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Artigos de revistas sobre o tema "Fracture mechanics"

Autor: Grafiati

Publicado: 4 de junho de 2021

Última modificação: 25 de julho de 2025

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1

Zhang, Ying, Kai He, Jianming Yang, et al. "Mechanical, Seepage, and Energy Evolution Properties of Multi-Shaped Fractured Sandstone Under Hydro-Mechanical Coupling: An Experimental Study." Minerals 15, no. 3 (2025): 215. https://doi.org/10.3390/min15030215.

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Rocks with multi-shaped fractures in engineering activities like mining, underground energy storage, and hydropower construction are often exposed to environments where stress and seepage fields interact, which heightens the uncertainty of instability and failure mechanisms. This has long been a long-standing challenge in the field of rock mechanics. Current research mainly focuses on the mechanical behavior, seepage, and energy evolution characteristics of single-fractured rocks under hydro-mechanical coupling. However, studies on the effects of multi-shaped fractures (such as T-shaped fractu

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2

Zhang, Hai Yong, Shun Li He, Guo Hua Luan, et al. "Influence of Fracture Parameters on the Productivity of Fractured Horizontal Well Based on Fluid Mechanics in Tight Gas Reservoir." Advanced Materials Research 886 (January 2014): 452–55. http://dx.doi.org/10.4028/www.scientific.net/amr.886.452.

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Multiple fractures are needed by hydraulic fracturing in order to improve the horizontal well productivity of a single well in tight gas reservoir. The calculation accuracy of productivity influences on the fracturing optimization results and the success ratio and effectiveness of fracturing treatment. This work focuses on analyzing the influence of fracture parameters on fractured horizontal well productivity in tight gas reservoir through establishing a productivity prediction model of fractured horizontal well, considering the interference between fracture and fracture and the wellbore pres

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3

Shi, Di, Liping Li, Jianjun Liu, Mingyang Wu, Yishan Pan, and Jupeng Tang. "Effect of discrete fractures with or without roughness on seepage characteristics of fractured rocks." Physics of Fluids 34, no. 7 (2022): 073611. http://dx.doi.org/10.1063/5.0097025.

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This study proposes a new fractal permeability model for fractured rocks that comprehensively accounts for the geometric fracture characteristics and the fluid transport mechanism. Then, the permeability changes of fractured rocks are analyzed using discrete fracture networks (DFNs) with or without roughness and different geometry parameters in the DFN modeling and finite element simulation. The results show that the proposed permeability model well agrees with the experimental data, and the established DFN numerical model more realistically reflects the fracture network in fractured rocks. Fl

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4

Liu, Chao, Xinggui Yang, Wenqi Cao, Jin Lin, Yuxuan Liu, and Hang Zhang. "Discrimination Model of Interaction Between Hydraulic Fracture and Natural Fracture Based on Energy Balance." Processes 13, no. 6 (2025): 1652. https://doi.org/10.3390/pr13061652.

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Hydraulic fracturing technology has been extensively applied for the efficient development of unconventional reservoirs. Influenced by geological discontinuities such as naturally fractured weak planes, the complex interaction behaviors between hydraulic fractures and natural fractures significantly challenge the prediction of hydraulic fracture propagation paths. Establishing interaction discrimination models to predict these behaviors proves crucial for characterizing post-stimulation fracture complexity. This study develops a discrimination model for hydraulic-natural fracture interactions

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5

VanCourt, RB, SE Byron, SJ Ali, and BD Caldwell. "Fracture mechanics. A comparison study of torsional stress on bone." Journal of the American Podiatric Medical Association 90, no. 4 (2000): 167–74. http://dx.doi.org/10.7547/87507315-90-4-167.

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Fractures that result from torsional loading of shafts in mechanical systems of nonbiologic materials generate a fracture line that forms a 45 degrees angle to an axis that is perpendicular to the direction of torsional loading on the shaft. As tension and compression are applied to these isotropic substances, the angle of fracture increases and decreases, respectively. Understanding how these forces, particularly compressive forces, generate elongation of a spiral fracture increases the ability to predict the extent of injury to bone. Fibular and metatarsal fractures are of primary importance

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6

Yuan, Yingzhong, Wende Yan, Fengbo Chen, Jiqiang Li, Qianhua Xiao, and Xiaoliang Huang. "Numerical Simulation for Shale Gas Flow in Complex Fracture System of Fractured Horizontal Well." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 3-4 (2018): 367–77. http://dx.doi.org/10.1515/ijnsns-2017-0135.

