The construction of complex fracture networks is essential for enlarging the stimulated reservoir volume (SRV) and enhancing hydrocarbon production in tight reservoirs. Variable-rate hydraulic fracturing induces periodic stress perturbations by modulating the injection rate, thereby redistributing the local stress field and facilitating the formation of secondary and branched fractures. To elucidate this mechanism, a numerical model of variable-rate fracturing based on the Continuum–Discontinuum Element Method (CDEM) was developed to simulate fracture initiation and propagation under various injection scenarios. The effects of cyclic rate amplitude, cycle duration, and horizontal stress difference on fracture evolution were systematically investigated. The simulation results indicate that, compared with constant-rate and stepwise-rate injection, cyclic fracturing significantly enhances the complexity of fracture networks in tight reservoirs. Increasing the rate amplitude and shortening the cycle duration promote fracture branching and development, thereby expanding the stimulated region. Conversely, an increase in horizontal stress difference reduces the effectiveness of cyclic injection and diminishes the resulting fracture network complexity. These findings provide theoretical insights for optimizing variable-rate fracturing parameters, enhancing the formation of complex fracture networks, and guiding hydraulic fracturing design under varying stress-field conditions.

Abstract Hydraulic fracturing is a critical technology for the efficient development of shale reservoirs. Induced by factors such as the preferred orientation of clay minerals, bedding planes, and natural fractures, shale exhibits pronounced transverse isotropy. The interaction between hydraulic fractures and these natural weak planes typically induces complex propagation behaviors. However, conventional studies often idealize shale reservoirs as isotropic media, neglecting the significant influence of transverse isotropy on fracture morphology. This study performs triaxial compression tests on Longmaxi formation shale to quantify mechanical anisotropy. Subsequently, a numerical model based on the global cohesive zone method is established to investigate fracture propagation across shale matrix, laminated shale, naturally fractured shale, and multicluster fracturing scenarios. Results demonstrate that Longmaxi shale exhibits strong mechanical anisotropy. Numerical simulations reveal that the transverse isotropy ratio ( k ) acts as a primary geometric control: increasing k significantly promotes vertical fracture height growth while simultaneously suppressing width opening due to the enhanced horizontal stiffness. This deformation behavior is accompanied by intensified horizontal stress disturbance and diminished vertical stress disturbance. The transverse isotropy characteristics and weak interfaces (bedding planes and natural fractures) jointly control the fracture propagation morphology. Laminae and natural fractures alter the hydraulic fracture propagation path, while the transverse isotropy ratio can regulate the propagation direction of the hydraulic fracture. When the ratio is between 1.5 and 2.0, the differences in horizontal and vertical stress disturbances are small, and hydraulic fractures easily communicate with laminae and natural fractures, forming a complex fracture network. Regarding multicluster fracturing, competitive propagation is primarily governed by cluster spacing and modulated by k . Cluster spacing determines the fundamental intensity of interference, whereas the anisotropic stress regime compels the restricted central fracture to redirect energy toward vertical extension, enabling it to attain a vertical height comparable to that of the side fractures. These findings offer theoretical insights for the optimization of hydraulic fracturing designs in shale reservoirs.

The mechanical properties of deep shale are influenced by various factors, including high-temperature and high-pressure conditions, as well as its bedding structure. To investigate the evolution of mechanical properties of deep shale under different environmental temperatures, this study takes the Longmaxi Formation shale as an example, conducting high-temperature and high-pressure triaxial tests. Additionally, a thermal-mechanical coupled particle flow model for deep shale with a bedding structure is established from both macroscopic and mesoscopic perspectives. Based on X-ray diffraction experiments to determine the mineral composition and content of the shale, the model assigns the number of grouped mineral particles and their thermal expansion coefficients. Meanwhile, smooth joint contact is incorporated to characterize the influence of bedding structure, and the model’s mesoscopic parameters are calibrated using high-temperature and high-pressure triaxial test results. Based on the triaxial experiments and the thermal-mechanical coupled model, this study investigates the variations in mesoscopic thermal damage, rock mechanical properties, and failure modes of layered shale under different environmental temperatures. The results indicate that high temperature conditions weaken the mechanical properties of shale, while high confining pressure reduces the anisotropy of layered shale. As temperature increases, thermal damage initially occurs at the bedding interfaces. When the temperature exceeds 150°C, mineral particles undergo shear displacement, leading to a sparse distribution of mesoscopic force chains, and macroscopic thermal cracks expand extensively. In high-temperature and high-pressure environments, the thermal-mechanical coupling effect causes a reduction in the peak strength and an increase in peak strain, with the failure mode transitioning from brittle failure to plastic-ductile failure. Meanwhile, bedding cracks branch and gradually extend into the matrix, forming a composite failure mode involving both the shale matrix and the bedding structure.

