[1] 贾承造.中国石油工业上游前景与未来理论技术五大挑战[J].石油学报,2024,45(1):1-14. Jia Chengzao.Prospects and five future theoretical and technical challenges of the upstream petroleum industry in China[J].Acta Petrolei Sinica,2024,45(1):1-14. [2] Carter B J,Desroches J,Ingraffea A R,et al.Simulating fully 3D hydraulic fracturing[J].Modeling in Geomechanics,2000,200:525-557. [3] 李莉,张兴勇,秦俐,等.储层改造三维物理模拟实验研究与应用[J].特种油气藏,2021,28(2):112-119. Li Li,Zhang Xingyong,Qin Li,et al.Study and application of 3D physical modeling experiment of reservoir stimulation[J].Special Oil & Gas Reservoirs,2021,28(2):112-119. [4] King G E,Haile L,Shuss J,et al.Increasing fracture path complexity and controlling downward fracture growth in the Barnett Shale[C].SPE119896-MS,2008:205-212. [5] 李玮,闫铁.二维条件下天然裂缝对压裂裂缝影响的分形分析[J].特种油气藏,2013,20(1):67-70. Li Wei,Yan Tie.Fractal analysis of the influence of natural fractures under 2D conditions on the fracturing fractures[J].Special Oil & Gas Reservoirs,2013,20(1):67-70. [6] Lecampion B,Detournay E.An implicit algorithm for the propagation of a hydraulic fracture with a fluid lag[J].Computer Methods in Applied Mechanics and Engineering,2007,196(49/50/51/52):4863-4880. [7] Rahman M M,Rahman M K.A review of hydraulic fracture models and development of an improved pseudo-3D model for stimulating tight oil/gas sand[J].Energy Sources,Part A:Recovery,Utilization,and Environmental Effects,2010,32(15):1416-1436. [8] Siebrits E,Peirce A P.An efficient multi-layer planar 3D fracture growth algorithm using a fixed mesh approach[J].International Journal for Numerical Methods in Engineering,2002,53(3):691-717. [9] 李小刚,何建冈,黄雁红,等.裂缝扩展与输砂动态耦合的缝内支撑剂铺置特征[J].特种油气藏,2023,30(4):146-155. Li Xiaogang,He Jian'gang,Huang Yanhong,et al.Characteristics of proppant placement in fractures dynamically coupled between fracture propagation and sand transport[J].Special Oil & Gas Reservoirs,2023,30(4):146-155. [10] Miehe C,Hofacker M,Welschinger F.A phase field model for rate-independent crack propagation:robust algorithmic implementation based on operator splits[J].Computer Methods in Applied Mechanics and Engineering,2010,199(45/46/47/48):2765-2778. [11] Wu J Y.A unified phase-field theory for the mechanics of damage and quasi-brittle failure[J].Journal of the Mechanics and Physics of Solids,2017,103:72-99. [12] Bourdin B,Francfort G A,Marigo J J.The variational approach to fracture[J].Journal of Elasticity,2008,91:5-148. [13] 易良平,张丹,杨若愚,等.基于相场法的裂缝性地层压裂裂缝延伸特征研究[J].油气藏评价与开发,2022,12(4):604-616. Yi Liangping,Zhang Dan,Yang Ruoyu,et al.Hydraulic fracture extension characteristics of fractured formation based on phase field method[J].Petroleum Reservoir Evaluation and Development,2022,12(4):604-616. [14] 易良平,胡滨,李小刚,等.基于相场法的煤砂互层水力裂缝纵向延伸计算模型[J].煤炭学报,2020,45(增刊2):706-716. Yi Liangping,Hu Bin,Li Xiaogang,et al.Calculation model of hydraulic crack vertical propagation in coal-sand inter-bedded formation based on the phase field method[J].Journal of China Coal Society,2020,45(S2):706-716. [15] 吴建营.固体结构损伤破坏统一相场理论、算法和应用[J].