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AbstractComplex fracture systems including natural fractures and hydraulic fractures exist in shale gas reservoir with fractured horizontal well development. The flow of shale gas is a multi-scale flow process from microscopic nanometer pores to macroscopic large fractures. Due to the complexity of seepage mechanism and fracture parameters, it is difficult to realize fine numerical simulation for fractured horizontal wells in shale gas reservoirs. Mechanisms of adsorption–desorption on the surface of shale pores, slippage and Knudsen diffusion in the nanometer pores, Darcy and non-Darcy seepag

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7

Wang, Yonggang, Xuejuan Zhang, Jie Zhang, et al. "Comparative Study on Artificial Fracture Modeling Schemes in Tight Reservoirs—For Enhancing the Production Efficiency of Tight Oil and Gas." Energies 17, no. 20 (2024): 5235. http://dx.doi.org/10.3390/en17205235.

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In order to improve the reliability of the deployment of production schemes after artificial fracturing in tight reservoirs, it is urgent to carry out research on the description of fractures after artificial fracturing. In this study, taking the Chang 61 oil formation group in the Wangyao South area of Ordos Basin as an example, three different fracture modeling schemes are used to establish the geological model of fractured reservoirs, and the fitting ratios of the respective reservoir models are calculated by using the method of reservoir numerical simulation of the initial fitting, and the

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8

Kubeyev, Amanzhol, Nathaniel Forbes Inskip, Tomos Phillips, et al. "Digital Image-Based Stress–Permeability Relationships of Rough Fractures Using Numerical Contact Mechanics and Stokes Equation." Transport in Porous Media 141, no. 2 (2022): 295–330. http://dx.doi.org/10.1007/s11242-021-01719-7.

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AbstractFlow in fractures is sensitive to their geometrical surface characteristics. The surface can undergo deformation if there is a change in stress. Natural fractures have complex geometries and rough surfaces which complicates the modelling of deformation and fluid flow. In this paper, we present a computational model that takes a digital image of a rough fracture surface and provides a stress–permeability relationship. The model is based on a first-principle contact mechanics approach at the continuum scale. Using this first principle approach, we investigate numerically the effect of fr

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9

Yu, Chaoyun, Bin Gong, Na Wu, Penglei Xu, and Xiankai Bao. "Simulation of the Fracturing Process of Inclusions Embedded in Rock Matrix under Compression." Applied Sciences 12, no. 16 (2022): 8041. http://dx.doi.org/10.3390/app12168041.

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Typical parallel fractures are often observed in the outcrops of inclusions in the field. To reveal the failure mechanism of inclusions embedded in rock matrix, a series of heterogeneous models are established and tested based on the damage mechanics, statistical strength theory, and continuum mechanics. The results show that, with the spacing between two adjacent fractures decreasing, the stress is firstly transferred from negative to positive, then from positive to negative. Stress transition is profound for the fracture spacing. Meanwhile, three types of fractures, i.e., consecutive fractur

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10

Abass, Hazim Abass, Chris Lamei Lamei, Kaveh Amini Amini, and Tadesse Teklu Teklu. "Hydraulic Fracturing Tight Reservoirs: Rock Mechanics and Transport Phenomena." Journal of Petroleum Research and Studies 8, no. 2 (2021): 122–43. http://dx.doi.org/10.52716/jprs.v8i2.239.

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Conventional reservoirs have been fracture stimulated using acid fracturing and proppant fracturing.Acid fracturing is performed to improve well productivity in acid-soluble formations such aslimestone, dolomite, and chalk. Hydrochloric acid is generally used to create an etched fracture,which is the main mechanism for maintaining the fracture open during the life of a well. Proppantfracturing is an alternative option that has been applied in carbonaceous and siliceous formations.There is no quantitative method to provide an answer of whether acid fracturing or proppantfracturing is an appropr

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11

Chen, Peng, Shuhan Yang, Xinyu Chen, Zeyu Li, Chuanbo Shen, and Huaning Qiu. "Multiscale Characterization of Fractures and Analysis of Key Controlling Factors for Fracture Development in Tight Sandstone Reservoirs of the Yanchang Formation, SW Ordos Basin, China." Applied Sciences 14, no. 21 (2024): 9676. http://dx.doi.org/10.3390/app14219676.

