Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

Borehole stability in naturally fractured rocks with drilling mud intrusion and associated fracture strength weakening:A coupled DFN-DEM approach

Borehole instability in naturally fractured rocks poses significant challenges to drilling.Drilling mud invades the surrounding formations through natural fractures under the difference between the wellbore pressure(P w)and pore pressure(P p)during drilling,which may cause wellbore instability.However,the weakening of fracture strength due to mud intrusion is not considered in most existing borehole stability analyses,which may yield significant errors and misleading predictions.In addition,only limited factors were analyzed,and the fracture distribution was oversimplified.In this paper,the impacts of mud intrusion and associated fracture strength weakening on borehole stability in fractured rocks under both isotropic and anisotropic stress states are investigated using a coupled DEM(distinct element method)and DFN(discrete fracture network)method.It provides estimates of the effect of fracture strength weakening,wellbore pressure,in situ stresses,and sealing efficiency on borehole stability.The results show that mud intrusion and weakening of fracture strength can damage the borehole.This is demonstrated by the large displacement around the borehole,shear displacement on natural fractures,and the generation of fracture at shear limit.Mud intrusion reduces the shear strength of the fracture surface and leads to shear failure,which explains that the increase in mud weight may worsen borehole stability during overbalanced drilling in fractured formations.A higher in situ stress anisotropy exerts a significant influence on the mechanism of shear failure distribution around the wellbore.Moreover,the effect of sealing natural fractures on maintaining borehole stability is verified in this study,and the increase in sealing efficiency reduces the radial invasion distance of drilling mud.This study provides a directly quantitative prediction method of borehole instability in naturally fractured formations,which can consider the discrete fracture network,mud intrusion,and associated weakening of fracture strength.The information provided by the numerical approach(e.g.displacement around the borehole,shear displacement on fracture,and fracture at shear limit)is helpful for managing wellbore stability and designing wellbore-strengthening operations.

Creep constitutive model considering nonlinear creep degradation of fractured rock

Stability analysis of underground constructions requires a model study of rock masses’ long-term performance. Creep tests under different stress conditions was conducted on intact granite and granite samples fractured at 30° and 45° angles. The experimental results indicate that the steady creep strain rates of intact and fractured rock present an exponential increase trend with the increase of stress level. A nonlinear creep model is developed based on the experimental results, in which the initial damage caused by fracture together with the damage caused by constant load have been taken into consideration. The fitting analysis results indicated that the model proposed is more accurate at identifying the full creep regions in fractured granite, especially the accelerated stage of creep deformation. The least-square fit error of the proposed creep model is significantly lower than that of Nishihara model by almost an order of magnitude. An analysis of the effects of elastic modulus, viscosity coefficient, and damage factors on fractured rock strain rate and creep strain is conducted. If no consideration is given to the effects of the damage, the proposed nonlinear creep model can degenerate into to the classical Nishihara model.

Identifying flow regime in the aquifer of fractured rock system in Germi Chai Basin,Iran

Considering the importance of fractured rock aquifers in the hydrogeologic process,this research aimed to analyze the flow regime,internal degree of karstification,and estimate storage volume in fractured rock aquifers of the Germi Chai Basin in northwest Iran,which is attributed to its active tectonics,erosion,and the lithological diversity.Given the geological setting,the hypothesis is that this basin is characterized by a high degree of karstification and diffuse or intermediate flow regime leading to variation in discharge flow rate.The hydrodynamic and hadrochemical analysis was conducted on 9 well distributed springs across the basin from 2019 to 2020.The maximum flow rate in most of the springs appeared in the early wet season despite their different levels of fluctuations on the monthly discharge time series.Analyzing the spring recession curve form revealed an aquifer containing multiple micro-regimes withαrecession coefficients and a degree of karstification ranging between 0.001 to 0.06 and 0.55 to 2.61,respectively.These findings indicated a dominant diffuse and intermediate flow system resulting from the development of a high density of fractures in this area.The electrical conductivity of the spring changes inversely proportional to the change in flow discharge,indicating the reasonable hydrological response of the aquifer to rainfall events.Hydrograph analysis revealed that the delay time of spring discharge after rainfall events mostly varies between 10 to 30 days.The total dynamic storage volume of the spring for a given period(2019-2020)was estimated to be approximately 1324 million cubic meters reflecting the long-term drainage potential and high perdurability of dynamic storage.Estimating the maximum and minimum ratio revealed that the springs recharging system in Germi Chai Basin comes under the slow aquifers category.This finding provides valuable insight into the hydrogeological properties of fractured rock aquifers contributing to effective water management strategy.

