页岩弹性模量非均质性对地应力及其损伤的影响
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摘要
页岩的应力非均质性对钻完井、压裂改造和气藏开发动态等过程具有显著影响,目前未给出合理的表征方法来刻画页岩水力压裂过程中力学非均质性引起的岩石损伤/破裂及"应力阴影"效应。采用Galerkin有限元数值方法,通过COMSOL Multiphysics求解器,利用Matlab脚本语言进行了二次开发;采用Weibull概率密度函数表示页岩力学非均质性,数值模拟了水力压裂过程中流固耦合条件下非均质性对页岩地应力分布、应变能密度、流压和损伤因子等因素的影响规律。当地层完全为均质时,Von-Mises应力、应变能密度和损伤因子递减分布曲线特征明显,随着地层非均质增强,它们的分布曲线呈现起伏波动的规律,且Von-Mises应力、应变能密度与损伤因子相关性较好。据此提出了二维平面应变条件下力学非均质性引起的岩石损伤/破裂及"应力阴影"效应表征方法,即用单点线处的Von-Mises应力或应变能密度刻画岩石的局部破裂程度或应力阴影效应的强弱,用单位面积的平均应变能密度刻画岩石整体的破裂程度或应力阴影效应的强弱。该研究对进一步改进页岩体积压裂设计和提高气井产能具有重要指导意义。
Shale heterogeneity has a significant effect on drilling and completions,hydraulic fracturing and hydrocarbon development performance,but it lacks representation of rock damage/failure caused by the mechanical heterogeneity and"stress shadow"effect during the hydraulic fracturing process.In this paper,Galerkin finite element method was adopted to numerically simulate the hydro-mechanical coupled interaction based on the solver in the COMSOL Multiphysics software and Matlab scripting development.The Weibull probability density function was used to represent the mechanical heterogeneity of gas shale.Under the condition of fully fluid-solid coupling during the fracking process,the effect of mechanical heterogeneity on von-Mises stress,strain energy density,damage factor and fluid pressure was numerically simulated in the gas shale wells.When the formation is completely homogeneous,their curves of von Mises stress,strain energy density and damage factor along a certain straight line showed obvious decreasing distribution.As the strata are heterogeneously enhanced,their distribution curves showed fluctuations,and von Mises stress and strain energy density respectively had a good relationship with damage factors.Accordingly,the method of rock damage/fracture and"stress shadow"effect caused by mechanic heterogeneity was put forward under the condition of 2D plane strain.That was to use,the von Mises stress or strain energy density at the single point or line to characterize the degree of local rupture or the shadow effect of stress,and the average strain energy density per unit area to characterize the degree of rupture of the rock or the intensity of the shadow effect.The study is of great significance to further improve the SRV fracturing design and the productivity of gas shale wells.
Shale heterogeneity has a significant effect on drilling and completions,hydraulic fracturing and hydrocarbon development performance,but it lacks representation of rock damage/failure caused by the mechanical heterogeneity and"stress shadow"effect during the hydraulic fracturing process.In this paper,Galerkin finite element method was adopted to numerically simulate the hydro-mechanical coupled interaction based on the solver in the COMSOL Multiphysics software and Matlab scripting development.The Weibull probability density function was used to represent the mechanical heterogeneity of gas shale.Under the condition of fully fluid-solid coupling during the fracking process,the effect of mechanical heterogeneity on von-Mises stress,strain energy density,damage factor and fluid pressure was numerically simulated in the gas shale wells.When the formation is completely homogeneous,their curves of von Mises stress,strain energy density and damage factor along a certain straight line showed obvious decreasing distribution.As the strata are heterogeneously enhanced,their distribution curves showed fluctuations,and von Mises stress and strain energy density respectively had a good relationship with damage factors.Accordingly,the method of rock damage/fracture and"stress shadow"effect caused by mechanic heterogeneity was put forward under the condition of 2D plane strain.That was to use,the von Mises stress or strain energy density at the single point or line to characterize the degree of local rupture or the shadow effect of stress,and the average strain energy density per unit area to characterize the degree of rupture of the rock or the intensity of the shadow effect.The study is of great significance to further improve the SRV fracturing design and the productivity of gas shale wells.
引文
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[15]Wang Wendong,Su Yuliang,Mu Lijun,et al.Influencing factors of stimulated reservoir volume of vertical wells in tight oil reservoirs[J].Journal of China University of Petroleum:Edition of Natural Science,2013,37(3):93-97.王文东,苏玉亮,慕立俊,等.致密油藏直井体积压裂储层改造体积的影响因素[J].中国石油大学学报:自然科学版,2013,37(3):93-97.
[16]Zhang J,Zhu D,Hill A D.Water-induced damage to proppedfracture conductivity in shale formations[J].SPE Production&Operations,2016,31(2):147-156.
[17]Zhang J,Ouyang L,Zhu D,et al.Experimental and numerical studies of reduced fracture conductivity due to proppant embedment in the shale reservoir[J].Journal of Petroleum Science and Engineering,2015,130:37-45.
