地热能作为一种分布广泛的可再生资源，已成为人类可利用的第三大可再生能源。干热岩型地热能因其储量巨大和清洁、高效、可再生的特点具有十分重要的研究意义。目前干热岩开采通常需要通过水力压裂实现，以提高干热岩储层渗透性。作为分布广泛的一种干热岩储层，花岗岩的水力压裂特征和渗流换热规律仍未系统揭示，需要进一步研究。本文以花岗岩为研究对象，研究了不同围压、温度下水力压裂特征；分析了压裂过程中声发射特征演化规律；阐明了裂隙扩展规律；厘清了水力压裂影响因素；揭示了水力压裂破裂机制和裂隙扩展准则；通过数值模拟手段研究了压裂裂隙渗透特性和裂隙岩体渗流换热规律。主要得到以下结论：

1.水力压裂曲线可以分为4个明显的阶段：（a）管孔充水；（b）钻孔增压；（c）压裂；（d）裂隙延伸。在压裂阶段可以同时观察到明显的孔压下降和围压上升。声发射信号的第一次大规模增加大致发生在孔压达到破裂压力时。声发射信号发生剧增意味着主裂隙的萌生，信号多次波动意味着裂隙的扩展。声发射手段监测裂隙的萌生与扩展相比孔压更灵敏，不仅可以监测宏观的破裂现象，也可以监测细观的微破裂。

2.压裂后的裂隙均沿着试样的钻孔方向竖向扩展，随着围压的增加，裂隙长度越来越大，裂隙路径越来越复杂。压裂裂隙并非从试样的顶部起裂，起裂于距离试样顶部的某个位置。裂隙较为粗糙且相当曲折，主裂隙周围有一定数量的次级裂隙，部分地方由于颗粒破碎，导致局部裂隙开度较大。裂隙既存在沿晶断裂，也存在穿晶断裂。

3.水力压裂特征受围压影响明显，结果表明：温度一定时，围压越大，破裂压力越大，二者的关系近似呈线性。围压越大，破裂时间越长。在热冲击现象不显著的情况下，围压一定时，温度越高，破裂压力越大。花岗岩水力压裂主导破裂机制为张拉破裂，但裂隙仍存在剪切破裂特征。破裂压力是围压、温度和岩石材料性质的函数。水力裂隙扩展集中的一部分区域称为优势裂隙扩展区。当裂隙尖端的应力强度因子K_I大于等于岩石的临界应力强度因子K_IC时，裂隙开始扩展。

4.不同入口压力工况下，压力数值都沿着轴向方向均匀减小。在流体流动通道的同一方向上，各工况下水的速度场分布近似相同，随着入口压力的不断增大，水渗流的整体速度明显增大。粗糙裂隙中的流态较为复杂，裂隙中的流速并非均匀，随着几何形貌的变化而变化。越靠近裂隙面突起处，渗流速度越大，越靠近裂隙面凹陷处，渗流速度越小。

5.裂隙水温沿长度方向逐渐增大，水流出口处，裂隙水温与岩体温度接近相等。越接近水流出口处，温度等值线越稀疏。入口温度的增大可以提高裂隙水温，但不会影响岩体的温度梯度，对出口温度的影响也不大。入口速度越大，换热面积越大，裂隙周边的岩体温度梯度越大，岩石和裂隙水换热充分性也越小，岩体整体温度越低。水流流速减小，可使水岩换热更为充分。入口速度越大，对流换热系数越大。增大入口速度可以大幅提高换热效率。

本研究结果为花岗岩水力压裂和渗流换热规律的研究提供了理论依据，为干热岩地热能的开采提供了一定的参考。

As a widely distributed renewable resource, geothermal energy has become the third renewable energy available to human beings. Hot dry rock geothermal energy is of great significance because of its huge reserves, clean, efficient and renewable characteristics. Currently, hot dry rock production is usually achieved through hydraulic fracturing to improve the permeability of hot dry rock reservoir. As a widely distributed hot dry rock reservoir, the hydraulic fracturing characteristics of granite and the law of seepage heat transfer have not been systematically revealed and need further study. In this paper, granite is taken as the research object to study the hydraulic fracturing characteristics under different confining pressures and temperatures. The evolution law of AE characteristics in fracturing process is analyzed. The law of crack propagation is expounded. The influencing factors of hydraulic fracturing are clarified. The fracture mechanism and fracture propagation criterion of hydraulic fracturing are revealed. The permeability characteristics of fractured fracture and the law of seepage heat transfer in fractured rock mass are studied by numerical simulation. The main conclusions are as follows:

(1)The hydraulic fracturing curve can be divided into four distinct stages: (a) water filling of pipe holes; (b) pressurization of boreholes; (c) fracturing; (d) fracture extension. A significant decrease in pore pressure and an increase in confining pressure can be observed at the same time during the fracturing stage. The first large scale increase of AE signal occurs roughly when pore pressure reaches breakdown pressure. The increase of AE signal means the initiation of the main crack, and the signal fluctuation means the expansion of the crack. AE method is more sensitive to monitoring the initiation and propagation of cracks than the pore pressure, which can not only monitor the macroscopic fracture phenomenon, but also monitor the microscopic micro-fracture.

(2)After fracturing, the fracture extends vertically along the drilling direction of the sample. With the increase of confining pressure, the fracture length becomes larger and the fracture path becomes more and more complex. The fracture fracture does not start at the top of the sample, but at a certain position away from the top of the sample. The cracks are rough and tortuous. There are a certain number of secondary cracks around the main crack, and the local crack is larger due to particle breakage in some places. There exists both intergranular fracture and transgranular fracture.

(3)The characteristics of hydraulic fracturing is obviously affected by confining pressure. The results show that the higher the confining pressure is, the greater the fracture stress is, and the relationship between them is approximately linear. The larger the confining pressure, the longer the breakdown time. When the thermal shock phenomenon is not significant and the confining pressure is constant, the higher the temperature, the greater the breakdown pressure. The dominant fracture mechanism of granite hydraulic fracturing is tensile fracture, but shear fracture still exists. Initiation pressure is a function of confining pressure, temperature and rock material properties. A region of the hydraulic fracture propagation concentration is called the dominant fracture propagation zone.When the stress intensity factor (K_I) at the crack tip is greater than or equal to the critical stress intensity factor (K_IC), the crack begins to expand.

(4)Under different inlet pressure conditions, the pressure value decreases uniformly along the axial direction. In the same direction of the fluid flow channel, the velocity field distribution of the water under different conditions is approximately the same. With the increasing of the inlet pressure, the overall velocity of water seepage increases obviously. The flow pattern in the rough crack is more complicated, and the velocity in the crack is not uniform, which changes with the change of the geometric morphology. The closer to the fracture surface protrusion, the larger the seepage velocity is, and the closer to the fracture surface depression, the smaller the seepage velocity is.

(5)The water temperature of the fissure increases gradually along the length direction, and the water temperature of the fissure is close to that of the rock mass at the flow outlet. The closer the flow outlet is, the thinner the temperature contour is. The increase of inlet temperature can improve the water temperature of crack, but it does not affect the temperature gradient of rock mass, and has little effect on outlet temperature. The larger the inlet velocity, the larger the heat transfer area, the larger the temperature gradient of rock mass around the fracture, the smaller the heat transfer adequacy of rock and fissure water, and the lower the overall temperature of rock mass. When the flow velocity decreases, the heat transfer between water and rock becomes more adequate. The larger the inlet velocity, the larger the convective heat transfer coefficient. Increasing the inlet speed can greatly improve the heat transfer efficiency.

The research results of this paper provide a theoretical basis for the study of granite hydraulic fracturing and seepage heat transfer law, and provide a certain reference for the exploitation of geothermal energy in hot dry rock.

[1] 李馨馨, 李典庆, 徐轶. 地热对井系统裂隙岩体三维渗流传热耦合的等效模拟方法[J]. 工程力学, 2019, 36(7): 238-247.

[2] 胡剑, 苏正, 吴能友, 等. 增强型地热系统热流耦合水岩温度场分析[J]. 地球物理学进展, 2014, 29(3): 1391-1398.

[3] 熊峰. 裂隙岩体非线性渗流特性及水热耦合模拟研究[D]. 武汉大学, 2020.

[4] 马兵. 热固耦合下储层岩石的地质力学特性及损伤演化规律研究[D]. 重庆大学, 2019.

[5] 雷治红. 青海共和盆地干热岩储层特征及压裂试验模型研究[D]. 吉林大学, 2020.

[6] 刘国军, 鲜学福, 周军平, 等. 超临界CO2致裂页岩实验研究[J]. 煤炭学报, 2017, 42(3): 694-701.