Multiscale modeling of gas-induced fracturing in anisotropic clayey rocks

In the context of repositories for nuclear waste,understanding the behavior of gas migration through clayey rocks with inherent anisotropy is crucial for assessing the safety of geological disposal facilities.The primary mechanism for gas breakthrough is the opening of micro-fractures due to high gas pressure.This occurs at gas pressures lower than the combined strength of the rock and its minimum principal stress under external loading conditions.To investigate the mechanism of microscale mode-I ruptures,it is essential to incorporate a multiscale approach that includes subcritical microcracks in the modeling framework.In this contribution,we derive the model from microstructures that contain periodically distributed microcracks within a porous material.The damage evolution law is coupled with the macroscopic poroelastic system by employing the asymptotic homogenization method and considering the inherent hydro-mechanical(HM)anisotropy at the microscale.The resulting permeability change induced by fracture opening is implicitly integrated into the gas flow equation.Verification examples are presented to validate the developed model step by step.An analysis of local macroscopic response is undertaken to underscore the influence of factors such as strain rate,initial damage,and applied stress,on the gas migration process.Numerical examples of direct tension tests are used to demonstrate the model’s efficacy in describing localized failure characteristics.Finally,the simulation results for preferential gas flow reveal the robustness of the two-scale model in explicitly depicting gas-induced fracturing in anisotropic clayey rocks.The model successfully captures the common behaviors observed in laboratory experiments,such as a sudden drop in gas injection pressure,rapid build-up of downstream gas pressure,and steady-state gas flow following gas breakthrough.

A method to interpret fracture aperture of rock slope using adaptive shape and unmanned aerial vehicle multi-angle nap-of-the-object photogrammetry

The aperture of natural rock fractures significantly affects the deformation and strength properties of rock masses,as well as the hydrodynamic properties of fractured rock masses.The conventional measurement methods are inadequate for collecting data on high-steep rock slopes in complex mountainous regions.This study establishes a high-resolution three-dimensional model of a rock slope using unmanned aerial vehicle(UAV)multi-angle nap-of-the-object photogrammetry to obtain edge feature points of fractures.Fracture opening morphology is characterized using coordinate projection and transformation.Fracture central axis is determined using vertical measuring lines,allowing for the interpretation of aperture of adaptive fracture shape.The feasibility and reliability of the new method are verified at a construction site of a railway in southeast Tibet,China.The study shows that the fracture aperture has a significant interval effect and size effect.The optimal sampling length for fractures is approximately 0.5e1 m,and the optimal aperture interpretation results can be achieved when the measuring line spacing is 1%of the sampling length.Tensile fractures in the study area generally have larger apertures than shear fractures,and their tendency to increase with slope height is also greater than that of shear fractures.The aperture of tensile fractures is generally positively correlated with their trace length,while the correlation between the aperture of shear fractures and their trace length appears to be weak.Fractures of different orientations exhibit certain differences in their distribution of aperture,but generally follow the forms of normal,log-normal,and gamma distributions.This study provides essential data support for rock and slope stability evaluation,which is of significant practical importance.

Discontinuity development patterns and the challenges for 3D discrete fracture network modeling on complicated exposed rock surfaces

Natural slopes usually display complicated exposed rock surfaces that are characterized by complex and substantial terrain undulation and ubiquitous undesirable phenomena such as vegetation cover and rockfalls.This study presents a systematic outcrop research of fracture pattern variations in a complicated rock slope,and the qualitative and quantitative study of the complex phenomena impact on threedimensional(3D)discrete fracture network(DFN)modeling.As the studies of the outcrop fracture pattern have been so far focused on local variations,thus,we put forward a statistical analysis of global variations.The entire outcrop is partitioned into several subzones,and the subzone-scale variability of fracture geometric properties is analyzed(including the orientation,the density,and the trace length).The results reveal significant variations in fracture characteristics(such as the concentrative degree,the average orientation,the density,and the trace length)among different subzones.Moreover,the density of fracture sets,which is approximately parallel to the slope surface,exhibits a notably higher value compared to other fracture sets across all subzones.To improve the accuracy of the DFN modeling,the effects of three common phenomena resulting from vegetation and rockfalls are qualitatively analyzed and the corresponding quantitative data processing solutions are proposed.Subsequently,the 3D fracture geometric parameters are determined for different areas of the high-steep rock slope in terms of the subzone dimensions.The results show significant variations in the same set of 3D fracture parameters across different regions with density differing by up to tenfold and mean trace length exhibiting differences of 3e4 times.The study results present precise geological structural information,improve modeling accuracy,and provide practical solutions for addressing complex outcrop issues.

