页岩水力压裂过程的态型近场动力学模拟研究
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摘要
水力压裂技术广泛使用于页岩气开采工程中。为了分析压裂过程中多裂缝扩展形成复杂裂缝网的机制,尝试将态型近场动力学理论引入页岩水平井水力压裂过程的力学建模与数值仿真,在物质点间相互作用力模型中加入等效水压力项以实现在新生裂缝面上跟踪施加水压力,建立了水力压裂过程的近场动力学分析模型。通过模拟页岩储层的水力压裂过程,可得到复杂的裂缝扩展路径、裂缝网络的形成过程以及裂缝扩展受射孔间距及页岩天然裂缝和层理的影响。研究结果表明:射孔间距过小会造成起裂干扰,使中心射孔的裂缝扩展受到抑制;在压裂压力一定的情况下适当增大射孔间距,可以显著增强页岩压裂形成裂缝网的能力;压裂过程中水平层理面可能张开形成水平裂缝,且天然裂缝会诱导形成更复杂的垂直裂缝。模型和方法可为页岩水力压裂过程和机制研究及工程实践提供参考。
Hydraulic fracturing technology is widely applied in shale gas extraction engineering. In this study, the state-based peridynamic theory was introduced into the modeling and analysis of hydraulic fracture in horizontal shale wells. The mechanism of the multi-fracture propagation and the formation of complex fracture networks were analyzed as well. An equivalent hydraulic pressure term was embedded in the constitutive function, which describes the interactive forces between material points, to track the applied hydraulic pressure on the new crack surfaces. Thus, a simplified state-based peridynamic model was established to describe the hydraulic fracturing. Through the proposed model, the hydraulic fracturing process of shale reservoirs was simulated to investigate the complex crack propagation paths, the formation process of crack networks, as well as the effects of natural stratification, cracks, and perforation spacing on the hydraulic crack propagation. Numerical results indicate that when the perforation spacing is sufficiently small, the cracking process is disturbed and the crack propagation along the central perforation is inhibited. Under certain fracturing pressure, a proper increase of perforation distance can significantly accelerate the hydraulic fracture process. During the hydraulic fracturing process, horizontal cracks may be formed in the horizontal stratification, and complex vertical cracks may be formed by the induction of natural cracks. The proposed model and numerical methods provide alternative and promising ways for the profound investigation into shale hydraulic fracturing and engineering applications.
Hydraulic fracturing technology is widely applied in shale gas extraction engineering. In this study, the state-based peridynamic theory was introduced into the modeling and analysis of hydraulic fracture in horizontal shale wells. The mechanism of the multi-fracture propagation and the formation of complex fracture networks were analyzed as well. An equivalent hydraulic pressure term was embedded in the constitutive function, which describes the interactive forces between material points, to track the applied hydraulic pressure on the new crack surfaces. Thus, a simplified state-based peridynamic model was established to describe the hydraulic fracturing. Through the proposed model, the hydraulic fracturing process of shale reservoirs was simulated to investigate the complex crack propagation paths, the formation process of crack networks, as well as the effects of natural stratification, cracks, and perforation spacing on the hydraulic crack propagation. Numerical results indicate that when the perforation spacing is sufficiently small, the cracking process is disturbed and the crack propagation along the central perforation is inhibited. Under certain fracturing pressure, a proper increase of perforation distance can significantly accelerate the hydraulic fracture process. During the hydraulic fracturing process, horizontal cracks may be formed in the horizontal stratification, and complex vertical cracks may be formed by the induction of natural cracks. The proposed model and numerical methods provide alternative and promising ways for the profound investigation into shale hydraulic fracturing and engineering applications.
引文
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[18]严成增,郑宏,孙冠华,等.模拟水压致裂的二维FDEM-flow方法[J].岩石力学与工程学报,2015,34(01):67-75.YAN Cheng-zeng,ZHENG Hong,SUN Guan-hua,et al.A 2D FDEM-flow method for simulation hydraulic fracturing[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(01):67-75.
[19]YAN C,ZHENG H,SUN G,et al.Combined finite-discrete element method for simulation of hydraulic fracturing[J].Rock Mechanics&Rock Engineering,2016,49(4):1389-1410.
[20]YAN C Z,ZHENG H.FDEM-flow3D:A 3Dhydro-mechanical coupled model considering the pore seepage of rock matrix for simulating three-dimensional hydraulic fracturing[J].Computers&Geotechnics,2017,81(1):212-228.
