Discrete Fracture Research Articles

Robust fracture intensity estimation from petrophysical logs and mud loss data: a multi-level ensemble modeling approach

This study presents a pioneering machine learning approach to continuously model fracture intensity in hydrocarbon reservoirs using solely conventional well logs and mud loss data. While machine learning has previously been applied to predict discrete fracture properties, this is among the first attempts to leverage well logs for continuous fracture intensity modeling leveraging advanced ensemble techniques. A multi-level stacked ensemble methodology systematically combines the strengths of diverse algorithms like gradient boosting, random forest and XGBoost through a tiered approach, enhancing predictive performance beyond individual models. Nine base machine learning algorithms generate initial fracture intensity predictions which are combined through linear regression meta-models and further stacked using ridge regression into an integrated super-learner model. This approach achieves significant improvements over individual base models, with the super-learner attaining a mean absolute error of 0.083 and R^2 of 0.980 on test data. By quantifying the crucial fracture intensity parameter continuously as a function of depth, this data-driven methodology enables more accurate reservoir characterization compared to traditional methods. The ability to forecast fracture intensity solely from conventional well logs opens new opportunities for rapid, low-cost quantification of this parameter along new wells without requiring advanced logging tools. When incorporated into reservoir simulators, these machine learning fracture intensity models can help optimize production strategies and recovery management. This systematic stacked ensemble framework advances continuous fracture intensity modeling exclusively from well logs, overcoming limitations of prior techniques. Novel insights gained via rigorous model evaluation deepen the understanding of naturally fractured reservoirs.

A new analytically modified embedded discrete fracture model for pressure transient analysis in fluid flow

In the past few decades, multi-stage hydraulic fracturing has emerged as a crucial technology for the commercial development of unconventional oil and gas (UOG) resources. It is crucial to accurately and efficiently characterize transient fluid flow near fractures, which is a critical concern for many researchers. Discrete fracture models (DFMs) are primarily used to analyze the pressure transient behaviors of fluid flow in naturally fractured porous media. DFMs can accurately capture transient fluid flow near fractures, but they require a substantial number of grids to ensure computational accuracy, leading to higher computational costs. On the other hand, standard embedded discrete fracture models (EDFMs) based on pseudo-steady-state assumptions are computationally efficient, but they struggle to model the early transient fluid flow near fractures accurately. To address this limitation, we propose a new analytically modified EDFM (AEDFM) with structured Cartesian grids for analyzing the pressure transient behaviors of fluid flow in naturally fractured porous media.The transmissibility between the matrix and fractures is adjusted by multiplying it with a transient factor. In addition, we have validated the accuracy and efficiency of our proposed model through comparisons with results from analytical models and a standard well-testing software package. The results demonstrate the significance of our proposed model in accurately capturing transient fluid flow around fractures and reducing computational costs. In this work, we analyze the pressure transient behaviors of fluid flow using various parameter values and further evaluate the significance of the proposed modifications. The results indicate that AEDFM can effectively match the early nonlinear pressure drop near fractures compared to the standard EDFM. This work presents a powerful tool for the fast and accurate analysis of pressure transient behaviors of fluid flow in naturally fractured porous media.

Influence of fractures and heat transmission on wormhole propagation in fractured carbonate rocks

