Some research advances in downhole tubular mechanics and control methods

GAO Deli; HUANG Wenjun

doi:10.6052/1000-0992-21-028

Volume 51 Issue 3

Sep. 2021

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Gao D L, Huang W J. Some research advances in downhole tubular mechanics and control methods. Advances in Mechanics, 2021, 51(3): 620-647 doi: 10.6052/1000-0992-21-028

Citation:

Gao D L, Huang W J. Some research advances in downhole tubular mechanics and control methods. Advances in Mechanics, 2021, 51(3): 620-647 doi: 10.6052/1000-0992-21-028

Gao D L, Huang W J. Some research advances in downhole tubular mechanics and control methods. Advances in Mechanics, 2021, 51(3): 620-647 doi: 10.6052/1000-0992-21-028

Citation:

Gao D L, Huang W J. Some research advances in downhole tubular mechanics and control methods. Advances in Mechanics, 2021, 51(3): 620-647 doi: 10.6052/1000-0992-21-028

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Some research advances in downhole tubular mechanics and control methods

doi: 10.6052/1000-0992-21-028

GAO Deli^,,
HUANG Wenjun

MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing 102249, China

More Information

Corresponding author: gaodeli_team@126.com
Received Date: 2021-05-17
Accepted Date: 2021-07-05

Available Online: 2021-07-20

Publish Date: 2021-09-25

Abstract

Abstract

Research on down-hole tubular mechanics has been more than 70 years so far. Many breakthrough research results have been obtained, and they have been successfully applied in drilling & completion engineering. However, due to the complexity of wellbore constraints and operating conditions, it has not been able to fully and accurately reveal the complicated mechanical behaviors of tubular strings in long and narrow wellbores. These facts also make the current design and control methods difficult to solve many complex engineering problems. First, this article reviews the overall development context of down-hole tubular mechanics and introduces the static deformation control equations of down-hole tubular strings. Next, research progress, the latest results and the existing problems of several important tubular mechanical problems are introduced, including down-hole tubular buckling, down-hole tubular friction and wear, safe operation limit of down-hole tubular strings, mechanics of bottom hole assembly and the corresponding design & control methods. Last, a summary and outlook on down-hole tubular mechanics are made. It is expected to provide some meaningful enlightenment for the development of down-hole tubular mechanics and control methods and the improvement of drilling & completion engineering technology.
- well engineering for oil & gas,
- drilling and completion,
- downhole tubular string,
- downhole tubular mechanics,
- downhole control engineering

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References(173)

