Mechanisms of fracture propagation from multi-cluster using a phase field based HMD coupling model in fractured reservoir

Natural fractures(NFs)are common in shale and tight reservoirs,where staged multi-cluster fracturing of horizontal wells is a prevalent technique for reservoir stimulation.While NFs and stress interference are recognized as significant factors affecting hydraulic fracture(HF)propagation,the combined influence of these factors remains poorly understood.To address this knowledge gap,a novel coupled hydromechanical-damage(HMD)model based on the phase field method is developed to investigate the propagation of multi-cluster HFs in fractured reservoirs.The comprehensive energy functional and control functions are established,while incorporating dynamic fluid distribution between multiple perforation clusters and refined changes in rock mechanical parameters during hydraulic fracturing.The HMD coupled multi-cluster HF propagation model investigates various scenarios,including single HF and single NF,reservoir heterogeneity,single HF and NF clusters,and multi-cluster HFs with NF clusters.The results show that the HMD coupling model can accurately capture the impact of approach angle(θ),stress difference and cementation strength on the interaction of HF and NF.The criterion of the open and cross zones is not fixed.The NF angle(a)is not a decisive parameter to discriminate the interaction.According to the relationship between approach angle(θ)and NF angle(a),the contact relationship of HF can be divided into three categories(θ=a,θ<a,andθ>a).The connected NF can increase the complexity of HF by inducing it to form branch fracture,resulting in a fractal dimension of HF as high as2.1280 at angles of±45°.Inter-fracture interference from the heel to the toe of HF shows the phenomenon of no,strong and weak interference.Interestingly,under the influence of NFs,distant HFs from the injection can become dominant fractures.However,as a gradually increases,inter-fracture stress interference becomes the primary factor influencing HF propagation,gradually superseding the dominance of NF induced fractures.

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.

The role of natural fracture activation in hydraulic fracturing for deep unconventional geo-energy reservoir stimulation

The presence of sealed or semi-sealed,multiscale natural fracture systems appears to be crucial for the successful stimulation of deep reservoirs.To explore the reaction of such systems to reservoir stimulation,a new numerical simulation approach for hydraulic stimulation has been developed,trying to establish a realistic model of the physics involved.Our new model successfully reproduces dynamic fracture activation,network generation,and overall reservoir permeability enhancement.Its outputs indicate that natural fractures facilitate stimulation far beyond the near-wellbore area,and can significantly improve the hydraulic conductivity of unconventional geo-energy reservoirs.According to our model,the fracture activation patterns are jointly determined by the occurrence of natural fractures and the in situ stress.High-density natural fractures,high-fluid pressure,and low effective stress environments promote the formation of complex fracture networks during stimulation.Multistage or multicluster fracturing treatments with an appropriate spacing also increase the stimulated reservoir area(SRA).The simulation scheme demonstrated in this work offers the possibility to elucidate the complex multiphysical couplings seen in the field through detailed site-specific modeling.

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 hydraulic fracture interacting with pre-existing fracture

Hydraulic fracturing is considered the main stimulation method to develop shale gas reservoirs. Due to its strong heterogeneity, the shale gas formation is typically embedded with geological discontinuities such as bedding planes and natural fractures. Many researchers realized that the interaction between natural fractures and hydraulic fractures plays a crucial role in generating a complex fracture network. In this paper, true tri-axial hydraulic fracturing tests were performed on polymethyl methacrylate (PMMA), on which pre-existing fracture was pre-manufactured to simulate natural fracture. A cohesive model has been developed to verify the results of the experimental tests. The key findings demonstrate that the experimental results agreed well with the numerical simulation outcomes where three main interaction modes were observed: crossing;being arrested by opening the pre-existing fracture;being arrested without dilating the pre-existing fracture. Crossing behavior is more likely to occur with the approaching angle, horizontal stress difference, and injection rate increase. Furthermore, the higher flow rate might assist in reactivating the natural fractures where both sides of the pre-existing fractures were reactivated as the injection rate increased from 5 to 20 mL/min. Additionally, hydraulic fractures show a tendency to extend vertically rather than along the direction of maximum horizontal stress when they are first terminated at the interface. This research may contribute to the field application of hydraulic fracturing in shale gas formation.