Carbonate reservoirs exhibit significant heterogeneity and often contain natural fractures. Matrix acidizing is a commonly used technique in fractured carbonate formations. Currently, the influences of natural fractures and the acid-rock molar reaction heat on wormhole propagation are rarely considered in acidizing models. In this paper, the two-scale continuum model, the embedded discrete fracture models (EDFM), and the heat transfer model are combined to develop a computational model of acidic fluid reactive flow in carbonate rocks with a complex fracture network that takes into account temperature variations. The model considers not only the temperature variation caused by the acid-rock molar reaction heat, but also simulates carbonate acidizing with any complex fracture network. Numerical simulations of the model were carried out to obtain the wormhole propagation patterns and the breakthrough curves under different conditions, and the simulation results were in good agreement with those of previous study. In particular, the sensitivity of fracture permeability, acid concentration, acid temperature and matrix porosity heterogeneity during acidizing is studied. The simulation results show that fractures can significantly alter the structure of wormholes and decrease the pore volume of acid required to reach the breakthrough (PVBT). However, fractures have minimal impact on the growth structure of wormholes prior to encountering fractures. During the reaction, the highest temperature was observed at the front end of the wormhole, and it was found that the optimum injection rate increased with the increase of the injected acid temperature. Lowering the temperature of the acid can enhance the efficiency of acidizing in fractured carbonate formations, particularly when applied at an optimal injection rate. When carbonate formations have well-developed fractures, the structure of the wormholes is insensitive to the heterogeneity of the matrix porosity, and they tend to grow along the fractures.

Meshfree multiscale method for the infiltration problem in permafrost

This study introduces a multiscale simulation approach, employing the Meshfree Generalized Multiscale Finite Element Method (GMsFEM), to numerically model fluid seepage in permafrost soil conditions. Combining Meshfree and Finite Element Methods, the coarse-grid system is addressed, while the standard Finite Element Method operates on the fine grid. For representing fractures at the fine grid level, the Discrete Fracture Model (DFM) is utilized. The findings demonstrate the method’s efficacy in accurately depicting soil heterogeneity and the impact of fractures on soil temperature.

A Practical probabilistic history matching framework for characterizing fracture network parameters of shale gas reservoirs

Simulating fluid flow in complex fracture systems encountered in subsurface systems, such as those encountered in tight or shale gas reservoirs, presents considerable challenges. Sophisticated numerical techniques and characterization approaches are required to integrate static and dynamic data from multiple sources to account for the intricate interplay between fractures and the surrounding rock matrix. A novel workflow using an indicator-based probability perturbation method (PPM) is applied to characterize uncertain discrete fracture network parameters. The posterior probability distributions of primary and secondary fracture transmissivity, aperture, length, height, and intensity of the secondary fracture are estimated according to the production (flow) histories. A case study based on the Horn River shale gas reservoir is presented. A pilot point scheme is formulated to update the distributions of P32L. The forward modelling entails upscaling each fracture model into a dual-porosity dual-permeability model and performing multiphase flow simulation. This approach produces an ensemble of history-matched discrete fracture and upscaled models by incorporating static and dynamic data. The results demonstrate the utility of the developed method for estimating secondary fracture parameters, which are not inferrable from other static information alone. The inference of both primary and secondary fractures offers a more comprehensive characterization of the fracture networks in tight or shale gas reservoirs. Integrating a pilot point parameterization technique and a sequential simulation approach into the PPM framework presents significant novelties in contributing to a comprehensive and effective method of simulating fluid flow in complex fracture systems, addressing the challenges associated with non-linear relationships between fracture model parameters and the corresponding flow response.

Algorithmic approach to discrete fracture network flow modeling in consideration of realistic connections in large-scale fracture networks

Analyzing rock mass seepage using the discrete fracture network (DFN) flow model poses challenges when dealing with complex fracture networks. This paper presents a novel DFN flow model that incorporates the actual connections of large-scale fractures. Notably, this model efficiently manages over 20,000 fractures without necessitating adjustments to the DFN geometry. All geometric analyses, such as identifying connected fractures, dividing the two-dimensional domain into closed loops, triangulating arbitrary loops, and refining triangular elements, are fully automated. The analysis processes are comprehensively introduced, and core algorithms, along with their pseudo-codes, are outlined and explained to assist readers in their programming endeavors. The accuracy of geometric analyses is validated through topological graphs representing the connection relationships between fractures. In practical application, the proposed model is employed to assess the water-sealing effectiveness of an underground storage cavern project. The analysis results indicate that the existing design scheme can effectively prevent the stored oil from leaking in the presence of both dense and sparse fractures. Furthermore, following extensive modification and optimization, the scale and precision of model computation suggest that the proposed model and developed codes can meet the requirements of engineering applications.

