Study on a Dual Embedded Discrete Fracture Model for Fluid Flow in Fractured Porous Media

Simulation of fluid flow in the fractured porous media is very important and challenging.Researchers have developed some models for fractured porous media.With the development of related research in recent years,the prospect of embedded discrete fracture model(EDFM)is more and more bright.However,since the size of the fractures in the actual reservoir varies greatly,a very fine grid should be used which leads to a huge burden to the computing resources.To address this challenge,in the present paper,an upscaling based model is proposed.In this model,the flow in large-scale fractures is directly described by the EDFM while that in the small-scale fractures is upscaled through local simulation by EDFM.The EDFM is used to simulate the large-and small-scale fractures independently two times,so the new model is called dual embedded discrete fracture model(D-EDFM).In this paper,the detailed implementation process of D-EDFM is introduced and,through test cases,it is found the proposed model is a feasible method to simulate the flow in fractured porous media.

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.

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.

A smart productivity evaluation method for shale gas wells based on 3D fractal fracture network model

The generation method of three-dimensional fractal discrete fracture network(FDFN)based on multiplicative cascade process was developed.The complex multi-scale fracture system in shale after fracturing was characterized by coupling the artificial fracture model and the natural fracture model.Based on an assisted history matching(AHM)using multiple-proxy-based Markov chain Monte Carlo algorithm(MCMC),an embedded discrete fracture modeling(EDFM)incorporated with reservoir simulator was used to predict productivity of shale gas well.When using the natural fracture generation method,the distribution of natural fracture network can be controlled by fractal parameters,and the natural fracture network generated coupling with artificial fractures can characterize the complex system of different-scale fractures in shale after fracturing.The EDFM,with fewer grids and less computation time consumption,can characterize the attributes of natural fractures and artificial fractures flexibly,and simulate the details of mass transfer between matrix cells and fractures while reducing computation significantly.The combination of AMH and EDFM can lower the uncertainty of reservoir and fracture parameters,and realize effective inversion of key reservoir and fracture parameters and the productivity forecast of shale gas wells.Application demonstrates the results from the proposed productivity prediction model integrating FDFN,EDFM and AHM have high credibility.

Well interference evaluation considering complex fracture networks through pressure and rate transient analysis in unconventional reservoirs

Severe well interference through complex fracture networks(CFNs)can be observed among multi-well pads in low permeability reservoirs.The well interference analysis between multi-fractured horizontal wells(MFHWs)is vitally important for reservoir effective development.Well interference has been historically investigated by pressure transient analysis,while it has shown that rate transient analysis has great potential in well interference diagnosis.However,the impact of complex fracture networks(CFNs)on rate transient behavior of parent well and child well in unconventional reservoirs is still not clear.To further investigate,this paper develops an integrated approach combining pressure and rate transient analysis for well interference diagnosis considering CFNs.To perform multi-well simulation considering CFNs,non-intrusive embedded discrete fracture model approach was applied for coupling fracture with reservoir models.The impact of CFN including natural fractures and frac-hits on pressure and rate transient behavior in multi-well system was investigated.On a logelog plot,interference flow and compound linear flow are two new flow regimes caused by nearby producers.When both NFs and frac-hits are present in the reservoir,frac-hits have a greater impact on well#1 which contains frac-hits,and NFs have greater impact on well#3 which does not have frac-hits.For all well producing circumstances,it might be challenging to see divergence during pseudosteady state flow brought on by frac-hits on the logelog plot.Besides,when NFs occur,reservoir depletion becomes noticeable in comparison to frac-hits in pressure distribution.Application of this integrated approach demonstrates that it works well to characterize the well interference among different multi-fractured horizontal wells in a well pad.Better reservoir evaluation can be acquired based on the new features observed in the novel model,demonstrating the practicability of the proposed approach.The findings of this study can help for better evaluating well interference degree in multi-well systems combing PTA and RTA,which can reduce the uncertainty and improve the accuracy of the well interference analysis based on both field pressure and rate data.

