动态内压力下油田超深井中厚壁套管的动力学响应和实验验证
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摘要
引入中间主应力系数和拉压强度比,采纳统一强度理论求解动态内压力下两封闭末端、两开放末端和平面应变厚壁套管弹塑性极限内压力的解析解。塑性流动最初发生在厚壁套管内壁,且被周围的弹性材料所约束。数值模拟表明,弹性极限内压力随拉压强度比的降低和中间主应力系数的增加而增加;两封闭末端厚壁套管的弹性极限内压力最大,两开放末端厚壁套管的最小,平面应变厚壁套管的在两开放末端和两封闭末端之间;分界面的临界半径随动态内压力的变大而变大;若动态内压力增加时,厚壁套管从弹性变形转变为弹塑性变形,分界面的临界半径自内半径增大至外半径;塑性极限内压力随拉压强度比的减少而增加;随外内直径比的变大,当相等的统一强度理论参数时,两封闭末端、两开放末端和平面应变厚壁套管的塑性极限内压力之间的差距变小;弹性极限内压力低于塑性极限内压力;塑性极限内压力的理论数据与测试数据之间的相对误差为-3%～-9%,国际标准化组织样板数据与测试数据之间的相对误差为-12%～-25%,美国石油协会平均线与测试数据之间的相对误差为-16%～-33%。比较显示,厚壁套管塑性极限内压力公式更接近测试数据。
Introducing the intermediate principal stress coefficient and tensile-to-compressive strength ratio,the analytical solutions for elastic and plastic ultimate inside pressures in thick-walled casing respectively with two closed ends,two open ends and plane strain under kinetic inside pressure are obtained using the unified strength theory.Plastic flow first occurs on inside wall of the thick-walled casing,and is restricted by the surrounding elastic material.Numerical emulation displays that the elastic ultimate inside pressure adds as the tensile-to-compressive strength ratio decreases and the intermediate principal stress coefficient enhances.The value of the elastic ultimate inside pressure for the thick-walled casing with two closed ends is largest,followed by value for the plane strain one,and value for one with two open ends is minimal.The interfacial critical radius becomes larger due to the increase of the kinetic inside pressure.If the kinetic inside pressure ascends,the thick-walled casing diverts from elastic deformation to elastoplastic deformation and the interfacial critical radius expands from inside radius to outside radius.The plastic ultimate inside pressure gains as the tensile-to-compressive strength ratio reduces.The differences among the plastic ultimate inside pressures of thick-walled casings with two closed ends,two open ends and plane strain become smaller with the increment of the outside-to-inside diameter ratio for the equivalent unified strength theory parameters.The elastic ultimate inside pressure is lower than plastic ultimate's.The relative error between theoretical values and test data for plastic ultimate inside pressure is between-3%～-9%.The relative warp between international standardization organization's template data and test data is between-12%～-25%.The relative windage between American petroleum institute's average lines and test data is between-16%～-33%.Comparisons show that the current plastic ultimate inside pressure's equation in thickwalled casing is closer to test data.
Introducing the intermediate principal stress coefficient and tensile-to-compressive strength ratio,the analytical solutions for elastic and plastic ultimate inside pressures in thick-walled casing respectively with two closed ends,two open ends and plane strain under kinetic inside pressure are obtained using the unified strength theory.Plastic flow first occurs on inside wall of the thick-walled casing,and is restricted by the surrounding elastic material.Numerical emulation displays that the elastic ultimate inside pressure adds as the tensile-to-compressive strength ratio decreases and the intermediate principal stress coefficient enhances.The value of the elastic ultimate inside pressure for the thick-walled casing with two closed ends is largest,followed by value for the plane strain one,and value for one with two open ends is minimal.The interfacial critical radius becomes larger due to the increase of the kinetic inside pressure.If the kinetic inside pressure ascends,the thick-walled casing diverts from elastic deformation to elastoplastic deformation and the interfacial critical radius expands from inside radius to outside radius.The plastic ultimate inside pressure gains as the tensile-to-compressive strength ratio reduces.The differences among the plastic ultimate inside pressures of thick-walled casings with two closed ends,two open ends and plane strain become smaller with the increment of the outside-to-inside diameter ratio for the equivalent unified strength theory parameters.The elastic ultimate inside pressure is lower than plastic ultimate's.The relative error between theoretical values and test data for plastic ultimate inside pressure is between-3%～-9%.The relative warp between international standardization organization's template data and test data is between-12%～-25%.The relative windage between American petroleum institute's average lines and test data is between-16%～-33%.Comparisons show that the current plastic ultimate inside pressure's equation in thickwalled casing is closer to test data.
引文
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[15]金乘武,王立忠,张永强.薄壁管道爆破压力的强度差异效应与强度准则影响[J].应用数学和力学,2012,33(11):1266-1274.Jin Chengwu,Wang Lizhong,Zhang Yongqiang.Strength differential effect and influence of strength criterion on burst pressure of thin-walled pipelines[J].Applied Mathematics and Mechanics,2012,33(11):1266-1274.