References

[1]	白家祉, 苏义脑. 1990. 井斜控制理论与实践. 北京: 石油工业出版社 Bai J Z, Su Y N. 1990. Well Deviation Control Theory and Practice. Beijing: Petroleum Industry Press.
[2]	柏景海, 张立功, 邸百英. 1994. 斜直井下部钻具组合受力分析. 石油钻探技术, 22: 22-23 (Bai J H, Zhang L G, Di B Y. 1994. Slant hole bottomhole assembly mechanics. Petroleum Drilling Techniques, 22: 22-23).
[3]	曹向峰, 孙启忠, 唐志军, 等. 2013. 水平井眼中双稳定器钻具组合的力学特性分析. 石油机械, 41: 16-19 (Cao X F, Sun Q Z, Tang Z J, et al. 2013. Mechanical property analysis of BHA with double stabilizer in horizontal hole. China Petroleum Machinery, 41: 16-19). doi: 10.3969/j.issn.1001-4578.2013.04.004
[4]	狄勤丰, 王文昌, 姚永汉, 等. 2010. 钻具组合动力学模型及涡动特性仿真. 中国石油大学学报(自然科学版), 34: 53-56 Di Q F, Wang W C, Yao Y H, et al. 2010. Dynamics model and whirl features’ simulation of bottom hole assembly. Journal of China University of Petroleum (Edition of Natural Science), 34: 53-56.
[5]	高宝奎, 高德利, 谢金稳. 1997. 钻柱涡动及其应用. 石油大学学报(自然科学版), 21: 25-27 Gao B K, Gao D L, Xie J W. 1997. Drillstring whirlingand its application. Journal of the University of Petroleum, China (Edition of Natural Science), 21: 25-27.
[6]	高德利, 刘希圣, 黄荣樽. 1989. 钻头与地层相互作用的三维宏观分析. 石油大学学报(自然科学版), 13: 23-31 (Gao D L, Liu X S, Huang R Z. 1989. Three-dimension macroanalysis of rock-bit interaction. Journal of the University of Petroleum, China (Edition of Natural Science), 13: 23-31).
[7]	高德利, 刘希圣. 1989. 钻头与地层相互作用的新模型. 石油钻采工艺, 11: 23-28 (Gao D L, Liu X S. 1989. A new method of rock-bit interaction. Oil Drilling & Production Technology, 11: 23-28).
[8]	高德利, 刘希圣. 1990a. 典型地层的各向异性钻井特性.石油大学学报(自然科学版), 14: 1-8 Gao D L, Liu X S. 1990a. Anisotropic drilling characteristic of typical formations. Journal of the University of Petroleum, China (Edition of Natural Science), 14: 1-8.
[9]	高德利, 刘希圣. 1990b. 正交各向异性地层对井斜的影响. 石油学报, 11: 98-105 (Gao D L, Liu X S. 1990b. The effect of an orthotropic formation on bore hole deviation. Acta Petrolei Sinica, 11: 98-105).
[10]	高德利, 徐秉业. 1992. 石油钻井底部钻具组合平面纵横弯曲大挠度分析. 工程力学, 9: 42-49 (Gao D L, Xu B Y. 1992. Planar analysis of the static behavior of a bottomhole assembly under large deflection. Chinese Engineering Mechanics, 9: 42-49).
[11]	高德利. 1993. 地层各向异性的评估方法. 石油学报, 14: 96-101 (Gao D L. 1993. A method for the evaluation of formation anisotropy. Acta Petrolei Sinica, 14: 96-101). doi: 10.7623/syxb199302012
[12]	高德利. 1994a. 钻头和地层各向异性钻井特性的一种表达方法. 石油学报, 15: 126-132 (Gao D L. 1994a. A diagrammatic method for drilling characteristics of formation anisotropy and drill bit. Acta Petrolei Sinica, 15: 126-132).
[13]	高德利, 刘希圣, 徐秉业. 1994b. 井眼轨迹控制. 东营: 石油大学出版社 Gao D L, Liu X S, Xu B Y. 1994b. Prediction and Control of Wellbore Trajectory. Dongying: China University of Petroleum Press
[14]	高德利, 徐秉业. 1995. 石油钻井底部钻具组合大挠度三维分析. 应用力学学报, 12: 53-62 (Gao D L, Xu B Y. 1995. Three-dimension analysis of the static behavior of BHA under large deflection. Chinese Journal of Applied Mechanics, 12: 53-62).
[15]	高德利. 1995a. 井眼轨迹控制力学模型. 力学学报, 27: 501-505 (Gao D L. 1995a. Mechanics models for prediction and control of the wellbore trajectory. Acta Mechanica Sinica, 27: 501-505).
[16]	高德利. 1995b. 钻柱力学若干基本问题的研究. 石油大学学报 (自然科学版), 19: 24-35 Gao D L. 1995b. Some basic problems of elastic drilling mechanics. Journal of China University of Petroleum (Edition of Natural Science), 19: 24-35.
[17]	高德利, 高宝奎, 谢金稳, 等. 1995. 钻压防斜技术的实践与理论探讨. 石油钻采工艺, 17: 1-6 (Gao D L, Gao B K, Xie J W, et al. 1995. Researching and practice of deviation control by increasing WOB. Oil Drilling & Production Technology, 17: 1-6).
[18]	高德利, 高宝奎, 耿瑞平. 1996. 钻柱涡动特性分析. 石油钻采工艺, 18: 9-13 (Gao D L, Gao B K, Geng R P. 1996. Analysis of drillstring whirling. Oil Drilling & Production Technology, 18: 9-13).
[19]	高德利. 1996. 井眼轨迹控制问题的力学分析方法. 石油学报, 17: 115-121 (Gao D L. 1996. A mechanical model for prediction and control of the wellbore trajectory. Acta Petrolei Sinica, 17: 115-121). doi: 10.7623/syxb199601016
[20]	高德利. 2005. 易斜地层防斜打快钻井理论与技术探讨. 石油钻探技术, 33: 16-19 (Gao D L. 2005. Discussions on theories and techniques about rapid drilling while preventing deviating in formations tending to deflecting. Petroleum Drilling Techniques, 33: 16-19). doi: 10.3969/j.issn.1001-0890.2005.02.005
[21]	高德利. 2006. 油气井管柱力学与工程. 北京: 中国石油大学出版社 Gao D L. 2006. Down Hole Tubular Mechanics and Its Applications. Beijing: China University of Petroleum Press
[22]	高德利. 2018. 复杂井工程力学与设计控制技术. 北京: 石油工业出版社 Gao D L. 2018. Downhole Mechanics and Design & Control Techniques in Critical Well Engineering. Beijing: Petroleum Industry Press
[23]	高德利, 黄文君, 李鑫. 2019. 大位移井钻井延伸极限研究与工程设计方法. 石油钻探技术, 47: 1-8 (Gao D L, Huang W J, Li X. 2019. Research on extension limits and engineering design methods for extended reach drilling. Petroleum Drilling Techniques, 47: 1-8). doi: 10.11911/syztjs.2019027
[24]	郭宗禄, 高德利, 杨文强, 等. 2014. 下部钻具组合上切点的位置确定方法. 石油钻探技术, 42: 46-51 (Guo Z L, Gao D L, Yang W Q, et al. 2014. A method for determining upper tangential point at bottomhole assembly. Petroleum Drilling Techniques, 42: 46-51). doi: 10.3969/j.issn.1001-0890.2014.01.009