The rapid advancement of electronic devices and wireless sensors has heightened the demand for energy sustainability and portable power solutions. Traditional human energy harvesters have limitations in harvesting energy from ultra-low-frequency human motion due to issues related to unstable energy output and wearing comfort. To address this challenge, a piezoelectric-electromagnetic hybrid energy harvesting (HP-EEH) structure designed for the hip joint area. This innovative design employs magnetically coupled frequency boosting alongside electromagnetic energy capture to achieve high output power. Firstly, the structure and principle of the energy capture device are introduced, and the electromechanical coupling model of the energy harvester is derived using Hamilton's principle. Furthermore, the system is numerically simulated, and the voltage output characteristics of the piezoelectric unit and the electromagnetic unit are analyzed by using the finite element analysis software. Finally, the experimental setup of the (HP-EEH) is constructed, and the voltage output characteristics are tested for different swinging angles and positions. The results show that two parts of energy can be captured simultaneously under ultra-low-frequency motion conditions. At a swing angle of 50 degrees, the piezoelectric and electromagnetic units achieved maximum output power values of 14.96 mu W at 0.8 Hz and 10.4 mu W at 1.2 Hz, respectively. Incorporating the output power of the electromagnetic unit aims to address the power consumption requirements of low-power devices better.

Summary Exploiting geothermal resources such as hot dry rocks (HDRs) requires directional drilling technology. Measurement-while-drilling (MWD) technology plays a crucial role in directional measurement. However, its high temperature and environment limit downhole measurement instruments in application. For this research, we designed an MWD system with a mechanical gravity tool face, and the fully mechanical structure was used to overcome the high-temperature constraints. The bias stabilization platform, gravity tool face coding method, and mud pulse generation structure were designed. The eccentric stable model and pulse generation structure model were established through numerical analysis, and a gravity tool face angle coding and identification method was also established. The experimental prototype testing system was built on theoretical analysis and hydrodynamics. The feasibility of the tool functions and the recognition algorithm were verified experimentally, with a maximum measurement error of 6° and an average measurement error of 2.6°. The average measurement error of the system in the well test is 6°, which verifies the reliability of the system.

Real-time measurement of the downhole information from sensors distributed along a slender drill-string plays an important role in oil and gas drilling. However, an urgent problem is how to provide power to the downhole sensor network. In this study, combining with the centrifugal softening effect and an oscillator with clearance, a bi-stable electromagnetic energy harvester (EMEH) is proposed to enhance the energy harvesting performance in the low-frequency rotation of the drill-string. The discrete dynamic equations of the coupled EMEHs & drill -string system are established by using the finite difference method and Lagrange's equations. The accuracy of the numerical simulation is validated through model test, and the effects of damping, excitation amplitude, speed and gravity on the performance of a single EMEH are analyzed through numerical simulation. Then, the coupled dynamic model is used to simulate and analyze the performance of the EMEHs in the drilling process of vertical wells and deviated wells. The numerical results show that the resonant frequency of EMEH is related to the excitation amplitude and rotating speed. It first decreases and then increases with the increase of the excitation amplitude, which can cover most frequencies below the resonant frequency of the linear system with delta(i0) = 0 mm. The variation range of the resonant frequency decreases with the increase of rotating speed. In vertical wells, the output power of EMEH increases with the increase of drill-string depth, and the maximum output power at the well bottom can reach 2.0 W. In deviated well, the output power is mainly generated by the continuous rotation of the drill-string and gravity, which increases with the increase of the well inclination. The results show that the output power of a single EMEH can meet the power demand of most downhole sensors.

