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深水平台钻井钻柱耦合振动及模拟分析
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摘要
深水钻井是当前国内外最前沿的钻井技术之一。由于海上钻井平台处于恶劣的自然环境下,海上钻井比陆上钻井难度大的多、复杂的多。随着世界油气储备的不断减少和需求量的增加,海底油气开采逐渐向深水域和超深水域发展,深水钻井技术问题也越来越引起人们的重视,深水钻井中的一些相关技术问题也成为研究的重点,其中深水钻井钻柱振动问题就是其一。
     首先,对半潜式钻井平台的振动问题进行了分析研究。以锚泊定位的半潜式钻井平台为例,分析了半潜式钻井平台的垂荡估算,利用有限元方法建立了半潜式钻井平台的各种平动、扭转振动及各种振动的耦合振动的模型,获得了半潜式钻井平台各种振动的规律。
     其次,对深水钻井中的隔水管的力学规律进行了研究。通过对隔水管的复杂力学环境的分析,利用线性微元法建立了隔水管的基本动力学微分方程。对平台漂移情况下隔水管的准静态状况进行了分析,获得了平台漂移情况下隔水管变形及受力的规律;通过隔水管的动态行为的研究,分析了隔水管的横向振动及在各种载荷作用下的动态响应,获得隔水管的横向振动频谱规律和振动模态形式以及平台漂移情况下的动态响应规律。
     再次,对深水钻井中钻柱的各种振动问题进行了研究。考虑到深水钻井工程的复杂情况,分别分析了钻井工程中水平井段钻柱轴向振动和直井段钻柱的轴向振动、水平井段钻柱的横向振动及直井段钻进中钻柱的横向振动、水平井段钻进中钻柱的扭转振动、大位移段钻柱的“粘滑”振动及直井段钻柱的扭转振动,利用线性、非线性及有限元等方法建立了各种振动的力学模型,获得了各种振动的频谱规律,并应用于实际。
     最后,分析了深水钻井中的各种耦合振动问题。用线性微元法分析了存在流体阻尼情况下钻柱的振动,获得了流体阻尼对钻柱各种振动影响的规律;分析了隔水管振动情况下钻柱的耦合振动,利用有限元法建立了隔水管和钻柱的随机接触的力学模型,分析了钻井平台漂移时隔水管和钻柱的变形及接触作用、隔水管和钻柱系统的横向振动规律以及平台动态行为对隔水管和钻柱系统影响;用有限元方法分析了钻柱的耦合振动,模拟了钻柱轴向、横向及扭转的耦合振动,获得钻柱的各种耦合振动规律;分析了平台振动对钻柱的动态行为的影响,利用有限元法建立了平台振动情况下钻柱动态响应力学模型,用解耦分析法获得了振动的规律。
     本文研究对深水钻井中的力学问题具有很强的针对性和实用性,其中涉及到钻井平台、隔水管及钻柱的振动问题,还涉及到各种耦合振动的问题,为深水钻井的设计和安全施工提供可靠的理论依据。
In presence, deep-water drilling is one of the advanced drilling technology at home and abroad. The bad oceanic environment brings very big difficulty to drilling engineering. With the world's decreasing for oil and gas reserves and demand increases, undersea oil and gas exploration has been developed to deep water and ultra deep-water gradually. Deep-water drilling technology problems have increasingly attracted people's attention, related technical problems in deep-water drilling also become a focus of the study, drillstring vibration problem for deep-water drilling is one of problems.
     First, the vibration problem of semi-submersible drilling platform has been analyzed. For anchor positioned semi-submersible drilling platform is example, semi-submersible drilling platform vertical vibration is estimated, by using finite element method a variety of translational, torsional vibration and various vibration coupled vibration model of semi-submersible drilling platform are established, the rule of various vibraiton are obtained.
     Second, the mechanical problems of the marine riser in deep-water drilling project are studied. Through the analysis of the complex mechanical environment of riser, the basic kinetic equation of marine riser has established using linear micro-element method. Under the across drift of the platform the marine riser for quasi-static conditions is analyzed, the laws of deformation and stress of marine riser are obtained under platform drift; the dynamic behavior of marine riser has been studied, lateral vibration of marine riser and dynamic response under a variety of loads are analysed, the lateral vibration spectrum, vibration mode and the law of the dynamic response under platform drift are obtained.