Sub-Homogeneous Peridynamic Model for Fracture and Failure Analysis of Roadway Surrounding Rock

The surrounding rock of roadways exhibits intricate characteristics of discontinuity and heterogeneity.To address these complexities,this study employs non-local Peridynamics(PD)theory and reconstructs the kernel function to represent accurately the spatial decline of long-range force.Additionally,modifications to the traditional bondbased PD model are made.By considering the micro-structure of coal-rock materials within a uniform discrete model,heterogeneity characterized by bond random pre-breaking is introduced.This approach facilitates the proposal of a novel model capable of handling the random distribution characteristics of material heterogeneity,rendering the PD model suitable for analyzing the deformation and failure of heterogeneous layered coal-rock mass structures.The established numerical model and simulation method,termed the sub-homogeneous PD model,not only incorporates the support effect but also captures accurately the random heterogeneous micro-structure of roadway surrounding rock.The simulation results obtained using this model show good agreement with field measurements from the Fucun coal mine,effectively validating the model’s capability in accurately reproducing the deformation and failure mode of surrounding rock under bolt-supported(anchor cable).The proposed subhomogeneous PD model presents a valuable and effective simulation tool for studying the deformation and failure of roadway surrounding rock in coal mines,offering new insights and potential advancements.

Grouting theories and technologies for the reinforcement of fractured rocks surrounding deep roadways

Grouting is an effective method to improve the integrity and stability of fractured rocks that surround deep roadways.After years of research and practice,various theories and a complete set of grouting technologies for deep roadways with fractured rocks have been developed and are widely applied in Chinese coal mining production.This paper systematically summarizes and analyzes the research results concerning the theory,design,materials,processes,and equipment for the grouting and reinforcement of fractured rocks surrounding deep roadways.Specifically,in terms of grouting methods,pregrouting,groutingwhile-excavation,and postgrouting methods are explored;in terms of grouting theory,backfill grouting,compaction grouting,infiltration grouting,and fracture grouting theories are studied.In addition,this paper also studies grouting borehole arrangement,water-cement ratio,grouting pressure,grouting volume,grout diffusion radius,and other grouting parameters and their determination methods.On this basis,this paper explores the physical and mechanical properties of organic and organic-inorganic composite grouting materials,and assess grouting reinforcement quality testing methods and instruments.Taken as the field cases,the application of pregrouting in front of heading faces,groutingwhile-excavation,and postgrouting in the Kouzidong coal mine are then introduced,and the effects of the grouting reinforcements are evaluated.This paper proposes a development direction for grouting technology based on problems existing in the grouting reinforcement of fractured rocks surrounding deep roadways.

Multi-domain equivalent method for prediction of elastic modulus of complex fractured rock mass

Reliable estimation of deformation and failure behaviors of fractured rock mass is important for practical engineering design.This study proposes a multi-domain equivalent method for fracture network to estimate the deformation properties of complex fractured rock mass.It comprehends both the advantages of the discrete fracture network model and the equivalent continuum model to capture the features of discontinuities explicitly while reducing computational intensity.The complex fracture network is stochastically split into a number of subfracture networks according to the domain,length or angle.An analytical solution is derived to infer theoretically the relationship between the elastic moduli of the original complex fractured rock mass and the split subfractured rock masses by introducing a correction term based on the deformation superposition principle.Numerical simulations are conducted to determine the elastic moduli of split subfractured rock masses using universal distinct element code(UDEC),while the elastic modulus of the original model is estimated based on the currently proposed analytical relationship.The results show that the estimation accuracy with the current domainbased splitting model is far superior compared to those with the other two splitting models.Thus,the estimation method of elastic modulus of complex fractured rock mass based on domain splitting mode of fracture network is identified as the multi-domain equivalent method proposed in this paper.The reliability of this method is evaluated,and its high computational efficiency is demonstrated through exemplification with regard to different geometric configurations for stochastically artificial discrete fracture network.The proposed multi-domain equivalent method constructs the theoretical framework except for the regression analysis hypothesis compared to the density-reduced model equivalent method.

