV). Modeling the SRV is complex and requires a synergetic approach between geophysics, petrophysics, and reservoir engineering. The objective of this paper is to characterize and evaluate the SRV in nine horizontal multilaterals covering the Muskwa, Otter Park, and Evie Formations in the Horn River Shale in Canada, with a view to match their production histories and to evaluate the effectiveness and potential problems of the multistage hydraulic-fracturing jobs performed in the nine laterals. To accomplish this goal, the HHF model is run in a numerical-simulation model to evaluate the SRV performance in planar and complex fracture networks using good-quality microseismicity data collected during 75 stages of hydraulic fracturing (out of 145 stages performed in nine laterals). The fracture-network geometry for each hydraulic-fracture (HF) stage is developed on the basis of microseismicity observations and the limits obtained in the fracture-propagation modeling. Post-fracturing production is appraised with rate-transient analysis (RTA) for determining effective permeability under flowing conditions. Results are compared with the HHF simulation and the hydraulic-fracturing design. The HHF modeling of the SRV leads to a good match of the post-fracturing production history. The HHF simulation indicates interference between stages. The vertical connectivity in the reservoir is larger than the horizontal connectivity. This is interpreted to be the result of the large height achieved by HFs, and the absence of barriers between the formations. It is concluded that the HHF model is a valuable tool for evaluating hydraulic-fracturing jobs and the SRV in shales of the Horn River Basin in Canada. Because of the generality of the Horn River application, the same approach might have application in other shale gas reservoirs around the world.

Unsteady advection-diffusion simulations in complex Discrete Fracture Networks with an optimization approach

It is widely recognized that the prediction of transport of contaminants in a fractured rock mass requires models that preserve several distinctive features of the inner fracture network, like heterogeneity and directionality; in this respect, Discrete Fracture Networks (DFNs) play a significant role. The solution of the associated equations would claim a high computational demand, that could be met only by using agile and robust numerical techniques. In this note a new numerical technique, fully validated from a mathematical standpoint, is applied to engineering problems, also introducing dispersion models for the description of non-stationary transport phenomena. The method results in a fast and scalable resolution tool, based on a PDE-constrained optimization approach designed to avoid mesh generation problems and allowing for transport simulations with an Eulerian approach. Examples are reported to show the quality of the solution obtained, even by using relatively coarse meshes and quite geometrically complex DFNs.