     Third, a variety of drillstring vibration problem of deep-water drilling has been studied. Taking into account the complexities of deep-water drilling project, drillstring axial vibration of horizontal part drilling and drillstring axial vibration of vertical part drilling are studied. Drill string lateral vibration of the horizontal part drilling and the lateral vibration of drill string of vertical part drilling are studied. Drill string torsional vibration of the horizontal part drilling, "stick-slip"of Extended Reach part and drill string torsional vibration of vertical part drilling are analyzed. The mechanical models are astablished by using linear, nonlinear and finite element method, the frequency rules are obtainend and the rules are used for actual problem.
     Forth, a variety of coupled vibration problem in deep-water drilling is analysed. The vibrations of drill string under the existence of fluid damping are studied by using linear micro-element method, the law of a variety of fluid damping vibration of the drill system is obtained. Coupled vibration of the drill string under marine riser vibration is studied, random contact mechanics model of the riser and the drill string is established by using FEM, the deformation and contact of riser and drill string under drilling platform drift are analyzed, and the effect about dynamic behavior of platform to the system of marine riser and drill string are studied. Various freedom degrees of coupled vibration of drill string is studied by using finite element method, the axial, lateral and torsional coupled vibration of drillstring are simulated, a variety of coupled vibration of drill string are obtained. The effect of vibration of the drilling platform to the dynamic behavior of drill string is analysed, the mechanical model of drill string dynamic response under platform vibration is established by using FEM, the rule of vibration is obtained using decoupled analysis.
     This paper has highly targeted and practical on mechanical issue of the deep-water drilling, includes the platform vibration, marine riser mechanics and drill string vibration, and a variaty of coupled vibraiton, it can provide reliable theoretical basis for the design and construction safety of deep-water drilling.
引文
[1]朱江.海洋钻井设备综述[J].中国海上油气工程,2000,12(6):44~47.
    [2]江怀友,乔卫杰.世界海洋钻井技术及装备现状与展望[J].环球石油,2008,27(6):24~30.
    [3] Tanaka S, Okada Y, Ichikaw Y. Offshore drilling and production equipment [J]. Civil engineering, 2005, 10: 103-134.
    [4]潘斌.移动式平台设计[M].上海:上海交通大学出版社,1995,26~106.
    [5] Bueno R C S, Morooka C K. Dynamic Analysis of Marine Riser[C]. 1994, SPE 28723.
    [6] Jogi P N, Macpherson J D, Neubert M. Field Verification of Model Derived Natual Frequencies of a Drill String[C]. 1999, ETCE99-6648.
    [7] Dubinsky V S, Baecker D R. An Interactive Drilling Dynamics Simulator for Drilling Optimization and Training[C]. 1998, SPE 49205.
    [8] Heisig G, Sancho J, Macpherson J D. Downhole Diagnosis of Drilling Dynamics Data Provide Bake Hugeses New Level Drilling Process Control to Driller[C]. 1998, SPE 49206.
    [9]陈新权.深海半潜式平台初步设计中的若干关键问题研究[D].上海:上海交通大学,2007.
    [10]马延德.大型半潜式钻井平台结构设计关键技术研究[J].中国海洋平台,2002,17(1):11~18.
    [11] Monk B G. Machinery vibration on offshore platforms[J]. Journal of Petroleum Technology, 1978, 30(4):627-638.
    [12] Ping Liu, Massie W W, Wolters J G and Blaauwnendraad J. Dynamics of Jack-up Structure[C]. 1992, SPE 22378.
    [13] Brogan M A, Wasserman K S. Tension Leg Platform Design Optimization for Vortex Induced Vibration[C]. Oceans proceedings , 2003.
    [14]彭熙民.“港海一号”自升式钻井平台结构静力分析[J].中国海洋平台,2000,15(4):21~24.
    [15]徐长航,陈国明等.自升式平台结构响应分析及可靠性评估研究综述[J].中国海洋平台,2003,18(4):6~12.
    [16]李茜,杨树耕.采用ANSYS程序的自升式平台结构有限元动力分析[J].中国海洋平台,2003,18(4):41~47.
    [17]桂洪斌,金咸定.海洋平台振动控制研究综述[J].中国海洋平台,2003,18(5):19~23.
    [18]邱世欣.FPSO整船有限元模型的瞬态动力分析[D].天津:天津大学建筑工程学院2005.