Stability Analysis of Jointed Rock Slopes Based on the Universal Elliptical Disc Model

A discrete fracture network (DFN) represents the random distribution of fractures within rock masses in three dimensions and has been widely used in the stability analysis of jointed rock slopes. This study introduces a novel method for constructing three-dimensional DFN models to address the limitations of traditional circular or polygon-based models. This method employs the universal elliptical disc (UED) model, combined with the discrete element method (DEM) in 3DEC, for the probabilistic analysis of jointed rock slope stability. The paper begins with an explanation of the fundamental principles of the UED model, and continues to detail the procedures for creating a three-dimensional DFN using the UED model and for analyzing slope stability using the DEM. An open-pit mine rock slope in the USA serves as a case study to illustrate the application of the proposed method. This approach facilitates the integration of the UED model into 3DEC and offers a more realistic depiction of the three-dimensional DFN, which enhances both the accuracy and efficiency of stability analysis in jointed rock slopes.

A novel multiphase and multicomponent model for simulating molecular diffusion in shale oil reservoirs with complex fracture networks

Molecular diffusion is critical for enhanced oil recovery (EOR) in shale oil reservoirs with complex fracture networks. Understanding the influence of fractures on diffusive mass transfer is crucial for predicting oil recovery and remaining oil distribution. Diffusive mass transfer between fractures and matrix is critical in comprehensively and effectively simulating molecular diffusion. Resolution of matrix cells significantly affects diffusion accuracy at the fracture–matrix interface. Low resolution results in multiple fractures in the same matrix cell, leading to decreased precision in calculating mass transfer by conventional methods. To address this, a novel multiphase and multicomponent model is proposed. The new model integrating the consideration of fracture spacing modifies molecular diffusion transmissibility between fracture and matrix in an embedded discrete fracture model. The discretization employs the two-point flux approximation in the finite-volume method. Validation compares the coarser mesh to the finest grid as a reliable reference. Results show the proposed model accurately captures diffusive mass transfer in a coarser mesh. Modified models study molecular diffusion's effects on EOR in shale oil reservoirs with complex fracture networks by CO2 huff and puff. Results indicate that increasing injection rates cannot improve oil recovery under extremely low porosity and permeability. Molecular diffusion facilitates CO2 penetration into the formation. This expands the swept CO2 volume and increases both volume expansion and formation energy. In addition, the light and heavy components of the crude oil are diffused into the fractures and eventually produced, which reduces gas production in the case of diffusion.

Study on the productivity and mechanism of physical field evolution of enhanced geothermal systems under different working fluid types and properties

The injected working fluid conditions directly affect the heat generation efficiency of a stimulated hot dry rock reservoir. Taking exploration well GR1 in the Gonghe Basin of Qinghai as the research object, a stochastic discrete fracture reservoir model was established around the main injection channel, and the productivity variation pattern of the enhanced geothermal system (EGS) and the spatiotemporal evolution mechanism of the reservoir fields were analyzed for CO2 and H2O working fluids. The interaction mechanism between the upper and lower rock formations and the reservoir during the heat mining process was discussed. This study obtained the following findings: (1) when the working fluid was CO2, after 20 years of heat recovery, the injection flow rate, output flow rate, and heat generation efficiency with a working fluid temperature of 60 °C reached 1.22 times, 1.18 times, and 1.92 times those with a working fluid temperature of 35 °C, respectively. The average subsidence and average geostress with the working fluid temperature of 60 °C were low, at only 90.61% and 95.96% of those with the working fluid temperature of 35 °C, respectively. However, high-temperature fluid injection increased flow loss. The changes in the various laws of H2O-EGS were similar to those of CO2-EGS. (2) When the working fluid temperature was 35 °C, after 20 years of heat recovery, the output flow rate and heat generation efficiency with the CO2-EGS reached 12.66 times and 1.28 times those with the H2O-EGS, respectively. However, the flow loss, average subsidence, and average geostress were higher with the CO2-EGS, reaching 6.58 times, 1.14 times, and 1.06 times those with the H2O-EGS, respectively. The patterns in these parameters observed at the other temperatures were similar to those observed at 35 °C. (3) The temperature decrease of the cushion layer was higher than that of the caprock, while the subsidence of the caprock was higher, and this phenomenon was more obvious when the working fluid temperature was lower. The conclusions obtained have important reference significance for the rational selection of working fluids.