[7] 贾海梁, 朱子贤, 周阳, 等. 砂−重晶石粉填料导热性能与传热机制研究[J]. 煤田地质与勘探, 2022, 50(11): 162-173.

[8] 亢方超, 唐春安, 李迎春, 等. 增强地热系统研究现状:挑战与机遇[J]. 工程科学学报, 2022, 44(10): 1767-1777.

[9] 周舟, 金衍, 曾义金, 等. 青海共和盆地干热岩地热储层水力压裂物理模拟和裂缝起裂与扩展形态研究[J]. 吉林大学学报：地球科学版, 2019, 49(5): 1425-1430.

[10] 尹乾, 靖洪文, 刘日成, 等. 三维粗糙单裂隙剪切渗流过程中临界水力梯度判据[C]. 中国力学大会-2017暨庆祝中国力学学会成立60周年大会论文集(A), 2017.

[11] 崔强, 冯夏庭, 薛强, 等. 化学腐蚀下砂岩孔隙结构变化的机制研究[J]. 岩石力学与工程学报, 2008, 27(6): 1209-1216.

[12] Shao H, Kabilan S, Childers M I,et al. Environmentally friendly, rheoreversible, hydraulic fracturing fluids for enhanced geothermal systems [J]. Geothermics, 2015, 58(11): 22-31.

[13] Kumari W G P, Ranjith P G, Perera M S A,et al. Experimental investigation of quenching effect on mechanical, microstructural and flow characteristics of reservoir rocks: Thermal stimulation method for geothermal energy extraction[J]. Journal of Petroleum Science and Engineering, 2018, 162: 419-433.

[14] 郭亮亮. 增强型地热系统水力压裂和储层损伤演化的试验及模型研究[D]. 吉林大学, 2016.

[15] 李全贵, 邓羿泽, 胡千庭, 等. 煤岩水力压裂物理试验研究综述及展望 [J]. 煤炭科学技术 2022, 50(12): 62-72.

[16] 吴拥政, 杨建威. 煤矿砂岩横向切槽真三轴定向水力压裂试验[J]. 煤炭学报, 2020, 45(3): 927-935.

[17] Zhou D, Zhang G, Zhao P,et al. Effects of post-instability induced by supercritical CO2 phase change on fracture dynamic propagation[J]. Journal of Petroleum Science and Engineering, 2018, 162: 358-366.

[18] 周雷, 李立, 夏彬伟, 等. 含径向水力割缝钻孔导向压裂裂缝形态及影响要素[J]. 煤炭学报, 2022, 47(4):1559-1570.

[19] Damani A, Sharma A, Sondergeld C,et al. Acoustic emission and SEM analyses of hydraulic fractures under triaxial stress conditions[M].2012: 1-5.

[20] Mao R B, Feng Z J, Liu Z H,et al. Laboratory hydraulic fracturing test on large-scale pre-cracked granite specimens[J]. Journal of Natural Gas Science and Engineering, 2017,44: 278-286.

[21] 杨典森, 周云, 周再乐. 含界面储层水力压裂试验与数值模拟研究进展[J]. 岩石力学与工程学报, 2022, 41(9): 1771-1794.

[22] 杨潇, 张广清, 刘志斌, 等. 压裂过程中水力裂缝动态宽度实验研究[J]. 岩石力学与工程学报, 2017, 36(9): 2232-2237.

[23] 邢岳堃, 黄炳香, 陈大勇, 等. 压裂裂缝非线性断裂的声发射全波形多参量监测[J]. 煤炭学报, 2021,46(11):3470-3487.

[24] Cha M, Yin X, Kneafsey T,et al. Cryogenic fracturing for reservoir stimulation – Laboratory studies[J]. Journal of Petroleum Science and Engineering, 2014, 124: 436-450.

[25] Fatahi H, Hossain M M, Fallahzadeh S H,et al. Numerical simulation for the determination of hydraulic fracture initiation and breakdown pressure using distinct element method[J]. Journal of Natural Gas Science and Engineering, 2016, 33: 1219-1232.

[26] Guo T K, Qu Z Q, Wang] Z. Research of fracture initiation and propagation in HDR fracturing under thermal stress from meso-damage perspective[J]. Energy, 2019(178): 508-521.

[27] Zoback M D, Rummel F, Jung R,et al. Laboratory hydraulic fracturing experiments in intact and pre-fractured rock[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1977, 14(2): 49-58.