    [19]周广利,白若阳.导管架平台的动力分析[J].中国海洋平台,2006,21(1):45~49.
    [20]王世圣,谢彬等.3000m深水半潜式钻井平台运动性能研究[J].中国海上油气,2007,19(4):277~284.
    [21]窦培举.海洋钻井平台HAZOP分析的研究[J].中国海洋平台,2007,22(1):43~46.
    [22]龚顺风,何勇,金伟良.海洋平台结构随机动力响应谱疲劳寿命可靠性分析[J].浙江大学学报(工学版),2007,41(1):12~17(3).
    [23]杨秀娟,闫相祯,高进伟.Ansys在导管架式海洋平台安全综合分析中的应用[C].Ansys-China,2006年用户年会论文.
    [24]潘子辉.深海半潜式钻井平台运动响应预报与分析[J].船舶,2008,19(1):231~36.
    [25]畅元江,陈国明,孙友义.基于波浪谱与钻井船RAO的钻井船运动模拟[J].系统仿真学报.2009,21(5):1310~1313.
    [26]崔振南,刘喜华,吴育华.基于ANSYS的海洋平台自振特性分析[J].JOURNAL OF QINGDAO UNWERSITY《Natural Science Edition》,2005,18(1):38~46.
    [27] Burke B G. An analysis of marine risers for deep water[C]. Offshore Technology Conference, 1973.
    [28] Egeland O, wiik T, Natvig B J. Dynamics Analysis of Marine Riser. 1975, SPE 10420.
    [29] Robert M Sexton, L K Agbezuge. Random wave and vessel motion effects on drilling riser dynamic[C]. Offshore Technology Conference , Houston ,1976.
    [30] Dareing D W. Natural Frequencies of Marine Drilling Risers[J]. JOURNAL OF PETROLEUM TECHNOLOGY, 1976, 28(7): 813-818.
    [31] Van Den Boom H J J, Dekker J N. Dynamic Aspects of offshore riser and mooring concepts[J]. Journal of petrolem technology,1988, 24(12):1609-1617.
    [32] Simmonds D G. Dynamic Analysis of Marine Riser[C]. 1980, SPE 9735.
    [33]贾星兰,方华灿.海洋钻井隔水管的动力响应[J].石油机械,1995,23(8):18~23.
    [34]熊汉桥,吴竞择.中、深水条件下隔水管频域动力响应精确数值分析[J].中国海洋平台,1996,11(5):210~216.
    [35]弓大为.海洋隔水管的受力分析[J].中国造船,2003,44(增刊):317~321.
    [36]李军强,刘宏昭,何钦象.波浪力作用下海洋钻井隔水管随机振动研究[J].机械科学与技术[J],2004, 23(1):7~10.
    [37]李中,杨进,曹式敬.深海水域钻井隔水管力学特性分析[J].石油钻采工艺,2007,29(1):19~23.
    [38]刘彩虹,杨进,曹式敬.海洋深水钻井隔水管力学特性分析[J].石油钻采工艺,2008, 30(2):28~31.
    [39]许亮斌,蒋世全,姜伟.深水钻井隔水管浮力块配置方法研究[J].中国海上油气,2009,21(1):51~54.
    [40]许亮斌,畅元江,蒋世全.深水钻井隔水管时域非线性动态响应分析技术研究[J].中国海上油气,2008,20(2):115~120.
    [41]王腾,张修占,朱为全.平台运动下深水钻井隔水管非线性动力响应研究[J].海洋工程,2008,26(3):21~27.
    [42] Lubinski A, Woods HB. Factors Affecting the Angle of Inclination and Dog-Legging in Rotary Bore Holes[M]. Drilling and Production Practice,1953: 222-242.
    [43] Lubinski A.A study of the buckling of rotary drilling string[M]. Drilling and Production Practice, 1950:178-214.
    [44] Finnie I, Bailey JJ. An Experimental Study of Drill String Vibration[J]. Journal of Engineering for Industry, 1960, 82(2):129-135.
    [45] Bailey JJ, Finnie I. An Analytical Study of Drill String Vibration[J]. Journal of Engineering for Industry, 1960, 82(2):122-128.
    [46] Dareing DW, Livesay BH. Longitudinal and Angular Drill String Vibrations With Damping[J]. Journal of Engineering for Industry, 1968,11:671-679.