Efficient production optimization for naturally fractured reservoir using EDFM

Naturally fractured reservoirs make important contributions to global oil and gas reserves and production.The modeling and simulation of naturally fractured reservoirs are different from conventional reservoirs as the existence of natural fractures.To address the development optimization problem of naturally fractured reservoirs,we propose an optimization workflow by coupling the optimization methods with the embedded discrete fracture model(EDFM).Firstly,the effective and superior performance of the workflow is verified based on the conceptual model.The stochastic simplex approximate gradient(StoSAG)algorithm,the ensemble optimization(EnOpt)algorithm,and the particle swarm optimization(PSO)algorithm are implemented for the production optimization of naturally fractured reservoirs based on the improved versions of the Egg model and the PUNQ-S3 model.The results of the two cases demonstrate the effectiveness of this optimization workflow by finding the optimal well controls which yield the maximum net present value(NPV).Compared to the initial well control guess,the final NPV obtained from the production optimization of fractured reservoirs based on all three optimization algorithms is significantly enhanced.Compared with the optimization results of the PSO algorithm,StoSAG and EnOpt have significant advantages in terms of final NPV and computational efficiency.The results also show that fractures have a significant impact on reservoir production.The economic efficiency of fractured reservoir development can be significantly improved by the optimization workflow.

Numerical Modeling of Natural Fracture Distributions in Shale

The production efficiency of shale gas is affected by the interaction between hydraulic and natural fractures.This study presents a simulation of natural fractures in shale reservoirs,based on a discrete fracture network(DFN)method for hydraulic fracturing engineering.Fracture properties of the model are calculated from core fracture data,according to statistical mathematical analysis.The calculation results make full use of the quantitative information of core fracture orientation,density,opening and length,which constitute the direct and extensive data of mining engineering.The reliability and applicability of the model are analyzed with regard to model size and density,a calculation method for dominant size and density being proposed.Then,finite element analysis is applied to a hydraulic fracturing numerical simulation of a shale fractured reservoir in southeastern Chongqing.The hydraulic pressure distribution,fracture propagation,acoustic emission information and in situ stress changes during fracturing are analyzed.The results show the application of fracture statistics in fracture modeling and the influence of fracture distribution on hydraulic fracturing engineering.The present analysis may provide a reference for shale gas exploitation.

Complex fracture propagation model and plugging timing optimization for temporary plugging fracturing in naturally fractured shale

In this paper,a viscoelasticity-plastic damage constitutive equation for naturally fractured shale is deduced,coupling nonlinear tensile-shear mixed fracture mode.Dynamic perforation-erosion on fluid re-distribution among multi-clusters are considered as well.DFN-FEM(discrete fracture network combined with finite element method)was developed to simulate the multi-cluster complex fractures propagation within temporary plugging fracturing(TPF).Numerical results are matched with field injection and micro-seismic monitoring data.Based on geomechanical characteristics of Weiyuan deep shale gas reservoir in Sichuan Basin,SW China,a multi-cluster complex fractures propagation model is built for TPF.To study complex fractures propagation and the permeability-enhanced region evolution,intersecting and competition mechanisms between the fractures before and after TPF treatment are revealed.Simulation results show that:fracture from middle cluster is restricted by the fractures from side-clusters,and side-clusters plugging is benefit for multi fractures propagation in uniformity;optimized TPF timing should be delayed within a higher density or strike of natural fractures;Within a reservoir-featured natural fractures distribution,optimized TPF timing for most clustered method is 2/3 of total fluid injection time as the optimal plugging time under different clustering modes.

Modeling flow in naturally fractured reservoirs： effect of fracture aperture distribution on dominant sub-network for flow

Fracture network connectivity and aperture （or conductivity） distribution are two crucial features controlling flow behavior of naturally fractured reservoirs. The effect of connectivity on flow properties is well documented. In this paper, however, we focus here on the influence of fracture aperture distribution. We model a two dimensional fractured reservoir in which the matrix is impermeable and the fractures are well connected. The fractures obey a power-law length distribution, as observed in natural fracture networks. For the aperture distribution, since the information from subsurface fracture networks is limited, we test a number of cases： log-normal distributions （from narrow to broad）, power-law distributions （from narrow to broad）, and one case where the aperture is pro- portional to the fracture length. We find that even a well- connected fracture network can behave like a much sparser network when the aperture distribution is broad enough （c~ 〈 2 for power-law aperture distributions and σ ≥ 0.4 for log-normal aperture distributions）. Specifically, most fractures can be eliminated leaving the remaining dominant sub-network with 90% of the permeability of the original fracture network. We determine how broad the aperture distribution must be to approach this behavior and the dependence of the dominant sub-network on the parameters of the aperture distribution. We also explore whether one can identify the dominant sub-network without doing flow calculations.

