采用俞茂宏统一强度理论求解套管的极限外压强
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摘要
充分考虑拉压强度比和中间主应力系数,根据俞茂宏统一强度理论推导出在外压强下闭端、开端和平面应变套管弹塑性极限外压强的统一算法。数值仿真显示:随拉压强度比的减小和中间主应力系数的增大,弹性极限外压强增大;开端套管的弹性极限外压强最大,平面应变套管的次之,闭端套管的最小;塑性区的半径随外压强的增大而增大;当外压强增大时,套管由弹性状态进入弹塑性状态,塑性区的半径逐渐从内半径扩展到外半径;塑性极限外压强随拉压强度比的减小而增大;随外内半径比的增大,在同样的统一强度理论参数下,闭端、开端和平面应变的塑性极限外压强之间的差异增大,且塑性极限外压强大于弹性极限外压强;塑性极限外压强的计算值与试验测试值之间的相对误差为-4%~-9%,而国际标准化组织样板数据与试验测试值之间的相对误差为-12%~-25%,美国石油协会推荐数据与试验测试值之间的相对误差为-17%~-30%,表明文中的套管塑性极限外压强公式更接近试验值。
With due consideration of the tensile-to-compressible strength ratio and intermediate principal stress coefficient,a unified algorithm of elastic and plastic ultimate outer pressures for the casing with close end,open end or plane strain under the outer pressure is obtained following Yu's unified strength theory.Numerical simulation reveals that the elastic ultimate outer pressure increases with the decreasing tensile-to-compressible strength ratio and the increasing intermediate principal stress coefficient.The elastic ultimate outer pressure of the open end casing reaches the maximum,that of the close end casing reaches the minimum,and that of the plane strain casing is between the extremums.The plastic zone radius increases due to the increase of the outer pressure.When the outer pressure increases,the casing diverts from elastic state to elastoplastic state,and the plastic zone radius expands gradually from the inner radius to the outer radius.The plastic ultimate outer pressure increases with the decrease in the tensile-tocompressible strength ratio.The plastic ultimate outer pressure differences among close end,open end and plane strain casings increase with the increasing outer-to-inner radius ratio for the same unified strength theory parameters,and the plastic ultimate outer pressure of casing isgreater than the elastic one.The relative error between the computational value of plastic ultimate outer pressure and the measured one lies within the range from-4% to-9%,the relative error between ISO template datum and the measured value lies between-12% and-25%,and the relative error between the commendatory datum from American Petroleum Institute and the measured value lies between-17% and-30%.These comparisons show that the present plastic ultimate outer pressure equation for casing is closer to the experimentally measured value than those in other references.
With due consideration of the tensile-to-compressible strength ratio and intermediate principal stress coefficient,a unified algorithm of elastic and plastic ultimate outer pressures for the casing with close end,open end or plane strain under the outer pressure is obtained following Yu's unified strength theory.Numerical simulation reveals that the elastic ultimate outer pressure increases with the decreasing tensile-to-compressible strength ratio and the increasing intermediate principal stress coefficient.The elastic ultimate outer pressure of the open end casing reaches the maximum,that of the close end casing reaches the minimum,and that of the plane strain casing is between the extremums.The plastic zone radius increases due to the increase of the outer pressure.When the outer pressure increases,the casing diverts from elastic state to elastoplastic state,and the plastic zone radius expands gradually from the inner radius to the outer radius.The plastic ultimate outer pressure increases with the decrease in the tensile-tocompressible strength ratio.The plastic ultimate outer pressure differences among close end,open end and plane strain casings increase with the increasing outer-to-inner radius ratio for the same unified strength theory parameters,and the plastic ultimate outer pressure of casing isgreater than the elastic one.The relative error between the computational value of plastic ultimate outer pressure and the measured one lies within the range from-4% to-9%,the relative error between ISO template datum and the measured value lies between-12% and-25%,and the relative error between the commendatory datum from American Petroleum Institute and the measured value lies between-17% and-30%.These comparisons show that the present plastic ultimate outer pressure equation for casing is closer to the experimentally measured value than those in other references.
引文
[1]YU Maohong.Twin shear stress yield criterion[J].Elsevier International Journal of Mechanical Sciences,1983,25(1):71-74.
[2]俞茂宏,宋凌宇,陈萍.双剪应力准则的一个推广[J].西安交通大学学报,1983,17(3):65-69.YU Maohong,SONG Lingyu,CHEN Ping.A generalization of the twin-shear-stress-yield-criterion[J].Journal of Xi’an Jiaotong University,1983,17(3):65-69.
[3]俞茂宏,何丽南,宋凌宇.双剪应力强度理论及其推广[J].中国科学:A辑,1985,28(12):1113-1120.