Shale reservoir is the research hotspot in the development of unconventional oil and gas resources. The properties of bedding plane have an important influence on the mechanical behavior of shale. According to the fracture characteristics of layered shale under Brazilian splitting load, the effects of bedding angle, bond strength ratio and natural fractures on the tensile strength and fracture pattern of layered shale in Brazilian splitting test were studied by particle flow code. The evolution mechanism of meso–macro fracture of shale is analyzed by combining the dynamic change process of particle mesoscopic force chain and crack. The results show that three types of fracture patterns are observed: splitting tensile failure of shale matrix, splitting tensile failure along bedding plane and tensile–shear composite failure along shale matrix and bedding plane. Mesoscopic cracks initiate at the top and bottom loading points of the disk. After the peak load, mesoscopic cracks propagate through and appear dense force chains until macroscopic failure occurs. The bond strength ratio of bedding plane affects the failure pattern and peak strength of the specimen. With the increase in bedding angle, the tensile strength decreases gradually. Considering the influence of natural fractures, the tensile strength of shale is lower, and the crack propagation is more complex. The research model and results provide theoretical basis for the mechanical properties evaluation and fracture pattern analysis of shale.

Fracture extension simulation is an important tool for studying hydraulic fracture characteristics. To solve the problem of mesh sensitivity of strain and fluid pressure during hydraulic crack propagation, the equivalent strain in the damage evolution equation was non-localized, and implicit gradient was performed. A hydraulic-mechanical coupling model based on implicit gradient non-local damage was established. Numerical simulation program was further developed. Comparison of simulation results with experimental data on 'L'-brittle material verified the validity of the program. The fracture propagation process of hydraulic fracturing in a perforated well was simulated. On this basis, the influence of internal length scale parameters and mesh size of the non-local model on the calculation results was analyzed. The influence of mesh size on hydraulic fracture morphology and damage variables is reduced by introducing an implicit gradient nonlocal model, which effectively alleviates the localization effect in hydraulic-mechanical coupling damage simulation. This new model achieves the nonlocalization of the fluid field by introducing the relationship among porosity-permeability and deformation and damage, which avoids the mesh sensitivity of equivalent strain, damage, fluid pressure, and improves the numerical stability. It provides a new method for simulating hydraulic fracture propagation and studying the failure behavior of porous media materials.

In order to explore the mechanical characteristics and porosity and permeability parameter of three kinds of rock (sandstone, granite and limestone) in high temperature environment, conventional triaxial compression experiments and porosity and permeability tests were conducted on three kinds of rocks under 25°C, 300°C and 500°C. The experimental results show that the high temperature environment increases the development degree of microcracks and pore structures in sandstone and limestone. As the temperature rises, the interpenetration length of triaxial compression shear crack of sandstone decreases gradually, and the angle between shear crack and horizontal direction increases gradually. Change of damage mode from single shear damage to tension shear damage (shear-dominated) in granite and limestone. The three rocks’ permeability and porosity increase as ambient temperature rises, and the permeability exhibits clear pressure-constricting sensitivity in a range of temperature settings. The results provide a reference for understanding and predicting the mechanical properties and porosity and permeability characteristics of rocks in high temperature environment.

In this paper, Particle flow code in two dimensions was used to simulate the failure behavior of shale rock under Brazilian test conditions. The meso-mechanism and failure characteristics of shale under different bedding dip angles and bedding cementation strength were studied. The results show that: (1) Three major failure patterns under Brazilian test are tensile failure along shale matrix, tensile failure occurs along the bedding and tensile and shear composite failure along shale matrix and bedding; (2) Microcracks begin at the top and bottom loading points of the disk. When the load reaches the peak strength, a large number of microcracks expand and appear dense force chains until macroscopic fractures are formed. (3) The tensile strength anisotropy of shale samples is obvious, and the tensile strength decreases with the increase of bedding angle; The failure mode and tensile strength of specimens under different cementation strength ratio of bedding plane are also quite different. In this paper, the micro-macro fracture evolution mechanism of layered shale is analyzed by combining the micro-crack and force chain evolution process, and the research results and models can provide theoretical basis for the analysis of mechanical properties of anisotropic rocks and reservoir fracturing.