Evaluating the mechanical properties of anisotropic shale containing bedding and natural fractures with discrete element modeling

Natural fracture data from one of the Carboniferous shale masses in the eastern Qaidam Basin were used to establish a stochastic model of a discrete fracture network and to perform discrete element simulation research on the size efect and mechanical parameters of shale.Analytical solutions of fctitious joints in transversely isotropic media were derived,which made it possible for the proposed numerical model to simulate the bedding and natural fractures in shale masses.The results indicate that there are two main factors infuencing the representative elementary volume(REV)size of a shale mass.The frst and most decisive factor is the presence of natural fractures in the block itself.The second is the anisotropy ratio:the greater the anisotropy is,the larger the REV.The bedding angle has little infuence on the REV size,whereas it has a certain infuence on the mechanical parameters of the rock mass.When the bedding angle approaches the average orientation of the natural fractures,the mechanical parameters of the shale blocks decrease greatly.The REV representing the mechanical properties of the Carboniferous shale masses in the eastern Qaidam Basin were comprehensively identifed by considering the infuence of bedding and natural fractures.When the numerical model size is larger than the REV,the fractured rock mass discontinuities can be transformed into equivalent continuities,which provides a method for simulating shale with natural fractures and bedding to analyze the stability of a borehole wall in shale.

Investigation of mechanical properties of fractured marbles by uniaxial compression tests

Uniaxial compression tests （UCTs） on 34 naturally fractured marble samples taken from the transportation tunnels of Jinping I1 hydropower station were carried out using the MTS815 Flex test GT rock testing system. Rockburst proneness index WET is determined for the marble samples with the UCTs. According to the number, size and spatial structure characteristics of the internal natural fractures of the marble samples, fractures are basically divided into 4 types, namely, single fracture, parallel fracture, intersectant fracture and mixed fracture. The mechanical properties of naturally fractured rocks （4 types） are analyzed and compared with those of intact rock samples （without natural fractures）. Experimental results indicate that failure characteristics of fractured rocks are appreciably controlled by fracture distribution or fracture patterns. In comparison with intact rocks, the failure of fractured marbles is a locally progressive failure process and finally rocks fail abruptly. Statistically, the uniaxial compressive strengths （UCSs） of rocks with single, parallel, intersectant and mixed fractures are 0.72, 0.69, 0.59 and 0.46 times those of the intact rocks, respectively. However, the elastic modulus of the fractured Yantang marbles is generally not different from that of intact rocks. But the elastic moduli of Baishan marble with single, intersectant and mixed fractures are 0.61, 0.62 and 0.45 times those of intact rocks, respectively. Experimental results also indicate that WEt of fractured marbles is generally smaller than that of intact marbles, which implies that rockburst intensity of fractured marble in field may be controlled to some extent. In addition, the bearing capacity of surrounding rocks is also reduced, thus the surrounding rocks should be supported or reinforced timely according to practical conditions.

A review of pressure transient analysis in reservoirs with natural fractures,vugs and/or caves

A review of the pressure transient analysis of flow in reservoirs having natural fractures,vugs and/or caves is presented to provide an insight into how much knowledge has been acquired about this phenomenon and to highlight the gaps still open for further research.A comparison-based approach is adopted which involved the review of works by several authors and identifying the limiting assumptions,model restrictions and applicability.Pressure transient analysis provides information to aid the identification of important features of reservoirs.It also provides an explanation to complex reservoir pressuredependent variations which have led to improved understanding and optimization of the reservoir dynamics.Pressure transient analysis techniques,however,have limitations as not all its models find application in naturally fractured and vuggy reservoirs as the flow dynamics differ considerably.Pollard’s model presented in 1953 provided the foundation for existing pressure transient analysis in these types of reservoirs,and since then,several authors have modified this basic model and come up with more accurate models to characterize the dynamic pressure behavior in reservoirs with natural fractures,vugs and/or caves,with most having inherent limitations.This paper summarizes what has been done,what knowledge is considered established and the gaps left to be researched on.

Techniques for improving fracture-controlled stimulated reservoir volume in ultra-deep fractured tight reservoirs: A case study of Kuqa piedmont clastic reservoirs, Tarim Basin, NW China

Based on analysis of the reasons for low efficiency and low production after fracturing of some wells in the ultra-deep fractured tight reservoirs of the Kuqa piedmont zone, Tarim Basin and the matching relationship between the in-situ stress field and natural fractures, technological methods for creating complex fracture networks are proposed. Through theoretical study and large-scale physical simulation experiments, the mechanical conditions for forming complex fracture network in the Kuqa piedmont ultra-deep reservoirs are determined. The effectiveness of temporary plugging and diversion, and multi-stage fracturing to activate natural fractures and consequently realize multi-stage diversion is verified. The coupling effect of hydraulic fractures and natural fractures activating each other and resulting in "fracture swarms" is observed. These insights provide theoretical support for improving fracture-controlled stimulated reservoir volume(FSRV) in ultra-deep tight reservoirs. In addition, following the concept of volume fracturing technology and based on the results of fracture conductivity experiments of different processes, fracturing technologies such as multi-stage fracture-network acid fracturing, "multi-stage temporary plugging + secondary fracturing", fracturing of multiple small layers by vertically softness-and-hardness-oriented subdivision, and weighted-fluid refracturing are proposed to increase the FSRV. New environment-friendly weighted-fluid with low cost and new fracturing fluid system with low viscosity and high proppant-carrying capacity are also developed. These techniques have achieved remarkable results in field application.