Predicting fluid flow in reservoirs: analysis of fracture clustering in outcrop analogues

Researchers have used lacunarity, a parameter that quantifies scale-dependent clustering in patterns, to differentiate fracture networks that belong to the same fractal system. In a previous study, the authors showed that lacunarity is efficient in representing connectivity and fluid flow in fractal-fracture models with the same fractal dimension. The objective of this research is to investigate if the concepts thus developed are applicable to outcrop analogues that are representative of subsurface fractured reservoirs. A set of nested fracture networks belonging to a single fractal system but mapped at different scales and resolutions is considered in this study. Lacunarity and connectivity values of these maps are evaluated using geospatial data analysis techniques. Fracture continuum (FC) models are built from these fracture maps and a streamline simulator, TRACE3D, is used to flow simulate these maps. Results show that although the fractal dimension of these maps is same, differences exist in the values of lacunarity, percolation connectivity and also fluid recovery values. It is further noted that the clustering, connectivity and fluid recovery values can be pairwise correlated very well for these natural fracture maps. Thus, the overall results indicate that connectivity in fracture maps, and hence their flow properties, are controlled by lacunarity or scale-dependent clustering attributes. Therefore, there could be novel applicability of the lacunarity parameter in calibrating discrete fracture network (DFN) models with respect to connectivity in natural fracture maps and the prediction of flow behaviour in fractured reservoirs. Thematic collection: This article is part of the Digitally enabled geoscience workflows: unlocking the power of our data collection available at: https://www.lyellcollection.org/topic/collections/digitally-enabled-geoscience-workflows

Data-driven hydraulic property analysis and prediction of two-dimensional random fracture networks

The large parameter space and uncertainty of the discrete fracture networks (DFNs) make the hydraulic characteristics have multiple possibilities. Statistical analysis of hydraulic characteristics based on a large amount of data is a standard practice and central to DFN methodology. The present study developed a two-dimensional (2D) DFN numerical seepage model based on Matlab and Comsol from modeling and parameter calculation to simulation to investigate the influence of parameters involved fracture network on seepage characteristics of DFNs. In total, 1728 2D DFN models were generated with increasing fracture density, fracture length, power-law exponent, fracture orientations, and fracture included angles, and 1728 × 3 = 5184 numerical simulations of fluid flow along the x-axis, y-axis, and center through the DFN models are conducted using a self-developed numerical code. The influence of fracture geometric features on connectivity and permeability are estimated, respectively. And to realize the prediction of permeability tensor by known geological data, a theoretical model based on the Snow model and a data mining model based on the back-propagation model are discussed. The analysis helps researchers and engineers can make informed decisions and develop effective strategies for addressing the challenges posed by uncertainty hydraulic property of the fractured rock masses.

Stochastic inversion of fracture networks using the reversible jump Markov chain Monte Carlo algorithm

Characterization of fracture networks is essential in the production optimization or storage calculation for enhanced geothermal systems or geologic carbon storage. A novel inversion approach is proposed for estimating the fracture networks in this research. The discrete fracture network technique is adopted to probabilistically describe various fracture parameters such as trace length, midpoint position or azimuthal angle. The reversible jump Markov chain Monte Carlo algorithm is applied to explore the target posterior distribution of model parameters of differing dimensionality, in which the number of fractures is assumed to be unknown. More specifically, the birth-death strategy is utilized to perturb the fracture number iteratively in the sampling process. The proposed methodology is applied with two different types of observational datasets, namely the head records from steady-state flow simulation and the acoustic impedance obtained from seismic inversion. The sampling results can successfully recover the fracture geometry in the observed domain, and the number of fractures in the system can be retrieved as well. Benchmarked on multiple Markov chain trials, the technique of parallel tempering can greatly improve the convergence efficiency and increase the diversity of sampled posterior models, through the random swapping of model states across the whole temperature ladder.