Analysis of fracture propagation and shale gas production by intensive volume fracturing

This paper presents an integrated study from fracture propagation modeling to gas flow modeling and a correlation analysis to explore the key controlling factors of intensive volume fracturing.The fracture propagation model takes into account the interaction between hydraulic fracture and natural fracture by means of the displacement discontinuity method(DDM)and the Picard iterative method.The shale gas flow considers multiple transport mechanisms,and the flow in the fracture network is handled by the embedded discrete fracture model(EDFM).A series of numerical simulations are conducted to analyze the effects of the cluster number,stage spacing,stress difference coefficient,and natural fracture distribution on the stimulated fracture area,fractal dimension,and cumulative gas production,and their correlation coefficients are obtained.The results show that the most influential factors to the stimulated fracture area are the stress difference ratio,stage spacing,and natural fracture density,while those to the cumulative gas production are the stress difference ratio,natural fracture density,and cluster number.This indicates that the stress condition dominates the gas production,and employing intensive volume fracturing(by properly increasing the cluster number)is beneficial for improving the final cumulative gas production.

Horizontal Well Interference Performance and Water Injection Huff and Puff Effect on Well Groups with Complex Fracture Networks:A Numerical Study

Well interference has become a common phenomenon with the increasing scale of horizontal well fracturing.Recent studies on well interference in horizontal wells do not properly reflect the physical model of the postfracturing well groups and the realistic fracturing process of infill wells.Establishing the correspondence between well interference causative factors and manifestations is of great significance for infill well deployment and secondary oil recovery.In this work,we develop a numerical model that considers low velocity non-Darcy seepage inshale reservoirs to study the inter-well interferencephenomenon that occurs in theSantanghufield,andconstruct an explicit hydraulic fracture and complex natural fracture network model with an embedded discrete fracture model,focusing on the effect of fracture network morphology on well interactions.The model also considers a multi-segment wellbore model to accommodate the effect of inter-well crossflow on wellbore tubular flow.The changes in formation pressure and water saturation during fracturing are performed by controlling the injection pressure and water injection rate.The result shows that the shape of the fracture network generated by the infill well with the old well determines the subsequent fluid and oil-increasing performance of the disturbed well.The synergistic production or competitive relationship formed by fractures with different connectivity between the two wells determines the positive and negative effects of the interference.The paper also investigates the adaptation study of water injection huff and puff schemes for well groups with different connectivity,and demonstrated a potential yield increase of up to 10.85%under adaptation injection.This method of identifying well interference based on the production dynamics of affected wells and the subsequent corresponding water injection method provides valuable references for the selection of secondary oil recovery measures.

A review of discrete modeling techniques for fracturing processes in discontinuous rock masses

The goal of this review paper is to provide a summary of selected discrete element and hybrid finitediscrete element modeling techniques that have emerged in the field of rock mechanics as simulation tools for fracturing processes in rocks and rock masses. The fundamental principles of each computer code are illustrated with particular emphasis on the approach specifically adopted to simulate fracture nucleation and propagation and to account for the presence of rock mass discontinuities. This description is accompanied by a brief review of application studies focusing on laboratory-scale models of rock failure processes and on the simulation of damage development around underground excavations.

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.

CO_(2)flooding in shale oil reservoir with radial borehole fracturing for CO_(2)storage and enhanced oil recovery

This study introduces a novel method integrating CO_(2)flooding with radial borehole fracturing for enhanced oil recovery and CO_(2)underground storage,a solution to the limited vertical stimulation reservoir volume in horizontal well fracturing.A numerical model is established to investigate the production rate,reservoir pressure field,and CO_(2)saturation distribution corresponding to changing time of CO_(2)flooding with radial borehole fracturing.A sensitivity analysis on the influence of CO_(2)injection location,layer spacing,pressure difference,borehole number,and hydraulic fractures on oil production and CO_(2)storage is conducted.The CO_(2)flooding process is divided into four stages.Reductions in layer spacing will significantly improve oil production rate and gas storage capacity.However,serious gas channeling can occur when the spacing is lower than 20 m.Increasing the pressure difference between the producer and injector,the borehole number,the hydraulic fracture height,and the fracture width can also increase the oil production rate and gas storage rate.Sensitivity analysis shows that layer spacing and fracture height greatly influence gas storage and oil production.Research outcomes are expected to provide a theoretical basis for the efficient development of shale oil reservoirs in the vertical direction.