Fracture Network Volume Fracturing Technology in High-temperature Hard Formation of Hot Dry Rock

It is more difficult for a hot dry rock to form a fracture network system than shale due to its special lithology, physical and mechanical properties under high temperature. The essential characteristics, rock mechanics and in-situ stress characteristics of a hot rock mass have been systematically studied by means of laboratory tests and true tri-axial physical simulation. The fracture initiation and propagation characteristics under different geological and engineering conditions are physically simulated, and the main controlling factors for the formation of a complex fracture network are revealed. The technology of low displacement for enhancing thermal cracking, gel fluid for expanding fracture and variable displacement cyclic injection for increasing a fracture network has been applied in the field, and good results have been achieved. Microseismic monitoring results demonstrate that complex fractures were formed in the field test, and the stimulation volume for heat exchanging reaches more than 3 million cubic meters. The research results play an important role in the stimulation technology of an enhanced geothermal system(EGS) and realize a breakthrough for power generation.

Failure Patterns and Mechanisms of Hydraulic Fracture Propagation Behavior in the Presence of Naturally Cemented Fractures

In this study,we use the extended finite element method(XFEM)with a consideration of junction enrichment functions to investigate the mechanics of hydraulic fractures related to naturally cemented fractures.In the proposed numerical model,the lubrication equation is adopted to describe the fluid flow within fractures.The fluid-solid coupling systems of the hydraulic fracturing problem are solved using the Newton-Raphson method.The energy release rate criterion is used to determine the cross/arrest behavior between a hydraulic fracture(HF)and a cemented natural fracture(NF).The failure patterns and mechanisms of crack propagation at the intersection of natural fractures are discussed.Simulation results show that after crossing an NF,the failure mode along the cemented NF path may change from the tensile regime to the shear or mixed-mode regime.When an advancing HF kinks back toward the matrix,the failure mode may gradually switch back to the tensile-dominated regime.Key factors,including the length of the upper/lower portion of the cemented NF,horizontal stress anisotropy,and the intersection angle of the crack propagation are investigated in detail.An uncemented or partially cemented NF will form a more complex fracture network than a cemented NF.This study provides insight into the formation mechanism of fracture networks in formations that contain cemented NF.

Naturally fractured hydrocarbon reservoir simulation by elastic fracture modeling

Accurate fluid flow simulation in geologically complex reservoirs is of particular importance in construction of reservoir simulators.General approaches in naturally fractured reservoir simulation involve use of unstructured grids or a structured grid coupled with locally unstructured grids and discrete fracture models.These methods suffer from drawbacks such as lack of flexibility and of ease of updating.In this study,I combined fracture modeling by elastic gridding which improves flexibility,especially in complex reservoirs.The proposed model revises conventional modeling fractures by hard rigid planes that do not change through production.This is a dubious assumption,especially in reservoirs with a high production rate in the beginning.The proposed elastic fracture modeling considers changes in fracture properties,shape and aperture through the simulation.This strategy is only reliable for naturally fractured reservoirs with high fracture permeability and less permeable matrix and parallel fractures with less cross-connections.Comparison of elastic fracture modeling results with conventional modeling showed that these assumptions will cause production pressure to enlarge fracture apertures and change fracture shapes,which consequently results in lower production compared with what was previously assumed.It is concluded that an elastic gridded model could better simulate reservoir performance.

Experimental verification of parameter m in Hoeke-Brown failure criterion considering the effects of natural fractures

HoekeBrown failure criterion is one of the widely used rock strength criteria in rock mechanics and mining engineering.Based on the theoretical expression of HoekeBrown parameter m of an intact rock,the parameter m has been modified by crack parameters for fractured rocks.In this paper,the theoretical value range and theoretical expression form of the parameter m in HoekeBrown failure criterion were discussed.A critical crack parameter B was defined to describe the influence of the critical crack when the stress was at the peak,while a parameter b was introduced to represent the distribution of the average initial fractures.The parameter m of a fractured rock contained the influences of critical crack(B),confining pressure(s3)and initial fractures(b).Then the triaxial test on naturally fractured limestones was conducted to verify the modification of the parameter m.From the ultrasonic test and loading test results of limestones,the parameter m can be obtained,which indicated that the confining pressure at a high level reduced the differences of m among all the specimens.The confining pressure s3 had an exponential impact on m,while the critical crack parameter B had a negative correlation with m.Then the expression of m for a naturally fractured limestone was also proposed.

