基于损伤理论的水力压裂人工裂缝应力场研究
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摘要
水力压裂施工是一个产层岩石中的各种孔洞和微裂纹等在强烈的压裂液作用下不断生长交叉并最终贯通汇合成宏观水力裂缝的过程，宏观裂纹以及岩石内生长的微裂纹组在一定程度上增加了储层的渗流体积进而提高了油气的渗流能力，同时也对整个岩石的力学性能造成了不可逆的损伤劣化。因此，完全可以借助损伤力学的研究方法和理论成果来对水力压裂施工过程中压裂液对地层岩体的这种劣化效果进行分析描述，进而能准确计算水力压裂裂缝的有效波及范围。
本文结合使用损伤力学和断裂力学的研究方法和理论成果来描述压裂过程中压裂裂缝对储层岩体的损伤劣化效果，对深入研究裂缝的产生机制，解决实际工程问题有一定的指导意义和创新性。
首先针对本文所使用的损伤力学的概念和理论进行简单介绍，重点论述了损伤变量的概念以及不同损伤变量的表述方法，对损伤力学的等效原理，尤其是等效应变原理进行分析和阐述；其次描述了压裂施工中裂缝周围岩石的受力特点，分析了岩石损伤的形成演化机理，在合理简化岩石的σ-ε曲线基础上，以此为前提并结合适当的假设推导出了基于损伤理论的地层岩石本构关系模型；假定岩体为双孔双渗介质，在综合考虑地应力场，渗流场的作用下，结合断裂力学理论，推导裂缝全场应力表达式，分析微元体受力，得出微分平衡方程；建立人工裂缝的损伤力学模型，将裂缝周围岩体划分为无损区、损伤区和破坏区，分别对各个区域的边界方程和应力状态进行计算求解，确定不同区域的延伸半径和岩体的应力分布，计算实际施工状态下裂缝的损伤应力状况并加以分析。
Hydraulic fracturing is a process in which a variety of holes and micro-crack growsunder the strong fracturing fluid cross and eventually through, into macro-hydraulic fractureand macroscopic crack growth within a rock micro crack group thereby increasing the seepa-ge of oil and gas reservoir seepage volume increased to a certain extent, but also cause irrev-ersible damage deterioration of the mechanical properties of the whole rock. With the researchmethods and theoretical results of the damage mechanics to hydraulic fracturing fracturingfluid in the construction process to analyze the effect of this degradation of the stratigraphicrock description, and thus can accurately calculate the effective spread range of hydraulicfractures.
In this paper, the author used methods and theoretical results in damage mechanics andfracture mechanics to describe the fracturing process of fracturing the reservoir rock damagedeterioration effect on the mechanism of in-depth study of cracks, to solve practical engineer-ing problems with some guiding significance and innovation.
First, a brief introduction to the concepts and theories of damage mechanics used in thisarticle, focusing on the formulation of the concept of the damage variable and damagevariable, the equivalence principle of damage mechanics, especially the analysis andelaboration of the equivalent strain principle; Second, it describes the mechanicalcharacteristics of the cracks in the rock surrounding the fracturing operation, a rock formationand evolution mechanism of injury, reasonable simplification σ-ε curve of rock on the basisof this premise, combined with appropriate assumptions derivation out based on the damagetheory of the formation rock constitutive model; assumed rock holes dual-permeability media,inthe considered stress field, seepage field effect, combined with fracture mechanics theoryderived expression of the cracks in the audience stress analysis element by the force, obtaineddifferential balance equations; damage mechanics model of artificial cracks, cracks thesurrounding rock mass is divided into non-destructive zone, damage zone and destruction zo-ne, all regions of the boundary equations and the stress state is calculated solving to determinethe different regions of extension of the radius and the stress distribution of the rock mass tocalculate the crackdamage stress conditions in the state of actual construction and analysis.