[25]	郭宗禄, 高德利, 刘书杰. 2019. 下部钻具组合稳定器的径向位置判断方法. 应用力学学报, 36: 1212-1219 (Guo Z L, Gao D L, Liu S J. 2019. A method for determining boundary conditions at stabilizers in bottom hole assembly analysis. Chinese Journal of Applied Mechanics, 36: 1212-1219).
[26]	管志川, 靳彦欣, 王以法. 2003. 直井底部钻柱运动状态的实验研究. 石油学报, 24: 102-106 (Guan Z C, Jin Y X, Wang Y F. 2003. Experimental research on motion behavior of bottom drill string in straight hole. Acta Petrolei Sinica, 24: 102-106). doi: 10.7623/syxb200306022
[27]	管志川, 邵冬冬, 温欣, 等. 2013. 水平井眼中旋转钻柱运动特性的实验研究. 工程力学, 30: 340-345 (Guan Z C, Shao D D, Wen X, et al. 2013. Experimental research on motion states of bottom drilling string in horizontal well. Engineering Mechanics, 30: 340-345). doi: 10.6052/j.issn.1000-4750.2011.07.0461
[28]	韩志勇. 2011. 液压环境下的油井管柱力学. 北京: 石油工业出版社 Han Z Y. 2011. Oil Well String Mechanics Under Hydraulic Conditions. Beijing: Petroleum Industry Press
[29]	槐庆林, 王洪英. 2008. 大位移井延伸极限预测技术研究. 西部探矿工程, 20: 73-76 (Huai Q L, Wang H Y. 2008. Study on extension limit prediction technology for extended reach wells. West-China Exploration Engineering, 20: 73-76). doi: 10.3969/j.issn.1004-5716.2008.11.024
[30]	黄文君. 2016. 旋转钻井机械延伸极限研究. [博士论文]. 北京: 中国石油大学(北京) Huang W J. 2016. Research on mechanical extending limits in rotary drilling. [PhD Thesis]. Beijing: China University of Petroleum-Beijing
[31]	黄文君, 石小磊, 高德利. 2020. 基于钻井延伸极限的管柱分段优化设计方法. 石油机械, 48: 1-8 (Huang W J, Shi X L, Gao D L. 2020. Piecewise optimal design method of tubular strings based on extended-reach drilling limits. China Petroleum Machinery, 48: 1-8).
[32]	姜伟. 2002. 渤海地区套管磨损问题的研究. 中国海上油气(工程), 14: 31-34 (Jiang W. 2002. Research on casing wear in the Bohai Sea. China Offshore Oil and Gas (Engineering), 14: 31-34).
[33]	刘凤梧, 高德利. 1999. 封隔器对油管螺旋屈曲的影响分析. 清华大学学报 (自然科学版), 39: 104-107 (Gao D L, Liu F W. 1999. Packer effect analysis of helical buckling of well tubing. Journal of Tsinghua University (Edition of Natural Science), 39: 104-107).
[34]	李子丰, 孔凡君. 1993. 钻柱拉力—扭矩模型述评. 石油机械, 21: 43-46 (Li Z F, Kong F J. 1993. Review of drillstring tension—torque model. China Petroleum Machinery, 21: 43-46).
[35]	刘巨保. 2003. 间隙元在钻柱接触非线性力学分析中的应用. 力学与实践, 25: 45-47 (Liu J B. 2003. The application of gap element to the nonlinear mechanics analysis of drillstring. Mechanics in Engineering, 25: 45-47). doi: 10.3969/j.issn.1000-0879.2003.01.016
[36]	林元华, 付建红, 施太和, 等. 2004. 套管磨损机理及其防磨措施研究. 天然气工业, 24: 58-61 (Lin Y H, Fu J H, Shi T H, et al. 2004. Research on casing wear mechanism and antiwear measures. Nature Gas Industry, 24: 58-61). doi: 10.3321/j.issn:1000-0976.2004.11.017
[37]	刘维凯. 2008. 大位移井钻柱力学分析及延伸能力研究. [博士论文]. 大庆: 大庆石油学院 Liu W K. 2008. Research on drillstem mechanic analysis and extension capacity extended reach well. [PhD Thesis]. Daqing: Daqing Petroleum Institute
[38]	李鑫, 高德利, 刁斌斌, 等. 2016. 基于赫巴流体的页岩气大位移水平井裸眼延伸极限分析. 天然气工业, 36: 85-92 (Li X, Gao D L, Diao B B, et al. 2016. Analysis on the open-hole extension limit of a shale-gas extended-reach horizontal well based on hershel–bulkley fluids. Nature Gas Industry, 36: 85-92). doi: 10.3787/j.issn.1000-0976.2016.10.011
[39]	李鑫, 高德利. 2017. 考虑延伸极限的大位移水平井最优钻井液排量设计. 石油钻采工艺, 39: 282-287 (Li X, Gao D L. 2017. Optimum drilling fluid displacement design of large displacement horizontal well considering extension limit. Oil Drilling & Production Technology, 39: 282-287).
[40]	李鑫. 2018. 大位移水平井裸眼延伸极限预测和控制技术基础研究. [博士论文]. 北京: 中国石油大学(北京) Li X. 2018. Basic research on prediction & control of maximum measured depth of open hole in horizontal extended-reach drilling. [PhD Thesis]. Beijing: China University of Petroleum-Beijing
[41]	廖明燕. 2007a. 基于神经网络和证据理论集成的钻井过程状态监测与故障诊断. 中国石油大学学报(自然科学版), 31: 136-140 (Liao M Y. 2007a. Drilling state monitoring and fault diagnosis based on integrating neural network and evidence theory. Journal of China University of Petroleum (Edition of Natural Science), 31: 136-140).
[42]	廖明燕. 2007b. 基于神经网络多参数融合的钻井过程状态监测与故障诊断. 中国石油大学学报(自然科学版), 31: 149-152 (Liao M Y. 2007b. Drilling state monitoring and fault diagnosis based on multi -parameter fusion by neural network. Journal of China University of Petroleum (Edition of Natural Science), 31: 149-152).
[43]	刘巨保, 张学鸿, 孙超, 等. 1997. 水平井BHA控制井斜与方位机理及影响因素分析. 大庆石油学院学报, 21: 70-74 (Liu J B, Zhang X H, Sun C, et al. 1997. Analysis of the theory and influence factors for the BHA to control inclination and azimuth in horizontal well. Journal of Daqing Petroleum Institute, 21: 70-74).
[44]	刘巨保, 冉祥利, 孟祥军, 等. 2002. 下部钻具纵横弯曲非线性有限元分析. 大庆石油学院学报, 26: 64-67 (Liu J B, Ran X L, Meng X J, et al. 2002. Nonlinear analysis of finite element for the sidewise and vertical bending of the bottom hole assembly (BHA). Journal of Daqing Petroleum Institute, 26: 64-67).
[45]	刘希圣, 高德利, 崔孝秉. 1988. 底部钻具组合三维静力分析的权余法. 石油大学学报(自然科学版), 12: 58-67 (Liu X S, Gao D L, Cui X B. 1988. Weighted residuals method for three-dimension static analysis of bottom hole assembly. Journal of the University of Petroleum, China (Edition of Natural Science), 12: 58-67).