通过对5种不同曲率半径的高密度聚乙烯(PE?HD)圆棒试样进行单轴拉伸试验,重点分析了曲率半径对工程应力?位移曲线的影响;同时对PE?HD平板试样进行冲压试验,分析了压头直径和冲压速度对载荷?位移曲线的影响;建立了3种基于冲压载荷预测PE?HD单轴屈服应力的经验公式.结果表明,同一拉伸速度下,屈服强度随曲率半径的减小而增大;同一冲压速度下,最大冲压载荷随压头直径的增大而增大;同一压头直径下,最大冲压载荷随冲压速度的增大而增大;基于压头直径为变量的经验公式预测得到的屈服强度可靠性最高,可以较为准确地表征PE?HD的力学性能.

In this paper, the equivalent strain is nonlocalized. The permeability is coupled through the damage variable into the Hydro-Mechanical coupling equation. So as to establish the fluid-driven nonlocal damage expansion model. It is used to solve the localization response problem of quasi-brittle material fracture failure finite element simulation process. So that it can effectively calculate the crack propagation process of rock mass under high pressure fluid. In view of this model, this paper first simulates and compares the experimental results of ‘L’ brittle material plate, and verifies the sensitivity of finite element mesh. Then, through the simulation of the influence of perforation angle on fracture propagation trajectory, the effectiveness of this model for Hydro-Mechanical coupling damage propagation is studied. The results show that the simulation results of the model are consistent with the experiment. It can significantly reduce the grid sensitivity difference caused by localization.

Aiming at the power supply problem of downhole measurement and control instruments, two kinds of vibration energy harvesters, axial vibration energy harvester and lateral vibration energy harvester, are designed in this paper to harvest the axial, lateral, and torsional vibration energy of the drillstring. The mathematical models of the two harvesters are established and the vibration coupling between the harvesters and the drillstring is realized by sharing the node with the drillstring. The performances of the two kinds of harvesters are numerically simulated. The results show that the output power of the axial harvester changes periodically with the change of its installation depth and the number of cycles increases with the increase of the drillstring length. The larger the natural frequency of the axial harvester, the smaller the amplitude of output power fluctuation with depth. When the rotating speed matches the natural frequency of the axial harvester, the maximum output power can reach 1.4 W. The outpower of the lateral VEH is maximum in the possible buckling section near the bit and the maximum output power is about 10 W. The results show that the output power of the designed vibration energy harvester can meet the power demand of most downhole measurement and control instruments.

In this paper, a dynamic method, which includes a coupled dynamic model of full-hole drill string and its numerical implementation approach, is developed to analyze the post buckling of drill string in vertical wells. The coupled dynamic model is established based on Lagrange's equations and finite difference method. Its numerical implementation approach is achieved by using the direct integration method and Rayleigh damping formula. Especially the developed dynamic method is able to consider the coupling of axial vibration, lateral vibration, torsional vibration and the effects of rotating speed, damping from the drilling fluid, the discontinuous contact and friction between drill string and borehole, which enable it to predict the post bucking behaviors of drill string in vertical wells more efficiently and accurately. The developed dynamic method is validated by the comparison with the static theoretical solution of drill string, and then it is used to calculate the dynamic post buckling of drill string in vertical wells. The calculation results show that the contact length increases with the increase of the friction coefficient when the weight on bit is stable. There are critical speeds to make the contact length take the extreme value, and the critical speeds vary with the change of weight on bit and drill string length. The increase of drill string length does not change the quasi-static contact length, but will make the dynamic contact length fluctuate greatly. The fluctuation of weight on bit and torque on bit make the contact length fluctuate near the quasi-static contact length under most weight on bit. This work provides important theoretical and technical support for the comprehensive analysis of the dynamic buckling characteristics of drill string in vertical wells.