[21]严成增.模拟水压致裂的另一种二维FDEM-flow方法[J].岩土力学,2017,38(6):1789-1796.YAN Cheng-zeng,A new two-dimensional FDEM-flow method for simulating hydraulic fracturing[J].Rock and Soil Mechanics,2017,38(6):1789-1796.
[22]YAN C,JIAO Y Y.A 2D fully coupled hydro-mechanical finite-discrete element model with real pore seepage for simulating the deformation and fracture of porous medium driven by fluid[J].Computers&Structures,2018,196(2):311-326.
[23]YAN C,JIAO Y Y,Zheng H.A fully coupled three-dimensional hydro-mechanical finite discrete element approach with real porous seepage for simulating3D hydraulic fracturing[J].Computers&Geotechnics,2017,96(4):73-89.
[24]SILLING S A.Reformulation of elasticity theory for discontinuities and long-range forces[J].Journal of the Mechanics and Physics of Solids,2000,48(1):175-209.
[25]黄丹,章青,乔丕忠,等.近场动力学方法及其应用[J].力学进展,2010,40(4):448-459.HUANG Dan,ZHANG Qing,QIAO Pi-zhong,et al.Areview on peridynamics method and its application[J].Advance in Mechanics,2010,40(4):448-459.
[26]顾鑫,章青,黄丹.基于近场动力学方法的混凝土板侵彻问题研究[J].振动与冲击,2016,35(6):52-58.GU Xin,ZHANG Qing,HUANG Dan.Peridynamics used in solving penetration problem of concrete slabs[J].Journal of Vibration and Shock,2016,35(6):52-58.
[27]HUANG D,ZHANG Q,QIAO P Z.Damage and progressive failure of concrete structures using non-local peridynamic modeling[J].Science China:Technological Science,2011,54(3):591-596.
[28]GERSTLE W,SAU N,SAKHAVAND N.On peridynamic computational simulation of concrete structures[J].American Concrete Institute,2009(65):245-264.
[29]HUANG D,LU G,QIAO P.An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis[J].International Journal of Mechanical Sciences,2015,94-95:111-122.
[30]吴凡,李书卉,段庆林,等.基于近场动力学方法的水力压裂过程数值模拟[J].计算机辅助工程,2017,26(1):1-6.WU Fan,LI Shu-hui,DUAN Qing-lin,et al.Numerical simulation of hydraulic fracturing process based on peridynamics method[J].Computer Aided Engineering,2017,26(1):1-6.
[31]SILLING S A,EPTON M,WECKNER O,et al.Peridynamic states and constitutive modeling[J].Journal of Elasticity,2007,88(2):151-184.
[32]WARREN T L,SILLING S A,ASKARI A,et al.Anon-ordinary state-based peridynamic method to model solid material deformation and fracture[J].International Journal of Solids and Structures,2009,46(5):1186-1195.
[33]刘肃肃,余音.复材非线性及渐进损伤的态型近场动力学模拟[J].浙江大学学报(工学版),2016,50(5):993-1000.LIU Su-su,YU Yin.State-based peridynamic modeling of nonlinear behavior and progressive damage of composites[J]Journal of Zhejiang University(Engineering Science),2016,50(5):993-1000.
[34]谷新保,周小平.裂纹扩展和连接过程的近场动力学数值模拟[J].岩土力学,2017,38(2):610-616.GU Xin-bao,ZHOU Xiao-ping.Numerical simulation of propagation and coalescence of cracks using peridynamic theory[J].Rock and Soil Mechanics,2017,38(2):610-616.
[35]KATIYAR A,FOSTER J T,OUCHI H,et al.Aperidynamic formulation of pressure driven convective fluid transport in porous media[J]Journal of Computational Physics,2014,261(3):209-229.
[36]LE Q V,CHAN W K,SCHWARTZ J.A two-dimensional ordinary,state-based peridynamic model for linearly elastic solids[J].International Journal for Numerical Methods in Engineering,2014,98(8):547-561.
[37]BOBARU F,HU W.The meaning,selection,and use of the peridynamic horizon and its relation to crack branching in brittle materials[J].International Journal of Fracture,2012,176(2):215-222.
[2]WENG X,KRESSE O,COHEN C E,et al.Modeling of hydraulic fracture network propagation in a naturally fractured formation[J].SPE Production&Operations,2011,26(4):368-380.
[3]TANG C A,THAM L G,LEE P K K,et al.Coupled analysis of flow,stress and damage(FSD)in rock failure[J].International Journal of Rock Mechanics&Mining Sciences,2002,39(4):477-489.
