Fracture Width Research Articles

Size Effects of Rough Fracture Seepage in Rocks of Different Scales

Percolation experiments were conducted on coal samples with various fracture lengths and inclination angles under different stress conditions using a gravity-loaded rock percolation test device. The goals of these experiments are (1) to improve the technology for protecting water resources while mining coal and (2) to enhance the research on how the size effects of fracture affect seepage. A three-dimensional seepage model was constructed using COMSOL numerical simulation software for larger fracture lengths ranging from 1 to 30 m to investigate the seepage pattern under the coupling of fracture roughness, fracture width, and other factors. Multiple regression analysis was used to investigate the effects of different factors on seepage from large and small fractures independently. The results show that, under laboratory conditions, for fracture lengths 10–70 mm (small length), permeability increases non-linearly with an increase in fracture length, and the overall increase is approximately 1.8 times. Whereas, for fracture lengths of 1–30 m (large length) in the simulation, permeability decreases and then increases with an increase in fracture length, and the overall change is approximately 0.03 times. The permeability varies in three stages (1–8 m obvious change, 8–23 m stabilization, 23–30 m stability) under different fracture lengths, widths, and roughness conditions. Acritical size was found to exist. The effect of fracture length on large length fracture seepage and small length fracture seepage was further verified by parameter sensitivity. The results of this study further reveal the mechanism of fracture seepage under coupling of fracture geometry size stress.

Optimization of process parameters for acid fracturing assisted herringbone well SAGD

Zhong18 wellblock of Fengcheng oilfield developed with low permeability interlayer and had strong heterogeneity, which caused steam chamber of conventional steam assisted gravity drainage (SAGD) process cannot extend lengthwise continuously and serious steam heat loss. To address this problem, a method of acid fracturing assisted SAGD process is proposed to enhance the oil drainage and improve oil recovery. Based on the herringbone well SAGD being used in Zhong18 wellblock, the orthogonal experimental design and oil reservoir numerical simulation are used to determine the significance level and fracture parameter optimization of the acid fracturing process. The priority of optimization sequence is: fracture permeability, fracture width, fracture half-length, fracture spacing. The optimal parameters are as: 3D fracture permeability, 2.8 mm fracture width, 80 m fracture half-length and 80 m fracture spacing. A 10-year simulation using optimized parameters can improve the recovery by 9.2 % compared with the conventional SAGD process. The result proved that acid fracturing assisted herringbone well SAGD process can effectively penetrate the low permeability interlayer, expand the sweep range of steam chamber, and improve the oil recovery degree of the reservoir.

Experimental and numerical modeling of deformation-cracking mechanics of 3D-printed rock samples with single fracture

The analysis of mechanical response and deformation-cracking behavior contributes to the high-efficiency extraction of geo-energy and long-term safety of underground engineering structures. Compared to natural cores, the mechanical properties of 3D-printed samples made from quartz sand as raw material are relatively homogeneous, and can be used for quantitative studies on the influence of natural defects on the mechanical properties of rocks. In this work, 3D-printed samples with single fractures of different crack angles, lengths and widths were fabricated and used for uniaxial compression tests. Adopting the digital image correlation method, the stress-strain distribution during uniaxial compression tests were visualized, and the influence of prefabricated fracture characteristics (dip angle, length, and width) on the deformation-failure process were studied. An extended finite element method subroutine for ABAQUS® software was modeled and used for the uniaxial compression simulation, which was validated by experiments. Then, the influence of mechanical parameters (Young’s modulus, Poisson’s ratio, cohesion, and internal friction angle) on the deformation-cracking mechanics were simulated and studied. The results indicate that, compared to the intact sample, fractures reduce the sample strength. With the extension of fracture length and width, or the decline of fracture angle, both the peak strain and strength of the 3D-printed samples decrease. The splitting tensile failure, or shear failure, or both were determined for the 3D-printed samples with different fracture angles. For the same axial strain, the extension length of the new crack increases linearly with rising Young’s modulus and decreases linearly with increasing Poisson’s ratio. The initial strain of new cracks decreases linearly with increasing Young’s modulus, while little variations are found in samples with different Poisson’s ratio. For the same axial displacement load, the peak stress increases linearly with growing internal friction angle and cohesion. Cited as: Song, R., Tian, J., Wu, M., Liu, J. Experimental and numerical modeling of deformation-cracking mechanics of 3D-printed rock samples with single fracture. Advances in Geo-Energy Research, 2023, 8(2): 126-135. https://doi.org/10.46690/ager.2023.05.06

