TIAN Jia-lin, WU Chun-ming, YANG Yong-wen, YAO Yu, YANG Zhi, YUAN Chang-fu, WU Bo. Numerical Analysis of Downhole Drill Strings With a Longitudinal and Lateral Coupled Vibration Model[J]. Applied Mathematics and Mechanics, 2017, 38(6): 685-695. doi: 10.21656/1000-0887.370214
 Citation: TIAN Jia-lin, WU Chun-ming, YANG Yong-wen, YAO Yu, YANG Zhi, YUAN Chang-fu, WU Bo. Numerical Analysis of Downhole Drill Strings With a Longitudinal and Lateral Coupled Vibration Model[J]. Applied Mathematics and Mechanics, 2017, 38(6): 685-695.

# Numerical Analysis of Downhole Drill Strings With a Longitudinal and Lateral Coupled Vibration Model

##### doi: 10.21656/1000-0887.370214
Funds:  The National Natural Science Foundation of China(51074202);The National Science and Technology Major Project of China(2016ZX05038)
• Rev Recd Date: 2016-08-19
• Publish Date: 2017-06-15
• Aimed at the complicated motion of the downhole drill string and based on the existing dynamics theory, the longitudinal and lateral coupled vibration model for the drill strings was established, and the numerical solution was obtained. According to the actual working condition of the downhole drill string, the entire drill string was regarded as the object of study. The concrete expressions of the dynamic stiffness, dynamic damping and the 1st 2 orders of natural frequencies were deduced with the analytical method and the dimensionless method in view of the coupled vibration characteristics of the downhole drill string. The research findings reveal that when the vibration frequency of the downhole drill string increases, the dynamic stiffness will periodically change with amplitude attenuation and the dynamic damping will periodically change with amplitude enhancement. The greater the length and the cross-sectional area of the downhole drill string are, the smaller the vibration amplitudes of the dynamic stiffness and the dynamic damping will be. Moreover, the Poisson’s ratio of the downhole drill string has no effect on the dynamic stiffness, the dynamic damping and the 1st 2 orders of natural frequencies. Meanwhile, the 2nd-order natural frequency of the drill string is always greater than the 1st. The proposed methods and model provide theoretical references and practical significances for further analysis and design optimization of the bottom-hole assembly (BHA).
•  [1] 胡育佳, 程昌钧, 杨骁. 水平振动下桩基的非线性动力学特性[J]. 应用数学和力学, 2005,26(6): 645-652. （HU Yu-jia, CHENG Chang-jun, YANG Xiao. Nonlinear dynamical characteristics of piles under horizontal vibration[J]. Applied Mathematics and Mechanics,2005,26(6): 645-652. （in Chinese）） [2] 胡以宝, 狄勤丰, 邹海洋, 等. 钻柱动力学研究及监控技术新进展[J]. 石油钻探技术, 2006,34(6)：7-10.（HU Yi-bao, DI Qing-feng, ZOU Hai-yang, et al. The new development of monitoring technology and researches on drill string dynamics[J]. Petroleum Drilling Technology,2006,34(6)：7-10.（in Chinese）） [3] 李子丰, 李志刚. 钻柱纵向振动分析[J]. 天然气工业, 2004,24(6): 10, 70-73.（LI Zi-feng, LI Zhi-gang. Analysis of longitudinal vibration of drill-string[J]. Natural Gas Industry,2004,24(6): 10, 70-73.（in Chinese）） [4] Gulyayev V I, Borshch O I. Free vibrations of drill strings in hyper deep vertical bore-wells[J]. Journal of Petroleum Science & Engineering,2011,78(3): 759-764. [5] 魏水平, 况雨春, 夏宇文. 基于 ANSYS 的钻柱纵向振动有限元分析及应用[J]. 河南石油, 2006,20(1): 66-68.（WEI Shui-ping, KUANG Yu-chun, XIA Yu-wen. ANSYS-based finite element analysis model of longitudinal vibration of drilling string and its application[J]. Henan Petroleum,2006,20(1): 66-68 .（in Chinese）） [6] 徐桃园, 张强, 陈灿, 等. 大位移井钻柱纵向振动理论分析与ANSYS计算[J]. 