Groundwater flow through fractured rocks and seepage control in geotechnical engineering: Theories and practices

Groundwater flow through fractured rocks has been recognized as an important issue in many geotechnical engineering practices.Several key aspects of fundamental mechanisms,numerical modeling and engineering applications of flow in fractured rocks are discussed.First,the microscopic mechanisms of fluid flow in fractured rocks,especially under the complex conditions of non-Darcian flow,multiphase flow,rock dissolution,and particle transport,have been revealed through a com-bined effort of visualized experiments and theoretical analysis.Then,laboratory and field methods of characterizing hydraulic properties(e.g.intrinsic permeability,inertial permeability,and unsaturated flow parameters)of fractured rocks in different flow regimes have been proposed.Subsequently,high-performance numerical simulation approaches for large-scale modeling of groundwater flow in frac-tured rocks and aquifers have been developed.Numerical procedures for optimization design of seepage control systems in various settings have also been proposed.Mechanisms of coupled hydro-mechanical processes and control of flow-induced deformation have been discussed.Finally,three case studies are presented to illustrate the applications of the improved theoretical understanding,characterization methods,modeling approaches,and seepage and deformation control strategies to geotechnical engi-neering projects.

In-situ observations of damage-fracture evolution in surrounding rock upon unloading in 2400-m-deep tunnels

The damage-fracture evolution of deep rock mass has obvious particularity,which is revealed in 2400-mdeep tunnels by field tests.The evolution of the excavation damaged zone depth is consistent with that of the fractured zone depth.The ratio of the excavation damaged zone depth to the excavation fractured zone depth is greater than 2.0 in a rock mass with both high strength and good integrity,but less than1.5 in a rock mass with lower strength or poor integrity.Zonal disintegration in a rock mass with high strength and fair integrity is more likely to occur when it contains more than two groups of primary fractures in damaged zones.Fractures develop outward in zonal disintegration but are totally different from the single-zone fracture,in which the fractures develop inward,and it is the starting position of the fractured zone when the excavation surface of the middle pilot is 7–9 m close to the pre-set borehole and it stops after the excavation surface of the baseplate is 11–14 m away.The most intense evolution occurs around 2–4 m from the pre-set borehole in the sidewall expansion stage.The research results provide a reference for the monitoring scheme and support design of CJPL-Ⅲin its future construction.

On the calibration and verification of Voronoi-based discontinuous deformation analysis for modeling rock fracture

Since its introduction,discontinuous deformation analysis(DDA)has been widely used in different areas of rock mechanics.By dividing large blocks into subblocks and introducing artificial joints,DDA can be applied to rock fracture simulation.However,parameter calibration,a fundamental issue in discontinuum methods,has not received enough attention in DDA.In this study,the parameter calibration of DDA for intact rock is carefully studied.To this end,a subblock DDA with Voronoi tessellation is presented first.Then,a modified contact constitutive law is introduced,in which the tensile and shear meso-strengths are modified to be independent of the bond lengths.This improvement can prevent the unjustified preferential failure of short edges.A method for imposing confining pressure is also introduced.Thereafter,sensitivity analysis is performed to investigate the influence of the calculated parameters and meso-parameters on the mechanical properties of modeled rock.Based on the sensitivity analysis,a unified calibration procedure is suggested for both cases with and without confining pressure.Finally,the calibration procedure is applied to two examples,including a biaxial compression test.The results show that the proposed Voronoi-based DDA can simulate rock fracture with and without confining pressure very well after careful parameter calibration.