Experimental evaluation and optimization of improved conductivity of gelling acid etched fractures in deep, low-permeability reservoirs

Stimulation technology is the key to efficient development of deep low-permeability carbonate reservoirs. For such reservoirs, where the porosity and permeability are low, or where the reservoir is far from the borehole. An efficient production increase can only be achieved by using a deep percolation gelling acid fracture technique, maximizing the length of the acid etched fracture to expand the percolation area, and improving the conductivity of the acid etched fracture. A quantitative experimental study of the conductivity of acid etch fracture based on an acid rock tiling instrument, a 3D laser scanner, and an acid etch fracture conductivity evaluation device identified three typical supporting morphologies of gelling acid etch fracture walls: spot, line, and sheet. A systematic quantitative description and evaluation of the etch morphology of rocks etched by acid has been performed. The fracture morphology of acid etchings has been quantitatively evaluated under various experimental conditions such as fracture width, temperature, acid fluid consumption, displacement, and different acid fracture processes and their laws affecting fracture conductivity. The conductivity of acid corrosion fracture increases with the decrease of fracture width, and decreases with the increase of closure stress. The greater the amount of acid used, the higher the fracture conductivity; With the increase of flow Reynolds number, the conductivity of acid corrosion fracture shows a trend of increasing first and then decreasing. The fracture conductivity was compared and analyzed for different property placement conditions under the acid sand carrying technique, and the main effect of the acid etch fracture conductivity was identified. Optimization of high conductivity and deep penetration gelling acid fracturing techniques can help guide the design of acid fracturing and improve stimulation and recovery effects, thus achieving the goal of efficient development of deep, low permeability carbonate reservoirs to increase reserves and production.

An updated numerical model of fracture fluid loss coupled with wellbore flow in managed pressure drilling

The loss of drilling fluids often occurs during reservoir extraction in fractured formations, and the prediction of natural fracture loss rate is vital for controlling drilling fluids loss. However, the coupling of loss model to wellbore flow has rarely been considered. Based on the non-Newtonian fluid loss dynamics theory, this study considers Herschel–Buckley fluid and develops an updated numerical model to couple the loss of fracture with wellbore flow. The roughness of the fracture is characterized using the continuous random accumulation method. The coupling model is verified by field data, and its simulated results show the average relative and maximum relative errors were 4.76% and 12.8%, respectively. A linear throttle valve is introduced to simulate the effect of regulating wellhead back pressure and pump displacement on drilling fluids loss in managed pressure drilling, and the results indicate that the impact of regulating wellhead back pressure is better than that of pump displacement. This paper studies the pressure fluctuates of the fractured borehole breathing mechanism in detail and has proposed two possible scenarios that may cause borehole breathing. Increasing the wellhead back pressure can convert the overflow into loss, while reducing the wellhead back pressure by too much at once may also turn a loss into an overflow. The orthogonal experiment design is performed to study the influence of eight parameters on the loss rate, and the order of influence is as follows: fracture width, fluidity index, fracture area, consistency factor, yield stress, drilling fluids density, circulating displacement, and fracture dip.