Comparison of numerical codes for coupled thermo-hydro-mechanical simulations of fractured media

Geo-energy and geo-engineering applications,such as improved oil recovery(IOR),geologic carbon storage,and enhanced geothermal systems(EGSs),involve coupled thermo-hydro-mechanical(THM)processes that result from fluid injection and production.In some cases,reservoirs are highly fractured and the geomechanical response is controlled by fractures.Therefore,fractures should explicitly be included into numerical models to realistically simulate the THM responses of the subsurface.In this study,we perform coupled THM numerical simulations of water injection into naturally fractured reservoirs(NFRs)using CODE_BRIGHT and TOUGH-UDEC codes.CODE_BRIGHT is a finite element method(FEM)code that performs fully coupled THM analysis in geological media and TOUGH-UDEC sequentially solves coupled THM processes by combining a finite volume method(FVM)code that solves nonisothermal multiphase flow(TOUGH2)with a distinct element method(DEM)code that solves the mechanical problem(UDEC).First,we validate the two codes against a semi-analytical solution for water injection into a single deformable fracture considering variable permeability based on the cubic law.Then,we compare simulation results of the two codes in an idealized conceptual model that includes one horizontal fracture and in a more realistic model with multiple fractures.Each code models fractures differently.UDEC calculates fracture deformation from the fracture normal and shear stiffnesses,while CODE_BRIGHT treats fractures as equivalent porous media and uses the equivalent Young’s modulus and Poisson’s ratio of the fracture.Finally,we obtain comparable results of pressure,temperature,stress and displacement distributions and evolutions for the single horizontal fracture model.Despite some similarities,the two codes provide increasingly different results as model complexity increases.These differences highlight the challenging task of accurately modeling coupled THM processes in fractured media given their high nonlinearity.

A method to experimentally investigate injection-induced activation of fractures

Natural fractures are generally well developed in most hydrocarbon and geothermal reservoirs,which can produce complex fracture networks due to the activation of fractures during hydraulic stimulation.The present paper is devoted to developing a method to investigate the activation characteristics of fracture under injection-shearing coupled condition at laboratory scale.The fluid is injected into the single-fractured granite until the fracture is activated based on the triaxial direct shear tests.The results show that injection process can significantly influence the shear stress distribution field,resulting in release of shear stress and relative slip between the opposite sides of the fractured surface.The injectioninduced activation of fracture is strongly dependent on the stress states.When the normal stress increases,the injection-induced activation pressure increases,and the comparatively high normal stress can restrain the fracture activation.The fracture deformation mechanisms during fluid injection are also discussed preliminarily with the experimental data.The sensitivity of shear stress to fluid injection increases with increase of shear stress level,while it decreases under high normal stress.The results can facilitate our understanding of the natural fracture activation behavior during fluid pressure stimulation.

A Review of the Dynamic Modeling Approaches for Characterizing Fluid Flow in Naturally Fractured Reservoirs

Fluid flow in fractured media has been studied for decades and received considerable attention in the oil and gas industry because of the high productivity of naturally fractured reservoirs.Due to formation complexity and reservoir heterogeneity,characterizing fluid flow with an appropriate reservoir model presents a challenging task that differs relatively from homogeneous conventional reservoirs in many aspects of view,including geological,petrophysical,production,and economics.In most fractured reservoirs,fracture networks create complex pathways that affect hydrocarbon flow,well performance,hence reservoir characterization.A better and comprehensive understanding of the available reservoir modeling approaches is much needed to accurately characterize fluid flow behavior in NFRs.Therefore,in this paper,a perspective review of the available modeling approaches was presented for fluid flow characterization in naturally fractured medium.Modeling methods were evaluated in terms of their description,application,advantages,and disadvantages.This study has also included the applications of these reservoir models in fluid flow characterizing studies and governing equations for fluid flow.Dual continuum models were proved to be better than single continuum models in the presence of large scale fractures.In comparison,discrete models were more appropriate for reservoirs that contain a smaller number of fractures.However,hybrid modeling was the best method to provide accurate and scalable fluid flow modeling.It is our understanding that this paper will bridge the gap between the fundamental understanding and application of NFRs modeling approaches and serve as a useful reference for engineers and researchers for present and future applications.