噪声与振动控制, 2010,30(2): 50-53.（XU Tao-yuan, ZHANG Qiang, CHEN Can, et al. Theoretical analysis and ANSYS calculation of longitudinal vibration of drill string[J]. Noise & Vibration Control,2010,30(2): 50-53.（in Chinese）） [7] Ghasemloonia A, Rideout D G, Butt S D. Analysis of multi-mode nonlinear coupled axial-transverse drillstring vibration in vibration assisted rotary drilling[J]. Journal of Petroleum Science & Engineering,2014,116(2): 36-49. [8] 丁天怀, 李成. 钻井液与钻柱的耦合纵向振动分析[J]. 机械工程学报, 2007,43(9): 215-219.（DING Tian-huai, LI Cheng. Analysis of coupling axial vibrations between drillling fluids and drillstring[J]. Chinese Journal of Mechanical Engineering,2007,43(9): 215-219.（in Chinese）） [9] 闫向宏, 孙建孟, 张美玲, 等. 钻柱扭转和纵向振动的等效网络分析[J]. 工程力学, 2011,28(2): 229-233, 245.（YAN Xiang-hong, SUN Jian-meng, ZHANG Mei-ling, et al. Analysis of torsional and longitudinal vibration of drill strings using equivalent network[J]. Engineering Mechanics,2011,28(2): 229-233, 245.（in Chinese）） [10] 徐鸿志, 王瑞和, 宋有胜, 等. 空气钻井条件下钻柱振动特性研究[J]. 天然气工业, 2011,31(6): 66-70, 128-129.（XU Hong-zhi, WANG Rui-he, SONG You-sheng, et al. Vibrating properties of the drill string during air drilling operations[J]. Natural Gas Industry,2011,31(6): 66-70, 128-129.（in Chinese）） [11] 孟庆华, 刘清友. 气体钻井钻柱气固耦合横向振动的数学建模与求解[J]. 应用力学学报, 2010,27(4): 830-833, 860.（MENG Qing-hua, LIU Qin-you. Mathematical model of lateral vibration of the drilling string with gas-solid coupling[J]. Chinese Journal of Applied Mechanics,2010,27(4): 830-833, 860.（in Chinese）） [12] 王鸿雁, 肖文生, 刘忠砚, 等. 钻井过程中钻柱的横-扭耦合振动分析[J]. 噪声与振动控制, 2014,34(1): 61-66. (WANG Hong-yan, XIAO Wen-sheng, LIU Zhong-yan, et al. Analysis of lateral-and-torsional coupled vibration of drill string during drilling process[J]. Noise & Vibration Control,2014,〖STHZ〗 34(1): 61-66.(in Chinese)) [13] 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(自然科学版), 2004,28(6): 68-71.（LI Mao-sheng, YAN Xang-zhen, GAO De-li. Influence of drilling fluid on natural frequency of drill string lateral vibration[J]. Journal of the University of Petroleum China,2004,28(6): 68-71.（in Chinese）） [14] 吴天新, 陆鑫森. 钻柱内外沿轴向流动的钻井液对钻柱横向振动的影响[J]. 振动与冲击, 1995(2): 1-6.（WU Tian-xin, LU Xin-shen. The influence of the annular and the internal drilling fluids flowing in axial on the lateral vibration of a drill collar[J]. Journal of Vibration and Shock,1995(2): 1-6.（in Chinese）） [15] Bukowitz D, Morán J, Bravo R. Computer model to predict drillstring lateral vibration modes and frequencies using the finite-element-method and modal analysis[J]. Revista Técnica de la Facultad de Ingeniería Universidad del Zulia,2008,31(2): 48-63. [16] 闫铁, 王雪刚, 李杉, 等. 钻柱轴向与横向耦合振动的有限元分析[J]. 石油矿场机械, 2012,41（3）: 39-42. （YAN Tie, WANG Xue-gang, LI Shan, et al. Finite element analysis of longitudinal and lateral coupled vibration of drilling[J]. Oil Field Equipment,2012,41（3）: 39-42.（in Chinese）） [17] 冯志鹏, 臧峰刚, 张毅雄. 三维横向流体诱发直管振动的数值模拟[J]. 应用数学和力学, 2013,34(12): 1311-1320.（FENG Zhi-peng, ZANG Feng-gang, ZHANG Yi-xiong. Numerical simulation of uniform tube vibration induced by 3-dimensional cross-flow[J]. Applied Mathematics and Mechanics,2013,34(12): 1311-1320. （in Chinese）） [18] REN Fu-shen, WANG Bao-jin, CHEN Su-li, et al. Nonlinear model and qualitative analysis for coupled axial/torsional vibrations of drill string[J]. Shock & Vibration,2016,2016(6): 1646814. [19] Musa N W, Gulyayev V I, Shevchuk L V, et al. Chaotic vibration analysis of the bottom rotating drill string[J]. Shock & Vibration,2014,49(1): 104-111.

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