    [47] Heisig G, Sancho J, Macpherson J D. Downhole Diagnosis of Drilling Dynamics Data Provide Bake Hugeses New Level Drilling Process Control to Driller[C]. 1998, SPE 49206.
    [48] Bradley WB. Factors Affecting the Control of Borehole Angle in Straight and Directional Wells[J]. Journal of Petroleum Technology, 1975, 27(6):679-688.
    [49] Dunayevsky V A, Judzis A, Mills W H. Dynamic Stability of Drillstrings Under Fluctating Weight-on-Bit[C]. 1985, SPE 14329.
    [50] Mitchell RF, Allen MB. Case Studies of BHA Vibration Failure[C]. 1987, SPE 16675.
    [51] Skaugen E. The Effects of Quasi-Random Drill Bit Vibration Upon Drillstring Dyanmic Bahavior[C]. 1987, SPE 16660.
    [52] Kyllingstad A, Halsey G W. A Study of Slip-Stick Motion of the Bit[C]. 1987, SPE 16659.
    [53] Dawson R, lin Y Q and Spanos P D. Drill String Stick-slip Oscillations[C]. Spring Conference of the Society for Experimental Mechanics, Texas, 1987, 6.
    [54] Leine R I, Van D H and Keultjes W J G. Stick-slip Whirl Interaction in Drillstring Dynamic[J]. Journal of Vibration and Acoustics, 2002, 124(2):209-220.
    [55] Halsey G W, Kyllingstad A, Kylling A. Torque Feedback used to Cure Slip-stick Motion[C]. 1988, SPE 18049: 277-282.
    [56] Hemphill T, Ravi K. Pipe Rotation and Hole Cleaning in an Eccentric Annulus[C]. 2006, IADC/SPE 99150.
    [57] Van den Steen L. Suppressing stick-slip-induced drillstring oscillations: a hyperstability approach[D]. The Netherlands: University of Twente, 1997.
    [58]黄根炉,韩志勇.大位移井钻柱粘滑振动机理分析及减振研究[J].石油钻探技术,2001,29(2):4~6.
    [59]黄根炉,韩志勇.大位移井钻柱扭转振动顶部扭矩负反馈减振研究[J].石油大学学报(自然科学版),2001,25(5):32~36.
    [60] Aldred W D, Sheppard M C. Drillstring Vibrations: A new Generation Mechanism and Control Strategies. 1992, SPE 24582.
    [61] Vandiver JK. Case Studies of the Bending Vibration and Whirling Motion of Drill Collars. 1990, SPE/IADC 18652.
    [62] Steven Taylor, Alain Besson, Djoko Minto. Unique PDC Bit Technologies Combine to Reduce Drilling Time in Interbedded Formations. 2000, SPE 64005.
    [63]赵国珍,龚伟安.钻井力学基础[M].北京:石油工业出版社,1988,101~112.
    [64]章扬烈.钻柱运动学与动力学[M].北京:石油工业出版社,2001,22~29.
    [65]王珍应,林建,施太和.钻柱振动特性分析与井底岩性识别方法初探[J].钻采工艺,2000,23(6):30~34.
    [66]帅健,蔡强康,吕英民.大斜度井中钻柱的有限元分析[J].石油机械,1995,23(3):25~29.
    [67] Zifeng Li, Baoyun Gao. Analysis of Longitudinal Vibration of Drillstring in Air and Gas Drilling. 2007, SPE 107697.
    [68]李子丰,马兴瑞.油气井杆管柱动力学基本方程[J].哈尔滨工业大学学报.1995,17(1):40~44.
    [69] Chi A, Zhang J. Prediction of Drillstring Fatigue Life Under Axial-Torsional Combined Vibration[C]. 2006, SPE 99356.
    [70]周守为,张钧.大位移井钻井技术及其在渤海湾油田的应用[M].北京:石油工业出版社,2002,1~10.
    [71]李瑞营,王大力,王洪英.大庆油田大位移井钻井完井技术应用前景分析[J].西部探矿工程,2006,18(5):159~161.
    [72]宋玉玲,姜德风,殷夜明译.国外大位移井钻井设计综述[J].国外油田工程,1999,1:33~36.
    [73] Bell R, McKee R, Zwald E. Single-Diameter Technology Capable of Increasing Extended-Reach Drilling by 50%[C].offshore technology conference, 2006, OTC 17828.