[28] 谢紫霄, 黄中伟, 熊建华, 等. 天然裂缝对干热岩水力压裂裂缝扩展的影响规律[J]. 天然气工业, 2022, 42(4):63-72.

[29] Tan P, Jin Y, Han K,et al. Analysis of hydraulic fracture initiation and vertical propagation behavior in laminated shale formation[J]. Fuel, 2017(206): 482-493.

[30] Chitrala Y, Moreno C, Sondergeld C,et al. An experimental investigation into hydraulic fracture propagation under different applied stresses in tight sands using acoustic emissions[J]. Journal of Petroleum Science and Engineering, 2013(108): 151-161.

[31] Sebastian B, Michael M, Ferdinand S C,et al.: Hydraulic and Sleeve Fracturing Laboratory Experiments on 6 Rock Types[C], Andrew P B, John M, Rob J, editor, Effective and Sustainable Hydraulic Fracturing, 2013: 20.

[32] Fallahzadeh S H, Rasouli V, Sarmadivaleh M. An Investigation of Hydraulic Fracturing Initiation and Near-Wellbore Propagation from Perforated Boreholes in Tight Formations[J]. Rock Mechanics and Rock Engineering, 2015, 48(2): 573-584.

[33] He J, Lin C, Li X,et al. Experimental Investigation of Crack Extension Patterns in Hydraulic Fracturing with Shale, Sandstone and Granite Cores[J]. Energy, 2016, 9(12): 1018.

[34] Xiang L, Feng Z, Gang H,et al. Breakdown pressure and fracture surface morphology of hydraulic fracturing in shale with H2O, CO2 and N2 [J]. Geomech. Geophys. Geoenergy Geo-resour, 2016, 2: 63-76.

[35] Yue Y, Peng S, Liu Y,et al. Investigation of acoustic emission response and fracture morphology of rock hydraulic fracturing under true triaxial stress[J]. Acta Geophysica, 2019, 67(4): 1017-1024.

[36] Zhang Y, Ma Y, Hu Z,et al. An experimental investigation into the characteristics of hydraulic fracturing and fracture permeability after hydraulic fracturing in granite[J]. Renewable Energy, 2019, 140(9): 615-624.

[37] Fallahzadeh S H, Cornwell A J, Rasouli V,et al. The impacts of fracturing fluid viscosity and injection rate on the near wellbore hydraulic fracture propagation in cased perforated wellbores[J], 2015.

[38] Lin C, He J, Li X,et al. An Experimental Investigation into the Effects of the Anisotropy of Shale on Hydraulic Fracture Propagation[J]. Rock Mechanics and Rock Engineering, 2017, 50(3): 543-554.

[39] Scholz C. Experimental Study of the Fracturing Process in Brittle Rock[J]. Journal of Geophysical Research, 1968, 73: 1447-1454.

[40] Renard F, Bernard D, Desrues J,et al. 3D imaging of fracture propagation using synchrotron X-ray microtomography[J]. Earth and Planetary Science Letters, 2009, 286(1): 285-291.

[41] Zhu H, Wang Q, Zhuang X. A nonlinear semi-concurrent multiscale method for fractures[J]. International journal of impact engineering, 2016(1): 67-82.

[42] Zhang S, Huang Z, Huang P,et al. Numerical and experimental analysis of hot dry rock fracturing stimulation with high-pressure abrasive liquid nitrogen jet[J]. Journal of Petroleum Science and Engineering, 2018, 163: 156-165.

[43] He J, Lin C, Li X,et al. Initiation, propagation, closure and morphology of hydraulic fractures in sandstone cores[J]. Fuel, 2017, 208: 65-70.

[44] 李连崇, 李根, 孟庆民, 等. 砂砾岩水力压裂裂缝扩展规律的数值模拟分析[J]. 岩土力学, 2013,34(5):1501-1507.

[45] Deng J Q, Lin C, Yang Q,et al. Investigation of directional hydraulic fracturing based on true tri-axial experiment and finite element modeling[J]. Computers and Geotechnics, 2016, 75: 28-47.

[46] Lin C, He J, Li X,et al. An Experimental Investigation into the Effects of the Anisotropy of Shale on Hydraulic Fracture Propagation[J], 2017,50(3):543-554.

[47] Fan T-G, Zhang G-Q. Laboratory investigation of hydraulic fracture networks in formations with continuous orthogonal fractures[J]. Energy, 2014, 74: 164-173.

