A new approach for flow simulation in complex hydraulic fracture morphology and its application:Fracture connection element method

Efficient flow simulation and optimization methods of hydraulic fracture morphology in unconventional reservoirs are effective ways to enhance oil/gas recovery.Based on the connection element method(CEM)and distribution of stimulated reservoir volume,the complex hydraulic fracture morphology was accurately described using heterogeneous node connection system.Then a new fracture connection element method(FCEM)for fluid flow in stimulated unconventional reservoirs with complex hydraulic fracture morphology was proposed.In the proposed FCEM,the arrangement of dense nodes in the stimulated area and sparse nodes in the unstimulated area ensures the calculation accuracy and efficiency.The key parameter,transmissibility,was also modified according to the strong heterogeneity of stimulated reservoirs.The finite difference and semi-analytical tracking were used to accurately solve the pressure and saturation distribution between nodes.The FCEM is validated by comparing with traditional numerical simulation method,and the results show that the bottom hole pressure simulated by the FCEM is consistent with the results from traditional numerical simulation method,and the matching rate is larger than 95%.The proposed FCEM was also used in the optimization of fracturing parameters by coupling the hydraulic fracture propagation method and intelligent optimization algorithm.The integrated intelligent optimization approach for multi-parameters,such as perforation number,perforation location,and displacement in hydraulic fracturing is proposed.The proposed approach was applied in a shale gas reservoir,and the result shows that the optimized perforation location and morphology distribution are related to the distribution of porosity/permeability.When the perforation location and displacement are optimized with the same fracture number,NPV increases by 70.58%,which greatly improves the economic benefits of unconventional reservoirs.This work provides a new way for flow simulation and optimization of hydraulic fracture morphology of multi-fractured horizontal wells in unconventional reservoirs.

Assessments of the effects of various fracture surface morphology on single fracture flow: A review

Natural rock joint permeability deviates from the classic fluid flow governing equations due to the inher-ent fracture surface roughness(i.e.,contact points,spatial correlation,matching,varying aperture,iso-lated voids,infilling material,tortuosity and channellings)and engineering disturbance such as excavations.To improve the accuracy of fracture permeability evaluation,many efforts have been made in analytical,experimental,and numerical methods.This study reviews the modified mathematical gov-erning equations of fluid flow and classifies them based on different influencing factors,such as friction factor,aperture,tortuosity,inertia,and various in situ stress effects.Various experimental and simulation techniques for the coupled normal-and shear-stress flow problems were assessed,and their advantages and disadvantages were also analysed.Furthermore,different surface roughness descriptions and their impacts on mechanical and hydraulic behaviours were discussed,followed by the potential research directions for fracture flow problems.

Experimental investigation of propagation mechanisms and fracture morphology for coalbed methane reservoirs

Fracture propagation mechanisms in coalbed methane(CBM) reservoirs are very complex due to the development of the internal cleat system. In this paper, the characteristics of initiation and propagation of hydraulic fractures in coal specimens at different angles between the face cleat and the maximum horizontal principal stress were investigated with hydraulic fracturing tests. The results indicate that the interactions between the hydraulic fractures and the cleat system have a major effect on fracture networks. "Step-like’’ fractures were formed in most experiments due to the existence of discontinuous butt cleats. The hydraulic fractures were more likely to divert or propagate along the butt cleat with an increase in the angles and a decrease in the horizontal principal stress difference. An increase in the injection rate and a decrease in the fracturing fluid viscosity were more conducive to fracture networks. In addition, the influence on fracture propagation of the residual coal fines in the wellbore was also studied. The existence of coal fines was an obstacle in fracturing, and no effective connection can be formed between fractures. The experimental investigation revealed the fracture propagation mechanisms and can provide guidance for hydraulic fracturing design of CBM reservoirs.

3D morphology and formation mechanism of fractures developed by true triaxial stress