Quantifying the impact of upscaled parameters on radionuclide transport in three-dimensional fracture-matrix systems

Assessing the long-term safety of geological repositories for high-level radioactive waste is critically dependent on understanding radionuclide transport in multi-scale fractured rocks. This study explores the influence of upscaled parameters on radionuclide movement within a three-dimensional fracture-matrix system using a discrete fracture-matrix (DFM) model. The developed numerical simulation workflow includes creating a random discrete fracture network, meshing of the fractures and matrix, assigning upscaled parameters, and conducting finite element simulations. We simulated the spatiotemporal evolution of radionuclide concentrations in the fractures and matrix over a century, revealing significant spatial heterogeneity driven by a heterogeneous seepage field. Employing geostatistics-based upscaling methods, we predicted the effective ranges of crucial solute transport parameters at the field scale. The matrix diffusion coefficient, matrix distribution coefficient, and longitudinal dispersivity were upscaled by factors of 2.0–3.0, 2.5–4.0, and 10–104, respectively, based on laboratory-scale measurements. Incorporating these upscaled parameters into the DFM model, we analyzed their impact on radionuclide transport. Our findings demonstrate that an upscaled matrix diffusion coefficient and matrix distribution coefficient result in a delayed transport of radionuclides in fractures by enhancing mass transfer between the fractures and rock matrix, while an upscaled longitudinal dispersivity accelerates transport by advancing the positions of concentration peaks. Sensitivity analysis revealed that the matrix distribution coefficient is the most impactful, followed by dispersivity and matrix diffusion coefficient. These insights are important for minimizing parameter uncertainties and enhancing the accuracy of predictions concerning radionuclide transport in multi-scale fractured rocks.

A New Simplified Discrete Fracture Model for Shearing of Intersecting Fractures and Faults

Shearing of fractures and faults is important because it can result in permeability change or even induce seismicity—both are keys for efficient and safe energy recovery and storage in Earth systems. Quantitative analysis of shearing of intersecting fractures and faults is challenging because it can involve dynamic frictional contacts that are complicated by deformation of the rock matrix. To predict the shearing of intersecting fractures/faults, we attempt to answer the question of how intersections impact the shearing of a fracture network and whether we can simplify the description as compared to classical discrete fracture network (DFN) models. To answer these questions, we conducted a series of numerical simulations on scenarios for variable numbers of intersecting fractures. All these examples yield consistent results: the results of using DFNs are consistent with those of using hypothetical major paths. This leads to a new model, which we name simplified discrete fracture network model, to analyze shearing of intersecting fractures/faults using major path(s). We found that the intersections of fractures do not fundamentally change the shearing of two intersecting fractures if the intersecting angles are small. Furthermore, increasing the number of fractures/faults may relax the stress as more fractures/faults become available for shearing and distributing the stress. The simplified DFN model, which can capture efficiently the shearing behavior of each major paths from a large number of intersecting fractures/faults, will be a promising conceptual model that is complementary to existing equivalent continuum and discrete fracture models to analyze shearing of intersecting fractures/faults.

Numerical methods for reinterpreted discrete fracture models with random inputs

This paper investigates the impact of uncertainty on the reinterpreted discrete fracture model (RDFM) for flow in porous media featuring fractures and barriers. The stochastic RDMF is formulated by parameterizing the uncertainty in the permeability, as well as the width of the fracture and barrier networks as random variables. To discretize these random variable, we adopt a stochastic collocation method based on a special choice of nodes. This collocation scheme offers optimal accuracy and easy implementation. The resulting collocation scheme is then combined with the local discontinuous Galerkin (LDG) method to accommodate the hybrid-dimensional Darcy’s law and the nature of the pressure/flux discontinuity. Additionally, a slope limiter is utilized to enhance stability. Numerical experiments are carried out to illustrate the accuracy and stability of the proposed scheme.