Numerical Simulation of Oil-Water Two-phase Conductivity in Hydraulic Fracturing Considering Proppant Crushing

Hydraulic fracturing can effectively increase reservoir productivity, and the effect depends on proppant behavior. Crushing of proppant during fracturing induces a series of changes in fracture width and the pore space formed between proppant particles, affecting reservoir fluid flow. For exploring the flow law of oil and water in proppant fractures, the discrete element method (DEM) and Tavares crushing model were combined to simulate the proppant crush process. At the same time, based on the formed pore space, the flow law of two phase fluid under the influence of such factors as the number of proppant placement, combination of particle size, closing pressure, and particle wettability was studied by fluid volume method(VOF). A series of data obtained through simulation show that with the increase of the average particle radius of single-layer and multilayer proppant is, the fracture conductivity and fracture width increase at the same closure pressure,. In the pore space formed by surface water-wet proppant, the ability of pore to transport oil phase increases; the higher of the number of closure pressure is, the larger the ability of pore to transport oil phase is.

Inclusion of anisotropy in understanding rock deformation and inter-well fracture growth in layered formation through CZM based XFEM

In layered formations such as the Wufeng-Longmaxi marine shale, mechanical rock properties may be uniform horizontally within a layer, but vary vertically, and from layer to layer. In this study, we implement Newton-Raphson method within a rigorous two-dimensional scheme for computing fluid-solid coupling at every time increment in an anisotropic rock frame. The investigated domain consists of intercalations of soft and hard rock layers with a consideration of a cluster of three horizontal wells. The linear convection equation describing the fluid flow is discretized using upwind scheme whose integration points are determined by the intersection between the crack geometry and the underlying discretization of the extended finite element method (XFEM). A normalized slurry concentration averaged over the fracture width is used to establish a basis for analysing fluid viscosity effects with subsequent XFEM computation indicating that an increased slurry concentration leads to increasing fracture aperture. We further conduct a thorough investigation of an inter-well fracture development with the analyses revealing that the fractures kink at the interfaces of the intercalations of soft and hard layers. It is also observed that, when the elastic contrast between the soft and hard strata decreases, fracture kinking reduces and the inter-well fracture interference mechanism switches to linking or coalescence. Before the linking, the fluid pressure fields inside the separate fractures are independent, whereas an equilibrated pressure field develops inside the inter-linked fracture system. Oriented initial perforations show no link-growth of fractures. However, we observe that the highest inclination angle, which is 75° in our case, yields the highest treatment pressure of 62.8 MPa, whereas the lowest inclination angle of 15° yields the lowest treatment pressure of 56.3 MPa. We validate our results through comparison with a triaxial fracturing cell experiment, and Kristianovich-Geertsma-de Klerk (KGD) fracture problem. In all cases, the findings agree with the numerical results.

Experimental Study on Acoustic Emission Characteristics of Uniaxial Compression of MICP-Filled Sandstone.

Rock masses are inherently heterogeneous, with numerous fractures that significantly affect their mechanical properties, fracture characteristics, and acoustic emission features due to the interactions between fractures or between fractures and the rock mass. Microbially induced calcite precipitation (MICP) technology, as an emerging non-destructive biological grouting reinforcement method, can repair fractured rock masses and alter their internal conditions. To investigate the mechanical properties, failure process evolution, and MICP repair effects of sandstone before and after repair, uniaxial compression tests were conducted on prefabricated, fractured (0.7-2.0 mm width) filled and unfilled rock samples, with acoustic emission monitoring throughout the process. Acoustic emission signal characteristics of the rock samples under stress were comparatively analyzed, determining the rock failure process and the microscopic failure types at compression-density stages, elastic stages, and destruction stages. The results show that the properties of the filled specimens improved, the failure process was mitigated, and the final failure stage was dominated by tension signals, accounting for over 60% of the total. The filling effect was better than 1.5-2.0 mm when the fracture width was 0.7-1.0 mm. The study deeply reveals the evolutionary process of compressive failure of the two types of rocks under different fracture widths, and by correlating the acoustic emission parameters with the stress-strain process, it provides a theoretical basis for repairing rock fractures using microbial engineering technology and offers experimental evidence and possible directions for the improvement and optimization of MICP technology.