As main part of underground rock mass,the three-dimensional(3D)morphology of natural fractures plays an important role in rock mass stability.Based on previous studies on 3D morphology,this study probes into the law and mechanism regarding the influence of the confining pressure constraints on 3D morphological features of natural fractures.First,fracture surfaces were obtained by true triaxial compression test and 3D laser scanning.Then 3D morphological parameters of fractures were calculated by using Grasselli’s model.The results show that the failure mode of granites developed by true triaxial stress can be categorized into tension failure and shear failure.Based on the spatial position of fractures,they can be divided into tension fracture surface,S-1 shear fracture surface,and S-2 shear fracture surface.Micro-failure of the tension fracture surface is dominated by mainly intergranular fracture;the maximum height of asperities on the fracture surface and the 3D roughness of fracture surfaces are influenced by σ_(3) only and they are greater than those of shear fracture surfaces,a lower overall uniformity than tension fracture surface.S-1 shear fracture surface and S-2 shear fracture surface are dominated by intragranular and intergranular coupling fracture.The maximum height of asperities on the fracture surface and 3D roughness of fracture surface are affected by σ_(1),σ_(2),and σ_(3).With the increase of σ_(2) or σ_(3),the cutting off of asperities on the fracture surface becomes more common,the maximum height of asperities and 3D roughness of fracture surface further decrease,and the overall uniformity gets further improved.The experimental results are favorable for selecting technical parameters of enhanced geothermal development and the safety of underground mine engineering.

Shear behavior of intact granite under thermo-mechanical coupling and three-dimensional morphology of shear-formed fractures

The shear failure of intact rock under thermo-mechanical(TM)coupling conditions is common,such as in enhanced geothermal mining and deep mine construction.Under the effect of a continuous engineering disturbance,shear-formed fractures are prone to secondary instability,posing a severe threat to deep engineering.Although numerous studies regarding three-dimensional(3D)morphologies of fracture surfaces have been conducted,the understanding of shear-formed fractures under TM coupling conditions is limited.In this study,direct shear tests of intact granite under various TM coupling conditions were conducted,followed by 3D laser scanning tests of shear-formed fractures.Test results demonstrated that the peak shear strength of intact granite is positively correlated with the normal stress,whereas it is negatively correlated with the temperature.The internal friction angle and cohesion of intact granite significantly decrease with an increase in the temperature.The anisotropy,roughness value,and height of the asperities on the fracture surfaces are reduced as the normal stress increases,whereas their variation trends are the opposite as the temperature increases.The macroscopic failure mode of intact granite under TM coupling conditions is dominated by mixed tensileeshear and shear failures.As the normal stress increases,intragranular fractures are developed ranging from a local to a global distribution,and the macroscopic failure mode of intact granite changes from mixed tensileeshear to shear failure.Finally,3D morphological characteristics of the asperities on the shear-formed fracture surfaces were analyzed,and a quadrangular pyramid conceptual model representing these asperities was proposed and sufficiently verified.

Is traumatic meniscal lesion associated with acute fracture morphology changes of tibia plateau? A series of arthroscopic analysis of 67 patients

BACKGROUND Computed tomography(CT)has become a routine preoperative examination for tibial plateau fractures(TPFs).Assessing the location of the fragment and intercondylar eminence fracture can provide clinicians with valuable information;however,the evaluation of traumatic meniscal lesion(TML)and arthroscopic management are controversial.AIM To predict TML by three-dimensional skeletal anatomy changes in unilateral TPF and bilateral TPF on preoperative thin layer CT.METHODS Acute fracture of tibial plateau patients undergoing arthroscopic surgery between December 2017 and December 2019 were included in this retrospective study.The type,zone,and location of TMLs were diagnosed based on the operation records and/or arthroscopic videos.Measurement of three-dimensional fracture morphology included the following:Frontal fragment width of plateau,sagittal fragment subsiding distance(FSD),sagittal fracture line distance,sagittal posterior tibial slope,and transversal area ratio of fragment area)on preoperative CT three-dimensional plane.The correlation of TML with skeletal values was calculated according to unicondylar TPFs and bicondylar TPFs.RESULTS A total of 67 patients were enrolled in this study,among which 30 patients had TMLs,lateral/medial(23/7).FSD was a particularly positive factor to predict TML,with odds ratio of 2.31(1.26-5.63).On sagittal view of CT,FSD degree of 8 mm and posterior tibial slope exceeding 11.74°implied enhanced risk of TML in bicondylar TPFs.On coronal view,once fragment width of plateau surpassed 3 cm,incidence of TML reached 100%.On transverse view,area ratio of fragment as enhanced risk of 5.5%and FSD>4.3 mm for predicting TML were observed in unicondylar TPFs.CONCLUSION TML can be predicted by different parameters on preoperative CT views according to unicondylar fractures and bicondylar TPFs.