Characteristics of electromagnetic vector field generated from rock fracturing

Rock fracturing is often accompanied by electromagnetic phenomenon.As a vector field,in addition to the intensity that is widely concerned,the generated electromagnetic field also has obvious direction-ality.To this end,a set of electromagnetic antennas capable of simultaneous three-axis measurement is used to monitor the electromagnetic vector field generated from rock fracturing based on Brazilian tests.The signal amplitude on each axis can represent the magnitude of actual magnetic flux density component on the three axes.The intensity and directional characteristics of electromagnetic signals received at different positions are studied using vector synthesis.The directionality of electromagnetic radiation measured using a three-axis electromagnetic antenna shows that the direction of the magnetic flux intensity generated by rock fracturing tends to be parallel to the crack surface,and the measured signal intensity is greater in a direction closer to the crack surface.

Enhance liquid nitrogen fracturing performance on hot dry rock by cyclic injection

Producing complex fracture networks in a safe way plays a critical role in the hot dry rock (HDR) geothermal energy exploitation. However, conventional hydraulic fracturing (HF) generally produces high breakdown pressure and results only in single main fracture morphology. Furthermore, HF has also other problems such as the increased risk of seismic events and consuption of large amount of water. In this work, a new stimulation method based on cyclic soft stimulation (CSS) and liquid nitrogen (LN2) fracturing, known as cyclic LN2 fracturing is explored, which we believe has the potential to solve the above issues related to HF. The fracturing performances including breakdown pressure and fracture morphology on granites under true-triaxial stresses are investigated and compared with cyclic water fracturing. Cryo-scanning electron microscopy (Cryo-SEM) tests and X-ray computed tomography (CT) scanning tests were used for quantitative characterization of fracture parameters and to evaluate the cyclic LN2 fracturing performances. The results demonstrate that the cyclic LN2 fracturing results in reduced breakdown pressure, with between 21% and 67% lower pressure compared with using cyclic water fracturing. Cyclic LN2 fracturing tends to produce more complex and branched fractures, whereas cyclic water fracturing usually produces a single main fracture under a low number of cycles and pressure levels. Thermally-induced fractures mostly occur around the interfaces of different particles. This study shows the potential benefits of cyclic LN2 fracturing on HDR. It is expected to provide theoretical guidance for the cyclic LN2 fracturing application in HDR reservoirs.

A post-peak dilatancy model for soft rock and its application in deep tunnel excavation

The dilation angle is the most commonly used parameter to study nonlinear post-peak dilatancy(PPD)behavior and simulate surrounding rock deformation;however,simplified or constant dilatancy models are often used in numerical calculations owing to their simple mathematical forms.This study developed a PPD model for rocks(rock masses)based on the Alejanoe-Alonso(A-A)dilatancy model.The developed model comprehensively reflects the influences of confining pressure(σ_(3))and plastic shear strain(γ^(p)),with the advantages of a simple mathematical form,while requiring fewer parameters and demonstrating a clear physical significance.The overall fitting accuracy of the PPD model for 11 different rocks was found to be higher than that of the A-A model,particularly for Witwatersrand quartzite and jointed granite.The applicability and reliability of the PPD model to jointed granites and different scaled Moura coals were also investigated,and the model was found to be more suitable for the soft and large-scale rocks,e.g.deep rock mass.The PPD model was also successfully applied in studying the mechanical response of a circular tunnel excavated in strain-softening rock mass,and the developed semi-analytical solution was compared and verified with existing analytical solutions.The sensitivities of the rock dilatancy to γ^(p) and σ_(3) showed significant spatial variabilities along the radial direction of the surrounding rock,and the dilation angle did not exhibit a monotonical increasing or decreasing law from the elasticeplastic boundary to the tunnel wall,thereby presenting the σ3-or γ^(p)-dominated differential effects of rock dilatancy.Tunnel deformation parabolically or exponentially increased with increasing in situ stress(buried depth).The developed PPD model is promising to conduct refined numerical and analytical analyses for deep tunneling,which produces extensive plastic deformation and exhibits significant nonlinear post-peak behavior.