Predicting the crack width of the engineered cementitious materials via standard machine learning algorithms

This study aims to develop various machine learning (ML) models to investigate the self-healing capacity of engineered cementitious composites (ECC) and to evaluate the effect of input parameters (raw materials and crack width before the healing process) on output parameters (crack width after the healing process) via Shapley additive explanations (SHAP) analysis. The combination of the individual and ensemble ML models has been introduced to check and compare the accuracy level towards the prediction of crack width after the healing process to access the most suitable model for this application. The support vector machine (SVM) from the individual, while XGBoost (XGB) and random forest (RF) from ensemble ML models have been investigated for prediction purposes. As per the obtained results, the RF model outperforms both the SVM and XGB algorithms in forecasting the fracture width after the healing process for the selected ECC in concrete material. The performance indicator, such as the coefficient of determination (R2), was reported as 0.97 for RF, 0.96 for XGB, and 0.93 for the SVM model. Statistical results and k-fold cross-validation for the employed ML models also confirm their legitimacy. It was also noted from the result of the SHAP analysis that the significant contribution was for the crack width before healing towards the prediction of crack width after the healing process. Furthermore, the ML models can also be utilized to anticipate the healing ability of the other ECC, such as soda glass powder, marble powder, and bagasse ash.

An improved Eulerian scheme for calculating proppant transport in a field-scale fracture for slickwater treatment

Field-scale proppant transport simulation is vital to the development of unconventional resources. Previous research on proppant transport and distribution has mainly focused on small-scale and experimental-scale proppant simulations, and few studies are related to field-scale proppant deployment. In this paper, through coupling of the slickwater flow, proppant flow, and dynamic crack propagation, an improved Eulerian scheme for calculating proppant transport in a field-scale fracture for slickwater treatment is presented. In the improved Eulerian scheme, the effect of the fracture width on the proppant settling rate and the effect of the increase in the settling bed height on the proppant bed build-up rate are taken into consideration. In addition, a new retardation coefficient is introduced to account for the effect of proppant retardation on the proppant flow. The Eulerian scheme is verified through comparison with published works, including experimental results and simulation results, and sensitivity analysis is conducted. Based on the results of this research, we conclude that the lower viscosity slickwater causes the proppant distribution to become more even, and thus, the proppant bed becomes longer and higher. As the proppant diameter increases, the proppant distribution in the fracture becomes more even, and the fracture area supported by the proppant becomes larger. The optimal initial proppant concentration for obtaining the largest propped fracture area is 0.15–0.25. The greater the density of the slickwater is, the more even the proppant distribution is, and the larger the propped fracture area is.

What is the Radiographic Factor Associated with Meniscus Injury in Tibial Plateau Factures? Multicenter Retrospective (TRON) Study.

Tibial plateau fracture (TPF) is a complex intra-articular injury involving comminution and depression of the joint, which can be accompanied by meniscal tears. The aims of this study were (1) to demonstrate the rate at which surgical treatment for lateral meniscal injury and (2) to clarify the explanatory radiographic factors associated with meniscal injury in patients with TPF. We extracted the patients who received surgical treatment for TPF from our multicenter database (named TRON) included from 2011 to 2020. We analyzed 79 patients who were received surgical treatment for TPF with Schatzker type II and III and evaluation for meniscal injury on arthroscopy. We investigated the rate at which surgical treatment of the lateral meniscus was required in patients with TPF and the explanatory radiographic factors associated with meniscal injury. Radiographs and CT scans were evaluated to measure the following parameters: tibial plateau slope, distance from lateral edge of the articular surface to fracture line (DLE), articular step, and width of articular bone fragment (WDT). Meniscus tears were classified according to whether surgery was necessary. The results were analyzed by multivariate Logistic analyses. We showed that 27.7% (22/79) of cases of TPF with Schatzker type II and III had lateral meniscal injury that required repair. WDT ≥ 10mm (odds ratio 10.9; p = 0.005) and DLE ≥ 5mm (odds ratio 5.7; p = 0.05) were independent explanatory factors for meniscal injury with TPF. Bone fragment size and the location of fracture line on radiographs in patients with TPF are associated with meniscus injuries requiring surgery. The online version contains supplementary material available at 10.1007/s43465-023-00888-5.