[4]YU Maohong,HE Linan,SONG Lingyu.Twin shear stress theory and its generalization[J].Scientia Sinica:Series A,1985,28(11):1174-1183.
[5]俞茂宏,何丽南,刘春阳.广义双剪应力屈服准则及其推广[J].科学通报,1992,37(2):182-185.
[6]YU Maohong.Advances in strength theories for materials under complex stress state in the 20th century[J].ASME Applied Mechanics Reviews,2002,55(3):169-218.
[7]张智,刘志伟,谢玉洪,等.井筒载荷-腐蚀耦合作用对碳钢套管服役寿命的影响[J].石油学报,2017,38(3):342-347,362.ZHANG Zhi,LIU Zhiwei,XIE Yuhong,et al.Influence of shaft load-corrosion coupling on the service life of carbon steel casing pipe[J].Acta Petrolei Sinica,2017,38(3):342-347,362.
[8]张微敬,郭媛媛,刘时伟.钢筋套筒挤压连接的预制RC柱抗震性能试验研究[J].工程力学,2016,33(12):119-127.ZHANG Weijing,GUO Yuanyuan,LIU Shiwei.Experimental research on seismic behavior of precast RCcolumns with steel bars spliced by compressive sleeves[J].Engineering Mechanics,2016,33(12):119-127.
[9]杨睿月,黄中伟,李根生,等.连续油管带筛管双重管柱岩屑运移模型研究[J].中国石油大学学报(自然科学版),2016,40(5):87-95.YANG Ruiyue,HUANG Zhongwei,LI Gensheng,et al.Slotted liner sheathing coiled tubing:a dual-pipe model for cuttings transport[J].Journal of China University of Petroleum(Edition of Natural Science),2016,40(5):87-95.
[10]刘波,刘璐璐,徐薇,等.基于统一强度理论的TBM斜井围岩弹塑性解[J].采矿与安全工程学报,2016,33(5):819-826.LIU Bo,LIU Lulu,XU Wei,et al.Elastic-plastic analytical solution of TBM inclined shaft based on unified strength criterion[J].Journal of Mining&Safety Engineering,2016,33(5):819-826.
[11]朱瑞林,朱国林.热预应力自增强厚壁圆筒研究[J].机械工程学报,2016,52(17):168-175.ZHU Ruilin,ZHU Guolin.Study on autofrettaged thick-walled cylinders with thermal pre-stresses[J].Journal of Mechanical Engineering,2016,52(17):168-175.
[12]陈梁,茅献彪,李明,等.基于Drucker-Prager准则的深部巷道破裂围岩弹塑性分析[J].煤炭学报,2017,42(2):484-491.CHEN Liang,MAO Xianbiao,LI Ming,et al.Elastoplastic analysis of cracked surrounding rock in deep roadway based on Drucker-Prager criterion[J].Journal of China Coal Society,2017,42(2):484-491.
[13]FANG Jun,WANG Yanbin,GAO Deli.On the collapse resistance of multilayer cemented casing in directional well under anisotropic formation[J].Elsevier Journal of Natural Gas Science and Engineering,2015,26:409-418.
[14]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.
[15]刘奎,高德利,王宴滨,等.局部载荷对页岩气井套管变形的影响[J].天然气工业,2016,36(11):76-82.LIU Kui,GAO Deli,WANG Yanbin,et al.Effects of local load on shale gas well casing deformation[J].Natural Gas Industry,2016,36(11):76-82.
[16]李宁波,钱稼茹,刘时伟,等.部分竖向分布钢筋套筒挤压连接的预制剪力墙抗震性能试验研究[J].土木工程学报,2016,49(7):36-48.LI Ningbo,QIAN Jiaru,LIU Shiwei,et al.Experimental study on seismic behavior of pre-cast shear walls with partial vertical distributed steel bars pressed sleeve splicing[J].China Civil Engineering Journal,2016,49(7):36-48.
[17]齐昌广,刘汉龙,陈永辉,等.塑料套管混凝土桩承载试验及沉降计算方法研究[J].岩土工程学报,2016,38(12):2302-2308.QI Changguang,LIU Hanlong,CHEN Yonghui,et al.Bearing capacity tests and settlement calculation method of plastic tube cast-in-place concrete pile[J].Chinese Journal of Geotechnical Engineering,2016,38(12):2302-2308.
[18]曹雪叶,赵均海,张常光.基于统一强度理论的冻结壁弹塑性应力分析[J].岩土力学,2017,38(3):769-774,809.CAO Xueye,ZHAO Junhai,ZHANG Changguang.Elastoplastic stress analysis of frozen soil wall based on unified strength theory[J].Rock and Soil Mechanics,2017,38(3):769-774,809.