SOLIDIFICATION MICROSTRUCTURE AND FRACTURE MORPHOLOGY OF SiCp/ZA27 COMPOSITE

Solidification microstructure and mechanical property are explored.Furthermore,tensile fracture and microstructure are analyzed by using SEM and JXA 840A electron probe.The results indicate that SiC particles in SiCp/ZA27 composite are mainly distributed on interfaces or between dendrites and surrounded by primary α phase.The dendrite of α phase is fined by SiCp.The tensile strength at room temperature decreases with the increasing of SiCp addition.The tensile strength at elevated temperature increases with the addition of SiCp.The fracture of SiCp/ZA27 composites is the mixture of tough and brittle fracture.The carck is prone to extend along the interface and the region of dispersed shrinkage.

Using fracture-based continuum modeling of coupled geomechanical-hydrological processes for numerical simulation of hydraulic fracturing

This paper describes numerical simulation of hydraulic fracturing using fracture-based continuum modeling(FBCM)of coupled geomechanical-hydrological processes to evaluate a technique for high-density fracturing and fracture caging.The simulations are innovative because of modeling discrete fractures explicitly in continuum analysis.A key advantage of FBCM is that fracture initiation and propagation are modeled explicitly without changing the domain grid(i.e.no re-meshing).Further,multiple realizations of a preexisting fracture distribution can be analyzed using the same domain grid.The simulated hydraulic fracturing technique consists of pressurizing multiple wells simultaneously:initially without permeating fluids into the rock,to seed fractures uniformly and at high density in the wall rock of the wells;followed by fluid injection to propagate the seeded fracture density hydraulically.FBCM combines the ease of continuum modeling with the potential accuracy of modeling discrete fractures and fracturing explicitly.Fractures are modeled as piecewise planar based on intersections with domain elements;fracture geometry stored as continuum properties is used to calculate parameters needed to model individual fractures;and rock behavior is modeled through tensorial aggregation of the behavior of discrete fractures and unfractured rock.Simulations are presented for previously unfractured rock and for rock with preexisting fractures of horizontal,shallow-dipping,steeply dipping,or vertical orientation.Simulations of a single-well model are used to determine the pattern and spacing for a multiple-well design.The results illustrate high-density fracturing and fracture caging through simultaneous fluid injection in multiple wells:for previously unfractured rock or rock with preexisting shallow-dipping or horizontal fractures,and in situ vertical compressive stress greater than horizontal.If preexisting fractures are steeply dipping or vertical,and considering the same in situ stress condition,well pressurization without fluid permeation appears to be the only practical way to induce new fractures and contain fracturing within the target domain.

Automatic fracture–vug identification and extraction from electric imaging logging data based on path morphology

We present a path morphology method to separate total rock pore space into matrix, fractures and vugs and derive their pore structure spectrum. Thus, we can achieve fine pore evaluation in fracture–vug reservoirs based on electric imaging logging data. We automatically identify and extract fracture–vug information from the electric imaging images by adopting a path morphological operator that remains flexible enough to fit rectilinear and slightly curved structures because they are independent of the structuring element shape. The Otsu method was used to extract fracture–vug information from the background noise caused by the matrix. To accommodate the differences in scale and form of the different target regions,including fracture and vug path, operators with different lengths were selected for their recognition and extraction at the corresponding scale. Polynomial and elliptic functions are used to fit the extracted fractures and vugs, respectively, and the fracture–vug parameters are deduced from the fitted edge. Finally, test examples of numerical simulation data and several measured well data have been provided for the verification of the effectiveness and adaptability of the path morphology method in the application of electric imaging logging data processing. This also provides algorithm support for the fine evaluation of fracture–vug reservoirs.

Microstructure and fracture morphology of Mo-Cu/Cr18-Ni8 brazed joint in vacuum

Mo-Cu composite and Cr18-Ni8 stainless steel were brazed with Ni-Cr-P filler metal in a vacuum of 10-4 Pa and a Mo-Cu/Cr18-Ni8 joint was obtained. Microstructure in Mo-Cu/Cr18-Ni8 joint was investigated by field-emission scanning electron microscope( FE-SEM) with energy dispersive spectrometer( EDS). Shear strength of Mo-Cu/Cr18-Ni8 lap joint was measured by electromechanical universal testing machine. An excellent Mo-Cu/Cr18-Ni8 joint with a shear strength of 155 MPa was achieved at 980 ℃ for 20 min. Brazed joint was mainly comprised of eutectic structure in the center of brazing seam,matrix structure and lump structure. Ni-Cu( Mo) and Ni-Fe solid solution were at the interface beside Mo-Cu composite and Cr18-Ni8 stainless steel,respectively. Shear fracture exhibited mixed ductile-brittle fracture feature with trans-granular fracture,ductile dimples and tearing edges. Fracture originated from the interface between brazing seam and Mo-Cu composite.