Numerical simulations of heat exchange and vapor flow in ice fractures on Enceladus

Cassini spacecraft observed plume of water vapor and ice particles above the south polar terrain (SPT) of Saturn's moon Enceladus in 2005. The area of the SPT is marked by four prominent linear depressions in the ice dubbed “tigers stripes” (TS) that appear to be the source of the plume. The area around TS is also the source of anomalously high heat flux. The current consensus based on analysis of Cassini observations and modeling suggests that TS are fractures in the ice that penetrate to warm sub-ice ocean. Escaping vapor laden with ice particles forms the visible plume and latent heat of condensing vapor serves as the source of the surface thermal anomaly. In the present work previously developed numerical model of vapor flow and heat exchange inside TS fractures is refined and used to explain Cassini observations. Model improvements include consideration of a possible snow layer on the surface and inclusion of surface ice sublimation into energy balance model. Results of the simulations with improved model suggest that Cassini observations of vapor mass flow and endogenic heat flux can be explained if the width of the ice fractures is in the range 0.05–0.1 m, similar to previously published results. Wider fractures are possible if only a small portion of TS total length produces vapor plume, but the whole ~500 km length of TS fractures still contributes to the surface thermal anomaly. Alternatively, wider fractures are also possible in fractures with high effective friction due to wall roughness or channel tortuosity. Simulated heat output of fractures with different widths and depths in the range of 1.5–3 km is ~2.5–3.0 GW and is only weakly dependent on fracture width. A 2-m-thick surface snow layer covering the fracture can significantly lower outgoing heat flux to 0.9–1.9 GW and reduce surface temperatures by 20–40 K. The total heat flow from different fractures (including conduction from the water-filled portion) is remarkably similar - it is ~3.3 GW and 2.3 GW for fractures without and with a surface snow layer, respectively. The simulated heat flow is lower than the observed heat flow, suggesting that each TS depression may host 2 to 6 narrow ice fractures. The long-standing puzzle of the large difference between the observed heat flow from near TS (~4.2 GW) and from the whole SPT (~15.8 GW) is explained by conduction of ~11 GW of heat from the ocean through the ~5 km-thick ice shell underlying the SPT. Predicted high surface temperatures near fracture exit result in high rates of ice sublimation, which may produce a secondary source of water vapor feeding the observed plume. Fracture outlet likely evolves into a cone-like cross-section widening towards the surface on timescales from 1 to 100 years.

Biomechanical evaluation of two internal fixation systems for the treatment of mandibular symphyseal fracture

Due to the disadvantage of maxillomandibular fixation, the semi-rigid and rigid internal fixations have been employed to provide early mouth motion. To find the proper fixation and adequate stability, the biomechanical performance of these systems was assessed using Finite Element (FE) method. The 3D mandible model with a symphyseal fracture, teeth, periodontal ligament, and fixation devices were created for the FE analyzes. The bone structure was determined as a transverse isotropic whereas the fixation devices were titanium. The load includes Masseter, Medial Pterygoid, and Temporalis muscular forces as well as the occlusal forces acting on first molars, canines, and incisors. The maximum stress occurs at the center of fixation devices at symphyseal fracture. The maximum stress values were 877.4 MPa for the reconstruction plate and 646.8 MPa for the mini-plates. The plates maintained the fracture width at mid-region better than superior and inferior. The maximum fracture gap were 1.10 and 0.78 mm for reconstruction plate and mini-plates, respectively. The fracture site's elastic strain stabilized with the reconstruction plate was 1089.0 microstrains and with the mini-plates was 399.6 microstrains. The treatment of a mandibular symphyseal fracture using a mini-plates provides more adequate fracture stability for new bone formation and mechanically safer than locking reconstruction plate. Mini-plates fixation was able to control the fracture gap better than the reconstruction plate. Mini-plates technique was considered as the first choice of internal fixation, however, a reconstruction plate can also be used in case of unavailability and complication related to mini-plating.