力学学报,2021,53(2):301-329. Wu Jianying.On the unified phase-field theory for damage and failure in solids and structures theoretical and numerical aspects[J].Chinese Journal of Theoretical and Applied Mechanics,2021,53(2):301-329. [16] Francfort G A,Marigo J J.Revisiting brittle fracture as an energy minimization problem[J].Journal of the Mechanics and Physics of Solids,1998,46(8):1319-1342. [17] Bourdin B,Francfort G A,Marigo J J.Numerical experiments in revisited brittle fracture[J].Journal of the Mechanics and Physics of Solids,2000,48(4):797-826. [18] Bourdin B,Chukwudozie C,Yoshioka K.A variational approach to the numerical simulation of hydraulic fracturing[C].SPE159154-MS,2012:213-221. [19] Tanne E,Bourdin B,Yoshioka K.On the loss of symmetry in toughness dominated hydraulic fractures[J].International Journal of Fracture,2022,237(1):189-202. [20] Chukwudozie C,Bourdin B,Yoshioka K.A variational phase-field model for hydraulic fracturing in porous media[J].Computer Methods in Applied Mechanics and Engineering,2019,347:957-982. [21] Lee S,Wheeler M F,Wick T.Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model[J].Computer Methods in Applied Mechanics and Engineering,2016,305:111-132. [22] Lee S,Mikelic A,Wheeler M F,et al.Phase-field modeling of two-phase fluid filled fractures in a poroelastic medium[J].Multiscale Modeling & Simulation,2018,16(4):1542-1580. [23] Lee S,Min B,Wheeler M F.Optimal design of hydraulic fracturing in porous media using the phase field fracture model coupled with genetic algorithm[J].Computational Geosciences,2018,22:833-849. [24] Zhou S W,Zhuang X Y,Rabczuk T.Phase-field modeling of fluid-driven dynamic cracking in porous media[J].Computer Methods in Applied Mechanics and Engineering,2019,350:169-198. [25] Zhou S W,Zhuang X Y,Rabczuk T.Phase field method for quasi-static hydro-fracture in porous media under stress boundary condition considering the effect of initial stress field[J].Theoretical and Applied Fracture Mechanics,2020,107:102523. [26] Yi D,Yi L P,Yang Z Z,et al.Coupled thermo-hydro-mechanical-phase field modelling for hydraulic fracturing in thermo-poroelastic media[J].Computers and Geotechnics,2024,166:105949. [27] Yi D,Yang Z Z,Yi L P,et al.Hydraulic fracturing phase-field model in porous viscoelastic media[J].International Journal of Mechanical Sciences,2024,272:109171. [28] Yi D,Yang Z Z,Yi L P,et al.Phase-field model of hydraulic fracturing in thermoelastic-plastic media[J].International Journal of Mechanical Sciences,2024,283:109750. [29] 李菊花,吴军龙,林海,等.基于相场法的英雄岭页岩水力压裂裂缝扩展规律研究[J].长江大学学报(自然科学版),2025,22(6):49-58. Li Juhua,Wu Junlong,Lin Hai,et al.Study on hydraulic fracture propagation laws in Yingxiongling Shale based on phase field method[J].Journal of Yangtze University(Natural Science Edition),2025,22(6):49-58. [30] 梁鑫,侯鹏,薛熠,等.基于相场法的岩石预制裂纹定向水力压裂裂纹扩展规律研究[J].岩土工程学报,2025,47(9):1865-1873. Liang Xin,Hou Peng,Xue Yi,et al.Propagation law of hydraulic-induced fractures in directional hydraulic fracturing with prefabricated cracks based on phase-field method[J].Chinese Journal of Geotechnical Engineering,2025,47(9):1865-1873. [31] Lee S,Mikelic A,Wheeler M F,et al.Phase-field modeling of proppant-filled fractures in a poroelastic medium[J].Computer Methods in Applied Mechanics and Engineering,2016,312:509-541. [32] Zhou S W,Zhuang X Y.Phase field modeling of hydraulic fracture propagation in transversely isotropic poroelastic media[J].Acta Geotechnica,2020,15(9):2599-2618. [33] Zhuang X Y,Zhou S W,Sheng M,et al.On the hydraulic fracturing in naturally-layered porous media using the phase field method[J].Engineering Geology,2020,266:105306. [34] Zhou S W,Rabczuk T,Zhuang X Y.Phase field modeling of quasi-static and dynamic crack propagation:COMSOL implementation and case studies[J].Advances in Engineering Software,2018,122:31-49. [35] Zhou S W,Zhuang X Y,Rabczuk T.Phase field