本文结合使用损伤力学和断裂力学的研究方法和理论成果来描述压裂过程中压裂裂缝对储层岩体的损伤劣化效果，对深入研究裂缝的产生机制，解决实际工程问题有一定的指导意义和创新性。
首先针对本文所使用的损伤力学的概念和理论进行简单介绍，重点论述了损伤变量的概念以及不同损伤变量的表述方法，对损伤力学的等效原理，尤其是等效应变原理进行分析和阐述；其次描述了压裂施工中裂缝周围岩石的受力特点，分析了岩石损伤的形成演化机理，在合理简化岩石的σ-ε曲线基础上，以此为前提并结合适当的假设推导出了基于损伤理论的地层岩石本构关系模型；假定岩体为双孔双渗介质，在综合考虑地应力场，渗流场的作用下，结合断裂力学理论，推导裂缝全场应力表达式，分析微元体受力，得出微分平衡方程；建立人工裂缝的损伤力学模型，将裂缝周围岩体划分为无损区、损伤区和破坏区，分别对各个区域的边界方程和应力状态进行计算求解，确定不同区域的延伸半径和岩体的应力分布，计算实际施工状态下裂缝的损伤应力状况并加以分析。
Hydraulic fracturing is a process in which a variety of holes and micro-crack growsunder the strong fracturing fluid cross and eventually through, into macro-hydraulic fractureand macroscopic crack growth within a rock micro crack group thereby increasing the seepa-ge of oil and gas reservoir seepage volume increased to a certain extent, but also cause irrev-ersible damage deterioration of the mechanical properties of the whole rock. With the researchmethods and theoretical results of the damage mechanics to hydraulic fracturing fracturingfluid in the construction process to analyze the effect of this degradation of the stratigraphicrock description, and thus can accurately calculate the effective spread range of hydraulicfractures.
In this paper, the author used methods and theoretical results in damage mechanics andfracture mechanics to describe the fracturing process of fracturing the reservoir rock damagedeterioration effect on the mechanism of in-depth study of cracks, to solve practical engineer-ing problems with some guiding significance and innovation.
First, a brief introduction to the concepts and theories of damage mechanics used in thisarticle, focusing on the formulation of the concept of the damage variable and damagevariable, the equivalence principle of damage mechanics, especially the analysis andelaboration of the equivalent strain principle; Second, it describes the mechanicalcharacteristics of the cracks in the rock surrounding the fracturing operation, a rock formationand evolution mechanism of injury, reasonable simplification σ-ε curve of rock on the basisof this premise, combined with appropriate assumptions derivation out based on the damagetheory of the formation rock constitutive model; assumed rock holes dual-permeability media,inthe considered stress field, seepage field effect, combined with fracture mechanics theoryderived expression of the cracks in the audience stress analysis element by the force, obtaineddifferential balance equations; damage mechanics model of artificial cracks, cracks thesurrounding rock mass is divided into non-destructive zone, damage zone and destruction zo-ne, all regions of the boundary equations and the stress state is calculated solving to determinethe different regions of extension of the radius and the stress distribution of the rock mass tocalculate the crackdamage stress conditions in the state of actual construction and analysis.
引文
[1]王鸿勋．水力压裂原理[M]．第一版，石油工业出版社，1987．
[2]张士诚，张劲．压裂开发理论与应用[M]．石油大学出版社，2003年第1版，27~37．
[3]杨秀夫，陈勉．国内外水力压裂技术现状及发展趋势[J]．钻采工艺，1998，21(4)：21~25．
[4]何艳青，王鸿勋．用数值模拟方法预测压裂井的生产动态[J]．石油大学学报，1990年，16~25．
[5] Chen, H. Y. Teufel, L. W, and Lee, R:"Coupled Fluid Flow and Geomechanics inReservoir Study-1.Theory and Governing Equations," paper SPE30752presented at theSPE Annual Technical Conference&Exhibition．Dallas, TX,22~25Oct.1995.