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Tight sandstone reservoirs, despite their low porosity and permeability, present considerable exploration potential as unconventional hydrocarbon resources. Natural fractures play a crucial role in hydrocarbon migration, accumulation, and present engineering challenges such as late-stage reformation in these reservoirs. This study examines fractures in the seventh member of the Triassic Yanchang Formation’s tight sandstone within the Ordos Basin using a range of methods, including field outcrops, core samples, imaging and conventional logging, thin sections, and scanning electron microscopy. T

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12

McClure, Mark W., Mohsen Babazadeh, Sogo Shiozawa, and Jian Huang. "Fully Coupled Hydromechanical Simulation of Hydraulic Fracturing in 3D Discrete-Fracture Networks." SPE Journal 21, no. 04 (2016): 1302–20. http://dx.doi.org/10.2118/173354-pa.

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Summary We developed a hydraulic-fracturing simulator that implicitly couples fluid flow with the stresses induced by fracture deformation in large, complex, 3D discrete-fracture networks (DFNs). The code is efficient enough to perform field-scale simulations of hydraulic fracturing in DFNs containing thousands of fractures, without relying on distributed-memory parallelization. The simulator can describe propagation of hydraulic fractures and opening and shear stimulation of natural fractures. Fracture elements can open or slide, depending on their stress state, fluid pressure, and mechanical

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13

Melvin, J. W. "Fracture Mechanics of Bone." Journal of Biomechanical Engineering 115, no. 4B (1993): 549–54. http://dx.doi.org/10.1115/1.2895538.

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This paper reviews the progress that has been made in applying the principles of fracture mechanics to the topic of fracture of long bones. Prediction of loading conditions which result in the propagation of fractures in bones has been of interest to the field of trauma biomechanics and orthopedics for over one hundred years. Independent verifications, by various investigators, of bone fracture mechanics parameters are reviewed and investigations of the effects of bone density and specimen thickness on the critical fracture mechanics parameters and of other factors such as critical crack lengt

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14

Wang, Wenhai, Yang Zhao, Lishuai Jiang, Jiacheng Zuo, Guangsheng Liu, and Hani S. Mitri. "Preliminary Study on Size Effect of Fractured Rock Mass with Sand Powder 3D Printing." Processes 10, no. 10 (2022): 1974. http://dx.doi.org/10.3390/pr10101974.

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The size effect has a significant effect on the mechanical behavior of rock, thereby fundamentally influencing the stability of rock excavations. The main challenge associated with the experimental research on the size effect of fractured rock mass lies in the difficulty of specimen preparation to represent the influence of size and fracture on the mechanical behavior of the rock material. In order to preliminarily explore the feasibility of 3D printing technology in the field of rock mechanics, fractured rock specimens of different sizes and different fracture characteristics were produced us

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15

Liu, Yang, Ping Chen, Bisheng Wu, et al. "Mechanics of Hydraulic-Fracture Growth from a Wellbore Intersecting Natural Fractures." SPE Journal 25, no. 02 (2019): 646–61. http://dx.doi.org/10.2118/198890-pa.

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Summary The creation and propagation of hydraulic fractures (HFs) emanating from a well in a naturally fractured rock is important not only to the success of fracturing treatments, but also for interpretation of the data from diagnostic fracture injection tests (DFITs). In this paper, we consider the reservoir rock to consist of an impermeable rock matrix and a system of discrete natural fractures (NFs) that are permeable. The well is assumed to intersect two sets of NFs at their midpoints, and injection into the wellbore might open the NFs and/or create new fractures that extend along the max

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16

Rice, J. R. "Fracture Mechanics." Applied Mechanics Reviews 38, no. 10 (1985): 1271–75. http://dx.doi.org/10.1115/1.3143689.

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Fracture mechanics is an active research field that is currently advancing on many fronts. This appraisal of research trends and opportunities notes the promising developments of nonlinear fracture mechanics in recent years and cites some of the challenges in dealing with topics such as ductile-brittle transitions, failure under substantial plasticity or creep, crack tip processes under fatigue loading, and the need for new methodologies for effective fracture analysis of composite materials. Continued focus on microscale fracture processes by work at the interface of solid mechanics and mater

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17

Erdogan, F. "Fracture mechanics." International Journal of Solids and Structures 37, no. 1-2 (2000): 171–83. http://dx.doi.org/10.1016/s0020-7683(99)00086-4.

