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.

Management and classification of the fracture of lateral process of talus:An overview and literature update

Fracture of the lateral process of the talus(FLPT)is uncommon in clinical practice and can be easily missed or misdiagnosed.In recent years,as researchers from all over the world have further deepened their research on FLPT,there has been a breakthrough in the classification,and the methods and principles of clinical management have changed accordingly;however,there is still no standardized guideline for the diagnosis and management of FLPT,and there have been few relevant literature review articles related to this kind of fracture in the past at least 5 years.In this article,we review the clinical classification,classification-based therapeutic recommendations,and prognosis of FLPT,with the aim of providing a reference for the clinical diagnosis and management of this infrequent fracture.

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.

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.

Beyond the imaging evaluation of fractures of the lateral process of the talus:Let’s not forget concomitant injuries

Fractures of the lateral process of the talus(FLPT)are uncommon fractures that represent a clinical challenge.Traditional radiological classification systems rely predominantly on radiographic findings.However,due to the high rate of FLPT misdiagnosis and the limited accuracy in evaluating concomitant talar injuries through plain radiographs,novel imaging classification systems have been developed that aim to enhance the diagnosis of concomitant talar injuries,thereby optimizing patient management and reducing the incidence of long-term complications.

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.

Epidemiologic investigation of pediatric distal humerus fractures: An American insurance claims database study

BACKGROUND Distal humerus elbow fractures are one of the most common traumatic fractures seen in pediatric patients and present as three main types:Supracondylar(SC),lateral condyle(LC),and medial epicondyle(ME)fractures.AIM To evaluate the epidemiology of pediatric distal humerus fractures(SC,LC,and ME)from an American insurance claims database.METHODS A retrospective review was performed on patients 17 years and younger with the ICD 9 and 10 codes for SC,LC and ME fractures based on the IBM Truven MarketScan®Commercial and IBM Truven MarketScan Medicare Supplemental databases.Patients from 2015 to 2020 were queried for treatments,patient age,sex,length of hospitalization,and comorbidities.RESULTS A total of 1133 SC,154 LC,and 124 ME fractures were identified.SC fractures had the highest percentage of operation at 83%,followed by LC(78%)and ME fractures(41%).Male patients were,on average,older than female patients for both SC and ME fractures.CONCLUSION In the insurance claims databases used,SC fractures were the most reported,followed by LC fractures,and finally ME fractures.Age was identified to be a factor for how a pediatric distal humerus fractures,with patients with SC and LC fractures being younger than those with ME fractures.The peak age per injury per sex was similar to reported historic central tendencies,despite reported trends for younger physiologic development.

Treatment of a femoral neck fracture combined with ipsilateral femoral head and intertrochanteric fractures: A case report

BACKGROUND This article presents a rare case of a complex hip fracture involving the ipsilateral femoral neck,trochanter,and femoral head,that was accompanied by hip dislocation.Currently,there is no established standard treatment method for this specific type of fracture.Therefore,it is crucial to comprehensively consider factors such as patient age,fracture type,and degree of displacement to achieve a successful outcome.CASE SUMMARY A 38-year-old man sustained a comminuted fracture of his right hip as a result of a car accident.The injuries included a fracture of the femoral head,a fracture of the femoral neck,an intertrochanteric fracture of the femur,and a posterior dislocation of the hip on the same side.We opted for a treatment approach combining the use of a proximal femoral locking plate,cannulated screws,and Kirschner wires.Following the surgery,we developed an individualized rehabil-itation program to restore patient limb function.CONCLUSION For this complex fracture,we selected appropriate internal fixation and for-mulated individualized rehabilitation,which ultimately achieved good results.

Production induced fracture closure of deep shale gas well under thermo-hydro-mechanical conditions

Deep shale gas reservoirs have geological characteristics of high temperature,high pressure,high stress,and inferior ability to pass through fluids.The multi-stage fractured horizontal well is the key to exploiting the deep shale gas reservoir.However,during the production process,the effectiveness of the hydraulic fracture network decreases with the closure of fractures,which accelerates the decline of shale gas production.In this paper,we addressed the problems of unclear fracture closure mechanisms and low accuracy of shale gas production prediction during deep shale gas production.Then we established the fluid—solid—heat coupled model coupling the deformation and fluid flow among the fracture surface,proppant and the shale matrix.When the fluid—solid—heat coupled model was applied to the fracture network,it was well solved by our numerical method named discontinuous discrete fracture method.Compared with the conventional discrete fracture method,the discontinuous discrete fracture method can describe the three-dimensional morphology of the fracture while considering the effect of the change of fracture surface permeation coefficient on the coupled fracture—matrix flow and describing the displacement discontinuity across the fracture.Numerical simulations revealed that the degree of fracture closure increases as the production time proceeds,and the degree of closure of the secondary fractures is higher than that of the primary fractures.Shale creep and proppant embedment both increase the degree of fracture closure.The reduction in fracture surface permeability due to proppant embedment reduces the rate of fluid transfer between matrix and fracture,which has often been overlooked in the past.However,it significantly impacts shale gas production,with calculations showing a 24.7%cumulative three-year yield reduction.This study is helpful to understand the mechanism of hydraulic fracture closure.Therefore,it provides the theoretical guidance for maintaining the long-term effectiveness of hydraulic fractures.