modeling of brittle compressive-shear fractures in rock-like materials:a new driving force and a hybrid formulation[J].Computer Methods in Applied Mechanics and Engineering,2019,355:729-752. [36] Zhuang X Y,Li X Y,Zhou S W.Three-dimensional phase field feature of longitudinal hydraulic fracture propagation in naturally layered rocks under stress boundaries[J].Engineering with Computers,2023,39(1):711-734. [37] Miehe C.Comparison of two algorithms for the computation of fourth-order isotropic tensor functions[J].Computers & Structures,1998,66(1):37-43. [38] Miehe C.Computation of isotropic tensor functions[J].Communications in Numerical Methods in Engineering,1993,9(11):889-896. [39] Yi D,Yang Z Z,Yi L P,et al.Simulation of dynamic pulse fracturing in elastoplastic media based on a mixed-mode fatigue phase-field model[J].Computers and Geotechnics,2025,179:107043. [40] Goswami S,Anitescu C,Rabczuk T.Adaptive fourth-order phase field analysis for brittle fracture[J].Computer Methods in Applied Mechanics and Engineering,2020,361:112808. [41] Yang Z Z,Liu J P,Yi L P,et al.Elastoplastic damage analysis and structural optimization of soluble bridge plug based on phase field method[J].Mechanics of Materials,2024,189:104899. [42] Kienle D,Keip M A.A variational minimization formulation for hydraulically induced fracturing in elastic-plastic solids[J].International Journal of Fracture,2022,237(1):203-227. [43] Liu C,Wang Z X.Numerical simulation of hydraulic fracture propagation in shale with plastic deformation[J].International Journal of Fracture,2022,238(2):115-132. [44] Zhao Y,Borja R I.A continuum framework for coupled solid deformation-fluid flow through anisotropic elastoplastic porous media[J].Computer Methods in Applied Mechanics and Engineering,2020,369:113225. [45] 曹玉玲,何强胜,刘闯.考虑页岩塑性变形的水力裂缝与天然裂缝相交模拟研究[J].应用数学和力学,2023,44(6):679-693. Cao Yuling,He Qiangsheng,Liu Chuang.Numerical Simulation of hydraulic fractures intersecting natural fractures in shale with plastic deformation[J].Applied Mathematics and Mechanics 2023,44(6):679-693. [46] 李金波.深部储层弹塑性力学表征及水力裂缝扩展机理研究[D].大庆:东北石油大学,2023:18-23. Li Jinbo.Research on elastoplastic mechanical characterization and hydraulic fracture propagation mechanism of deep reservoir[D].Daqing:Northeast Petroleum University,2023:18-23. [47] 赵金洲,雍锐,胡东风,等.中国深层—超深层页岩气压裂:问题、挑战与发展方向[J].石油学报,2024,45(1):295-311. Zhao Jinzhou,Yong Rui,Hu Dongfeng,et al.Deep and ultra deep shale gas fracturing in China:problems,challenges and directions[J].Acta Petrolei Sinica,2024,45(1):295-311. [48] 侯冰,张其星,陈勉.页岩储层压裂物理模拟技术进展及发展趋势[J].石油钻探技术,2023,51(5):66-77. Hou Bing,Zhang Qixing,Chen Mian.Status and tendency of physical simulation technology for hydraulic fracturing of shale reservoirs[J].Petroleum Drilling Techniques,2023,51(5):66-77. [49] Chang C,Zoback M D.Creep in unconsolidated shale and its implication on rock physical properties[C].ARMA-08-130,2008:1-8. [50] An C,Killough J,Xia X Y.Investigating the effects of stress creep and effective stress coefficient on stress-dependent permeability measurements of shale rock[J].Journal of Petroleum Science and Engineering,2021,198:108155. [51] Chen Y J,Mobasher M E,You T,et al.Non-local continuum damage model for poro-viscoelastic porous media[J].International Journal of Rock Mechanics and Mining Sciences,2022,159:105212. [52] 胡小飞,张鹏,姚伟岸.断裂相场法[M].