[46]	刘永升, 高德利, 王镇全, 等. 2017. 斜直井眼中钻柱横向动态运动非线性模型研究. 振动与冲击, 36: 1-6 (Liu Y S, Gao D L, Wang Z Q, et al. 2017. Nonlinear dynamic model of drill-string transverse motion in a deviated well. Journal of Vibration and Shock, 36: 1-6).
[47]	刘永升. 2019. 钻柱及底部钻具组合系统非线性动力学特性研究. [博士论文]. 北京: 中国石油大学(北京) Liu Y S. 2019. Study on nonlinear dynamic characteristics of drill string and BHA system. [PhD Thesis]. Beijing: China University of Petroleum-Beijing
[48]	任文希, 王煜, 程纯勇, 等. 2014. 长水平段水平井机械水力延伸能力研究. 石油化工应用, 33: 18-21 (Ren W X, Wang Y, Cheng C Y, et al. 2014. The research on mechanical-hydraulic extension ability of long horizontal section well. Petrochemical Industry Application, 33: 18-21). doi: 10.3969/j.issn.1673-5285.2014.02.005
[49]	孙连忠. 2012. 复杂结构井管柱摩阻磨损预测与控制方法研究. [博士论文]. 北京: 中国石油大学(北京) Sun L Z. 2012. Calculation Methods for Prediction and Control of Down-Hole Tubular Torque & Drag and Casing Wear in Complex-Structure Wells. [PhD Thesis]. Beijing: China University of Petroleum-Beijing
[50]	署恒木, 吕英民, 蔡强康. 1990. 有限元法在底部钻具组合动态分析中的应用. 石油大学学报(自然科学版), 14: 54-61 (Shu H M, Lv Y M, Cai Q K. 1990. Application for finite element method in dynamic analysis of bottom hole assembly. Journal of China University of Petroleum (Edition of Natural Science), 14: 54-61).
[51]	谭雷川, 高德利, ADEEB Samer, 等. 2018. 基于钻柱正弦屈曲的套管磨损预测模型. 中国石油大学学报(自然科学版), 43: 69-74 (Tan L C, Gao D L, ADEEB Samer, et al. 2018. Casing wear prediction model in consideration of sinusoidal buckled drill string. Journal of China University of Petroleum (Edition of Natural Science), 43: 69-74).
[52]	唐波, 赵金海, 王敏生, 等. 2008. 气体钻井钟摆钻具组合的有限元分析法. 石油钻探技术, 36: 20-24 (Tang B, Zhao J H, Wang M S, et al. 2008. Finite element analysis on pendulum bottom hole assembly on gas wells. Petroleum Drilling Techniques, 36: 20-24). doi: 10.3969/j.issn.1001-0890.2008.01.006
[53]	汪志明, 郭晓乐. 2008. 大位移井水力延伸极限研究. 钻采工艺, 31: 1-3 (Wang Z M, Guo X L. 2008. Hydraulic extended limitation of extended-reach well. Drilling & Production Technology, 31: 1-3). doi: 10.3969/j.issn.1006-768X.2008.01.001
[54]	闫铁, 张凤民, 刘维凯, 等. 2010. 大位移井钻井极限延伸能力的研究. 钻采工艺, 33: 4-7 (Yan T, Zhang F M, Liu W K, et al. 2010. Mechanical analysis on the limit extended capacity for an extended reach well. Drilling & Production Technology, 33: 4-7). doi: 10.3969/j.issn.1006-768X.2010.01.002
[55]	闫铁, 李庆明, 王岩, 等. 2011. 水平井钻柱摩阻扭矩分段计算模型. 大庆石油学院学报, 35: 69-72 (Yan T, Li Q M, Wang Y, et al. 2011. Segmental calculation model for torque and drag of drillstring in horizontal wells. Journal of Daqing Petroleum Institute, 35: 69-72).
[56]	邹红华. 2002. 斜直井钻柱屈曲的研究. [硕士论文]. 北京: 中国石油大学(北京) Zou H H. 2002. Study on buckling of pipe string in inclined vertical well. [Master Thesis]. Beijing: China University of Petroleum-Beijing
[57]	张广清, 陈勉, 路永明. 2001. 斜直井段旋转钻柱稳定性试验研究. 石油钻采工艺, 23: 23-25 (Zhang G Q, Chen M, Lu Y M. 2001. Test study on drilling stem stability of rotary drilling in the slant hole. Oil Drilling & Production Technology, 23: 23-25). doi: 10.3969/j.issn.1000-7393.2001.01.006
[58]	祝效华, 童华, 刘清友, 等. 2007. 旋转钻柱与井壁的碰撞摩擦边界问题研究. 中国机械工程, 18: 1833-1837 (Zhu X H, Tong H, Liu Q Y, et al. 2007. Research on the dynamic boundary condition between revolving drill string and borehole wall. China Mechanical Engineering, 18: 1833-1837). doi: 10.3321/j.issn:1004-132x.2007.15.018
[59]	祝效华, 张智, 常学军, 等. 2015. 复杂结构井磨损套管连接螺纹的三维力学行为. 石油学报, 36: 748-753 (Zhu X H, Zhang Z, Chang X J, et al. 2015. Three-dimensional mechanical behavior of worn casing connecting thread in complex structural well. Acta Petrolei Sinica, 36: 748-753). doi: 10.7623/syxb201506012
[60]	祝效华, 李波, 李柯, 等. 2019. 大斜度井钻柱动态摩阻扭矩快速求解方法. 石油学报, 40: 611-620 (Zhu X H, Li B, Li K. 2019. Quick solution method for dynamic friction torque of drilling string in a highly-deviated well. Acta Petrolei Sinica, 40: 611-620). doi: 10.7623/syxb201905011
[61]	Alfsen T E, Heggen S, Blikra H, et al. 1995. Pushing the limits for extended reach drilling: new world record from platform Statfjord C, Well C2. SPE Drilling & Completion, 10: 71-76.
[62]	Apostal M C, Haduch G A, Williams J B. 1990. A study to determine the effect of damping on finite-element-based, forced-frequency-response models for bottomhole assembly vibration analysis//65th SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana. SPE-20458-MS.
[63]	Aslaksen H, Annand M, Duncan R, et al. 2006. Integrated FEA modeling offers system approach to drillstring optimization//IADC/SPE Drilling Conference, Miami, Florida, USA. SPE-99018-MS.
[64]	Aston M S, Hearn P J, McGhee G. 1998. Techniques for solving torque and drag problems in today's drilling environment//SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana. SPE-48939-MS.
[65]	Bradley W B, Fontenot J E. 1975. The prediction and control of casing wear. SPE Journal of Petroleum Technology, 27: 233-245. doi: 10.2118/5122-PA