    [74]苏义脑.水平井井眼轨道控制[M].北京:石油工业出版社,2000, 1~88.
    [75]阎铁,韩春杰.斜井眼内钻柱轴向振动的有限元分析[J].石油钻探技术,2006,34(4):5~7.
    [76]韩春杰,阎铁.水平井侧钻过程中钻柱横向振动规律的研究[J].石油机械,2005,33(1):8~10.
    [77]楼一珊.深井钻柱临界转速的计算方法[J].钻采工艺,1999,22(4):3~5.
    [78]刘巨保,丁皓江,张学鸿.间隙元在钻柱瞬态动力学分析中的应用[J].计算力学学报,2002,19(4):456~460.
    [79]管志川,靳彦欣,王以法.直井底部钻柱运动状态的实验研究[J].石油学报,2003,24(6):102~106.
    [80]袁光杰,王青华,姚振强,等.冲旋钻井中钻柱纵向振动模型的建立与求解方法[J].石油钻探技术,2002,30(5):20~22.
    [81]韩春杰,阎铁.深井钻柱振动规律的分析及应用[J].天然气工业,2005,25(9):76~79.
    [82]韩致信,李钫,杨莉玲.钻柱纵向自由振动研究[J].甘肃工业大学学报,2002,28(2):50~52.
    [83]阎铁.优选参数钻井理论与实践[J].哈尔滨工业大学出版社,1994(2):21~35.
    [84]张子明,杜成斌,周星德等.结构动力学[M].北京:清华大学出版社,2008,70~80.
    [85] Payne, Michael Lyle. Drilling Bottom-Hole Assembly Dynamics[D]. Houston, Texas: Rice University, 1992.
    [86] Heisig G,Neubert M.Lateral drillstring vibration in Extended-Reach Wells[C].2000,IADC/SPE 59235.
    [87] Sophianopoulos D S, Michaltsos G T. Combomed Torsional-Lateral Vibration of Beam under Vehicular Loading[J]. The sientific jourmal Facta Universities, 1999, 2(9): 877-886.
    [88] Spanos P D, Chevallier A M, Politis N P. Nonlinear Stochastic Drill-String Vibrations. Journal of Vibration and Acoustics, 2002, 124(10): 512-518.
    [89]刘清友,黄本生.牙轮钻头横向振动模型的建立及求解[J].钻井工程,2001,21(4):55~56.
    [90] Susumu Katayama, Yasuko Ogawa. Total Analysis Computer for a Semi-submersible Offshore Unit[C]. 1984, SPE 12438.
    [91]韩凌,杜勤.深水半潜式钻井平台锚泊系统技术概论[J].海洋工程,2007,36(3):82~86.
    [92] Hjelle A, Teige T G. World-Record ERD Well Drilled From a Floating Installation in the North Sea[C]. 2006, IADC/SPE 98945.
    [93]朱伯芳.有限单元法原理与应用[M].北京:中国水利水电出版社,2000,1~54.
    [94]加拉霍夫,利托诺夫,阿利谢依奇克(苏).王轲,方学,管光东译.浮动钻井平台[M].北京:国防工业出版社,1988,121~136.
    [95]关晓晶,周国强,郭奕珊.海洋石油钻机井架动力特性分析[J].大庆石油学院学报,2005,29(3):53~59.
    [96]薛继军,许爱荣,赵志丽.钻机井架有限元模态分析[J].石油矿场机械,2001,30(6):44~46.
    [97]周国强,刘金梅.勘探三号海洋钻井井架动力特性测试与安全评估[J].石油矿藏机械,2008,37(8):14~18.
    [98]邹龙庆.石油钻机井架动态响应分析[D].哈尔滨:哈尔滨工程大学,2006.
    [99]王海峡,赵广慧.波流极值载荷作用下隔水管的非线性分析[J].石油矿场机械,2008,37(11):6~10.
    [100]许士菊,王长华.梁振动方程的一个稳定的有限差分近似[J].吉林化工学院学报,2007,24(1):79~82.
    [101]余爱晖,金怡.关于一类二阶边值问题的有限差分方法[J].杭州师范学院学报(自然科学版),2007,6(5):351~354.
    [102]许芝卉,王凤艳.用差分方法求解两点边值问题[J].山西大同大学学报(自然科学版),2009,25(4):10~13.
    [103]王大斌,马双红.一类四阶差分方程边值问题的正解[J].兰州理工大学学报2006,23(4):138~142.