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18

Aliabadi, M. "Fracture mechanics." Engineering Analysis with Boundary Elements 6, no. 2 (1989): 114. http://dx.doi.org/10.1016/0955-7997(89)90009-x.

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19

Parker, A. P. "Fracture mechanics." Journal of Mechanical Working Technology 18, no. 1 (1989): 123. http://dx.doi.org/10.1016/0378-3804(89)90115-0.

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20

OHJI, Kiyotsugu. "Fracture Mechanics." Journal of the Society of Mechanical Engineers 90, no. 823 (1987): 706–7. http://dx.doi.org/10.1299/jsmemag.90.823_706.

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21

Ferri Aliabadi, M. H. "Fracture mechanics." Engineering Analysis with Boundary Elements 20, no. 3 (1997): 269–71. http://dx.doi.org/10.1016/s0955-7997(97)00053-2.

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22

Sakamoto, Haruo. "Fracture Mechanics in Design Guidance and Practice." Key Engineering Materials 353-358 (September 2007): 182–85. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.182.

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This paper describes the state of the art in design codes and guidance using fracture mechanics. In Germany, a railroad accident occurred in June, 1998, which resulted in about 100 passenger deaths due to a wheel fracture. In September, 1999, a water leak accident due to a crack in a pipe happened at the Tsuruga nuclear plant in Japan. Such serious accidents are the result of fracture events. Fracture mechanics is thought to be a tool to avoid such catastrophic fracture accidents. The state of the art in designing mechanical components or structures applying fracture mechanics was reviewed. Th

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23

Zeng, Qingdong, Taixu Li, Long Bo, Xuelong Li, and Jun Yao. "Comprehensive Investigation of Factors Affecting Acid Fracture Propagation with Natural Fracture." Energies 17, no. 21 (2024): 5386. http://dx.doi.org/10.3390/en17215386.

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Acid fracturing is a crucial stimulation technique to enhance hydrocarbon recovery in carbonate reservoirs. However, the interaction between acid fractures and natural fractures remains complex due to the combined effects of mechanical, chemical, and fluid flow processes. This study extends a previously developed hydro-mechano-reactive flow coupled model to analyze these interactions, focusing on the influence of acid dissolution. The model incorporates reservoir heterogeneity and simulates various scenarios, including different stress differences, approaching angles, injection rates, and acid

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24

Xu, Qianghui, Xiongyu Chen, Junyu Yang, Zhiying Liu, and Lin Shi. "Pore-scale study of coke combustion in a matrix-fracture system based on the micro-continuum approach." Physics of Fluids 34, no. 3 (2022): 036603. http://dx.doi.org/10.1063/5.0082518.

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In situ combustion is an advanced recovery technique used to exploit heavy oil in the fractured reservoirs that make up approximately one-third of global heavy-oil resources. However, the mesoscopic mechanisms of coke combustion in the multiscale matrix-fracture system are not well understood because of the difficulty of performing pore-resolved simulations. In the present study, a pore-resolved micro-continuum approach was used to investigate fully coupled thermal and reactive flows through fractured media that contain nanometer-range coke pores, micrometer-range matrix pores, and sub-millime

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25

Wu, Kan, and Jon E. Olson. "Simultaneous Multifracture Treatments: Fully Coupled Fluid Flow and Fracture Mechanics for Horizontal Wells." SPE Journal 20, no. 02 (2014): 337–46. http://dx.doi.org/10.2118/167626-pa.

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Summary Successfully creating multiple hydraulic fractures in horizontal wells is critical for unconventional gas production economically. Optimizing the stimulation of these wells will require models that can account for the simultaneous propagation of multiple, potentially nonplanar, fractures. In this paper, a novel fracture-propagation model (FPM) is described that can simulate multiple-hydraulic-fracture propagation from a horizontal wellbore. The model couples fracture deformation with fluid flow in the fractures and the horizontal wellbore. The displacement discontinuity method (DDM) is

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26

Gong, Diguang, Junbin Chen, Cheng Cheng, Yuanyuan Kou, Haiyan Jiang, and Jianhong Zhu. "Numerical Simulation on Radial Well Deflagration Fracturing Based on Phase Field Method." Energies 16, no. 12 (2023): 4758. http://dx.doi.org/10.3390/en16124758.