Effect of current pulses on fracture morphology in superplastic deformation of 2091 Al Li alloy

The effect of current pulses on the fracture morphology in the superplastic deformation of 2091 Al Li alloy at two kinds of initial strain rate ( 1=3.33×10 -3 s -1 ; 2=3.33×10 -2 s -1 ) was investigated.Experimental results show that current pulse turns fracture of superplastic deformation at low strain rate from local interior fracture morphology to typical fracture by growth and interlinkage of cavities, and at high strain rate from rough grain boundary surface to smooth grain boundary surface. It is indicated that the characteristic, that current pulse promotes atomic diffusion, maintains an equiaxial grain microstructure at low strain rate, and accelerates the development of diffusional type of cavity and relaxes stress concentration at triple junction of grain boundaries at high strain rate, and makes the superplastic deformation at two kinds of strain rate show a normal superplastic fracture morphology.

The Morphology of Rolling Contact Fatigue Fracture of Hardened Steels

Rolling Contact Fatigue(RCF) is a cumulative damage phenomenon when metals are subjected to repeated contact stresses. The fomation of pitting on the contact surface is the result of the rolling contact fatigue. The morphologies of rolling contact fatigue fracture of the har- dened steels (86CrHoV7, 42CrMo) show that strong resemblance in fractuye mechanisms exists between rolling contact fatigue and uni-axial fatigue. Since fatigue striations are hardly observed in hardened steels under uni-axial fatigue, it is interesting to note that the state of stress in rolling contact fatigue is more favor- able to ductile fractures than in uni-axial fatigue.

Quantitative investigation of multi-fracture morphology during TPDF through true tri-axial fracturing experiments and CT scanning

Due to the reservoir heterogeneity and the stress shadow effect, multiple hydraulic fractures within one fracturing segment cannot be initiated simultaneously and propagate evenly, which will cause a low effectiveness of reservoir stimulation. Temporary plugging and diverting fracturing(TPDF) is considered to be a potential uniform-stimulation method for creating multiple fractures simultaneously in the oilfield. However, the multi-fracture propagation morphology during TPDF is not clear now. The purpose of this study is to quantitatively investigate the multi-fracture propagation morphology during TPDF through true tri-axial fracturing experiments and CT scanning. Critical parameters such as fracture spacing, number of perforation clusters, the viscosity of fracturing fluid, and the in-situ stress have been investigated. The fracture geometry before and after diversion have been quantitively analyzed based on the two-dimensional CT slices and three-dimensional reconstruction method. The main conclusions are as follows:(1) When injecting the high viscosity fluid or perforating at the location with low in-situ stress, multiple hydraulic fractures would simultaneously propagate. Otherwise, only one hydraulic fracture was created during the initial fracturing stage(IFS) for most tests.(2) The perforation cluster effectiveness(PCE) has increased from 26.62% during the IFS to 88.86% after using diverters.(3) The diverted fracture volume has no apparent correlation with the pressure peak and peak frequency during the diversion fracturing stage(DFS) but is positively correlated with water-work.(4) Four types of plugging behavior in shale could be controlled by adjusting the diverter recipe and diverter injection time, and the plugging behavior includes plugging the natural fracture in the wellbore, plugging the previous hydraulic fractures, plugging the fracture tip and plugging the bedding.

Medial tibial plateau morphology and stress fracture location:A magnetic resonance imaging study

AIM To determine the location of medial tibial plateau stress fractures and its relationship with tibial plateau morphology using magnetic resonance imaging(MRI).METHODS A retrospective review of patients with a diagnosis of stress fracture of the medial tibial plateau was performed for a 5-year period. Fourteen patients [three female and 11 male, with an average age of 36.4 years(range, 15-50 years)], who underwent knee MRI, were included. The appearance of the tibial plateau stress fracture and the geometry of the tibial plateau were reviewed and measured on MRI.RESULTS Thirteen of 14 stress fractures were linear, and one of them stellated on MRI images. The location of fractures was classified into three types. Three fractures were located anteromedially(AM type), six posteromedially(PM type), and five posteriorly(P type) at the medial tibial plateau. In addition, tibial posterior slope at the medial tibial plateau tended to be larger when the fracture was located more posteriorly on MRI.CONCLUSION We found that MRI showed three different localizations of medial tibial plateau stress fractures, which were associated with tibial posterior slope at the medial tibial plateau.

