Experimental and Numerical Simulation Research on the Nonlinear Coupled Longitudinal-torsional Vibration of a Drill-string

doi:10.3901/JME.2025.23.134

Abstract

Abstract: The nonlinear coupled longitudinal-torsional vibration of a drill-string is investigated by using a novel multifunctional experimental drilling rig capable of simulating key vibration modes, including stick-slip, bit-bounce, whirling, and helical buckling. Experimental and parametric studies first elucidate the stick-slip vibration mechanism and the longitudinal-torsional coupling effects. Results demonstrate that increasing the driving speed and reducing the effective weight-on-bit can help to alleviate the torsional vibration of drill-string and even eliminate the stick-slip phenomenon. Subsequently, steady-state drilling experiments examine bit-rock interaction, leading to the development of a mathematical model with characteristic parameter identification. Based on these findings, a lumped parameter model incorporating stick-slip, bit-bounce, and the regeneration effect of rock-breaking is established. The model's validity is confirmed through excellent agreement between simulations and experimental data, enabling further numerical analysis of nonlinear coupled longitudinal-torsional vibration. The research results provide theoretical basis for optimizing drill-string structure and drilling parameters to suppress harmful vibration and enhance drilling efficiency.

Key words: drill-string system, coupled longitudinal-torsional vibration, stick-slip vibration properties, bit-rock interaction, lumped parameter model

CLC Number:

TE38

XIE Dou, WU Qinyao, SHE Lunyuan, ZOU Min, WANG Changcheng, LI Weicheng. Experimental and Numerical Simulation Research on the Nonlinear Coupled Longitudinal-torsional Vibration of a Drill-string[J]. Journal of Mechanical Engineering, 2025, 61(23): 134-144.