[6]闫建文，王群嶷，张士诚．低渗透油田压裂注水采油整体优化方法[J]．大庆石油地质与开发，2000年第5期，50~52．
[7] Degue. K. M.and Ladamyi．B．Effect of fluid penetration and pressurizing rate onhydraulic fracturing． Pacific Rocks2000． Girad． Liebman． Breeds andDoe(eds)．Balkema．Rotterdam．2000:181~188.
[8][美]米卡尔J．埃克诺米德斯，肯尼斯G．诺尔特编著；张保平，蒋阗，张汝生等译．油藏增产措施[M]．第三版，北京石油工业出版社，2002，230~310．
[9]王鸿勋，张士诚，水力压裂设计数值计算方法[M]．石油工业出版社，1998年第1版，342~353．
[10] Van Dam D. B. Papanastasiou P.de Pater C.J Impact of rock plasticity on hydraulicfracture propagation and closure[R]．SPE63172.
[11]刘建军，杜广林，薛强．水力压裂的连续损伤模型初探[J]．机械强度，2004，26(S)，134~137．
[12]余寿文，冯西桥编著．损伤力学[M]．清华大学出版社，1997，12，第1版．
[13]李兆霞．损伤力学及其应用[M]．北京：科学出版社：2002．
[14] Lemaitre. How to use damage mechanics. Nuclear Engineering and Design,1984,80(3):233~245.
[15] J Lemaitre, Sermage J P, Desmorat R.A two scale damage concept applied to fatigue.International Journal of Fracture,1999,97(1-4):67~81.
[16]村上澄男．损伤力学-材料损伤与断裂的连续介质力学处理[J]．材料(日)：1982：2~22．
[17]余天庆，混凝土分段线性损伤模型[J]．岩石、混凝土断裂与强度．1982，2，14～16．
[18]易顺民，朱德珍．裂隙岩体损伤力学导论[M]．科学出版社．2005，9．
[19]冯西桥，余寿文著．准脆性材料细观损伤力学[M]．高等教育出版社，2002．
[20]杨天鸿，唐春安，梁正召，等．脆性岩石破裂过程损伤与渗流耦合数值模型研究[J]．力学学报，2003，35(5)：533~541．
[21]杨天鸿，徐涛，唐春安，冯启言．脆性岩石破裂过程渗透性演化试验研究[J]．东北大学学报，2003，24(10)：974~977．
[22]杨天鸿，赵兴东．开采引起围岩渗透性演化规律的数值模拟[J]．岩石力学与工程学报，2003，22(S1)：2386~2389．
[23]李连崇，杨天鸿，唐春安．岩石水压致裂过程的耦合分析[J]．岩石力学与工程学报，2003，22(7)：1060~1066．
[24]陈要辉．海拉尔油田凝灰质储层水力压裂力学理论研究[D]．大庆石油学院博士学位论文，2008．
[25]张平，赵金洲，郭大立．水力压裂裂缝三维延伸数值模拟研究[J]．石油钻采工艺，1997，19（3）：53~59．
[26] B． A dibhatla, K． K． Mohanty Oil Recovery From Fractured Carbonates bySurfactant-Aided Gravity Drainage Laboratory Experiments and MechanisticSimulations[R]. SPE.997732008.
[27] R. Pongratz, M. Stanojcic, V. Martysevich．Pin Point Multistage Fracturing StimulationGlobal Applications and Case Histories from Russia[R]. SPE114786.
[28] Pijush Paul and Mark Zoback, and Peter Hennings, ConovoPhillips, Fluid Flow in aFractured Reservoir Using a Geomachanically-Constrained Fault Zone Damage Modelfor Reservoir Simulation[R].SPE110542.
[29] Wright, C. A. and Conant, R.A:"Hydraulic Fracture Reorientation in Primary andSecondary Recovery from low-permeability Reservoirs," paper SPE30494presented atthe1995SPE Annual and Technical Conference and Exhibition,Dallas,Oct.22~25.