Visualization and characterization of experimental hydraulic fractures interacting with karst fracture-cavity distributions

Karst fracture-cavity carbonate reservoirs,in which natural cavities are connected by natural fractures to form cavity clusters in many circumstances,have become significant fields of oil and gas exploration and exploitation.Proppant fracturing is considered as the best method for exploiting carbonate reservoirs;however,previous studies primarily focused on the effects of individual types of geological formations,such as natural fractures or cavities,on fracture propagation.In this study,true-triaxial physical simulation experiments were systematically performed under four types of stress difference conditions after the accurate prefabrication of four types of different fracture-cavity distributions in artificial samples.Subsequently,the interaction mechanism between the hydraulic fractures and fracture-cavity structures was systematically analyzed in combination with the stress distribution,cross-sectional morphology of the main propagation path,and three-dimensional visualization of the overall fracture network.It was found that the propagation of hydraulic fractures near the cavity was inhibited by the stress concentration surrounding the cavity.In contrast,a natural fracture with a smaller approach angle(0°and 30°)around the cavity can alleviate the stress concentration and significantly facilitate the connection with the cavity.In addition,the hydraulic fracture crossed the natural fracture at the 45°approach angle and bypassed the cavity under higher stress difference conditions.A new stimulation effectiveness evaluation index was established based on the stimulated reservoir area(SRA),tortuosity of the hydraulic fractures(T),and connectivity index(CI)of the cavities.These findings provide new insights into the fracturing design of carbonate reservoirs.

A modified 3D mean strain energy density criterion for predicting shale mixed-mode I/III fracture toughness

The fracture toughness of rocks is a critical fracturing parameter in geo-energy exploitation playing a significant role in fracture mechanics and hydraulic fracturing.The edge-notched disk bending(ENDB)specimens are employed to measure the entire range of mixed-modeⅠ/Ⅲfracture toughness of Longmaxi shale.To theoretically interpret the fracture mechanisms,this research first introduces the detailed derivations of three established fracture criteria.By distinguishing the volumetric and distortional strain energy densities,an improved three-dimensional mean strain energy density(MSED)criterion is proposed.As the critical volumetric to distortional MSED ratio decreases,the transition from tensiondominated fracture to shear-dominated fracture is observed.Our results indicate that both peak load and applied energy increase significantly with the transition from pure mode I(i.e.,tension)to pure modeⅢ(i.e.,torsion or tearing)since mode-Ⅲcracking happens in a twisted manner and mode-Ⅰcracking occurs in a coplanar manner.The macroscopic fracture signatures are consistent with those of triaxial hydraulic fracturing.The average ratio of pure mode-Ⅲfracture toughness to pure mode-Ⅰfracture toughness is 0.68,indicating that the obtained mode-Ⅲfracture resistance for a tensionbased loading system is apparent rather than true.Compared to the three mainstream fracture criteria,the present fracture criterion exhibits greater competitiveness and can successfully evaluate and predict mixed-modeⅠ/Ⅲfracture toughness of distinct materials and loading methods.

Nanoscale Morphology in Tensile Fracture of a Brittle Amorphous Ribbon

The paper reports on the observation of nanoscale morphology on the tensile fracture surface of a brittle amorphous Fe-based ribbon. The formation of nanoscale damage cavity structure is a main characteristic morphology on the fracture surfaces. Approaching the ribbon boundary, these damage cavities assemble and form the nanoscale periodic corrugations, which are neither Wallner lines nor crack front waves. The periodic corrugations result from the interactions between the reflected elastic waves by the boundaries of amorphous ribbon and the stress fields of the crack tip.

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.

Management of geriatric acetabular fractures:Contemporary treatment strategies

Acetabular fractures in the geriatric population are typically low-energy fractures resulting from a fall from standing height.Compromised bone quality in the elderly,as well as this population’s concomitant medical comorbidities,render the management of such fractures challenging and controversial.Non-operative management remains the mainstay of treatment,although such a choice is associated with numerous and serious complications related to both the hip joint as well as the general condition of the patient.On the other hand,operatively treating acetabular fractures(e.g.,with osteosynthesis or total hip arthroplasty)is gaining popularity.Osteosynthesis can be performed with open reduction and internal fixation or with minimally invasive techniques.Total hip arthroplasty could be performed either in the acute phase combined with osteosynthesis or as a delayed procedure after a period of non-operative management or after failed osteosynthesis of the acetabulum.Regardless of the implemented treatment,orthogeriatric co-management is considered extremely crucial,and it is currently one of the pillars of a successful outcome after an acetabular fracture.