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A radial well has a unique wellbore configuration. Fracture propagation in radial well deflagration fracturing is studied rarely. The mechanism of interaction between deflagration fractures, natural fractures, and micro-fractures is still unknown. Based on continuum mechanics, damage mechanics, and variational principles, a numerical model of fracture propagation in deflagration fracturing is established with the Hamilton principle and phase-field fracture theory. The effects of horizontal principal stress difference, natural fracture distribution, and micro-fractures around the wellbore on fr

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27

Dubey, Prashant K., Sushil Kumar, Khushboo Havelia, and Savitri Yadav. "Integrated deterministic and predictive discrete fracture network modeling for an Eocene carbonate reservoir, Bengal Basin, India." Leading Edge 38, no. 4 (2019): 274–79. http://dx.doi.org/10.1190/tle38040274.1.

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Prediction of fracture porosity and permeability remains a challenge for fractured carbonate reservoirs. As natural fractures are heterogeneous and subseismic in scale, core data and image logs only provide partially sampled data, leading to sparse information on fracture length, height, orientation, spacing, and aperture. In the present study, an integrated discrete fracture network was generated that is capable of predicting fracture porosity in Eocene carbonates of the Bengal Basin in northeastern India. The predictive fracture modeling method used 3D kinematic and geomechanical restoration

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28

Bart, M., J. F. Shao, D. Lydzba, and M. Haji-Sotoudeh. "Coupled hydromechanical modeling of rock fractures under normal stress." Canadian Geotechnical Journal 41, no. 4 (2004): 686–97. http://dx.doi.org/10.1139/t04-018.

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In this paper, a nonlinear poromechanical model is developed for a single rock fracture under normal stress. The fracture is represented by a set of voids, and the progressive fracture displacement is considered as a modification process of void space. Based on experimental data obtained from three representative rock fractures, the constitutive model is formulated through an extension of Biot poroelasticity theory to a saturated fracture. A generalized poroelastic coupling coefficient is introduced to describe the interaction between pore fluid pressure and fracture deformation. This coeffici

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29

Zhao, Xueping, and R. Paul Young. "Numerical modeling of seismicity induced by fluid injection in naturally fractured reservoirs." GEOPHYSICS 76, no. 6 (2011): WC167—WC180. http://dx.doi.org/10.1190/geo2011-0025.1.

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The interaction between hydraulic and natural fractures is of great interest for the energy resource industry because natural fractures can significantly influence the overall geometry and effectiveness of hydraulic fractures. Microseismic monitoring provides a unique tool to monitor the evolution of fracturing around the treated rock reservoir, and seismic source mechanisms can yield information about the nature of deformation. We performed a numerical modeling study using a 2D distinct-element particle flow code ([Formula: see text]) to simulate realistic conditions and increase understandin

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Men, Xiaoxi, and Jiren Li. "Numerical Investigation of Fracture Network Formation under Multiple Wells." Mathematical Problems in Engineering 2020 (August 20, 2020): 1–11. http://dx.doi.org/10.1155/2020/1763713.

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A two-step fracturing method is proposed to investigate the hydraulic fracture evolution behavior and the process of complex fracture network formation under multiple wells. Simulations are conducted with Rock Failure Process Analysis code. Heterogeneity and permeability of the rocks are considered in this study. In Step 1, the influence of an asymmetric pressure gradient on the fracture evolution is simulated, and an artificial structural plane is formed. The simulation results reflect the macroscopic fracture evolution induced by mesoscopic failure; these results agree well with the characte

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31

FAN, L. F., X. W. YI, and G. W. MA. "NUMERICAL MANIFOLD METHOD (NMM) SIMULATION OF STRESS WAVE PROPAGATION THROUGH FRACTURED ROCK MASS." International Journal of Applied Mechanics 05, no. 02 (2013): 1350022. http://dx.doi.org/10.1142/s1758825113500221.

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The present work is devoted to the simulation of stress wave propagation through fractured elastic media, such as rock mass, by using the numerical manifold method (NMM). A single fracture is used to verify the capability and accuracy of the NMM in modeling fractured rock mass. The frequency-dependence on stress wave transmission across a fracture is analyzed. The influence of the fracture specific stiffness on the wave attenuation and effective wave velocity is discussed. The results from the NMM have a good agreement with those obtained from a theoretical displacement discontinuity method (D

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32

Li, Xin, Xiang Li, Dongxiao Zhang, and Rongze Yu. "A Dual-Grid, Implicit, and Sequentially Coupled Geomechanics-and-Composition Model for Fractured Reservoir Simulation." SPE Journal 25, no. 04 (2020): 2098–118. http://dx.doi.org/10.2118/201210-pa.