[66]	Bradley W B. 1975. Factors affecting the control of borehole angle in straight and directional wells. Journal of Petroleum Technology, 27: 679-688. doi: 10.2118/5070-PA
[67]	Birades M, Gazaniol D. 1989. ORPHEE 3D: Original results on the directional behavior of BHA's with bent subs//SPE Offshore Europe, Aberdeen, UK. SPE-19244-MS.
[68]	Brett J F, Beckett A D, Holt C A, et al. 1989. Uses and limitations of drillstring tension and torque models for monitoring hole conditions. SPE Drilling Engineering, 4: 223-229. doi: 10.2118/16664-PA
[69]	Chen Y C, Lin Y H, Cheatham J B. 1990. Tubing and casing buckling in horizontal wells. Journal of Petroleum Technology, 42: 140-191. doi: 10.2118/19176-PA
[70]	Chen X Y, Gao D L. 2018. The maximum-allowable well depth while performing ultra-extended-reach drilling from shallow water to deepwater target. SPE Journal, 23: 224-236. doi: 10.2118/183025-PA
[71]	Christine I N, Jerome J S. 2018. The role of machine learning in drilling operations; a review//SPE Eastern Regional Meeting, Pittsburgh, Pennsylvania, USA. SPE-191823-18ERM-MS.
[72]	Cunha J C S. 1995. Buckling behavior of tubulars in oil and gas wells: A theoretical and experimental study with emphasis on the torque effect. [PhD Thesis]. Oklahoma, OU: University of Tulsa.
[73]	Daily J S, Ring L, Hajianmaleki M, et al. 2013. Critical buckling load assessment of drill strings in different wellbores using the explicit finite element method//SPE Offshore Europe Oil and Gas Conference and Exhibition, Aberdeen, UK. SPE-166592-MS.
[74]	Di Q F, Zhu W P, Yao J L, et al. 2007. Dynamic model of bottom hole assembly used in pre-bending dynamic vertical and fast drilling technology. Acta Petrolei Sinica, 28: 118-121. doi: 10.1111/j.1745-7254.2007.00484.x
[75]	Dunayevsky V, Abbassian F, Judzis A. 1993. Dynamic stability of drillstrings under fluctuating weight on bit. SPE Drilling & Completion, 8: 84-92.
[76]	Gao D L, Liu F W, Xu B Y. 1998. An analysis of helical buckling of long tubulars in horizontal wells//SPE International Oil and Gas Conference and Exhibition in China, Beijing. SPE-50931-MS.
[77]	Gao D L, Tan C J, Tang H X. 2009. Limit analysis of extended reach drilling in South China Sea. Petroleum Science, 6: 166-171. doi: 10.1007/s12182-009-0026-8
[78]	Gao D L, Sun L Z, Lian J H. 2010. Prediction of casing wear in extended-reach drilling. Petroleum Science, 7: 494-501. doi: 10.1007/s12182-001-0098-6
[79]	Gao D L, Sun L Z. 2012. New method for predicting casing wear in horizontal drilling. Petroleum Science and Technology, 30: 883-892. doi: 10.1080/10916466.2010.493909
[80]	Gao D L, Huang W J. 2015. A review on down-hole tubular string buckling in well engineering. Petroleum Science, 12: 443-457. doi: 10.1007/s12182-015-0031-z
[81]	Gao G H, Miska S Z. 2009. Effects of boundary conditions and friction on static buckling of pipe in a horizontal well. SPE Journal, 14: 782-796. doi: 10.2118/111511-PA
[82]	Gao G H, Miska S Z. 2010a. Dynamic buckling and snaking motion of rotating drilling pipe in a horizontal well. SPE Journal, 15: 867-877. doi: 10.2118/113883-PA
[83]	Gao G H, Miska S. 2010b. Effects of friction on post-buckling behavior and axial load transfer in a horizontal well. SPE Journal, 15: 1104-1118. doi: 10.2118/120084-PA
[84]	Gao G H, Di Q F, Miska S Z, et al. 2011. Stability analysis of pipe with connectors in horizontal wells. SPE Journal, 17: 931-941.
[85]	Ghasemloonia A, Geoff R D, Butt S D. 2014. Analysis of multi-mode nonlinear coupled axial-transverse drillstring vibration in vibration assisted rotary drilling. Journal of Petroleum Science and Engineering, 116: 36-49. doi: 10.1016/j.petrol.2014.02.014
[86]	Hajianmaleki M, Daily J S. 2014. Critical-buckling-load assessment of drillstrings in different wellbores by use of the explicit finite-element method. SPE Drilling & Completion, 29: 256-264.
[87]	Hall R W, Jr, Garkasi A, Deskins G, et al. 1994. Recent advances in casing wear technology//SPE/IADC Drilling Conference. Dallas, Texas, USA. SPE-27532-MS.
[88]	Hall R W, Malloy K P. 2005. Contact pressure threshold: an important new aspect of casing wear//SPE Production Operations Symposium. Oklahoma City, Oklahoma, USA. SPE-94300-MS.
[89]	He X, Kyllingstad A. 1995. Helical buckling and lock-up conditions for coiled tubing in curved wells. SPE Drilling & Completion, 10: 10-15.
[90]	Huang W J, Gao D L. 2014a. Sinusoidal buckling of a thin rod with connectors constrained in a cylinder. Journal of Natural Gas Science and Engineering, 18: 237-246. doi: 10.1016/j.jngse.2014.03.003
[91]	Huang W J, Gao D L. 2014b. Helical buckling of a thin rod with connectors constrained in a cylinder. International Journal of Mechanical Sciences, 84: 189-198. doi: 10.1016/j.ijmecsci.2014.04.022
[92]	Huang W J, Gao D L. 2015. Helical buckling of a thin rod with connectors constrained in a torus. International Journal of Mechanical Sciences, 98: 14-28. doi: 10.1016/j.ijmecsci.2015.04.010