    [104]孙友义,陈国明,畅元江.深水铝合金隔水管涡激振动疲劳特性[J].中国石油大学学报(自然科学版),2008,32(1):100~105.
    [105]朱宝华.杆系结构理论[M].上海:同济大学出版社,1993,421~471.
    [106]屈展,刘德涛.钻柱振动问题极其理论进展[J].石油机械,1996,24(2):54~57.
    [107]蔡亚系,施太和,王幼金.连续油管柱振动分析[J].西南石油学院学报,1998,20(2):59~60.
    [108]陈涛平,胡靖邦.石油工程[M].北京:石油工业出版社,2000,50~103.
    [109]胡少伟,苗同臣.结构振动理论及其应用[M].北京:中国建筑工业出版社,2005,100~118.
    [110] Chur Claus, Bendzko Thomas. KTB-4 Years Experence at the Limits of Drilling Technology[C]. 1995, SPE/IADC 29412.
    [111] M.B.Allen. BHA Lateral vibrations: Case Studies and Evaluation of Important Parameters. 1987, SPE/IADC 16110.
    [112]李茂生,闫相祯,高德利.钻井液对钻柱横向振动固有频率的影响[J].石油大学学报,2004,28(6):68~71.
    [113] Li C, Jiang Han. Analytical Study of Drill string vibration. 1987, SPE 15979.
    [114]刘清友,马德坤,钟青.钻柱扭转振动模型的建立及求解[J].石油学报,2000,21(2):78~82.
    [115] Ford Brett J. The Genesis of Torsional Drillstring Vibration. 1992, SPE 21943.
    [116] Bernd Schmalhorst, Baker Hughes INTEQ, Eberhard Brommundt. Drilling Dynamics in the Presence of Mud Flow[C]. 2000, IADC/SPE:59236.
    [117] Taylor S, Besson A, Minto D. Unique PDC Bit Technologies Combine to Consistently Reduce Drilling Time in Interbedded Formations[C]. 1998, IADC/SPE 47778: 75-82.
    [118]邱国虎,付建红.三维定向井轨迹优化设计[J].钻采工艺,1997,20(5):26~29.
    [119]欧珠光.工程振动[M].湖北:武汉大学出版社,2003,90~95.
    [120]杨海波,赵新瑞.侧钻水平井钻柱动力学分析及应用[J].石油钻采工艺,2001,23(3):24~27.
    [121]殷朝阳,王光远.钻柱动力学有限元分析及室内轴向试验结果对比[J].哈尔滨建筑大学学报,2000,33(3):6~10.
    [122]王秀亭,刘延强.大位移井钻柱的动态分析[J].石油大学学报(自然科学版),2004,28(1):41~43.
    [123]刘峰,王鑫伟.水平井中钻柱屈曲的非线性有限元分析[J].机械科学与技术,2005,24(8):917~920.
    [124]韩志勇.定向井设计与计算[M].北京:石油工业出版社,1989,120~150.
    [125]李鹤林,李平全,冯耀荣.石油钻柱失效分析及预防[M].北京:石油工业出版社,1999,214~220.
    [126]石晓兵.大位移井中利用钻柱旋转作用清除岩屑床的机理研究[J].天然气工业,2000,20(2):50~54.
    [127]李克向,周煜辉,苏义脑.国外大位移井钻井技术[M].北京:石油工业出版社,1998,111~113.
    [128]艾秋波,李培佳,杨长路.G780一P15大位移近水平井钻进技术.钻井承包商协会论文集,中国钻井网,2005,12.
    [129] Menand S, Sellami H. Advancements in 3D Drillstring Mechanics: From the Bit to the Topdrive[C]. 2006, IADC/SPE 98965.
    [130]管志川,靳彦欣,王以法.直井底部钻柱运动状态的实验研究[J].石油学报,2003,24(6):102~106.
    [131] Bueno R C S, Petrobras S A, Morooka C K. Analysis Method for Contact Forces Between Drillstring-Well-Riser[C]. 1994, SPE 28723.
    [132]钱俊梅,江晓红.浅谈基于ANSYS软件的接触分析问题[J].煤矿机械,2006,27(7):62~64.
    [133]鲁世强,吴厚钰.有摩擦有间隙的三维接触间题有限元法及应用[J].应用力学学报.1996,13(7):56~63.

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