[48] Pradhan S, Stroisz A M, Fjær E,et al. Stress-Induced Fracturing of Reservoir Rocks: Acoustic Monitoring and μCT Image Analysis[J]. Rock Mechanics and Rock Engineering, 2015, 48(6): 2529-2540.

[49] 王金安, 谢和平. 剪切过程中岩石节理粗糙度分形演化及力学特征[J]. 岩土工程学报, 1997, 19(4): 2-9.

[50] 杨金保, 冯夏庭, 潘鹏志, 等. 三轴压应力-化学溶液渗透作用下单裂隙花岗岩裂隙开度演化[J]. 岩石力学与工程学报, 2012, 31(9): 1869-1878.

[51] 王媛, 速宝玉. 单裂隙面渗流特性及等效水力隙宽[J]. 水科学进展, 2002, 13(1): 61-68.

[52] 吴金花, 李守巨, 刘迎曦. 具有分形表面裂隙的渗流特性研究[C]. 中国力学学会学术大会2009论文摘要集, 2009.

[53] 张鑫. 粗糙单裂隙渗流与岩体应力特性分析[D]. 西安理工大学, 2019.

[54] 陈禹, 杜时贵. JRC修正直边法的数学表达[J]. 工程地质学报, 1996,4(2): 36-43.

[55] Barton N, Choubey V. The shear strength of rock joints in theory and practice[J]. Rock Mechanics and Rock Engineering, 1977, 10(1):1-54.

[56] Bandis S C B N R C M. Application of a new numerical model of joint behaviour to rock mechanics problems[J]. International Journal of Rock Mechanics Mining sciences andGeomechanics Abstracts, 1986, 24(4): 345-356.

[57] Rutqvist J, Stephansson O. The role of hydromechanical coupling in fractured rock engineering[J]. Hydrogeology Journal, 2003, 11(1): 7-40.

[58] 王伟. 不同接触状态下节理应力-渗流耦合特性的研究[D]. 同济大学, 2009.

[59] 熊祥斌, 张楚汉, 王恩志. 岩石单裂隙稳态渗流研究进展[J]. 岩石力学与工程学报, 2009, 28(9): 1839-1847.

[60] Miao T, Yu B, Duan Y,et al. A fractal analysis of permeability for fractured rocks[J]. International Journal of Heat and Mass Transfer, 2015, 81: 75-80.

[61] Zhang C, Shu L, Lu C,et al. Experimental determination of fractures and conduits and the applicability of Cubic law in closed fractures[J]. Experimental Thermal and Fluid Science, 2015, 69: 1-7.

[62] Zuloaga-Molero P, Yu W, Xu Y,et al. Simulation Study of CO2-EOR in Tight Oil Reservoirs with Complex Fracture Geometries[J]. Scientific Reports, 2016, 6(1): 33445.

[63] 熊峰, 孙昊, 姜清辉, 等. 粗糙岩石裂隙低速非线性渗流模型及试验验证[J]. 岩土力学, 2018, 39(9): 3294-3302.

[64] Snow D T. A parallel plate model of fractured permeable media[J]. Berkeley:University of California of Berkeley, 1965.

[65] Zimmerman R W, Kumar S, Bodvarsson G S. Lubrication theory analysis of the permeability of rough-walled fractures[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1991, 28(4): 325-331.

[66] Yeo I W, Ge S. Applicable range of the Reynolds equation for fluid flow in a rock fracture[J]. Geosciences Journal, 2005, 9(4): 347-352.

[67] Barton N. Rock Quality, Seismic Velocity, Attenuation and Anisotropy[J], Environmental & Engineering Geoscience, 2009, 15(1):50-52.

[68] Jianping S, Zhao Z. Influences of Fracture Aperture and Roughness on Hydraulic Conductivity in Fractured Rock Mass[J], 2011, 1376-1384.

[69] 李文亮, 周佳庆, 贺香兰, 等. 不同围压下破碎花岗岩非线性渗流特性试验研究[J]. 岩土力学, 2017, 38(S1): 140-150.

[70] 孟如真, 胡少华, 陈益峰, 等. 高渗压条件下基于非达西流的裂隙岩体渗透特性研究[J]. 岩石力学与工程学报, 2014, 33(9): 1756-1764.

[71] Xiong F, Jiang Q, Ye Z,et al. Nonlinear flow behavior through rough-walled rock fractures: The effect of contact area[J]. Computers and Geotechnics, 2018, 102(OCT.): 179-195.