[93]	Huang W J, Gao D L, Wei S L, et al. 2015a. A generalized quasi-static model of drill string system. Journal of Natural Gas Science and Engineering, 23: 208-220. doi: 10.1016/j.jngse.2015.01.038
[94]	Huang W J, Gao D L, Liu F W. 2015b. Buckling analysis of tubular strings in horizontal wells. SPE Journal, 20: 405-416. doi: 10.2118/171551-PA
[95]	Huang W J, Gao D L, Wei S L, et al. 2015c. Boundary conditions: A key factor in tubular-string buckling. SPE Journal, 20: 1409-1420. doi: 10.2118/174087-PA
[96]	Huang W J, Gao D L, Liu Y H. 2016. A study of tubular string buckling in vertical wells. International Journal of Mechanical Sciences, 118: 231-253. doi: 10.1016/j.ijmecsci.2016.09.035
[97]	Huang W J, Gao D L, Liu Y H. 2017. Inter-helical and intra-helical buckling analyses of tubular strings with connectors in horizontal wellbores. Journal of Petroleum Science and Engineering, 152: 182-192. doi: 10.1016/j.petrol.2017.03.004
[98]	Huang W J, Gao D L, Liu Y H. 2018a. Buckling analysis of tubular strings with connectors constrained in vertical and inclined wellbores. SPE Journal, 23: 301-327. doi: 10.2118/180613-PA
[99]	Huang W J, Gao D L, Liu Y H. 2018b. A study of mechanical extending limits for three-section directional wells. Journal of Natural Gas Science and Engineering, 54: 163-174. doi: 10.1016/j.jngse.2018.03.031
[100]	Huang W J, Gao D L, Liu Y H. 2018c. Mechanical model and optimal design method of tubular strings with connectors constrained in extended-reach and horizontal wells. Journal of Petroleum Science and Engineering, 166: 948-961. doi: 10.1016/j.petrol.2018.01.072
[101]	Huang W J, Gao D L. 2019. Combined effects of wellbore curvature, connector, and friction force on tubular buckling behaviors. SPE Journal, 24: 2083-2096. doi: 10.2118/195680-PA
[102]	Huang W J, Gao D L. 2020. Local-integral coupling model of tubular strings with connectors and its application in periodic sticking analyses, SPE Journal, in press.
[103]	Ho H S. 1986. General formulation of drillstring under large deformation and its use in BHA analysis//61st SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA. SPE-15562-MS.
[104]	Ho H S. 1987. Prediction of drilling trajectory in directional wells via a new rock-bit interaction model//62nd SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA, SPE-16658-MS.
[105]	Ho H S. 1988. An improved modeling program for computing the torque and drag in directional and deep wells//SPE Annual Technical Conference and Exhibition, Houston, Texas, USA. SPE-18047-MS.
[106]	Jansen J D. 1991. Non-linear rotor dynamics as applied to oilwell drillstring vibrations. Journal of Sound & Vibration, 147: 115-135.
[107]	Jansen J D. 1992. Whirl and chaotic motion of stabilized drill collars. SPE Drilling & Completion, 7: 107-114.
[108]	Johancsik C A, Friesen D B, Dawson R. 1984. Torque and drag in directional wells-prediction and measurement. Journal of Petroleum Technology, 36: 987-992. doi: 10.2118/11380-PA
[109]	Juvkam-Wold H C, Wu J. 1992. Casing deflection and centralizer spacing calculations. SPE Drilling Engineering, 7: 268-274. doi: 10.2118/21282-PA
[110]	Kyllingstad A. 1995. Buckling of tubular strings in curved wells. Journal of Petroleum Science and Engineering, 12: 209-218. doi: 10.1016/0920-4105(94)00046-7
[111]	Lesage M, Falconer I G, Wick C J. 1988. Evaluating drilling practice in deviated wells with torque and weight data. SPE Drilling Engineering, 3: 248-252. doi: 10.2118/16114-PA
[112]	Li X, Gao D L, Zhou Y C, et al. 2016a. General approach for the calculation and optimal control of the extended-reach limit in horizontal drilling based on the mud weight window. Journal of Natural Gas Science and Engineering, 35: 964-979. doi: 10.1016/j.jngse.2016.09.049
[113]	Li X, Gao D L, Zhou Y C, et al. 2016b. Study on open-hole extended-reach limit model analysis for horizontal drilling in shales. Journal of Natural Gas Science and Engineering, 34: 520-533. doi: 10.1016/j.jngse.2016.07.026
[114]	Li X, Gao D L, Zhou Y C, et al. 2016c. A model for extended-reach limit analysis in offshore horizontal drilling based on formation fracture pressure. Journal of Petroleum Science and Engineering, 146: 400-408. doi: 10.1016/j.petrol.2016.06.004
[115]	Li X, Gao D L, Chen X Y. 2017a. A comprehensive prediction model of hydraulic extended-reach limit considering the allowable range of drilling fluid flow rate in horizontal drilling. Scientific Reports, 7: 1-11. doi: 10.1038/s41598-016-0028-x
[116]	Li X, Gao D L, Zhou Y C, et al. 2017b. Study on the prediction model of the open-hole extended-reach limit in horizontal drilling considering the effects of cuttings. Journal of Natural Gas Science and Engineering, 40: 159-167. doi: 10.1016/j.jngse.2017.02.013
[117]	Li X, Gao D L, Lu B P, et al. 2019. Study on the prediction model of extended-reach limit length in horizontal drilling with dual-channel drillpipe in shale formation. Journal of Petroleum Science and Engineering, 177: 570-578. doi: 10.1016/j.petrol.2019.02.083