From Streamline to Pathline: Visualizing Particle Trajectories Under Changing Velocity Fields

Summary Monitoring of subsurface fluid motion is critical for optimizing hydrocarbon production and CO2 sequestration. Streamlines are frequently used to visualize fluid flow; however, they provide only an instantaneous snapshot of the velocity field and do not offer an exact representation of fluid movement under varying field conditions. In contrast, pathlines are constructed by tracking individual particles within the fluid, enabling us to trace the movement of these particles as they traverse through changing velocity fields. Pathline is the trajectory that an individual fluid particle follows in the reservoir. It can be thought of as “recording” the path of a fluid element in the flow field for a given time interval. Pathlines are distinct from streamlines which represent a snapshot of the velocity field at a given instant. The direction the path takes is determined by the streamlines at a specific instant. To start with, streamlines are traced based on the grid face fluxes of finite-difference simulation. Streamline tracing continues till the time of flight equals the current time. The endpoints of the current streamlines become the starting points for the next tracing period. Thus, our formulation incorporates changing flow fields, and the process is repeated for each time interval until the end. The proposed injection monitoring method is tested using a 3D field-scale model with complex geologic features to demonstrate its power and utility. The pathlines were compared with streamlines, as well as the water saturation distribution. Three scenarios are tested: a constant well schedule, a changing well schedule with partial shut-in, and a changing well schedule with a whole field cessation. Results indicate that the pathline provides a more accurate swept volume, consistent with saturation distribution. The robustness of our algorithm and implementation is demonstrated with a complex embedded discrete fracture model (EDFM) to visualize flow patterns in discrete facture network. Pathlines display the fluid flow across fractures and are subsequently used to explore the sweep efficiency and the well connectivity.

Effects of Geo-Stress and Natural Fracture Strength on Hydraulic Fracture Propagation in a Deep Fractured Tight Sandstone Reservoir.

Hydraulic fracturing technology has been widely used in the tight reservoir reconstruction. Unfortunately, with the deepening of mining depth and the increase of geo-stress, the propagation mechanism of medium-pressure fractures in the reservoir is significantly different from that of conventional shallow reservoirs. Based on the combined finite discrete element method, this paper conducts numerical simulation research on deep tight sandstone reservoirs in the west. The discrete fracture network modeling method is used to establish a tight sandstone reservoir model with natural bedding, and the influence of geo-stress difference and natural fracture strength on hydraulic fracture propagation law in a high geo-stress environment is discussed in detail. The results show that the difference between geo-stress and the strength of natural fractures has a significant effect on the shape and expansion of hydraulic fractures under the high geo-stress conditions. The greater the difference in ground stress, the more obvious the tendency of the main fractures of the reservoir, and the shorter the branch fractures. With the increase of natural fracture strength, the changes in propagation pressure, fracture length, area, and width, which can be fitted with a linear function with a goodness of fit as high as 0.99. In addition, the morphological results of hydraulic fractures in the simulation are not only affected by the constitutive parameters of the model but also may be affected by the randomness of the natural fracture network, thus, showing a certain degree of dispersion. Therefore, it is extremely necessary to build a reservoir fracturing model in a specific area based on more detailed geological monitoring data to guide actual construction. The above achievements have certain reference significance for the field operation of deep tight sandstone reservoirs.