[30]夏海帮，陈刚，韦建伟．苏北地区低渗储层压裂改造工艺技术及效果评价[J]．工程论坛，2006，3．
[31]王群嶷，冯立．大庆低渗透油田薄差油层勘探开发整体压裂优化设计应用与实践[J]．中国石油勘探，2005年第6期，56~60．
[32] Arthur S. Metcalf, and Juan Coronado, A Case Study of Hydraulically Fractured EddyCounty, New Mexico, Horizontal Wolfcamp Producers[R]. SPE116646.
[33]侯洪涛，邹群．先进的多层压裂技术[J]．国外油田工程，2007，2(23)，2
[34] Adib A. Al-Mumen, Mohammedl. Al-Umran and Pradeep Agrawal. Unique Solution forFracture Isolation Resolves Water Gas Breakthrough Challenges in Horizontal Slim HoleWell[R]. SPE115270.
[35]姜瑞忠，蒋廷学，汪永利．水力压裂技术的近期发展及展望[J]．石油钻采工艺，2004，4，vol26，4．
[36]刘伟．水力压裂压力动态试井分析与增产效果提高方法研究[D]．中国地质大学(北京)博士学位论文，2005，5.
[37]李凡磊，张志海，刘更新．转向压裂技术在江苏油田的应用[J]．油气井测试，2006，2(15)，1．
[38] Liu He, Wang Zhong guo, Wang Qingping, Yao Hongtian, ect-Study and Application ofthe Technology of subdivision Controlled Limited entry Fracturing in Reservoir withMany Thin Layers[R].SPE115371.
[39]吴月先．国内大型压裂技术再创新记录[J]．Oil FIELD EQUIPMENT，2006，vol35，1．
[40] E. Artun, T. Ertekin, and R. Watson, ect, Optimized Design of Cyclic Pressure Pulsing ina Depleted, Naturally Fractured Reservoir[R].SPE117762.
[41] V. S. Mironov, I．R．Diyashev, and A. V. Brovchuk, ect Determination of FractureAzimuth in Palnikovskoye Field Western Siberia Using Tiltmeter Technology[R]SPE117097
[42] R. J. Curtice and Carlson, and M. Stahl Relative-Permeability Modifiers Used inConjunction With Hydraulic Fracturing Can Increase Hydrocarbon Production andReduce Water Production[R] SPE117603.
[43]唐庆春．整体压裂垂直裂缝数值模拟方法研究[D]．吉林大学硕士学位论文，2006年．
[44]钟显，赵立志，杨旭．生化处理压裂返排液的试验研究[J]．石油与天然气化工，2006，35，1．
[45] Krajcinovic D. Damage Mechanics. Mech Mater,1989(8):117~119．
[46] Dougill J W, Lau J and N J. Mechanics in Eng. ASCE. EMD.,1976:222～355.
[47] Dragon A and Mroz Z. A continuum model for plastic behavior of rock and concrete. Int.J. Engineering Science.1979,17:121～137.
[48] LemaitreJ.and Chaboche J.L.Aspect phenomen~ologique dela Ruptrue Parendommagement.J.demec.APPl.Vol.2,No.3,1978.
[49] LemaitreJ. How to use damage mechanics. Nuelear engineering and design, Vol.80,PP233~245,1984.
[50] ChaboeheJ. L. Lifetime predictions and cumulative damage under high temperatureonditionsInt. Sum P. on low cycle fatigue and life prediction, Firming. Franee ASTMST P.770(1980).
[51] ChaboeheJ. L. Continuous damage mechanics: a tool to describe phenomena beforecrack initiation. Nuclear Engineering and design，Vol．64，PP．233~247，1981.
[52] Orsten Friedel, George Michedlishvili, Aron Behr, SPE, Hans Dieter Voigt, FriederHafner, Freiberg University, Comparative Analysis of Damage Mechanisms inFractured Gas Wells[R], SPE107662.
[53] Hassan Chaabouni, Scholumberger, Pierrer Baux, Dasa Manalu, Muhammead Sobirin,Tobal E&P Indonesie, Philippe Enkababian, Schlumberger, A Case Study of Oil BasedMud Effect on Horizontal Well Productivity[R],SPE112077.