Assessing the readability of online information about jones fracture

BACKGROUND Hand in hand with technological advancements,treatment modalities continue to grow.With the turn of the century,the internet has become the number one source of information for almost every topic.Thus,many patients look toward the internet as their primary source of information to learn about their respective medical conditions.The American Medical Association and National Institute of Health strongly recommend that online medical information be written at the 6th to 8th-grade level to aid comprehension by patients of all literacy backgrounds.AIM To assess the readability of online information regarding Jones fracture.Our hypothesis is that the reading level of medical information published on websites far exceeds the recommended reading level of 6th-8th grade as proposed by the American Medical Associate and National Institute of Health.The result of this study can help us formulate improved recommendations for publishing more comprehensible material and,thus,eventually improve patient compliance and clinical outcomes.METHODS The exact phrase“Jones fracture”was queried on the three most common search engines,Google,Yahoo!,and Bing,on December 28,2022.As of December 2022,Google held 84%,Bing held 9%,and Yahoo!held 2%of the worldwide search engine market share.Web pages uniform resource locator from the first three pages of search results were recorded from each search engine.These web pages were classified according to academic,physician-sponsored,governmental and non-government organizations(NGO),commercial,and unspecified as per formally defined categories.Websites associated with an educational institution or medical organization were classified as academic.Websites with products for sale,corporate sponsorship,or advertisements were classified as commercial.Governmental websites or NGOs comprised those that received government subsidies or grants.Webpages that were independently owned by physicians or physician groups were respectively classed as physician sponsored.The remainder of websites that did not fall under the above categories were classified as unspecified.RESULTS A total of 93 websites were analyzed for reading assessment.A whopping 44%of websites were commercial,followed by 22%of physician-sponsored websites.Third place belonged to non-government organization websites holding a 15%share.The academic website held a meager 9%portion,while unspecified sites were 3%.The table illustrates mean readability scores,along with average cumulative grade level.The average grade level was 10.95±2.28 for all websites,with a range of 6.18 to 18.90.Since P values were more than 0.05,there was not a significant statistical difference between the first page results and the results of all pages.Thus,we can rationalize that readability scores are consistent throughout all pages of a website.CONCLUSION Hand in hand with technological advancements,treatment modalities continue to grow.With the turn of the century,the internet has become the number one source of information for almost every topic.Thus,many patients look towards the internet as the primary source of information to learn about their respective medical conditions.Our study demonstrates that current online medical information regarding Jones fracture is written at an extraordinarily high-grade level,with an average grade level of all websites at 10.95,nearly an 10th-grade educational level.The American Medical Association and National Institute of Health strongly recommend that online medical information should be written at the 6th to 8th-grade level to aid comprehension by patients of all literacy backgrounds.On the contrary,most of the medical information evaluated was at an 10th-grade level,which far exceeds recommendations by AMA and NIH.This is particularly relevant because readability scores are directly proportional to the level of comprehension attained by readers,thus directly impacting patient outcomes.In conclusion,we suggest and encourage that all online reading materials should be re-written at the 6th to 8th-grade level in a public service effort to increase compliance with treatment goals and raise awareness of preventive measures.

Multiple damage zones around hydraulic fractures generated by high-frequency pulsating hydraulic fracturing

Pulsating hydraulic fracturing(PHF)is a promising fracturing method and can generate a dynamic periodic pressure.The periodic pressure can induce fatigue failure of rocks and decrease initiation pressure of fracture.If the frequency of periodic pressure exceeds 10 Hz,the distribution of pressure along the main fracture will be heterogeneous,which is much different from the one induced by the common fracturing method.In this study,the impact of this special spatial feature of pressure on hydraulic fracture is mainly investigated.A coupled numerical simulation model is first proposed and verified through experimental and theoretical solutions.The mechanism of secondary fracture initiation around the main fracture is then discovered.In addition,sensitivity studies are conducted to find out the application potential of this new method.The results show that(1)this coupled numerical simulation model is accurate.Through comparison with experimental and theoretical data,the average error of this coupled model is less than 1.01%.(2)Even if a reservoir has no natural fracture,this heterogeneous distribution pressure can also cause many secondary fractures around the main fracture.(3)The mechanism of secondary fracture initiation is that this heterogeneous distribution pressure causes tensile stress at many locations along the main fracture.(4)Through adjusting the stimulation parameters,the stimulation efficiency can be improved.The average and amplitude of pressure can increase possibility of secondary fracture initiation.The frequency of this periodic pressure can increase number of secondary fractures.Even 6 secondary fractures along a 100 m-length main fracture can be generated.(5)The influence magnitudes of stimulation parameters are larger than ones of geomechanical properties,therefore,this new fracturing method has a wide application potential.