[118]	Li X, Gao D L, Lu B P, et al. 2019a. Study on modified maximum extension length prediction model for horizontal wells considering differential sticking. Journal of Petroleum Science and Engineering, 183: 1-13.
[119]	Li X, Gao D L, Lu B P, et al. 2019b. A prediction model of the shortest drilling time for horizontal section in extended-reach well. Journal of Petroleum Science and Engineering, 182: 1-11.
[120]	Li X, Gao D L. 2019. Study on mud weight window prediction model and safety additional value of horizontal well in shales considering effects of well's extended-reach limit. Journal of Petroleum Science and Engineering, 173: 579-587. doi: 10.1016/j.petrol.2018.10.054
[121]	Li X, Hu Z Q, Gao D L., et al. 2020. Study on prediction model of maximum hydraulic extension depth for ultra deep wells considering effects of temperature. Science China, 63: 1792-1807.
[122]	Liu Y S, Gao D L. 2017. A nonlinear dynamic model for characterizing downhole motions of drill-string in a deviated well. Journal of Natural Gas Science and Engineering, 38: 466-474. doi: 10.1016/j.jngse.2017.01.006
[123]	Liu Y S, Gao D L, Tan L C, et al. 2018. How is the dynamic of drillstring going under internal & external countercurrent-axial flows? //Society of Petroleum Engineers - Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, UAE. SPE-193084-MS
[124]	Lubinski A. 1950. A study of the buckling of rotary drilling strings. API Drilling & Production Practice, 5: 178-214.
[125]	Lubinski A, Woods H B. 1953. Factors affecting the angle of inclination and dog-legging in rotary bore holes. Drilling and Production Practice, 1: 222-250.
[126]	Lubinski A, Woods H B. 1955. Use of stabilizers in controlling hole deviation. Drilling and Production Practice, 1: 165-182.
[127]	Lubinski A, Althouse W. 1962. Helical buckling of tubing sealed in packers. Journal of Petroleum Technology, 14: 655-670. doi: 10.2118/178-PA
[128]	Lubinski A. 1977. Fatigue of range 3 drill pipe. Oil & Gas Science and Technology, 32: 209-232.
[129]	Maidla E E, Wojtanowicz A K. 1987. Field comparison of 2-D and 3-D methods for the borehole friction evaluation in directional wells//62nd SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA. SPE-16663-MS.
[130]	Martins A L, Aragão A, Calderon. A, et al. 2004. Hydraulic limits for drilling and completing long horizontal deepwater wells//SPE International Thermal Operations and Heavy Oil Symposium and Western Regional Meeting, Bakersfield, California, USA. SPE-86923-MS.
[131]	Mason C J, Judzis A. 1998. Extended-reach drilling: what is the limit//SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA. SPE-48943-MS.
[132]	McCann R C, Suryanarayana P V R. 1994. Experimental study of curvature and frictional effects on buckling//OTC Offshore Technology Conference, Houston, Texas, USA. OTC-7568-MS.
[133]	McSpadden A, Newman K. 2002. Development of a stiff-string forces model for coiled tubing//SPE/ICoTA Coiled Tubing Conference and Exhibition, Houston, Texas, USA. SPE-74831-MS.
[134]	Meader T, Allen F, Riley G. 2000. To the limit and beyond: the secret of world-class extended-reach drilling performance at Wytch Farm//IADC/SPE Drilling Conference, New Orleans, Louisiana, USA. SPE-59204-MS.
[135]	Meertens R, Kloss P. 1994. Drilling to the limit/long reach oil strike extended reach appraisal/development Well Tern TA05//the European Petroleum Conference, London, United Kingdom. SPE-28833-MS.
[136]	Melakhessou H, Berlioz A, Ferraris G. 2003. A nonlinear well-drillstring interaction model. Journal of Vibration and Acoustics, 125: 46-52. doi: 10.1115/1.1523071
[137]	Menand S, Sellami H, Tijani M, et al. 2006. Advancements in 3D drillstring mechanics: from the bit to the topdrive//IADC/SPE Drilling Conference, Miami, Florida, USA. SPE-98965-MS.
[138]	Millheim K K, Apostal M C. 1981. The effect of bottomhole assembly dynamics on the trajectory of a bit. Journal of Petroleum Technology, 33: 2323-2338. doi: 10.2118/9222-PA
[139]	Wu M, Chen D C K. 2006. A generic solution to BHA (bottomhole-assembly) modeling//SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA. SPE-101186-MS.
[140]	Miska S, Qiu W, Volk L, et al. 1996. An improved analysis of axial force along coiled tubing in inclined/horizontal wellbores//SPE International Conference on Horizontal Well Technology, Calgary, Alberta, Canada. SPE-37056-MS.
[141]	Mitchell R F. 1982. Buckling behavior of well tubing: the packer effect. Society of Petroleum Engineers Journal, 22: 616-624. doi: 10.2118/9264-PA
[142]	Mitchell R F. 1999. A buckling criterion for constant-curvature wellbores. SPE Journal, 4: 349-352. doi: 10.2118/57896-PA
[143]	Mitchell R F. 2003. Lateral buckling of pipe with connectors in horizontal wells. SPE Journal, 8: 124-137. doi: 10.2118/84950-PA
[144]	Mitchell R F. 2005. The pitch of helically buckled pipe//SPE/IADC Drilling Conference, Amsterdam, Netherlands. SPE-92212-MS.