[19]YIN Fei,GAO Deli.Prediction of sustained production casing pressure and casing design for shale gas horizontal wells[J].Elsevier Journal of Natural Gas Science and Engineering,2015,25:159-165.
[20]HUANG Wenjun,GAO Deli.A theoretical study of the critical external pressure for casing collapse[J].Elsevier Journal of Natural Gas Science and Engineering,2015,27:290-297.
[21]XU S Q,YU M H.The effect of the intermediate principal stress on the ground response of circular openings in rock mass[J].Springer Rock Mechanics and Rock Engineering,2006,39(2):169-181.
[22]CHEN Zhanfeng,ZHU Weiping,DI Qinfeng,et al.Numerical and theoretical analysis of burst pressures for casings with eccentric wear[J].Elsevier Journal of Petroleum Science and Engineering,2016,145:585-591.
[23]ZHANG Hongkun,SUN Baojiang,YAN Guomin,et al.Distribution laws and effects analysis of casing external pressure taking elastic parameters matching into account[J].Elsevier Petroleum,2016,2(1):108-115.
[24]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.
[25]田红亮,彭文昱,何孔德,等.采用俞茂宏统一强度理论求解圆筒和球壳的极限值[J].西安交通大学学报,2018,52(3):1-11.TIAN Hongliang,PENG Wenyu,HE Kongde,et al.Solving limit values of cylinder and spherical shell adopting Yu’s unified strength theory[J].Journal of Xi’an Jiaotong University,2018,52(3):1-11.
[26]Petroleum and natural gas industries:formulae and calculation for casing,tubing,drill pipe and line pipe properties:ISO 10400[S].6th ed.Geneva,Switzerland:International Organization for Standardization,2007.
[27]Bulletin on formulas and calculations for casing,tubing,drill pipe,and line pipe properties:API Bulletin5C3[S].6th ed.Washington,USA:American Petroleum Institute,1994.
[28]ASBILL W T,CRABTREE S,PAYNE M L.DEA-130 modernization of tubular collapse performance properties[R].San Antonio,USA:Southwest Research Institute,2002.
[2]俞茂宏,宋凌宇,陈萍.双剪应力准则的一个推广[J].西安交通大学学报,1983,17(3):65-69.YU Maohong,SONG Lingyu,CHEN Ping.A generalization of the twin-shear-stress-yield-criterion[J].Journal of Xi’an Jiaotong University,1983,17(3):65-69.
[3]俞茂宏,何丽南,宋凌宇.双剪应力强度理论及其推广[J].中国科学:A辑,1985,28(12):1113-1120.
[4]YU Maohong,HE Linan,SONG Lingyu.Twin shear stress theory and its generalization[J].Scientia Sinica:Series A,1985,28(11):1174-1183.
[5]俞茂宏,何丽南,刘春阳.广义双剪应力屈服准则及其推广[J].科学通报,1992,37(2):182-185.
[6]YU Maohong.Advances in strength theories for materials under complex stress state in the 20th century[J].ASME Applied Mechanics Reviews,2002,55(3):169-218.
[7]张智,刘志伟,谢玉洪,等.井筒载荷-腐蚀耦合作用对碳钢套管服役寿命的影响[J].石油学报,2017,38(3):342-347,362.ZHANG Zhi,LIU Zhiwei,XIE Yuhong,et al.Influence of shaft load-corrosion coupling on the service life of carbon steel casing pipe[J].Acta Petrolei Sinica,2017,38(3):342-347,362.
[8]张微敬,郭媛媛,刘时伟.钢筋套筒挤压连接的预制RC柱抗震性能试验研究[J].工程力学,2016,33(12):119-127.ZHANG Weijing,GUO Yuanyuan,LIU Shiwei.Experimental research on seismic behavior of precast RCcolumns with steel bars spliced by compressive sleeves[J].Engineering Mechanics,2016,33(12):119-127.
[9]杨睿月,黄中伟,李根生,等.连续油管带筛管双重管柱岩屑运移模型研究[J].中国石油大学学报(自然科学版),2016,40(5):87-95.YANG Ruiyue,HUANG Zhongwei,LI Gensheng,et al.Slotted liner sheathing coiled tubing:a dual-pipe model for cuttings transport[J].Journal of China University of Petroleum(Edition of Natural Science),2016,40(5):87-95.
[10]刘波,刘璐璐,徐薇,等.基于统一强度理论的TBM斜井围岩弹塑性解[J].采矿与安全工程学报,2016,33(5):819-826.LIU Bo,LIU Lulu,XU Wei,et al.Elastic-plastic analytical solution of TBM inclined shaft based on unified strength criterion[J].Journal of Mining&Safety Engineering,2016,33(5):819-826.