[4]ADACHI J,SIEBRITS E,PEIRCE A,et al.Computer simulation of hydraulic fractures[J].International Journal of Rock Mechanics and Mining Sciences,2007,44(5):739-757.
[5]金衍,程万,陈勉.页岩气储层压裂数值模拟技术研究进展[J].力学与实践,2016,38(1):1-9.JIN Yan,CHENG Wan,CHEN Mian.A review of numerical simulations of hydro-fracking in shale gas reservoir[J].Mechanics in Engineering,2016,38(1):1-9.
[6]潘林华,程礼军,张烨,等.页岩水平井多段分簇压裂起裂压力数值模拟[J].岩土力学,2015,36(12):3639-3648.PAN Lin-hua,CHENG Li-jun,ZHANG Ye,et al.Numerical simulation of fracturing pressure in multiple clusters staged hydraulic fracture of shale horizontal well[J].Rock and Soil Mechanics,2015,36(12):3639-3648.
[7]刘玉章,杨立峰,王欣,等.页岩气水力压裂裂缝缝网完善程度概论[J].天然气工业,2017,37(7):34-39.LIU Yu-zhang,YANG Li-feng,WANG Xin,et al.Introduction to the completion degree of hydraulic fracture networks in shale gas reservoirs[J].Natural Gas Industry,2017,37(7):34-39.
[8]龚迪光,曲占庆,李建雄,等.基于ABAQUS平台的水力裂缝扩展有限元模拟研究[J].岩土力学,2016,37(5):1512-1520.GONG Di-guang,QU Zhan-qing,LI Jian-xiong,et al.Extended finite element simulation of hydraulic fracture based on ABAQUS platform[J].Rock and Soil Mechanics,2016,37(5):1512-1520.
[9]JIAO Y Y,ZHANG H Q,ZHANG X L,et al.A twodimensional coupled hydromechanical discontinuum model for simulating rock hydraulic fracturing[J].International Journal for Numerical&Analytical Methods in Geomechanics,2015,39(5):457-481.
[10]MORGAN W E,ARAL M M.An implicitly coupled hydro-geomechanical model for hydraulic fracture simulation with the discontinuous deformation analysis[J].International Journal of Rock Mechanics and Mining Sciences,2015,73:82-94.
[11]顾颖凡,卢毅,刘兵,等.基于离散元法的水力压裂数值模拟[J].高校地质学报,2016,22(1):194-199.GU Ying-fan,LU Yi,LIU Bing,et al.Numerical simulation of hydraulic fracturing based on discrete element method[J].Geological Journal of China Universities,2016,22(1):194-199.
[12]TORRES S A,CASTANO J D.Simulation of the hydraulic fracture process in two dimensions using a discrete element method[J].Physical Review E:Statistical Nonlinear&Soft Matter Physics,2007,75(6Pt 2):066109.
[13]CHOI S O.Interpretation of shut-in pressure in hydrofracturing pressure-time records using numerical modeling[J].International Journal of Rock Mechanics and Mining Sciences,2012,50(2):29-37.
[14]姚池,赵明,杨建华,等.基于改进刚体弹簧方法的二维水压致裂模型[J].岩石力学与工程学报,2017,36(9):2169-2176.YAO Chi,ZHAO Ming,YANG Jian-hua,et al.Improved method of rigid body spring for 2D hydraulic fracturing simulation[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(9):2169-2176.
[15]ZHANG L,ZHOU J,HAN Z.Hydraulic fracturing process by using a modified two-dimensional particle flow code-case study[J].Progress in Computational Fluid Dynamics,2017,17(1):13-26.
[16]ZHOU J,ZHANG L,PAN Z,et al.Numerical investigation of fluid-driven near-borehole fracture propagation in laminated reservoir rock using PFC 2D[J].Journal of Natural Gas Science&Engineering,2016,36(A):719-733.
[17]严成增,郑宏,孙冠华,等.基于FDEM-flow研究地应力对水力压裂的影响[J].岩土力学,2016,37(1):237-246.YAN Cheng-zeng,ZHENG Hong,SUN Guan-hua,et al.Effect of in-situ stress on hydraulic fracturing based on FDEM-flow[J].Rock and Soil Mechanics,2016,37(1):237-246.
[18]严成增,郑宏,孙冠华,等.模拟水压致裂的二维FDEM-flow方法[J].岩石力学与工程学报,2015,34(01):67-75.YAN Cheng-zeng,ZHENG Hong,SUN Guan-hua,et al.A 2D FDEM-flow method for simulation hydraulic fracturing[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(01):67-75.