[16]Zhu Xiankui,Leis Brian N.Influence of yield-to-tensile strength ratio on failure assessment of corroded pipelines[J].Transactions of the ASME Journal of Pressure Vessel Technology,2005,127(4):436-442.
[17]徐栓强,俞茂宏.厚壁圆筒安定问题的统一解析解[J].机械工程学报,2004,40(9):23-27.Xu Shuanqiang,Yu Maohong.Unified analytical solution to shakedown problem of thick-walled cylinder[J].Chinese Journal of Mechanical Engineering,2004,40(9):23-27.
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[20]齐念,叶继红.弹塑性DEM方法在杆系结构中的应用研究[J].振动工程学报,2017,30(6):929-937.Qi Nian,Ye Jihong.Application of discrete element method in member structures:elastoplastic analysis[J].Journal of Vibration Engineering,2017,30(6):929-937.
[21]俞茂宏.强度理论新体系:理论、发展和应用[M].第2版.西安:西安交通大学出版社,2011:152-165,340.
[22]田红亮,何孔德,陈从平,等.采用俞茂宏统一强度理论求解套管的极限外压强[J].西安交通大学学报,2018,52(5):1-11,87.Tian Hongliang,He Kongde,Chen Congping,et al.Solving ultimate outer pressure of casing by Yu's unified strength theory[J].Journal of Xi'an Jiaotong U-niversity,2018,52(5):1-11,87.
[23]图马Jan J,沃尔什Ronald A.工程数学手册[M].欧阳芳锐,张玉平,译.第4版.北京:科学出版社和美国麦格劳-希尔教育出版亚洲集团,2002:727,741.Tuma Jan J,Walsh Ronald A.Engineering Mathematics Handbook[M].Ouyang Fangrui,Zhang Yuping,translation.4th ed.Beijing:Science Press and USAMcGraw-Hill Education Press Asia Companies Incorporated,2002:727,741.
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[25]ISO 10400.PD CEN ISO/TR 10400,Petroleum and natural gas industries-equations and calculations for the properties of casing,tubing,drill pipe and line pipe used as casing or tubing[S].6th ed.Genève,Switzerland:International Organization for Standardization,2011.
[26]API Bulletin 5C3.Order No.G5C3S1,Bulletin on formulas and calculations for casing,tubing,drill pipe,and line pipe properties[S].6th ed.Washington District of Columbia,USA:American Petroleum Institute,1994.
[2]田红亮,刘芙蓉,方子帆,等.引入各向同性虚拟材料的固定结合部模型[J].振动工程学报,2013,26(4):561-573.Tian Hongliang,Liu Furong,Fang Zifan,et al.Immovable joint surface's model using isotropic virtual material[J].Journal of Vibration Engineering,2013,26(4):561-573.
[3]南波,武岳,孙浩田.缠绕型CFRP圆管轴压力学性能[J].工程力学,2017,34(1):92-100.Nan Bo,Wu Yue,Sun Haotian.Mechanical properties of filament-wound CFRP tube under axially compressive load[J].Engineering Mechanics,2017,34(1):92-100.
[4]陈朝伟.流变性地层套管等效外挤力[J].石油学报,2012,33(4):702-705.Chen Zhaowei.Equivalent external casing pressure in rheological strata[J].Acta Petrolei Sinica,2012,33(4):702-705.
[5]殷有泉,陈朝伟.软化材料厚壁筒的解析解及其稳定性分析[J].力学学报,2010,42(1):56-64.Yin Youquan,Chen Zhaowei.The analytical solutions of thick-walled cylinder of softening material and its stability[J].Chinese Journal of Theoretical and Applied Mechanics,2010,42(1):56-64.
[6]林元华,邓宽海,孙永兴,等.基于统一强度理论的套管全管壁屈服挤毁压力[J].石油勘探与开发,2016,43(3):462-468.Lin Yuanhua,Deng Kuanhai,Sun Yongxing,et al.Through-wall yield collapse pressure of casing based on unified strength theory[J].Petroleum Exploration and Development,2016,43(3):462-468.
[7]陈江,江学良,祝中林,等.偏压隧道模型振动台试验与数值模拟研究[J].振动工程学报,2017,30(4):660-669.Chen Jiang,Jiang Xueliang,Zhu Zhonglin,et al.Shaking table test and numerical simulation study on unsymmetrical loading tunnel model[J].Journal of Vibration Engineering,2017,30(4):660-669.
[8]张冠军,李天匀,朱翔.偏心柱壳自由振动的级数变换求解方法[J].振动工程学报,2017,30(6):947-954.Zhang Guanjun,Li Tianyun,Zhu Xiang.Series transformation method for the free vibration of eccentric cylindrical shell[J].Journal of Vibration Engineering,2017,30(6):947-954.
[9]Deng Kuanhai,Lin Yuanhua,Qiang Hu,et al.New high collapse model to calculate collapse strength for casing[J].Elsevier Engineering Failure Analysis,2015,58:295-306.