[54] R.A. Holicek, J. Adachi, L. A. Viloria, A. I. Mese, and Y. Traore, Schlumberger, and A. P.Singh and R. Hanssen, TOTAL, Surveillance and Diagnostics of Permanent BottomholeGauge Data Coupled With Geomechanical Modeling to Identify Sources of FormationDamage[R],SPE112429.
[55] Michael Byrne, Ian Patey, and Justin Green, Corex UK, A New Tool for Exploration andAppraisal~Formation Damage Evaluation[R], SPE107557.
[56] Krajcinovic D.Constitutive equation for damaging materials.J Appl Mech,1983(50):355~360.
[57] Gurson A L.Continuum theory of ductile rupture in void nucleation and growth partI:yield criteria and flow rules for porous ductile media.J Eng Mater Tech,1977(4):2~15.
[58] Krajeinovc D. Constitiltlve theories for solid with defective micro struture，damagemechanics and continuum modeling(Eds: N. Stubks and D.Krajeinovc),ASCE,NewYork.PP.39~56，1985
[59]马青．基于损伤理论的圆形水工压力隧洞围岩应力场分析[D]．长安大学硕士学位论文，2009．
[60]赵万春．水力压裂岩体非线性损伤演化研究[D]．东北石油大学博士学位论文，2009．
[61]李玉伟．水力压裂井井眼围岩损伤力学模型[D]．东北石油大学硕士学位论文，2009．
[62]张晓光．基于损伤理论重复压裂应力场研究[D]．东北石油大学硕士学位论文，2009．
[2]张士诚，张劲．压裂开发理论与应用[M]．石油大学出版社，2003年第1版，27~37．
[3]杨秀夫，陈勉．国内外水力压裂技术现状及发展趋势[J]．钻采工艺，1998，21(4)：21~25．
[4]何艳青，王鸿勋．用数值模拟方法预测压裂井的生产动态[J]．石油大学学报，1990年，16~25．
[5] Chen, H. Y. Teufel, L. W, and Lee, R:"Coupled Fluid Flow and Geomechanics inReservoir Study-1.Theory and Governing Equations," paper SPE30752presented at theSPE Annual Technical Conference&Exhibition．Dallas, TX,22~25Oct.1995.
[6]闫建文，王群嶷，张士诚．低渗透油田压裂注水采油整体优化方法[J]．大庆石油地质与开发，2000年第5期，50~52．
[7] Degue. K. M.and Ladamyi．B．Effect of fluid penetration and pressurizing rate onhydraulic fracturing． Pacific Rocks2000． Girad． Liebman． Breeds andDoe(eds)．Balkema．Rotterdam．2000:181~188.
[8][美]米卡尔J．埃克诺米德斯，肯尼斯G．诺尔特编著；张保平，蒋阗，张汝生等译．油藏增产措施[M]．第三版，北京石油工业出版社，2002，230~310．
[9]王鸿勋，张士诚，水力压裂设计数值计算方法[M]．石油工业出版社，1998年第1版，342~353．
[10] Van Dam D. B. Papanastasiou P.de Pater C.J Impact of rock plasticity on hydraulicfracture propagation and closure[R]．SPE63172.
[11]刘建军，杜广林，薛强．水力压裂的连续损伤模型初探[J]．机械强度，2004，26(S)，134~137．
[12]余寿文，冯西桥编著．损伤力学[M]．清华大学出版社，1997，12，第1版．
[13]李兆霞．损伤力学及其应用[M]．北京：科学出版社：2002．
[14] Lemaitre. How to use damage mechanics. Nuclear Engineering and Design,1984,80(3):233~245.
[15] J Lemaitre, Sermage J P, Desmorat R.A two scale damage concept applied to fatigue.International Journal of Fracture,1999,97(1-4):67~81.