Identifying the real fracture hidden in rock microcrack zone by acoustic emission energy

Identifying the real fracture of rock hidden in acoustic emission(AE)source clusters(AE-depicted microcrack zone)remains challenging and crucial.Here we revealed the AE energy(representing dissipated energy)distribution rule in the rock microcrack zone and proposed an AE-energy-based method for identifying the real fracture.(1)A set of fracture experiments were performed on granite using wedgeloading,and the fracture process was detected and recorded by AE.The microcrack zone associated with the energy dissipation was characterized by AE sources and energy distribution,utilizing our selfdeveloped AE analysis program(RockAE).(2)The accumulated AE energy,an index representing energy dissipation,across the AE-depicted microcrack zone followed the normal distribution model(the mean and variance relate to the real fracture path and the microcrack zone width).This result implies that the nucleation and coalescence of massive cracks(i.e.,real fracture generation process)are supposed to follow a normal distribution.(3)Then,we obtained the real fracture extension path by joining the peak positions of the AE energy normal distribution curve at different cross-sections of the microcrack zone.Consequently,we distinguished between the microcrack zone and the concealed real fracture within it.The deviation was validated as slight as 1–3 mm.

Laboratory visualization of damage asymmetry formation of rock fracture via acoustic emission and digital imaging correlation

Rock fracture mechanics and accurate characterization of rock fracture are crucial for understanding a variety of phenomena interested in geological engineering and geoscience.These phenomena range from very large-scale asymmetrical fault structures to the scale of engineering projects and laboratory-scale rock fracture tests.Comprehensive study can involve mechanical modeling,site or post-mortem investigations,and inspection on the point cloud of the source locations in the form of earthquake,microseismicity,or acoustic emission.This study presents a comprehensive data analysis on characterizing the forming of the asymmetrical damage zone around a laboratory mixed-mode rock fracture.We substantiate the presence of asymmetrical damage through qualitative analysis and demonstrate that measurement uncertainties cannot solely explain the observed asymmetry.The implications of this demonstration can be manifold.On a larger scale,it solidifies a mechanical model used for explaining the contribution of aseismic mechanisms to asymmetrical fault structures.On a laboratory scale,it exemplifies an alternative approach to understanding the observational difference between the source location and the in situ or post-mortem inspection on the rock fracture path.The mechanical model and the data analysis can be informative to the interpretations of other engineering practices as well,but may face different types of challenges.

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.

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.

Experimental and numerical investigation of droplet flow mechanisms at fracture intersections

Understanding unsaturated flow behaviors in fractured rocks is essential for various applications.A fundamental process in this regard is flow splitting at fracture intersections.However,the impact of geometrical properties of fracture intersections on flow splitting is still unclear.This work investigates the combined influence of geometry(intersection angle,fracture apertures,and inclination angle),liquid droplet length,inertia,and dynamic wetting properties on liquid splitting dynamics at fracture intersections.A theoretical model of liquid splitting is developed,considering the factors mentioned above,and numerically solved to predict the flow splitting behavior.The model is validated against carefullycontrolled visualized experiments.Our results reveal two distinct splitting behaviors,separated by a critical droplet length.These behaviors shift from a monotonic to a non-monotonic trend with decreasing inclination angle.A comprehensive analysis further clarifies the impacts of the key factors on the splitting ratio,which is defined as the percentage of liquid volume entering the branch fracture.The splitting ratio decreases with increasing inclination angle,indicating a decrease in the gravitational effect on the branch fracture,which is directly proportional to the intersection angle.A non-monotonic relationship exists between the splitting ratio and the aperture ratio of the branch fracture to the main fracture.The results show that as the intersection angle decreases,the splitting ratio increases.Additionally,the influence of dynamic contact angles decreases with increasing intersection angle.These findings enhance our understanding of the impact of geometry on flow dynamics at fracture intersections.The proposed model provides a foundation for simulating and predicting unsaturated flow in complex fractured networks.

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.