High-Precision Flow Numerical Simulation and Productivity Evaluation of Shale Oil Considering Stress Sensitivity

Continental shale oil reservoirs,characterized by numerous bedding planes and micro-nano scale pores,feature significantly higher stress sensitivity compared to other types of reservoirs.However,research on suitable stress sensitivity characterization models is still limited.In this study,three commonly used stress sensitivity models for shale oil reservoirs were considered,and experiments on representative core samples were conducted.By fitting and comparing the data,the“exponential model”was identified as a characterization model that accurately represents stress sensitivity in continental shale oil reservoirs.To validate the accuracy of the model,a two-phase seepage mathematical model for shale oil reservoirs coupled with the exponential model was introduced.The model was discretely solved using the finite volume method,and its accuracy was verified through the commercial simulator CMG.The study evaluated the productivity of a typical horizontal well under different engineering,geological,and fracture conditions.The results indicate that considering stress sensitivity leads to a 13.57%reduction in production for the same matrix permeability.Additionally,as the fracture half-length and the number of fractures increase,and the bottomhole flowing pressure decreases,the reservoir stress sensitivity becomes higher.

Ensemble-based optimization of hydraulically fractured horizontal well placement in shale gas reservoir through Hough transform parameterization

Shale gas reservoirs have been successfully developed due to the advancement of the horizontal well drilling and multistage hydraulic fracturing techniques.However,the optimization design of the horizontal well drilling,hydraulic fracturing,and operational schedule is a challenging problem.An ensemble-based optimization method(EnOpt)is proposed here to optimize the design of the hydraulically fractured horizontal well in the shale gas reservoir.The objective is to maximize the net present value(NPV)which requires a simulation model to predict the cumulative shale gas production.To accurately describe the geometry of the hydraulic fractures,the embedded discrete fracture modeling method(EDFM)is used to construct the shale gas simulation model.The efects of gas absorption,Knudsen difusion,natural and hydraulic fractures,and gas-water two phase fow are considered in the shale gas production system.To improve the parameter continuity and Gaussianity required by the EnOpt method,the Hough transformation parameterization is used to characterize the horizontal well.The results show that the proposed method can efectively optimize the design parameters of the hydraulically fractured horizontal well,and the NPV can be improved greatly after optimization so that the design parameters can approach to their optimal values.

Numerical analysis of the hydraulic fracture communication modes in fracture-cavity reservoirs

The fracture-cavity carbonate reservoirs in the Tahe Oilfield in China are mainly exploited by fracturing.We need the hydraulic fractures to communicate with caves to create a flow channel.However,due to the existence of the fracture-cavity systems,the hydraulic fracture propagation morphology is complicated,while the propagation characteristics are not clear.To analyze the hydraulic fracture propagation in fracture-cavity carbonate formations,based on the discontinuous discrete fracture model,we developed a solid-seepage-freeflow coupled fracturing model for fracture-cavity formations,which can simulate the complex interaction behavior of fractures and caves.Based on the simulation results,we found the interaction rule between hydraulic fractures and fracture-cavity systems:the stress concentration around caves is the main factor that determines the fracture propagation path.Deflection due to stress concentration is usually not conducive to communication,while natural fractures distributed around caves could break the rejection action.Increasing the hydraulic energy in the hydraulic fracture can make fracture propagate directly and reduce the influence of deflection.The steering fracture formed by temporary plugging is beneficial to the communication of fracture-cavity systems in the non-principal stress direction.According to the simulation results of different fracture-cavity characteristics,we raised four optimization communication modes for fracture-cavity carbonate formation to provide references for fracturing optimization design and parameter optimization.

Development of a DFN-based probabilistic block theory approach for bench face angle design in open pit mining

In open pit mining,uncontrolled block instabilities have serious social,economic and regulatory consequences,such as casualties,disruption of operation and increased regulation difficulties.For this reason,bench face angle,as one of the controlling parameters associated with block instabilities,should be carefully designed for sustainable mining.This study introduces a discrete fracture network(DFN)-based probabilistic block theory approach for the fast design of the bench face angle.A major advantage is the explicit incorporation of discontinuity size and spatial distribution in the procedure of key blocks testing.The proposed approach was applied to a granite mine in China.First,DFN models were generated from a multi-step modeling procedure to simulate the complex structural characteristics of pit slopes.Then,a modified key blocks searching method was applied to the slope faces modeled,and a cumulative probability of failure was obtained for each sector.Finally,a bench face angle was determined commensurate with an acceptable risk level of stability.The simulation results have shown that the number of hazardous traces exposed on the slope face can be significantly reduced when the suggested bench face angle is adopted,indicating an extremely low risk of uncontrolled block instabilities.