[72] 周新, 盛建龙, 叶祖洋, 等. 岩体粗糙裂隙几何特征对其Forchheimer型渗流特性的影响[J]. 岩土工程学报, 2021, 43(11): 2075-2083.

[73] Javadi M, Sharifzadeh M, Shahriar K,et al. Critical Reynolds number for nonlinear flow through rough-walled fractures: The role of shear processes[J]. Water Resources Research, 2014, 50(2): 1789-1804.

[74] Jiang P, Zhang L, Xu R. Experimental study of convective heat transfer of carbon dioxide at supercritical pressures in a horizontal rock fracture and its application to enhanced geothermal systems[J]. Applied Thermal Engineering, 2017, 117: 39-49.

[75] Huang Y, Zhang Y, Yu Z,et al. Experimental investigation of seepage and heat transfer in rough fractures for enhanced geothermal systems[J]. Renewable Energy, 2019, 135: 846-855.

[76] Zhang L, Jiang P, Wang Z,et al. Convective heat transfer of supercritical CO2 in a rock fracture for enhanced geothermal systems[J]. Applied Thermal Engineering, 2017, 115: 923-936.

[77] Bai B, He Y, Hu S,et al. An Analytical Method for Determining the Convection Heat Transfer Coefficient Between Flowing Fluid and Rock Fracture Walls[J]. Rock Mechanics and Rock Engineering, 2017, 50(7): 1787-1799.

[78] Ranjith P G. An experimental study of single and two-phase fluid flow through fractured granite specimens[J]. Environmental Earth Sciences, 2010, 59(7): 1389-1395.

[79] Zhao Z. On the heat transfer coefficient between rock fracture walls and flowing fluid[J]. Computers and Geotechnics, 2014, 59: 105-111.

[80] Luo S, Zhao Z, Peng H,et al. The role of fracture surface roughness in macroscopic fluid flow and heat transfer in fractured rocks[J]. International Journal of Rock Mechanics and Mining Sciences, 2016, 87: 29-38.

[81] Gringarten A C, Witherspoon P A, Ohnishi Y. Theory of heat extraction from fractured hot dry rock[J]. Journal of Geophysical Research (1896-1977), 1975, 80(8): 1120-1124.

[82] Ghassemi A, Tarasovs S, H.-D. Cheng A. An integral equation solution for three-dimensional heat extraction from planar fracture in hot dry rock[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2003, 27(12): 989-1004.

[83] Mohais R, Xu C, Dowd P. Fluid Flow and Heat Transfer Within a Single Horizontal Fracture in an Enhanced Geothermal System[J]. Journal of Heat Transfer, 2010, 132(8):1063-1069.

[84] Chen J, Jiang F. A numerical study of EGS heat extraction process based on a thermal non-equilibrium model for heat transfer in subsurface porous heat reservoir[J]. Heat and Mass Transfer, 2016, 52(2): 255-267.

[85] 李帅. 超临界CO2在裂隙储层中的渗流-传热特性的数值研究[D]. 天津大学, 2019.

[86] Luo J, Zhu Y, Guo Q,et al. Experimental investigation of the hydraulic and heat-transfer properties of artificially fractured granite[J]. Scientific Reports, 2017, 7(1): 39882.

[87] Shaik A R, Rahman S S, Tran N H,et al. Numerical simulation of Fluid-Rock coupling heat transfer in naturally fractured geothermal system[J]. Applied Thermal Engineering, 2011, 31(10): 1600-1606.

[88] 赵坚. 岩石裂隙中的水流-岩石热传导[J].岩石力学与工程学报, 1999, 18(2):119-123.

[89] 黄诗冰, 刘泉声, 程爱平, 等. 低温裂隙岩体水-热耦合模型研究及数值分析[J]. 岩土力学, 2018, 39(2): 735-744.

[90] 杨更社, 申艳军, 贾海梁, 等. 冻融环境下岩体损伤力学特性多尺度研究及进展[J]. 岩石力学与工程学报, 2018, 37(3): 545-563.

[91] Jia H, Ding S, Wang Y,et al. An NMR-based investigation of pore water freezing process in sandstone[J]. Cold Regions Science and Technology, 2019, 168: 102893.

[92] Kumari W G P, Ranjith P G, Perera M S A,et al. Hydraulic fracturing under high temperature and pressure conditions with micro CT applications: Geothermal energy from hot dry rocks[J]. Fuel, 2018, 230: 138-154.