Study on the Impact of Massive Refracturing on the Fracture Network in Tight Oil Reservoir Horizontal Wells

Class III tight oil reservoirs have low porosity and permeability,which are often responsible for low production rates and limited recovery.Extensive repeated fracturing is a well-known technique to fix some of these issues.With such methods,existing fractures are refractured,and/or new fractures are created to facilitate communication with natural fractures.This study explored how different refracturing methods affect horizontal well fracture networks,with a special focus on morphology and related fluid flow changes.In particular,the study relied on the unconventional fracture model(UFM).The evolution of fracture morphology and flow field after the initial fracturing were analyzed accordingly.The simulation results indicated that increased formation energy and reduced reservoir stress differences can promote fracture expansion.It was shown that the length of the fracture network,the width of the fracture network,and the complexity of the fracture can be improved,the oil drainage area can be increased,the distance of oil and gas seepage can be reduced,and the production of a single well can be significantly increased.

Fracture network types revealed by well test curves for shale reservoirs in the Sichuan Basin,China

Pressure buildup testing can be used to analyze fracture network characteristics and conduct quantitative interpretation of relevant parameters for shale gas wells,thus providing bases for assessing the well productivity and formulating proper development strategies.This study establishes a new well test interpretation model for fractured horizontal wells based on seepage mechanisms of shale reservoirs and proposes a method for identifying fracturing patterns based on the characteristic slopes of pressure buildup curves and curve combination patterns.The pressure buildup curve patterns are identified to represent three types of shale reservoirs in the Sichuan Basin,namely the moderately deep shale reservoirs with high pressure,deep shale reservoirs with ultra-high pressure,and moderately deep shale reservoirs with normal pressure.Based on this,the relationship between the typical pressure buildup curve patterns and the fracture network types are put forward.Fracturing effects of three types of shale gas reservoir are compared and analyzed.The results show that typical flow patterns of shale reservoirs include bilinear flow in primary and secondary fractures,linear flow in secondary fractures,bilinear flow in secondary fractures and matrix,and linear flow in matrix.The fracture network characteristics can be determined using the characteristic slopes of pressure buildup curves and curve combinations.The linear flow in early secondary fractures is increasingly distinct with an increase in primary fracture conductivity.Moreover,the bilinear flow in secondary fractures and matrix and the subsequent linear flow in the matrix occur as the propping and density of secondary fractures increase.The increase in the burial depth,in-situ stress,and stress difference corresponds to a decrease in the propping of primary fractures that expand along different directions in the shale gas wells in the Sichuan Basin.Four pressure buildup curve patterns exist in the Sichuan Basin and its periphery.The pattern of pressure buildup curves of shale reservoirs in the Yongchuan area can be described as 1/2/→1/4,indicating limited stimulated reservoir volume,poorly propped secondary fractures,and the forming of primary fractures that extend only to certain directions.The pressure buildup curves of shale reservoirs in the main block of the Fuling area show a pattern of 1/4/→1/2 or 1/2,indicating greater stimulated reservoir volume,well propped secondary fractures,and the forming of complex fracture networks.The pattern of pressure buildup curves of shale reservoirs in the Pingqiao area is 1/2/→1/4→/1/2,indicating a fracturing effect somewhere between that of the Fuling and Yongchuan areas.For reservoirs with normal pressure,it is difficult to determine fracture network characteristics from pressure buildup curves due to insufficient formation energy and limited liquid drainage.

Pulp health and calcific healing of a complicated crown–root fracture with additional root fracture in a maxillary incisor: A case report

BACKGROUND Complicated crown–root fracture (CRF) involves severe injury to the crown, root,and pulp, and may be accompanied by multiple root fractures. The loss of a toothhas lifelong consequences for children and teenagers, but the maintenance of pulphealth and the calcific healing of multiple root fractures are rarely reported in theliterature.CASE SUMMARY This case reports healing of a permanent tooth with complicated crown–root andadditional root fractures, in which pulp health was maintained. A 10-year-old girlfell and fractured the root of her maxillary left central incisor at the cervical level.After the coronal fragment was repositioned, the tooth was splinted until thetooth was no longer mobile, 2 years later. Eight years after treatment, the toothhas remained asymptomatic with vital pulp and localized gingival overgrowth.Cone-beam computed tomography revealed not only calcified healing of the CRFbut also spontaneous healing in an additional undiagnosed root fracture. Thefracture line on the enamel could not be healed by hard tissue and formed agroove in the cervical crown. It was speculated that the groove was related to thelocalized gingival overgrowth.CONCLUSION This case provides a clinical perspective of the treatment of a tooth with acomplicated CRF and an additional root fracture.