北京:科学出版社,2022:113-141. Hu Xiaofei,Zhang Peng,Yao Weian.Phase field method for fracture[M].Beijing:Science Press,2022:113-141. [53] Xia L,Yvonnet J,Ghabezloo S.Phase field modeling of hydraulic fracturing with interfacial damage in highly heterogeneous fluid-saturated porous media[J].Engineering Fracture Mechanics,2017,186:158-180. [54] Li H, Lei H W,Yang Z J,et al.A hydro-mechanical-damage fully coupled cohesive phase field model for complicated fracking simulations in poroelastic media[J].Computer Methods in Applied Mechanics and Engineering,2022,399:115451. [55] Li H,Yang Z J,Zhang X X,et al.A hydro-thermo-damage-mechanical fully coupled cohesive phase-field model for fracking in quasi-brittle thermo-poroelastic media[J].Engineering Fracture Mechanics,2024,301:110018. [56] Liu J P,Yi L P,Yang Z Z,et al.A phase-field model of hydraulic fractures in acidized porous media with strain-softening properties[J].Computers and Geotechnics,2024,171:106392. [57] Liu J P,Yang Z Z,Yi L P,et al.Cohesive phase-field model for dynamic fractures in coal seams[J].International Journal of Mechanical Sciences,2024,282:109617. [58] 吕茂淋,朱珍德,周露明,等.基于相场法的预制双裂隙岩体水力压裂扩展数值模拟研究[J].岩土力学,2024,45(6):1850-1862. Lyu Maolin,Zhu Zhende,Zhou Luming,et al.Numerical simulation of hydraulic fracture propagation in rock masses with pre-existing double fractures using the phase field method[J].Rock and Soil Mechanics,2024,45(6):1850-1862. [59] 戴一凡,侯冰,廖志豪.基于相场法的深层干热岩储层水力压裂模拟研究[J].石油钻探技术,2024,52(2):229-235. Dai Yifan,Hou Bing,Liao Zhihao.Simulation of hydraulic fracturing in deep hot dry rock reservoir based on phase-field method[J].Petroleum Drilling Techniques,2024,52(2):229-235. [60] Li Y W,Peng G B,Tang J Z,et al.Thermo-hydro-mechanical coupling simulation for fracture propagation in CO2 fracturing based on phase-field model[J].Energy,2023,284:128629. [61] Feng Y X,Firoozabadi A.Phase-field simulation of hydraulic fracturing by CO2 and water with consideration of thermos poroelasticity[J].Rock Mechanics and Rock Engineering,2023,56(10):7333-7355. [62] Xu W L,Yu H,Zhang J N,et al.Phase-field method of crack branching during SC-CO2 fracturing:a new energy release rate criterion coupling pore pressure gradient[J].Computer Methods in Applied Mechanics and Engineering,2022,399:115366. [63] 魏兵,陈海龙,刘帅,等.页岩储层CO2吸附解吸行为及弥散特征[J].天然气工业,2024,44(12):176-186. Wei Bing,Chen Hailong,Liu Shuai,et al.CO2 adsorption/desorption behaviors and dispersion characteristics in shale reservoirs[J].Natural Gas Industry,2024,44(12):176-186. [64] 李玉杰.考虑应力敏感和多尺度流动的页岩气渗流模型[J].非常规油气,2025,12(1):117-122. Li Yujie.Shale gas flow model considering stress sensitivity and multi-scale flow[J].Unconventional Oil & Gas,2025,12(1):117-122. [65] Zhou Z Q,Bi J,Zhao Y,et al.Thermal-mechanical coupling smooth particle hydrodynamics-phase field method modelling of cracking in rocks[J].Computers and Geotechnics,2024,173:106476. [66] Hakimzadeh M,Mora-corral C,Walkington N,et al.Phase-field modeling of fracture under compression and confinement in anisotropic geomaterials[J].International Journal for Numerical and Analytical Methods in Geomechanics,2025,49(4):1319-1335. [67] Miehe C,Aldakheel F,Raina A.Phase field modeling of ductile fracture at finite strains:a variational gradient-extended plasticity-damage theory[J].International Journal of Plasticity,2016,84:1-32. [68] Zhang D,Yi L P,Yang Z Z,et al.Phase field model for simulating hydraulic fracture propagation and oil-water two-phase flow in reservoir[J].Computer Methods in Applied Mechanics and Engineering,2023,404:115838. |