[145]	Mitchell R F, Bjorset A, Grindhaug G. 2015. Drillstring analysis with a discrete torque/drag model. SPE Drilling & Completion, 30: 5-16.
[146]	Nandakumar K, Wiercigroch M. 2013. Stability analysis of a state dependent delayed, coupled two DOF model of drill-stringvibration. Journal of Sound and Vibration, 332: 2575-2592. doi: 10.1016/j.jsv.2012.12.020
[147]	Paslay P R, Bogy D B. 1964. The stability of a circular rod laterally constrained to be in contact with an inclined circular cylinder. Journal of Applied Mechanics, 31: 605-610. doi: 10.1115/1.3629721
[148]	Paslay P R, Cernocky E P. 1991. Bending stress magnification in constant curvature doglegs with impact on drillstring and casing//66th SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA. SPE-22547-MS.
[149]	Prince O, Juan C V, Roman S. 2019. Estimating downhole vibration via machine learning techniques using only surface drilling parameters//SPE Western Regional Meeting, San Jose, California, USA. SPE-195334-MS.
[150]	Qui W, Miska S, Volk L. 1998. Drill pipe/coiled tubing buckling analysis in a hole of constant curvature//SPE Permian Basin Oil and Gas Recovery Conference, Midland, Texas, USA. SPE-39795-MS.
[151]	Rocha L A S, Junqueira P, Roque J L. 2003a. Overcoming deep and ultra deepwater drilling challenges//Offshore Technology Conference, Houston, Texas, USA. OTC-15233-MS.
[152]	Rocha L A S, Andrade R, Soffried K. 2003b. How water depth affects extended reach drilling//Offshore Technology Conference, Houston, Texas, USA. OTC-15326-MS.
[153]	Rodman D W, Swietlik G. 1997. Extended reach drilling limitations: a shared solution//Offshore Europe Conference, Aberdeen, Scotland, UK. SPE-38466-MS.
[154]	Salies J B, Cunha J C S, Azar J J, et al. 1994. Experimental and analytical study of sinusoidal buckling in vertical wells//SPE Eastern Regional Meeting Charleston, West Virginia, USA. SPE-29164-MS.
[155]	Salies J B. 1994. Experimental study and mathematical modeling of helical buckling of tubulars in inclined wellbores [PhD Thesis]. Oklahoma, OU: University of Tulsa.
[156]	Schamp J H, Estes B L, Keller S R. 2006. Torque reduction techniques in ERD Wells//IADC/SPE Drilling Conference. Miami, Florida, USA. SPE-98969-MS.
[157]	Schoenmakers J M. 1987. Prediction of casing wear due to drillstring rotation: field validation of laboratory simulations. SPE Drilling Engineering, 2: 375-381. doi: 10.2118/14761-PA
[158]	Sheppard M C, Wick C, Burgess T. 1987. Designing well paths to reduce drag and torque. SPE Drilling Engineering, 2: 344-350. doi: 10.2118/15463-PA
[159]	Sorenson K G, Cheatham J B. 1986. Post-buckling behavior of a circular rod constrained within a circular cylinder. Journal of applied mechanics, 53: 929-934. doi: 10.1115/1.3171883
[160]	Sun L Z, Gao D L, Zhu K L. 2012. Models & tests of casing wear in drilling for oil & gas. Journal of Natural Gas Science & Engineering, 4: 44-47.
[161]	Sun L Z, Gao D L. 2012. Optimum placement of friction reducer in extended reach well. Applied Mechanics and Materials, 101-102: 339-342.
[162]	Tikhonov V, Valiullin K, Nurgaleev A, et al. 2014. Dynamic model for stiff-string torque and drag. SPE Drilling & Completion, 29: 279-294.
[163]	Tan L C, Gao D L, Zhou J H. 2018a. Casing wear prediction with considering initial internal casing eccentricity. Arabian Journal for Science and Engineering, 43: 2593-2603. doi: 10.1007/s13369-017-2890-7
[164]	Tan L C, Gao D L, Zhou J H. 2018b. A prediction model of casing wear in extended-reach drilling with buckled drillstring. Journal of Applied Mechanics, 85: 1-11.
[165]	Tan L C, Gao D L. 2018. Casing wear prediction model based on casing ellipticity in oil & gas well-drilling with complex structures. Journal of Applied Mechanics, 85: 1-16.
[166]	Walker B H. 1973. Some technical and economic aspects of stabilizer placement. SPE Journal of Petroleum Technology, 25: 663-672. doi: 10.2118/4263-PA
[167]	Williamson J S, Lubinski A. 1987. Predicting bottomhole assembly performance. SPE Drilling & Completion, 2: 37-46.
[168]	White J P, Dawson R. 1987. Casing wear: laboratory measurements and field predictions. SPE Drilling Engineering, 2: 56-62. doi: 10.2118/14325-PA
[169]	Wu J. 1992. Buckling behavior of pipes in directional and horizontal wells. [PhD Thesis]. Texas, AM: A&M University.
[170]	Wu J, Juvkam-Wold H C. 1995a. The effect of wellbore curvature on tubular buckling and lockup. Journal of Energy Resources Technology, 117: 214-218. doi: 10.1115/1.2835343
[171]	Wu J, Juvkam-Wold H C. 1995b. Coiled tubing buckling implication in drilling and completing horizontal wells. SPE Drilling & Completion, 10: 16-21.
[172]	Wu J. 1995. Slack-off load transmission in horizontal and inclined wells//SPE Production Operations Symposium, Oklahoma, OK, USA. SPE-29496-MS.
[173]	Zhang H, Di Q F, Qin G X, et al. 2017. Quick solution method for lateral vibration response of pre-bent bottom-hole assembly. Acta Petrolei Sinica, 38: 1441-1447.