[18]Zhang J,Zhu D,Hill A D.A new theoretical method to calculate shale fracture conductivity based on the population balance equation[J].Journal of Petroleum Science and Engineering,2015,134:40-48.
[19]Zhang J,Kamenov A,Zhu D,et al.Measurement of realistic fracture conductivity in the Barnett shale[J].Journal of Unconventional Oil and Gas Resources,2015,11(11):44-52.
[2]Wei Chenhui.Damage Model for Coal and Rock Under Coupled Thermal-Hydraulic-Mechanical Conditions and Its Applications[D].Shenyang:Northeastern University,2012:13-36.魏晨慧.热流固耦合条件下煤岩体损伤模型及其应用[D].沈阳:东北大学,2012:13-36.
[3]Lu Yinlong,Wang Lianguo.Numerical modeling of mining-induced fracturing and flow evolution in coal seam floor based on micro-crack growth[J].Journal of Mining &Safety Engineering,2015,32(6):889-897. 陆银龙,王连国.基于微裂纹演化的煤层底板损伤破裂与渗流演化过程数值模拟[J].采矿与安全工程学报,2015,32(6):889-897.
[4]Wang Yongliang,Zhuang Zhuo,Liu Zhanli,et al.Finite element analysis of transversely isotropic rock with mechanicalchemical-damage coupling[J].Engineering Mechanics,2016,30(1):105-113. 王永亮,庄茁,柳占立,等.横观各向同性岩石力学—化学—损伤耦合有限元分析[J].工程力学,2016,30(1):105-113.
[5]Mi Kaihua.Numerical Simulation of Meso-damage and Fracture of Full-graded Concrete[D].Kunming:Kunming University of Science and Technology,2015:78-79.糜凯华.全级配混凝土细观损伤及断裂数值模拟研究[D].昆明:昆明理工大学,2015:78-79.
[6]Zhu W C,Tang C A.Micromechanical model for simulating the fracture process of rock[J].Rock Mechanics and Rock Engineering,2004,37(1):25-56.
[7]Wang J H,Elsworth D,Zhu W C,et al.The influence of fracturing fluids on fracturing processes:A comparison between gas and water[C]∥American Rock Mechanics Association.49th US Rock Mechanics/Geomechanics Symposium.California:American Rock Mechanics Association,2015:1-9.
[8]Lu Y L,Elsworth D,Wang L G.Microcrack-based coupled damage and flow modeling of fracturing evolution in permeable brittle rocks[J].Computers and Geotechnics,2013,49:226-244.
[9]Pogacnik J,Elsworth D,O’Sullivan M,et al.A damage mechanics approach to the simulation of hydraulic fracturing/shearing around a geothermal injection well[J].Computers and Geotechnics,2016,71:338-351.
[10]Li X,Wang J H,Elsworth D.Stress redistribution and fracture propagation during restimulation of gas shale reservoirs[J].Journal of Petroleum Science and Engineering,2017,154:150-160.
[11]Wang Y,Liu Z,Yang H,et al.FE analysis of rock with hydraulic-mechanical coupling based on continuum damage evolution[J].Mathematical Problems in Engineering,2016,2016:1-9.
[12]Oh C S,Kim N H,Kim Y J,et al.A finite element ductile failure simulation method using stress-modified fracture strain model[J].Engineering Fracture Mechanics,2011,78(1):124-137.
[13]Gasch T,Ansell A.Cracking in quasi-brittle materials using isotropic damage mechanics[C]//Comsol.Proceedings of 2016Comsol Conference.Munich:Comsol,2016:1-25.
[14]Wang Wendong,Zhao Guangyuan,Su Yuliang,et al.Application of network fracturing technology to tight oil reservoirs[J].Xinjiang Petroleum Geology,2013,34(3):345-348.王文东,赵广渊,苏玉亮,等.致密油藏体积压裂技术应用[J].新疆石油地质,2013,34(3):345-348.
[15]Wang Wendong,Su Yuliang,Mu Lijun,et al.Influencing factors of stimulated reservoir volume of vertical wells in tight oil reservoirs[J].Journal of China University of Petroleum:Edition of Natural Science,2013,37(3):93-97.王文东,苏玉亮,慕立俊,等.致密油藏直井体积压裂储层改造体积的影响因素[J].中国石油大学学报:自然科学版,2013,37(3):93-97.
[16]Zhang J,Zhu D,Hill A D.Water-induced damage to proppedfracture conductivity in shale formations[J].SPE Production&Operations,2016,31(2):147-156.
[17]Zhang J,Ouyang L,Zhu D,et al.Experimental and numerical studies of reduced fracture conductivity due to proppant embedment in the shale reservoir[J].Journal of Petroleum Science and Engineering,2015,130:37-45.
[18]Zhang J,Zhu D,Hill A D.A new theoretical method to calculate shale fracture conductivity based on the population balance equation[J].Journal of Petroleum Science and Engineering,2015,134:40-48.
[19]Zhang J,Kamenov A,Zhu D,et al.Measurement of realistic fracture conductivity in the Barnett shale[J].Journal of Unconventional Oil and Gas Resources,2015,11(11):44-52.