References

[1] BERLIOZ A,DER HAGOPIAN J,DUFOUR R,et al. Dynamic behavior of a drill-string:Experimental investigation of lateral instabilities[J]. Journal of Vibration and Acoustics,1996,118(3):292-298.
[2] ZAMUDIO C A,TLUSTY J L,DAREING D W. Self-excited vibrations in drill strings[C]//SPE Annual Technical Conference and Exhibition,September 27-30,1987,Dallas,Texas,SPE no. 16661.
[3] SPANOS P D,CHEVALLIER A M,POLITIS N P,et al. Oil and gas well drilling:A vibrations perspective[J]. The Shock and Vibration Digest,2003,35(2):85-103.
[4] GUPTA S K,WAHI P. Tuned dynamics stabilizes an idealized regenerative axial-torsional model of rotary drilling[J]. Journal of Sound and Vibration,2018,412:457-473.
[5] LIU J,WANG J,GUO X,et al. Investigation on axial-lateral-torsion nonlinear coupling vibration model and stick-slip characteristics of drilling string in ultra-HPHT curved wells[J]. Applied Mathematical Modelling,2022,107:182-206.
[6] GHASEMLOONIA A,RIDEOUT D G,BUTT S D. A review of drillstring vibration modeling and suppression methods[J]. Journal of Petroleum Science and Engineering,2015,131:150-164.
[7] LI Z,ZHANG C,SONG G. Research advances and debates on tubular mechanics in oil and gas wells[J]. Journal of Petroleum Science and Engineering,2017,151:194-212.
[8] 狄勤丰,杨赫源,王文昌,等. 钻柱动力学研究进展及发展趋势[J]. 石油科学通报,2024,9(2):224-239. DI Qinfeng,YANG Heyuan,WANG Wenchang,et al. Research advances and development trend of drill string dynamics[J]. Petroleum Science Bulletin,2024,9(2):224-239.
[9] RICHARD T,GERMAY C,DETOURNAY E. Self-excited stick-slip oscillations of drill bits[J]. Comptes Rendus Mécanique,2004,332(8):619-626.
[10] RICHARD T,GERMAY C,DETOURNAY E. A simplified model to explore the root cause of stick-slip vibrations in drilling systems with drag bits[J]. Journal of Sound and Vibration,2007,305(3):432-456.
[11] NANDAKUMAR K,WIERCIGROCH M. Stability analysis of a state dependent delayed,coupled two DOF model of drill-string vibration[J]. Journal of Sound and Vibration,2013,332(10):2575-2592.
[12] YAN Y,WIERCIGROCH M. Dynamics of rotary drilling with non-uniformly distributed blades[J]. International Journal of Mechanical Sciences,2019,160:270-281.
[13] GUPTA S K,WAHI P. Criticality of bifurcation in the tuned axial-torsional rotary drilling model[J]. Nonlinear Dynamics,2018,91:113-130.
[14] GUPTA S K,WAHI P. Bifurcations in the axial-torsional state-dependent delay model of rotary drilling[J]. International Journal of Non-Linear Mechanics,2018,99:13-30.
[15] ZHANG H,DETOURNAY E. An alternative formulation for modeling self-excited oscillations of rotary drilling systems[J]. Journal of Sound and Vibration,2020,474:115241.
[16] 张鹤,狄勤丰,王文昌,等. 基于状态依赖时滞的钻柱动力学稳定性分析[J]. 振动与冲击,2022,41(22):233-240,283. ZHANG He,DI Qinfeng,WANG Wenchang,et al. Numerical stability analysis of the rotary drilling system on the basis of state-dependent delay[J]. Journal of Vibration and Shock,2022,41(22):233-240,283.
[17] LIU X,VLAJIC N,LONG X,et al. Nonlinear motions of a flexible rotor with a drill bit:stick-slip and delay effects[J]. Nonlinear Dynamics,2013,72:61-77.
[18] XIE D,HUANG Z,MA Y,et al. Nonlinear dynamics of lump mass model of drill-string in horizontal well[J]. International Journal of Mechanical Sciences,2020,174:105450.
[19] MILLHEIM K,JORDAN S,RITTER C J. Bottom-hole assembly analysis using the finite-element method[J]. Journal of Petroleum Technology,1978,30(2):265-274.
[20] GERMAY C,DENOËL V,DETOURNAY E. Multiple mode analysis of the self-excited vibrations of rotary drilling systems[J]. Journal of Sound and Vibration,2009,325(1-2):362-381.
[21] LIU X,LONG X,ZHENG X,et al. Spatial-temporal dynamics of a drill string with complex time-delay effects:Bit bounce and stick-slip oscillations[J]. International Journal of Mechanical Sciences,2020,170:105338.
[22] XIE D,WU Q,XI Y,et al. Global modelling of nonlinear spatiotemporal dynamics of a drill-string with multiple regenerative effects[J]. Applied Mathematical Modelling,2023,114:114-132.