Stress Interferences between Fractures and Fracturing Stages of a Horizontal Well in a Sandy Conglomerate Reservoir in Junggar Basin, Northwest China

The sandy conglomerate reservoirs in the Mahu oilfield located in the Junggar Basin of Northwest China are featured by a significant horizontal stress difference between two directions, making formations easy to form double-wing fractures upon hydraulic fracturing instead of creating a complex fracture network. In addition, as the well spacing or interval cluster spacing decreases, the stress interferences between hydraulic fractures strengthen accordingly, leading to more difficulties in the prediction of fracture propagation patterns. Given the geological characteristics in the study area, an extended finite element method (XFEM) based hydraulic fracture model that can handle fracturing fluid flow distribution was proposed to evaluate the seepage, stress, and damage of the formation under hydraulic fracturing. The influences of the initial stress difference, cluster spacing, and fracturing stage sequence on the hydraulic fracture stress interference and the fracture propagation were investigated, producing discoveries that include: (1) as the fractures propagate, the stress difference between two fractures changes as well, and such change is also affected by the initial stress difference and the fracture distance; (2) the postfracturing stress difference first decreases but then increases with the increase in cluster spacing; (3) as the cluster spacing increases, the interfracture stress interference decreases. In addition, the outer fractures suppress the length of the middle fractures, thus limiting the stimulated reservoir area (SRA); (4) for the cases of creating multistage fractures, the later fracturing stage experiences both the interfracture and the interstage stress interferences from the prefracturing stage. As the fracture width changes with time, the nonplanar fracture feature of the later fracturing stage becomes more evident while the corresponding SRA decreases.

EXPERIMENTALLY VALIDATED COMPUTER SIMULATIONS OF LOCKING PLATE FIXATIONS FOR SURGICAL EDUCATION

Surgical education of fracture fixation biomechanics relies mainly on simplified illustrations to distill the essence of the underlying principles. These mostly consist of textbook drawings or hands-on exercises during courses, both with unique advantages such as broad availability and haptics, respectively. Computer simulations are suited to bridge these two approaches; however, the validity of such simulations must be guaranteed to teach the correct aspects. Therefore, the aim of this study was to validate finite element (FE) simulations of bone-plate constructs to be used in surgical education in terms of fracture gap movement and implant surface strain.The validation procedure was conducted in a systematic and hierarchical manner with increasing complexity. First, the material properties of the isolated implant components were determined via four-point bending of the plate and three-point bending of the screw. Second, stiffness of the screw-plate interface was evaluated by means of cantilever bending to determine the properties of the locking mechanism. Third, implant surface strain and fracture gap motion were measured by testing various configurations of entire fixation constructs on artificial bone (Canevasit) in axial compression. The determined properties of the materials and interfaces assessed in these experiments were then implemented into FE models of entire fixation constructs with different fracture width and screw configurations. The FE-predicted implant surface strains and fracture gap motions were compared with the experimental results.The simulated results of the different construct configurations correlated strongly with the experimentally measured fracture gap motions (R2>0.99) and plate surface strains (R2>0.95).In a systematic approach, FE model validation was achieved successfully in terms of fracture gap motion and implant deformation, confirming trustworthiness for surgical education. These validated models are used in a novel online education tool OSapp (https://osapp.ch/) to illustrate and explain the biomechanical principles of fracture fixations in an interactive manner.

Research on the cone-beam CT of the fracture morphology and location of a single oblique complicated crown-root fracture of maxillary incisors