基于国家油气发展战略和工程教育背景,开发了油气管道应变测试实验平台,提出了基于应变检测的安全评价方法,并将其用于自主设计实验和开放型实验教学,为工科学生创造了良好的实践条件.结果表明,管道安全评价实践有助于学生掌握应变的检测原理、过程及在石油工程领域的应用,加深了学生对专业知识在实际应用的认识,提高了其对于专业知识学习的兴趣,培养了团队合作意识和探索积极性.

For processes such as water injection in deep geothermal production, heat transfer and fluid flow are coupled and affect one another, which leads to numerous challenges in wellbore structure safety. Due to complicated wellbore structures, consisting of casing, cement sheaths, and formations under high temperature, pressure, and in situ stress, the effects of thermo-hydro-mechanical (THM) coupling are crucial for the instability control of geothermal wellbores. A THM-coupled model was developed to describe the thermal, fluid, and mechanical behavior of the casing, cement sheath, and geological environment around the geothermal wellbore. The results show that a significant disturbance of effective stress occurred mainly due to the excess pore pressure and temperature changes during cold water injection. The effective stress gradually propagated to the far-field and disrupted the integrity of the wellbore structure. A serious thermal stress concentration occurred at the junction of the cased-hole and open-hole section. When the temperature difference between the injected water and the formation was up to 160 °C, the maximum hoop tensile stress in the granite formation reached up to 43.7 MPa, as high as twice the tensile strength, which may increase the risk of collapse or rupture of the wellbore structure. The tensile radial stress, with a maximum of 31.9 MPa concentrated at the interface between the casing and cement sheath, can cause the debonding of the cementing sheath. This study provides a reference for both the prediction of THM responses and the design of drilling fluid density in geothermal development.

针对致密油层体积压裂过程中缝内注入压力与缝间应力场耦合响应问题,建立了多簇裂缝扩展流-固耦合模型,采用裂缝扩展单元表征岩层破裂与渐进扩展,协同计算多个求解域、模拟多裂缝同步延伸,研究多簇裂缝扩展过程中缝内注入压力与缝间应力场的动态变化,定量评价射孔簇间距对流-固耦合响应的影响规律.研究结果表明:多簇裂缝扩展缝间应力场干扰导致裂缝延伸压力上升,而缝内高压流体诱导缝间应力场转向;减小射孔簇间距有利于增大缝间应力干扰,但导致多裂缝延伸压力差异显著;应优化射孔方案调控流-固耦合影响,促进多裂缝均衡扩展.本文研究成果可为水平井多簇裂缝均衡扩展调控提供理论依据.

The wellbore stability of soft mudstone formation is strongly affected by thermal and hydraulic loadings due to its low strength and high plasticity under high-pressure and high-temperature conditions.A nonlinear coupled thermalhydraulic-mechanical (THM) model was proposed to evaluate the influence of temperature and fluid factors on wellbore stability located in deep and complex soft mudstone formations.The evolution of near-wellbore formation strength and permeability was quantitatively described by introducing a plastic damage variable in the THM model.The influence of mud pressure and temperature on the stress and plastic damage distribution near the wellbore zone was analyzed using the THM model.The accuracy of the models was verified by comparing the radial/hoop stress results with those from classical thermopore elastic theory.Results show that the plastic failure of the near-wellbore zone and wellbore stability are mainly controlled by the coupling effects of thermal and hydraulic deformations of the soft mudstone.Specifically, the size of the damage zone is enlarged by 2.7 mm when the mud temperature increases by 40 °C.By contrast, the damage scale is reduced by 1.7 mm as the temperature decrease by 40 °C due to the compaction effects in the nearwellbore region.The mechanical behavior of the soft mudstone wellbore is time dependent, that is, with the increase in time, the damage gradually extends to the periphery of the wellbore after the plastic equilibrium state near the wellbore is reached.This study provides a THM modelling framework for understanding the mechanism of soft mudstone wellbore instability and formulating corresponding preventive measures.