Verification of Particle Tracking and In Situ Tracer Experiment for the Gravel and Cholan Formation Composite in Northwest Taiwan

This paper presents the verification results of an experimental site that employed a particle tracking algorithm to assess the transport of tracers through the composite formation of gravel and Cholan in northwest Taiwan. A suitable hydrogeological conceptual model that describes the flow characteristics of the gravel formation and Cholan formation is essential to evaluate groundwater flow and management at this site. Continuous porous medium (CPM) can be easily applied in the gravel formation, while the Cholan formation, characterized by argillaceous sandstone, is commonly treated as a porous medium. However, this study obtains its fracture distribution through geological surveys, and the key fracture parameters are also collected, analyzed, and incorporated into the model. Four hydrogeological conceptual models, including CPM, discrete fracture network (DFN), equivalent continuous porous medium (ECPM), and hybrid DFN/ECPM, are generated for this complex formation. This study combines the conceptual models of the gravel and Cholan formation into four cases to describe the characteristics of the composite formation. The groundwater flow field of four cases is simulated, and the particle tracking method is employed to model the tracer transport. Simulation results from the four hybrid models all yielded a breakthrough curve (BTC) for the first 15 h, indicating that the tracer arrived at the designated outlet within this timeframe and primarily flowed through the gravel formation, while long-time particle tracking revealed a possible flow path through the Cholan formation after 15 h. The breakthrough curve of the four cases shows that the ECPM model is more suitable for representing the heterogeneity of the Cholan formation than the common CPM model. This study provides a suitable numerical algorithm of the conceptual model of the Cholan formation based on strong evidence by considering different models and comparing them with in situ tracer tests.

A three-dimensional numerical well-test model for pressure transient analysis in fractured horizontal wells with secondary fractures

During oil and gas reservoir development, multi-stage horizontal wells (MFHWs) and hydraulic fracturing techniques can effectively increase estimated ultimate recovery. However, there still lacks an understanding of the three-dimensional (3D) pressure transient behaviors of multi-stage fractured horizontal wells with secondary fractures. To narrow this gap, a three-dimensional numerical well-test model based on a discrete fracture model and unstructured tetrahedral grids is developed to study the pressure transient behaviors of MFHWs with secondary fractures. The pressure transient solutions of MFHWs with secondary fractures have been demonstrated by model verifications. The results show that the proposed model can accurately capture the complex transient flow around fractures, including early radial flow that is not easily captured by two-dimensional numerical well test models. The proposed model classifies the flow regimes of a MFHW as: wellbore storage and skin effects, early radial flow, bilinear flow, linear flow, elliptical flow, pseudo radial flow, and pseudo-boundary dominated flow. It is found that the fracture geometry has a relatively large effect on the shape of the pressure derivative curve in this work. The hydraulic fracture half-length has the greatest impact on the pressure transient behaviors of the MFHW, followed by fracture height and secondary fracture half-length, as found in this study. Additionally, fracture parameters are evaluated, and actual well testing data are interpreted, taking into account the fracture height. This work is meaningful to understand the three-dimensional pressure transient behaviors of MFHWs with secondary fractures.

An extended discontinuous deformation analysis for simulation of grouting reinforcement in a water-rich fractured rock tunnel

Grouting has been the most effective approach to mitigate water inrush disasters in underground engineering due to its ability to plug groundwater and enhance rock strength. Nevertheless, there is a lack of potent numerical tools for assessing the grouting effectiveness in water-rich fractured strata. In this study, the hydro-mechanical coupled discontinuous deformation analysis (HM-DDA) is inaugurally extended to simulate the grouting process in a water-rich discrete fracture network (DFN), including the slurry migration, fracture dilation, water plugging in a seepage field, and joint reinforcement after coagulation. To validate the capabilities of the developed method, several numerical examples are conducted incorporating the Newtonian fluid and Bingham slurry. The simulation results closely align with the analytical solutions. Additionally, a set of compression tests is conducted on the fresh and grouted rock specimens to verify the reinforcement method and calibrate the rational properties of reinforced joints. An engineering-scale model based on a real water inrush case of the Yonglian tunnel in a water-rich fractured zone has been established. The model demonstrates the effectiveness of grouting reinforcement in mitigating water inrush disaster. The results indicate that increased grouting pressure greatly affects the regulation of water outflow from the tunnel face and the prevention of rock detachment face after excavation.