A three-dimensional feature extraction-based method for coal cleat characterization using X-ray μCT and its application to a Bowen Basin coal specimen

Cleats are the dominant micro-fracture network controlling the macro-mechanical behavior of coal.Improved understanding of the spatial characteristics of cleat networks is therefore important to the coal mining industry.Discrete fracture networks(DFNs)are increasingly used in engineering analyses to spatially model fractures at various scales.The reliability of coal DFNs largely depends on the confidence in the input cleat statistics.Estimates of these parameters can be made from image-based three-dimensional(3D)characterization of coal cleats using X-ray micro-computed tomography(m CT).One key step in this process,after cleat extraction,is the separation of individual cleats,without which the cleats are a connected network and statistics for different cleat sets cannot be measured.In this paper,a feature extraction-based image processing method is introduced to identify and separate distinct cleat groups from 3D X-ray m CT images.Kernels(filters)representing explicit cleat features of coal are built and cleat separation is successfully achieved by convolutional operations on 3D coal images.The new method is applied to a coal specimen with 80 mm in diameter and 100 mm in length acquired from an Anglo American Steelmaking Coal mine in the Bowen Basin,Queensland,Australia.It is demonstrated that the new method produces reliable cleat separation capable of defining individual cleats and preserving 3D topology after separation.Bedding-parallel fractures are also identified and separated,which has his-torically been challenging to delineate and rarely reported.A variety of cleat/fracture statistics is measured which not only can quantitatively characterize the cleat/fracture system but also can be used for DFN modeling.Finally,variability and heterogeneity with respect to the core axis are investigated.Significant heterogeneity is observed and suggests that the representative elementary volume(REV)of the cleat groups for engineering purposes may be a complex problem requiring careful consideration.

Slope stability assessment of an open pit using lattice-spring-based synthetic rock mass (LS-SRM) modeling approach

Discontinuity waviness is one of the most important properties that influence shear strength of jointed rock masses,and it should be incorporated into numerical models for slope stability assessment.However,in most existing numerical modeling tools,discontinuities are often simplified into planar surfaces.Discrete fracture network modeling tools such as MoFrac allow the simulation of non-planar discontinuities which can be incorporated into lattice-spring-based geomechanical software such as Slope Model for slope stability assessment.In this study,the slope failure of the south wall at Cadia Hill open pit mine is simulated using the lattice-spring-based synthetic rock mass(LS-SRM)modeling approach.First,the slope model is calibrated using field displacement monitoring data,and then the influence of different discontinuity configurations on the stability of the slope is investigated.The modeling results show that the slope with non-planar discontinuities is comparatively more stable than the ones with planar discontinuities.In addition,the slope becomes increasingly unstable with the increases of discontinuity intensity and size.At greater pit depth with higher in situ stress,both the slope models with planar and non-planar discontinuities experience localized failures due to very high stress concentrations,and the slope model with planar discontinuities is more deformable and less stable than that with non-planar discontinuities.

Optimization of operational strategies for rich gas enhanced oil recovery based on a pilot test in the Bakken tight oil reservoir

Horizontal well drilling and multistage hydraulic fracturing have been demonstrated as effective approaches for stimulating oil production in the Bakken tight oil reservoir.However,after multiple years of production,primary oil recovery in the Bakken is generally less than 10%of the estimated original oil in place.Gas huff‘n’puff(HnP)has been tested in the Bakken Formation as an enhanced oil recovery(EOR)method;however,most field pilot test results showed no significant incremental oil production.One of the factors affecting HnP EOR performance is premature gas breakthrough,which is one of the most critical issues observed in the field because of the presence of interwell fractures.Consequently,injected gas rapidly reaches adjacent production wells without contacting reservoir rock and increasing oil recovery.Proper conformance control is therefore needed to avoid early gas breakthrough and improve EOR performance.In this study,a rich gas EOR pilot in the Bakken was carefully analyzed to collect the essential reservoir and operational data.A simulation model with 16 wells was then developed to reproduce the production history and predict the EOR performance with and without conformance control.EOR operational strategies,including single-and multiple-well HnP,with different gas injection constraints were investigated.The simulation results of single-well HnP without conformance control showed that a rich gas injection rate of at least 10 MMscfd was needed to yield meaningful incremental oil production.The strategy of conformance control via water injection could significantly improve oil production in the HnP well,but injecting an excessive amount of water also leads to water breakthrough and loss of oil production in the offset wells.By analyzing the production performance of the wells individually,the arrangement of wells was optimized for multiple-well HnP EOR.The multiwell results showed that rich gas EOR could improve oil production up to 7.4%by employing conformance control strategies.Furthermore,replacing rich gas with propane as the injection gas could result in 14%of incremental oil production.