[11]朱瑞林,朱国林.热预应力自增强厚壁圆筒研究[J].机械工程学报,2016,52(17):168-175.ZHU Ruilin,ZHU Guolin.Study on autofrettaged thick-walled cylinders with thermal pre-stresses[J].Journal of Mechanical Engineering,2016,52(17):168-175.
[12]陈梁,茅献彪,李明,等.基于Drucker-Prager准则的深部巷道破裂围岩弹塑性分析[J].煤炭学报,2017,42(2):484-491.CHEN Liang,MAO Xianbiao,LI Ming,et al.Elastoplastic analysis of cracked surrounding rock in deep roadway based on Drucker-Prager criterion[J].Journal of China Coal Society,2017,42(2):484-491.
[13]FANG Jun,WANG Yanbin,GAO Deli.On the collapse resistance of multilayer cemented casing in directional well under anisotropic formation[J].Elsevier Journal of Natural Gas Science and Engineering,2015,26:409-418.
[14]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.
[15]刘奎,高德利,王宴滨,等.局部载荷对页岩气井套管变形的影响[J].天然气工业,2016,36(11):76-82.LIU Kui,GAO Deli,WANG Yanbin,et al.Effects of local load on shale gas well casing deformation[J].Natural Gas Industry,2016,36(11):76-82.
[16]李宁波,钱稼茹,刘时伟,等.部分竖向分布钢筋套筒挤压连接的预制剪力墙抗震性能试验研究[J].土木工程学报,2016,49(7):36-48.LI Ningbo,QIAN Jiaru,LIU Shiwei,et al.Experimental study on seismic behavior of pre-cast shear walls with partial vertical distributed steel bars pressed sleeve splicing[J].China Civil Engineering Journal,2016,49(7):36-48.
[17]齐昌广,刘汉龙,陈永辉,等.塑料套管混凝土桩承载试验及沉降计算方法研究[J].岩土工程学报,2016,38(12):2302-2308.QI Changguang,LIU Hanlong,CHEN Yonghui,et al.Bearing capacity tests and settlement calculation method of plastic tube cast-in-place concrete pile[J].Chinese Journal of Geotechnical Engineering,2016,38(12):2302-2308.
[18]曹雪叶,赵均海,张常光.基于统一强度理论的冻结壁弹塑性应力分析[J].岩土力学,2017,38(3):769-774,809.CAO Xueye,ZHAO Junhai,ZHANG Changguang.Elastoplastic stress analysis of frozen soil wall based on unified strength theory[J].Rock and Soil Mechanics,2017,38(3):769-774,809.
[19]YIN Fei,GAO Deli.Prediction of sustained production casing pressure and casing design for shale gas horizontal wells[J].Elsevier Journal of Natural Gas Science and Engineering,2015,25:159-165.
[20]HUANG Wenjun,GAO Deli.A theoretical study of the critical external pressure for casing collapse[J].Elsevier Journal of Natural Gas Science and Engineering,2015,27:290-297.
[21]XU S Q,YU M H.The effect of the intermediate principal stress on the ground response of circular openings in rock mass[J].Springer Rock Mechanics and Rock Engineering,2006,39(2):169-181.
[22]CHEN Zhanfeng,ZHU Weiping,DI Qinfeng,et al.Numerical and theoretical analysis of burst pressures for casings with eccentric wear[J].Elsevier Journal of Petroleum Science and Engineering,2016,145:585-591.
[23]ZHANG Hongkun,SUN Baojiang,YAN Guomin,et al.Distribution laws and effects analysis of casing external pressure taking elastic parameters matching into account[J].Elsevier Petroleum,2016,2(1):108-115.
[24]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.
[25]田红亮,彭文昱,何孔德,等.采用俞茂宏统一强度理论求解圆筒和球壳的极限值[J].西安交通大学学报,2018,52(3):1-11.TIAN Hongliang,PENG Wenyu,HE Kongde,et al.Solving limit values of cylinder and spherical shell adopting Yu’s unified strength theory[J].Journal of Xi’an Jiaotong University,2018,52(3):1-11.
[26]Petroleum and natural gas industries:formulae and calculation for casing,tubing,drill pipe and line pipe properties:ISO 10400[S].6th ed.Geneva,Switzerland:International Organization for Standardization,2007.
[27]Bulletin on formulas and calculations for casing,tubing,drill pipe,and line pipe properties:API Bulletin5C3[S].6th ed.Washington,USA:American Petroleum Institute,1994.
[28]ASBILL W T,CRABTREE S,PAYNE M L.DEA-130 modernization of tubular collapse performance properties[R].San Antonio,USA:Southwest Research Institute,2002.