[16]村上澄男．损伤力学-材料损伤与断裂的连续介质力学处理[J]．材料(日)：1982：2~22．
[17]余天庆，混凝土分段线性损伤模型[J]．岩石、混凝土断裂与强度．1982，2，14～16．
[18]易顺民，朱德珍．裂隙岩体损伤力学导论[M]．科学出版社．2005，9．
[19]冯西桥，余寿文著．准脆性材料细观损伤力学[M]．高等教育出版社，2002．
[20]杨天鸿，唐春安，梁正召，等．脆性岩石破裂过程损伤与渗流耦合数值模型研究[J]．力学学报，2003，35(5)：533~541．
[21]杨天鸿，徐涛，唐春安，冯启言．脆性岩石破裂过程渗透性演化试验研究[J]．东北大学学报，2003，24(10)：974~977．
[22]杨天鸿，赵兴东．开采引起围岩渗透性演化规律的数值模拟[J]．岩石力学与工程学报，2003，22(S1)：2386~2389．
[23]李连崇，杨天鸿，唐春安．岩石水压致裂过程的耦合分析[J]．岩石力学与工程学报，2003，22(7)：1060~1066．
[24]陈要辉．海拉尔油田凝灰质储层水力压裂力学理论研究[D]．大庆石油学院博士学位论文，2008．
[25]张平，赵金洲，郭大立．水力压裂裂缝三维延伸数值模拟研究[J]．石油钻采工艺，1997，19（3）：53~59．
[26] B． A dibhatla, K． K． Mohanty Oil Recovery From Fractured Carbonates bySurfactant-Aided Gravity Drainage Laboratory Experiments and MechanisticSimulations[R]. SPE.997732008.
[27] R. Pongratz, M. Stanojcic, V. Martysevich．Pin Point Multistage Fracturing StimulationGlobal Applications and Case Histories from Russia[R]. SPE114786.
[28] Pijush Paul and Mark Zoback, and Peter Hennings, ConovoPhillips, Fluid Flow in aFractured Reservoir Using a Geomachanically-Constrained Fault Zone Damage Modelfor Reservoir Simulation[R].SPE110542.
[29] Wright, C. A. and Conant, R.A:"Hydraulic Fracture Reorientation in Primary andSecondary Recovery from low-permeability Reservoirs," paper SPE30494presented atthe1995SPE Annual and Technical Conference and Exhibition,Dallas,Oct.22~25.
[30]夏海帮，陈刚，韦建伟．苏北地区低渗储层压裂改造工艺技术及效果评价[J]．工程论坛，2006，3．
[31]王群嶷，冯立．大庆低渗透油田薄差油层勘探开发整体压裂优化设计应用与实践[J]．中国石油勘探，2005年第6期，56~60．
[32] Arthur S. Metcalf, and Juan Coronado, A Case Study of Hydraulically Fractured EddyCounty, New Mexico, Horizontal Wolfcamp Producers[R]. SPE116646.
[33]侯洪涛，邹群．先进的多层压裂技术[J]．国外油田工程，2007，2(23)，2
[34] Adib A. Al-Mumen, Mohammedl. Al-Umran and Pradeep Agrawal. Unique Solution forFracture Isolation Resolves Water Gas Breakthrough Challenges in Horizontal Slim HoleWell[R]. SPE115270.
[35]姜瑞忠，蒋廷学，汪永利．水力压裂技术的近期发展及展望[J]．石油钻采工艺，2004，4，vol26，4．
[36]刘伟．水力压裂压力动态试井分析与增产效果提高方法研究[D]．中国地质大学(北京)博士学位论文，2005，5.
[37]李凡磊，张志海，刘更新．转向压裂技术在江苏油田的应用[J]．油气井测试，2006，2(15)，1．
[38] Liu He, Wang Zhong guo, Wang Qingping, Yao Hongtian, ect-Study and Application ofthe Technology of subdivision Controlled Limited entry Fracturing in Reservoir withMany Thin Layers[R].SPE115371.
[39]吴月先．国内大型压裂技术再创新记录[J]．Oil FIELD EQUIPMENT，2006，vol35，1．
[40] E. Artun, T. Ertekin, and R. Watson, ect, Optimized Design of Cyclic Pressure Pulsing ina Depleted, Naturally Fractured Reservoir[R].SPE117762.