[93] Zhuang L, Kim K Y, Jung S G,et al. Effect of Water Infiltration, Injection Rate and Anisotropy on Hydraulic Fracturing Behavior of Granite[J], 2018(3): 1-15.

[94] Zhuang L, Kwang Yeomjung, Sung Gyudiaz, Melvinmin, Ki-Bokzang, Arnostephansson, Ovezimmerman, Guenteryoon, Jeoung-Seokhofmann, Hannes. Cyclic hydraulic fracturing of pocheon granite cores and its impact on breakdown pressure, acoustic emission amplitudes and injectivity[J]. International Journal of Rock Mechanics Mining Sciences, 2019, 122：104065.

[95] 张玉良, 吴必胜, 赵高峰. 基于声发射监测的岩石热损伤实时演化研究[J]. 中南大学学报（自然科学版）2021, 52(8): 2945-2958.

[96] 梁卫国, 贺伟, 阎纪伟. 超临界CO2致煤岩力学特性弱化与破裂机理[J]. 煤炭学报, 2022(007):2557-2568.

[97] Stephen, Rassenfoss. Digging Up New Information On What Fractures Really Look Like[J]. Journal of Petroleum Technology, 2018, 70(3): 38-39.

[98] Chen Y, Nagaya Y, Ishida T. Observations of Fractures Induced by Hydraulic Fracturing in Anisotropic Granite[J]. Rock Mechanics Rock Engineering, 2015,48(4):1455-1461.

[99] 杜广盛, 陈世江, 常建平, 等. 矿物组构对花岗岩抗拉强度影响分析[J]. 矿业研究与开发, 2020(011): 76-82.

[100] 陈芳, 秦昊. 细观尺度下岩石沿晶断裂应力强度因子计算研究[J]. 岩土力学, 2011, 32(3): 941-945.

[101] 甘一雄, 吴顺川, 任义, 等. 基于声发射上升时间/振幅与平均频率值的花岗岩劈裂破坏评价指标研究[J]. 岩土力学, 2020(007): 2324-2332.

[102] 徐严波. 水平井水力压裂基础理论研究[D]. 西南石油学院, 2004.

[103] 周代余. 大位移井水力压裂的基础理论和设计方法研究[D]. 西南石油学院, 2002.

[104] Closmann P J, Phocas D M. Thermal stresses near a heated fracture in a transversely isotropic medium[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1976, 16(1): 59-74.

[105] 杨红. 水力喷射压裂裂缝形态的探讨[D]. 西安石油大学, 2009.

[106] A W G P K, A P G R, A M S a P B,et al. Hydraulic fracturing under high temperature and pressure conditions with micro CT applications: Geothermal energy from hot dry rocks[J], Fuel, 2018, 230: 138-154.

[107] Wanniarachchillage W, Ranjith G, Mandadige P,et al. Investigation of Depth and Injection Pressure Effects on Breakdown Pressure and Fracture Permeability of Shale Reservoirs: An Experimental Study[J], Applied Sciences, 2017, 7(7): 664.

[108] Patel S M, Sondergeld C H, Rai C S. Hydraulic fracture permeability estimation using stimulation pressure data[J]. International Journal of Rock Mechanics and Mining Sciences, 2018, 101: 50-53.

[109] Crank J. The Mathematics of Diffusion[J]. Clarendon Press, Oxford, Second Ed., 1975, 44.

[110] Shapiro S A, Patzig R, Rothert E,et al. Triggering of Seismicity by Pore-pressure Perturbations: Permeability-related Signatures of the Phenomenon[J]. Pure and Applied Geophysics, 2003, 160(5): 1051-1066.

[111] 贺立新. 高温后岩石孔隙-裂隙组合非线性渗流特性研究[D]. 中国矿业大学, 2019.

[112] 李广林. 干热岩水力压裂下储层物性及其渗透性研究[D]. 太原理工大学, 2018.

[113] 李维溪. 裂隙岩体渗流-传热耦合的有限元模拟研究[D]. 北京交通大学, 2015.

[114] 李正伟, 张延军, 张驰, 等. 花岗岩单裂隙渗流传热特性试验[J]. 岩土力学, 2018, 39(9): 3261-3269.

[115] 肖鹏, 窦斌, 田红, 等. 地热储层单裂隙岩体渗流传热数值模拟研究[J]. 钻探工程, 2021,48(2):16-28