[23] 朱才朝,冯代辉,陆波,等. 钻柱结构与井壁岩石互作用下系统耦合非线性动力学研究[J]. 机械工程学报,2007,43(5):145-149. ZHU Caichao,FENG Daihui,LU Bo,et al. Nonlineaer study on dynamic action of integrated drill string-well rock system[J]. Journal of Mechanical Engineering,2007,43(5):145-149.
[24] 程载斌,姜伟,任革学,等. 全井钻柱系统多体动力学模型[J]. 石油学报,2013,34(4):753-758. CHENG Zaibin,JIANG Wei,REN Gexue,et al. A multibody dynamical model of full-hole drillstring system[J]. Acta Petrolei Sinica,2013,34(4):753-758.
[25] 郭晓强,柳军,王建勋,等. 超高温高压曲井钻柱纵-横-扭耦合振动模型及黏滑振动特性研究[J]. 机械工程学报,2022,58(5):119-135. GUO Xiaoqiang,LIU Jun,WANG Jianxun,et al. Study on axial-lateral-torsion coupling vibration model and stick-slip characteristics of drilling string in ultra-HPHT curved wells[J]. Journal of Mechanical Engineering,2022,58(5):119-135.
[26] 陈益丽,柳军,梁爽. 钻井液流变性对转盘钻井钻柱耦合振动抑制的参数影响研究[J]. 机械工程学报,2024,60(5):183-195. CHEN Yili,LIU Jun,LIANG Shuang. Influence of rheological parameters of drilling fluid on the coupling vibration suppression of drillstring in rotary table drilling[J]. Journal of Mechanical Engineering,2024,60(5):183-195.
[27] LOBO D M,RITTO T G,CASTELLO D A,et al. On the calibration of drill-string models based on hysteresis cycles data[J]. International Journal of Mechanical Sciences,2020,177:105578.
[28] FINNIE I,BAILEY J J. An experimental study of drill-string vibration[J]. Journal of Engineering for Industry,1960,82(2):129-135.
[29] JOGI P N,MACPHERSON J D,NEUBERT M. Field verification of model-derived natural frequencies of a drill string[J]. Journal of Energy Resources Technology,2002,124(3):154-162.
[30] SHEN Y,ZHANG Z,ZHAO J,et al. The origin and mechanism of severe stick-slip[C]//SPE Annual Technical Conference and Exhibition,October 9-11,2017,San Antonio,Texas,SPE no. 187457.
[31] PATIL P A,TEODORIU C. A comparative review of modelling and controlling torsional vibrations and experimentation using laboratory setups[J]. Journal of Petroleum Science and Engineering,2013,112:227-238.
[32] MELAKHESSOU H,BERLIOZ A,FERRARIS G. A nonlinear well-drillstring interaction model[J]. Journal of Vibration and Acoustics,2003,125(1):46-52.
[33] KHULIEF Y A,AL-SULAIMAN F A. Laboratory investigation of drillstring vibrations[J]. Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2009,223(10):2249-2262.
[34] ALZIBDEH A,ALQARADAWI M,BALACHANDRAN B. Effects of high frequency drive speed modulation on rotor with continuous stator contact[J]. International Journal of Mechanical Sciences,2017,131-132:559-571.
[35] ELSAYED M A. A novel approach to dynamic representation of drill strings in test rigs[J]. Journal of Energy Resources Technology,2007,129(4):281-288.
[36] REAL F F,LOBO D M,RITTO T G,et al. Experimental analysis of stick-slip in drilling dynamics in a laboratory test-rig[J]. Journal of Petroleum Science and Engineering,2018,170:755-762.
[37] KAPITANIAK M,HAMANEH V V,CHÁVEZ J P,et al. Unveiling complexity of drill-string vibrations:Experiments and modelling[J]. International Journal of Mechanical Sciences,2015,101-102:324-337.
[38] KAPITANIAK M,VAZIRI V,CHÁVEZ J P,et al. Experimental studies of forward and backward whirls of drill-string[J]. Mechanical Systems and Signal Processing,2018,100:454-465.
[39] MACLEAN J D J,VAZIRI V,APHALE S S,et al. Suppressing stick-slip oscillations in drill-strings by modified integral resonant control[J]. International Journal of Mechanical Sciences,2022,228:107425.
[40] YUAN Y,CHEN W,WIERCIGROCH M. Experimentally calibrated FE modelling of helical buckling of anisotropic slender shafts[J]. International Journal of Mechanical Sciences,2024,275:109320.
[41] LIN W,CHÁVEZ J P,LIU Y,et al. Stick-slip suppression and speed tuning for a drill-string system via proportional-derivative control[J]. Applied Mathematical Modelling,2020,82:487-502.
[42] HUANG Z,XIE D,XIE B,et al. Investigation of PDC bit failure base on stick-slip vibration analysis of drilling string system plus drill bit[J]. Journal of Sound and Vibration,2018,417:97-109.
[43] TUCKER R W,WANG C. Torsional vibration control and cosserat dynamics of a drill-rig assembly[J]. Meccanica,2003,38:145-161.
[44] XUE Q,LEUNG H,WANG R,et al. The chaotic dynamics of drilling[J]. Nonlinear Dynamics,2016,83:2003-2018.