Effect of hydraulic fracture deformation hysteresis on CO_(2)huff-n-puff performance in shale gas reservoirs

As a promising enhanced gas recovery technique,CO_(2)huff-n-puff has attracted great attention recently.However,hydraulic fracture deformation hysteresis is rarely considered,and its effect on CO_(2)huff-n-puff performance is not well understood.In this study,we present a fully coupled multi-component flow and geomechanics model for simulating CO_(2)huff-n-puff in shale gas reservoirs considering hydraulic fracture deformation hysteresis.Specifically,a shale gas reservoir after hydraulic fracturing is modeled using an efficient hybrid model incorporating an embedded discrete fracture model(EDFM),multiple porosity model,and single porosity model.In flow equations,Fick’s law,extended Langmuir isotherms,and the Peng-Robinson equation of state are used to describe the molecular diffusion,multi-component adsorption,and gas properties,respectively.In relation to geomechanics,a path-dependent constitutive law is applied for the hydraulic fracture deformation hysteresis.The finite volume method(FVM)and the stabilized extended finite element method(XFEM)are applied to discretize the flow and geomechanics equations,respectively.We then solve the coupled model using the fixed-stress split iterative method.Finally,we verify the presented method using several numerical examples,and apply it to investigate the effect of hydraulic fracture deformation hysteresis on CO_(2)huff-n-puff performance in a 3D shale gas reservoir.Numerical results show that hydraulic fracture deformation hysteresis has some negative effects on CO_(2)huff-n-puff performance.The effects are sensitive to the initial conductivity of hydraulic fracture,production pressure,starting time of huff-n-puff,injection pressure,and huff-n-puff cycle number.

Impact of Fractures and Diagenesis on Reservoir Potential of Inner Ramp Paleocene Carbonates Exposed in Western Part of the Lesser Himalayas of Pakistan

The outcrop investigations provide a better comprehension to interrelate facies-diagenesis and fracture networks for the evaluation of reservoir potential of the carbonate rocks.In this paper,we targeted Kahi-Section(Nizampur Basin)and Peeran Tangai-Section(Kalachitta Range)to analyze structural-kinematics,Discrete Fracture Network Modelling,microfacies identification and diagenesis to interpret their impact on reservoir potential of Lockhart Limestone(Paleocene).The structural grain within the study area mostly represents the typical east-west trending tight to overturned folds and north-dipping thrust faults that mimic the north-south Indo-Eurasian collision.However,a second phase of deformation related to east-west compressions also identified which rotated the axes of preexisting structures.Fracture analysis revealed that extensional fractures are oriented at high angle to bedding and are differentiated into three orthogonal sets trending northeast-southwest,northwest-southeast and east-west,whereas,the shear fractures formed two conjugate sets trending northeastsouthwest.The Lockhart Limestone was deposited in the inner ramp setting and microfacies types are packstone,wackestone and wacke-packstone with seven sub-microfacies types.It has been identified that the Lockhart Limestone has the heterogeneous distribution of diagenetic and tectonic features throughout its extent.The observed diagenetic sequence is micritization,calcite cementation,dissolution,neomorphism,pyritization and compaction.The results highlight that open and partially filled fractures may provide an interconnected network to promote fluid mobility,leading to higher values of fracture permeability.The porosity values of the pore matrix were greater than fracture,resulting a significant impact on reservoir storage capacity.In contrast,a negative impact on reservoir potential has been shown by stylolites,veins and dissolution seams.However,based on the overall studies,the Lockhart Limestone revealed the prospect of a good reservoir unit in the study area.