[41] V. S. Mironov, I．R．Diyashev, and A. V. Brovchuk, ect Determination of FractureAzimuth in Palnikovskoye Field Western Siberia Using Tiltmeter Technology[R]SPE117097
[42] R. J. Curtice and Carlson, and M. Stahl Relative-Permeability Modifiers Used inConjunction With Hydraulic Fracturing Can Increase Hydrocarbon Production andReduce Water Production[R] SPE117603.
[43]唐庆春．整体压裂垂直裂缝数值模拟方法研究[D]．吉林大学硕士学位论文，2006年．
[44]钟显，赵立志，杨旭．生化处理压裂返排液的试验研究[J]．石油与天然气化工，2006，35，1．
[45] Krajcinovic D. Damage Mechanics. Mech Mater,1989(8):117~119．
[46] Dougill J W, Lau J and N J. Mechanics in Eng. ASCE. EMD.,1976:222～355.
[47] Dragon A and Mroz Z. A continuum model for plastic behavior of rock and concrete. Int.J. Engineering Science.1979,17:121～137.
[48] LemaitreJ.and Chaboche J.L.Aspect phenomen~ologique dela Ruptrue Parendommagement.J.demec.APPl.Vol.2,No.3,1978.
[49] LemaitreJ. How to use damage mechanics. Nuelear engineering and design, Vol.80,PP233~245,1984.
[50] ChaboeheJ. L. Lifetime predictions and cumulative damage under high temperatureonditionsInt. Sum P. on low cycle fatigue and life prediction, Firming. Franee ASTMST P.770(1980).
[51] ChaboeheJ. L. Continuous damage mechanics: a tool to describe phenomena beforecrack initiation. Nuclear Engineering and design，Vol．64，PP．233~247，1981.
[52] Orsten Friedel, George Michedlishvili, Aron Behr, SPE, Hans Dieter Voigt, FriederHafner, Freiberg University, Comparative Analysis of Damage Mechanisms inFractured Gas Wells[R], SPE107662.
[53] Hassan Chaabouni, Scholumberger, Pierrer Baux, Dasa Manalu, Muhammead Sobirin,Tobal E&P Indonesie, Philippe Enkababian, Schlumberger, A Case Study of Oil BasedMud Effect on Horizontal Well Productivity[R],SPE112077.
[54] R.A. Holicek, J. Adachi, L. A. Viloria, A. I. Mese, and Y. Traore, Schlumberger, and A. P.Singh and R. Hanssen, TOTAL, Surveillance and Diagnostics of Permanent BottomholeGauge Data Coupled With Geomechanical Modeling to Identify Sources of FormationDamage[R],SPE112429.
[55] Michael Byrne, Ian Patey, and Justin Green, Corex UK, A New Tool for Exploration andAppraisal~Formation Damage Evaluation[R], SPE107557.
[56] Krajcinovic D.Constitutive equation for damaging materials.J Appl Mech,1983(50):355~360.
[57] Gurson A L.Continuum theory of ductile rupture in void nucleation and growth partI:yield criteria and flow rules for porous ductile media.J Eng Mater Tech,1977(4):2~15.
[58] Krajeinovc D. Constitiltlve theories for solid with defective micro struture，damagemechanics and continuum modeling(Eds: N. Stubks and D.Krajeinovc),ASCE,NewYork.PP.39~56，1985
[59]马青．基于损伤理论的圆形水工压力隧洞围岩应力场分析[D]．长安大学硕士学位论文，2009．
[60]赵万春．水力压裂岩体非线性损伤演化研究[D]．东北石油大学博士学位论文，2009．
[61]李玉伟．水力压裂井井眼围岩损伤力学模型[D]．东北石油大学硕士学位论文，2009．
[62]张晓光．基于损伤理论重复压裂应力场研究[D]．东北石油大学硕士学位论文，2009．
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