An open-end high-power microwave-induced fracturing system for hard rock

Microwave pre-treatment is considered as a promising technique for alleviating cutter wear. This paper introduces a high-power microwave-induced fracturing system for hard rock. The test system consists of a high-power microwave subsystem (100 kW), a true triaxial testing machine, a dynamic monitoring subsystem, and an electromagnetic shielding subsystem. It can realize rapid microwave-induced fracturing, intelligent tuning of impedance, dynamic feedback under strong microwave fields, and active control of microwave parameters by addressing the following issues: the instability and insecurity of the system, the discharge breakdown between coaxial lines during high-power microwave output, and a lack of feedback of rock-microwave response. In this study, microwave-induced surface and borehole fracturing tests under true triaxial stress were carried out. Experimental comparisons imply that high-power microwave irradiation can reduce the fracturing time of hard rock and that the fracture range (160 mm) of a 915-MHz microwave source is about three times that of 2.45 GHz. After microwave-induced borehole fracturing, many tensile cracks occur on the rock surface and in the borehole: the maximum reduction of the P-wave velocity is 12.8%. The test results show that a high-power microwave source of 915 MHz is more conducive to assisting mechanical rock breaking and destressing. The system can promote the development of microwave-assisted rock breaking equipment.

Comprehensive assessment on dynamic roof instability under fractured rock mass conditions in the excavation disturbed zone

The damage process of fractured rock mass showed that the fracture in rocks induced roof collapse in Yangchangwan Coal Mine, China. The rock mass was particularly weak and fractured. There occurred 6 large-scale dynamical roof falls in the excavation disturbed zone （EDZ） with the collapsing volume of 216 m^3. First, the field detailed geological environment, regional seismic dynamics, and dynamic instability of roadways were generally investigated. Second, the field multiple-index monitoring measurements for detecting the deep delamination of the roof, convergence deformation, bolt-cable load, acoustic emission （AE） characteristic parameters, total AE events, AE energy-releasing rate, rock mass fracture, and damage were arranged. Finally, according to the time-space-strength relations, a quantitative assessment of the influence of rock-mass damage on the dynamic roof instability was accomplished.

A 3D analysis of the occurrence of fractures in hot dry rock reservoirs based on the spatial distribution of natural fractures

Hot dry rock(HDR)geothermal energy is a kind of widely distributed clean energy with huge reserves.However,its commercial development has been constrained by reservoir stimulation.In the early stage of HDR geothermal energy development,properly determining spatial distribution patterns of natural fractures in HDR reservoirs can effectively guide reservoir stimulation.This study analyzes the spatial distribution of natural fractures by using FracMan software based on the actual geological data and log data of well M-2 in the Matouying Uplift area,Hebei Province.The fracture parameters are counted and Monte Carlo simulation technique is introduced to optimize the parameters,which makes the natural fracture model more accurate and reliable.Furthermore,this study simulates hydraulic fracturing using the model combined with the actual in-situ stress parameters and the construction scheme.As verified by fitting the changes in simulated wellhead pressure during hydraulic fracturing with the actual wellhead pressure data detected during construction,the methods for natural fracture modeling used in this study are scientific and reasonable.The preliminary prediction results show that the displacement design scheme with a pump displacement of 2.0-3.0 m^(3)/min,4.0-5.5 m^(3)/min and 6-7 m^(3)/min in the early,middle and late stages,respectively,has good fracturing effect.The results of this study can be utilized as a reference for preparing development schemes for HDR reservoirs.

Visualization of drained rock volume(DRV) in hydraulically fractured reservoirs with and without natural fractures using complex analysis methods(CAMs)

The drainage areas(and volumes)near hydraulically fractured wells,computed and visualized in our study at high resolution,may be critically affected by the presence of natural fractures.Using a recently developed algorithm based on complex analysis methods(CAMs),the drained rock volume(DRV)is visualized for a range of synthetic constellations of natural fractures near hydraulic fractures.First,flow interference effects near a single hydraulic fracture are systematically investigated for a variety of natural fracture sets.The permeability contrast between the matrix and the natural fractures is increased stepwise in order to better understand the effect on the DRV.Next,a larger-scale model investigates flow interference for a full hydraulically fractured well with a variety of natural fracture sets.The time of flight contours(TOFCs)outlining the DRV are for all cases with natural fractures compared to a base case without any natural fractures.Discrete natural fractures,with different orientations,hydraulic conductivity,and fracture density,may shift the TOFC patterns in the reservoir region drained by the hydraulically fractured well,essentially shifting the location of the well’s drainage area.The CAM-based models provide a computationally efficient method to quantify and visualize the drainage in both naturally and hydraulically fractured reservoirs.