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Summary In the development of fractured reservoirs, geomechanics is crucial because of the stress sensitivity of fractures. However, the complexities of both fracture geometry and fracture mechanics make it challenging to consider geomechanical effects thoroughly and efficiently in reservoir simulations. In this work, we present a coupled geomechanics and multiphase-multicomponent flow model for fractured reservoir simulations. It models the solid deformation using a poroelastic equation, and the solid deformation effects are incorporated into the flow model rigorously. The noticeable features

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Liu, Hong, Lin Wang, Yu Wu Zhou, and Xi Nan Yu. "A Mathematical Model for Natural Fracture Evolution in Water-Flooding Oil Reservoir." Advanced Materials Research 868 (December 2013): 535–41. http://dx.doi.org/10.4028/www.scientific.net/amr.868.535.

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The fractured low permeability reservoirs develop complex fracture network. As the of waterflooding recovery heightens, excessive high injection pressures and excessive water injection rate will result in open, initiation, propagation and coalescence of micro-fracture, connecting injection with production form the high permeability zone, which results in a one-way onrush of waterflooding, water cut in oil well water rise quickly, causing a severe oil well flooding and channeling, thereby reducing the ultimate oil recovery efficiency. The effect of the waterflooding seepage within natural fract

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Mehrabian, Amin. "The Stability of Inclined and Fractured Wellbores." SPE Journal 21, no. 05 (2016): 1518–36. http://dx.doi.org/10.2118/180910-pa.

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Summary The theory of linear-elastic fracture mechanics is used to develop an analytical solution for a wellbore in an isotropic elastic medium when drilled inclined to a general state of 3D far-field stress, and attached to which are an arbitrary number of N straight and axially aligned fractures. Axial alignment refers to the special case where the borehole axis is the existing common interface of all planes defined by the fracture faces. The solution uses a familiar load decomposition and coordinate-transform scheme. Within the fracture-mechanics context of the analysis, this scheme transla

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Liu, Xue-wei, Quan-sheng Liu, Shi-bing Huang, Lai Wei, and Guang-feng Lei. "Fracture Propagation Characteristic and Micromechanism of Rock-Like Specimens under Uniaxial and Biaxial Compression." Shock and Vibration 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/6018291.

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This paper presents a set of uniaxial and biaxial compression tests on the rock-like material specimens with different fracture geometries through a rock mechanics servo-controlled testing system (RMT-150C). On the basis of experimental results, the characteristics of fracture propagation under different fracture geometries and loading conditions are firstly obtained. The newly formed fractures are observed propagating from or near the preexisting crack tips for different specimens, while the propagation paths are affected by the loading condition obviously. Then, by adopting acoustic emission

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Atluri, S. N., M. H. Aliabadi, and D. P. Rooke. "Numerical Fracture Mechanics." Mathematics of Computation 63, no. 208 (1994): 825. http://dx.doi.org/10.2307/2153308.

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Sih, G. C., L. Faria, and C. H. Popelar. "Fracture Mechanics Methodology." Journal of Applied Mechanics 52, no. 2 (1985): 500. http://dx.doi.org/10.1115/1.3169086.

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Kanninen, Melvin F., Carl H. Popelar, and A. J. McEvily. "Advanced Fracture Mechanics." Journal of Engineering Materials and Technology 108, no. 2 (1986): 199. http://dx.doi.org/10.1115/1.3225862.

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Lewandowski, John J. "Modern fracture mechanics." Philosophical Magazine 93, no. 28-30 (2013): 3893–906. http://dx.doi.org/10.1080/14786435.2013.812811.

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Kanninen, M. F., C. A. Popelar, and H. Saunders. "Advanced Fracture Mechanics." Journal of Vibration and Acoustics 110, no. 3 (1988): 419–20. http://dx.doi.org/10.1115/1.3269540.

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Newman, J. C., and Uwe Zerbst. "Engineering Fracture Mechanics." Engineering Fracture Mechanics 70, no. 3-4 (2003): 367–69. http://dx.doi.org/10.1016/s0013-7944(02)00124-8.

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Freund, L. B., and John W. Hutchinson. "Dynamic Fracture Mechanics." Journal of Applied Mechanics 59, no. 1 (1992): 245. http://dx.doi.org/10.1115/1.2899458.

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