[10]Klever Frans J,Tamano Toshitaka.A new OCTGstrength equation for collapse under combined loads[J].Society of Petroleum Engineers Drilling and completion,2006,21(3):164-171,174-179.
[11]Sun Yongxing,Lin Yuanhua,Wang Zhongsheng,et al.A new OCTG strength equation for collapse under external load only[J].Transactions of the ASMEJournal of Pressure Vessel Technology,2011,133(1):011702-1-011702-5.
[12]Han Jianzeng,Shi Taihe.Equations calculate collapse pressures for casing strings[J].Oil and Gas Journal,2001,99(4):44-49.
[13]赵均海,李艳,张常光,等.基于统一强度理论的石油套管柱抗挤强度[J].石油学报,2013,34(5):969-976.Zhao Junhai,Li Yan,Zhang Changguang,et al.Collapsing strength for petroleum casing string based on unified strength theory[J].Acta Petrolei Sinica,2013,34(5):969-976.
[14]李艳,赵均海,李楠,等.基于统一强度理论的厚壁套管柱三轴抗拉强度[J].工程力学,2015,32(1):234-240.Li Yan,Zhao Junhai,Li Nan,et al.Tri-axial tension strength of thick-walled casing strings based on unified strength theory[J].Engineering Mechanics,2015,32(1):234-240.
[15]金乘武,王立忠,张永强.薄壁管道爆破压力的强度差异效应与强度准则影响[J].应用数学和力学,2012,33(11):1266-1274.Jin Chengwu,Wang Lizhong,Zhang Yongqiang.Strength differential effect and influence of strength criterion on burst pressure of thin-walled pipelines[J].Applied Mathematics and Mechanics,2012,33(11):1266-1274.
[16]Zhu Xiankui,Leis Brian N.Influence of yield-to-tensile strength ratio on failure assessment of corroded pipelines[J].Transactions of the ASME Journal of Pressure Vessel Technology,2005,127(4):436-442.
[17]徐栓强,俞茂宏.厚壁圆筒安定问题的统一解析解[J].机械工程学报,2004,40(9):23-27.Xu Shuanqiang,Yu Maohong.Unified analytical solution to shakedown problem of thick-walled cylinder[J].Chinese Journal of Mechanical Engineering,2004,40(9):23-27.
[18]Xu Shuanqiang,Yu Maohong.Shakedown analysis of thick-walled cylinders subjected to internal pressure with the unified strength criterion[J].Elsevier International Journal of Pressure Vessels and Piping,2005,82(9):706-712.
[19]刘鸿文.材料力学Ⅰ[M].第6版.北京:高等教育出版社,2017:222.Liu Hongwen.Mechanics of MaterialsⅠ[M].6th ed.Beijing:Higher Education Press,2017:222.
[20]齐念,叶继红.弹塑性DEM方法在杆系结构中的应用研究[J].振动工程学报,2017,30(6):929-937.Qi Nian,Ye Jihong.Application of discrete element method in member structures:elastoplastic analysis[J].Journal of Vibration Engineering,2017,30(6):929-937.
[21]俞茂宏.强度理论新体系:理论、发展和应用[M].第2版.西安:西安交通大学出版社,2011:152-165,340.
[22]田红亮,何孔德,陈从平,等.采用俞茂宏统一强度理论求解套管的极限外压强[J].西安交通大学学报,2018,52(5):1-11,87.Tian Hongliang,He Kongde,Chen Congping,et al.Solving ultimate outer pressure of casing by Yu's unified strength theory[J].Journal of Xi'an Jiaotong U-niversity,2018,52(5):1-11,87.
[23]图马Jan J,沃尔什Ronald A.工程数学手册[M].欧阳芳锐,张玉平,译.第4版.北京:科学出版社和美国麦格劳-希尔教育出版亚洲集团,2002:727,741.Tuma Jan J,Walsh Ronald A.Engineering Mathematics Handbook[M].Ouyang Fangrui,Zhang Yuping,translation.4th ed.Beijing:Science Press and USAMcGraw-Hill Education Press Asia Companies Incorporated,2002:727,741.
[24]Asbill W Tom,Livesay Ron,Crabtree Stephen,et al.DEA-130 modernization of tubular collapse performance properties[R].Drilling Engineering Association-130joint industry program,San Antonio,USA:Technical and Quality Solutions Incorporated,2002,26-31.
[25]ISO 10400.PD CEN ISO/TR 10400,Petroleum and natural gas industries-equations and calculations for the properties of casing,tubing,drill pipe and line pipe used as casing or tubing[S].6th ed.Genève,Switzerland:International Organization for Standardization,2011.
[26]API Bulletin 5C3.Order No.G5C3S1,Bulletin on formulas and calculations for casing,tubing,drill pipe,and line pipe properties[S].6th ed.Washington District of Columbia,USA:American Petroleum Institute,1994.