Objective: To study the morphological pattern of single oblique complex crown fracture and its relative location to periodontal hard tissues from a three-dimensional perspective by using cone-beam CT, which provides a more intuitive and comprehensive understanding for the pathological features and rules of single oblique complex crown fracture. Methods: Primary cone-beam CT images of 56 maxillary permanent anterior teeth with oblique complex crown root fractures were collected from the Department of Integrated Emergency Dental Care, Capital Medical University School of Stomatology during January 2015 to January 2019. Fracture pattern, fracture angle, fracture depth, fracture width, and the relative location of the fracture line to the crest of the adjacent alveolar ridge were retrospectively analyzed. Independent samples t-test was used to compare the differences in angle, depth and width of fractures between sexes and tooth locations, as well as the pre-and post-fracture crown-to-root ratios between different tooth locations. Then the affected teeth were divided into juvenile group (≤18 years), young group (19-34 years) and middle-aged and elderly group (≥35 years). One-way ANOVA was applied to compare the differences in angle, depth and width of fracture between age groups, and Fisher exact test to compare the differences in fracture pattern of the teeth and the relative position of the fracture line to the crest of the adjacent alveolar ridge. Results: There were 35 males and 21 females in 56 patients, aged (28.2±13.2) years. Among the 56 affected teeth, forty-six were maxillary central incisors and 10 were lateral incisors. According to the patients' age and growing stage, they could be divided into the juvenile group (19 cases), the young group (14 cases), and the middle-aged and elderly group (23 cases). Forty-six (82%) affected teeth had an S-shaped fracture pattern, and ten (18%) had a diagonal pattern, in which the fracture angle of the S-shaped fracture line (47.85°±10.02°) was significantly greater than that of the diagonal line (28.30°±8.07°) (P<0.001). The fracture nadir was flush with or below the top of the alveolar crest in 98% (55/56) of cases. The fracture depth was significantly greater in the juvenile group [(1.75±0.73) mm] than in the young group [(1.21±0.68) mm](P=0.042) and in the middle-aged and elderly group [(1.12±0.90) mm] (P=0.001). The width of fractures among 56 patients was (4.75±1.44) mm, which had no statistically significant differences between different age, sex and tooth location groups (P>0.05). There were no statistically significant differences in the crown-to-root ratios after fracture of maxillary central incisors (1.18±0.13) compared to maxillary lateral incisors (1.14±0.20) (t=1.90, P=0.373). Conclusions: The fracture patterns of single oblique complex crown fracture were mainly S-shaped and oblique alignment; the fracture nadir was mostly located within 2.0 mm below the palatal alveolar crest.

Experimental Study on Plugging Behavior of Degradable Diverters in Partially Open Fracture in Temporary Plugging and Diverting Fracturing.

Temporary plugging and diverting fracturing technology (TPDF) has been successfully applied to improve reservoir productivity. In real reservoirs, a considerable number of fractures have relatively rapidly decreasing fracture widths and closed ends. However, the plugging behavior of diverters in this typical fracture called the partially open fracture (POF) is still unclear because of the few related studies. This paper aims to investigate the plugging behavior of diverters at the fracture tip. The 3D-printed fracture model was used to reproduce the partially open fracture, and the morphological characteristics of the partially open fracture and the open fracture were compared based on the scan data. A series of plugging experiments were conducted to monitor the transport behavior of the diverter in partially open fractures through multiple pressure sensors on the fracture model and to investigate the influence of diverter formula and fracture type on plugging behavior. Finally, based on the experimental results, the plugging mechanism of diverters in partially open fractures was analyzed. The plugging experiments show that a higher-pressure distribution appears at the fracture tip when using a combination of fibers and particles, indicating that it is beneficial for the diverter to transport to the tip and form plugging in the fracture, and it should be noted that small changes in particle size and concentration had a significant influence on the plugging performance. Therefore, it is recommended to use a combination of fibers and particles of multiple sizes (maximum particle size not exceeding half of the fracture width) to achieve a better plugging effect. In addition, the plugging behaviors of partially open fractures and open fractures are different. For partially open fractures with widths of 1, 2, and 4 mm, the recommended formula of the diverter is 1 wt % fibers + 1 wt % 0.15 mm particles, 1 wt % fibers + 1 wt % 0.15 mm particles + 1 wt % 1 mm particles, and 1 wt % fibers + 1 wt % 0.15 mm particles + 1 wt % 1 mm particles + 1 wt % 2 mm particles, respectively. The above experimental results provide an experimental and theoretical basis for the application of TPDF in the field.