[19]YAN C,ZHENG H,SUN G,et al.Combined finite-discrete element method for simulation of hydraulic fracturing[J].Rock Mechanics&Rock Engineering,2016,49(4):1389-1410.
[20]YAN C Z,ZHENG H.FDEM-flow3D:A 3Dhydro-mechanical coupled model considering the pore seepage of rock matrix for simulating three-dimensional hydraulic fracturing[J].Computers&Geotechnics,2017,81(1):212-228.
[21]严成增.模拟水压致裂的另一种二维FDEM-flow方法[J].岩土力学,2017,38(6):1789-1796.YAN Cheng-zeng,A new two-dimensional FDEM-flow method for simulating hydraulic fracturing[J].Rock and Soil Mechanics,2017,38(6):1789-1796.
[22]YAN C,JIAO Y Y.A 2D fully coupled hydro-mechanical finite-discrete element model with real pore seepage for simulating the deformation and fracture of porous medium driven by fluid[J].Computers&Structures,2018,196(2):311-326.
[23]YAN C,JIAO Y Y,Zheng H.A fully coupled three-dimensional hydro-mechanical finite discrete element approach with real porous seepage for simulating3D hydraulic fracturing[J].Computers&Geotechnics,2017,96(4):73-89.
[24]SILLING S A.Reformulation of elasticity theory for discontinuities and long-range forces[J].Journal of the Mechanics and Physics of Solids,2000,48(1):175-209.
[25]黄丹,章青,乔丕忠,等.近场动力学方法及其应用[J].力学进展,2010,40(4):448-459.HUANG Dan,ZHANG Qing,QIAO Pi-zhong,et al.Areview on peridynamics method and its application[J].Advance in Mechanics,2010,40(4):448-459.
[26]顾鑫,章青,黄丹.基于近场动力学方法的混凝土板侵彻问题研究[J].振动与冲击,2016,35(6):52-58.GU Xin,ZHANG Qing,HUANG Dan.Peridynamics used in solving penetration problem of concrete slabs[J].Journal of Vibration and Shock,2016,35(6):52-58.
[27]HUANG D,ZHANG Q,QIAO P Z.Damage and progressive failure of concrete structures using non-local peridynamic modeling[J].Science China:Technological Science,2011,54(3):591-596.
[28]GERSTLE W,SAU N,SAKHAVAND N.On peridynamic computational simulation of concrete structures[J].American Concrete Institute,2009(65):245-264.
[29]HUANG D,LU G,QIAO P.An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis[J].International Journal of Mechanical Sciences,2015,94-95:111-122.
[30]吴凡,李书卉,段庆林,等.基于近场动力学方法的水力压裂过程数值模拟[J].计算机辅助工程,2017,26(1):1-6.WU Fan,LI Shu-hui,DUAN Qing-lin,et al.Numerical simulation of hydraulic fracturing process based on peridynamics method[J].Computer Aided Engineering,2017,26(1):1-6.
[31]SILLING S A,EPTON M,WECKNER O,et al.Peridynamic states and constitutive modeling[J].Journal of Elasticity,2007,88(2):151-184.
[32]WARREN T L,SILLING S A,ASKARI A,et al.Anon-ordinary state-based peridynamic method to model solid material deformation and fracture[J].International Journal of Solids and Structures,2009,46(5):1186-1195.
[33]刘肃肃,余音.复材非线性及渐进损伤的态型近场动力学模拟[J].浙江大学学报(工学版),2016,50(5):993-1000.LIU Su-su,YU Yin.State-based peridynamic modeling of nonlinear behavior and progressive damage of composites[J]Journal of Zhejiang University(Engineering Science),2016,50(5):993-1000.
[34]谷新保,周小平.裂纹扩展和连接过程的近场动力学数值模拟[J].岩土力学,2017,38(2):610-616.GU Xin-bao,ZHOU Xiao-ping.Numerical simulation of propagation and coalescence of cracks using peridynamic theory[J].Rock and Soil Mechanics,2017,38(2):610-616.
[35]KATIYAR A,FOSTER J T,OUCHI H,et al.Aperidynamic formulation of pressure driven convective fluid transport in porous media[J]Journal of Computational Physics,2014,261(3):209-229.
[36]LE Q V,CHAN W K,SCHWARTZ J.A two-dimensional ordinary,state-based peridynamic model for linearly elastic solids[J].International Journal for Numerical Methods in Engineering,2014,98(8):547-561.
[37]BOBARU F,HU W.The meaning,selection,and use of the peridynamic horizon and its relation to crack branching in brittle materials[J].International Journal of Fracture,2012,176(2):215-222.