Optimization of Hydraulic Fracture Treatment Parameters for Normally Pressured Longmaxi and Wufeng Shales in the Southeastern Sichuan Basin in China

Lower Silurian Longmaxi and Upper Ordovician Wufeng shales are gas-producing formations. These formations have ultralow porosity and permeability in the southeastern Sichuan Basin and have normal formation pressures with pressure coefficients of less than 1.2. Hydraulic fracturing has been proven as the best development strategy to produce gas. But choosing hydraulic fracture treatment parameters becomes challenging due to strong reservoir heterogeneity, significant horizontal stress contrast and high in situ stress in this region. We employed the pseudo-three-dimensional (P3D) model to study fracturing fluid types, injection rates, and proppant sizes to optimize the fracturing design of these shale formations. First, this model was solved in the simulator by the finite element method (FEM) to obtain the fracture height, length, and width. Then the results were validated by 3D Tip dominated model, and the perkins-kern-nordgren (PKN) and khristianovic-geertsma-deklerk (KGD) analytical models, which are popular and most used in designing hydraulic fractures. It was found that as the volumetric injection rate and gel loading in the fracturing fluid rise, so do the generated fracture length and width. Furthermore, the formations’ stress contrast affected the shape of the fracture, the interval with lower stress had a wider fracture compared to the interval with higher stress. Also, the higher stress in the layers above and below the shale formations contained the fracture height, which favored the growth of fracture in the shale formations. Lastly, it is suggested that a fluid with gel loading of 60 ppgt, proppant with 12/20 mesh size and an injection rate of 6.36 m3/min be used in these shale formations with normal reservoir pressure. These parameters’ combinations created the most extended propped fracture length of 264.8 m, and the average width was 1.06 cm.

Optimization of a multi-fractured multilateral well network in advantageous structural positions of ultralow-permeability hydrate reservoirs

In this study, we propose a production enhancement strategy that combines multiplanar fractures with a multilateral well network, namely multi-fractured multilateral well network (MMWN), to improve the production efficiency of ultralow-permeability hydrate reservoirs (ULPHs). Considering that natural gas hydrate is generally disseminated in nonhorizontal strata, the influence of topography on the productivity of multilateral wells was first revealed, and then the stimulation effects of MMWN with different geometries and properties in advantageous structural positions of ULPHs on gas production were systematically analyzed. Results indicate that gas extraction from multilateral wells is good at the structural low of ULPHs. MMWN significantly increased the stimulated reservoir volume, leading to an increase in gas production by more than 23 times compared to using the depressurization method alone. Using the MMWN did not require extra energy and caused no ice formation. Improving the planar fracture number, area, width, and permeability effectively facilitated gas recovery. Enlarged fracture spacing is suitable for long-term production. Gas production is not influenced by porosity, overlarge width, or high permeability (over 10 D) of planar fractures. This novel study suggests that the combination of multilateral well networks and highly intensive reconstruction is an effective method to produce gas hydrates.

Characterization of fracture development in geometrical similar ultra-high-performance concrete (UHPC) beams using acoustic emission (AE) technique

The acoustic emission (AE) technique is a common method for evaluating the fracture and damage properties of materials. This study utilized the AE technique to analyze the fracture behavior of ultra-high-performance concrete (UHPC) beams. Experiments were conducted on three differently sized beam specimens that were geometrically similar. The center point bending tests were carried out under crack mouth opening displacement (CMOD) control to study the fracture properties of the UHPC beams. Based on the experimental study, the fracture properties such as crack propagation, parametric-based properties, and fracture process zone (FPZ) length and width were predicted in the present work. The AE waves generated during the cracking can readily differentiate between the concrete matrix failure and fiber bridging following the post-peak response in the UHPC beam. In this work, the AE parameters were used to detect the source location, fracture mode, the position of the crack, and strain localization near the crack tip. The presence of steel fibers in concrete provides complexity in identifying the source localization, and wave dispersion results in attenuation and distortion of the AEs. The occurrence of AE events was observed to increase in the post-peak part compared to pre-peak possibly due to fiber bridging, demonstrating the energy absorption capacity. Based on AE results, the length and width of the fracture process zone were found to increase with the specimen size.