Dynamic Simulation of Drilling String System Based on Fluid-Structure Coupling

doi:10.12068/j.issn.1005-3026.2022.01.008

Abstract

Abstract: The nonlinear dynamics of the drilling string system is studied， and the fluid-structure coupling dynamic equation of the drilling string system is established. With the Galerkin truncation method， a set of partial differential equations are diverted into ordinary differential equations. Numerical simulation is carried out by using the Runge-Kutta integration method and the effects of parameters such as pulsating frequency， pulsation amplitude and mass ratio on the dynamic characteristics of the drilling string system are investigated. The results show that there are various dynamic behaviors for the model in different parametric excitation such as periodic motion， quasi-periodic motion， chaotic motion and jump discontinuous phenomenon. Besides， the path from chaotic motion to periodic motion is in the form of period-doubling inverse bifurcation， and the support stiffness can cause a certain change in the inherent characteristics of the system， which has a complex impact on the nonlinear dynamic behavior of the system.

Key words: drilling string system; nonlinear dynamics; fluid-structure coupling; parametric excitation; Galerkin method

CLC Number:

TH113

WANG Rong-peng， SONG Gui-qiu， ZHOU Shi-hua. Dynamic Simulation of Drilling String System Based on Fluid-Structure Coupling[J]. Journal of Northeastern University(Natural Science), 2022, 43(1): 56-64.

References

[1]李子丰.油气井杆管柱力学研究进展与争论［J］.石油学报，2016，37(4):53l-556.(Li Zi-feng.Research advances and debates on tubular mechanics in oil and gas wells［J］.Acta Petrolei Sinica，2016，37(4):531-556.)
[2]Ghasemloonia A，Rideout D G，Butt S D.A review of drilling string vibration modeling and suppression methods［J］.Journal of Petroleum Science and Engineering，2015，131(4):150-164.
[3]刘永升，高德利，王镇全，等.斜直井眼中钻柱横向动态运动非线性模型研究［J］.振动与冲击，2017，36(24):1-6.(Liu Yong-sheng，Gao De-li，Wang Zhen-quan，et a1.Nonlinear dynamic model of drilling string transverse motion in a deviated well ［J］.Journal of Vibration and Shock，2017，36(24):1-6.)
[4]王长进，李子丰，李银朋，等.充满液体的圆筒中受压屈曲杆柱旋转实验［J］.石油学报，2018，39(3):341-348.(Wang Chang-jin，Li Zi-feng，Li Yin-peng，et a1.Experiment on the rotation of compressional buckling column in the liquid-filled cylinder［J］.Acta Petrolei Sinica，2018，39(3):341-348.)
[5]王文龙，胡群爱，刘化伟，等.钻柱纵向振动分析与应用［J］.振动与冲击，2011，30(6):229-233.(Wang Wen-long，Hu Qun-ai，Liu Hua-wei，et a1.Analysis on longitudinal vibration of drill string and the corresponding application［J］.Journal of Vibration and Shock，2011，30(6):229-233.)
[6]王尊策，曹梦雨，徐德奎，等.基于梁-梁接触理论的管柱屈曲分析［J］.中国石油大学学报(自然科学版)，2017，41(2):132-138.(Wang Zun-ce，Cao Meng-yu，Xu De-kui，et al.Post-buckling analysis of tubes based on beam-to-beam contact theory［J］.Journal of China University of Petroleum(Natural Science Edition)，2017，41(2):132-138.)
[7]李子丰.钻柱涡动理论研究的必由之路钻井液动力润滑学与钻柱动力学相结合［J］.石油学报，2013，34(3):607-610.(Li Zi-feng.An inevitable way in drill-string whirling research:combinaton of drilling fluid power lubrication with drill string dynamics［J］.Acta Petrolei Sinica，2013，34(3):607-610.)
[8]Liu Y，Chávez J P，Sa R D，et al.Numerical and experimental studies of stick-slip oscillationsin drill-strings［J］.Nonlinear Dynamics，2017，90(4):2959-2978.
[9]Real F F，Batou A，Ritto T G.et al.Hysteretic bit/rock interaction model to analyze the torsional dynamics of a drill string aguiare［J］.Mechanical Systems and Signal Processing，2018，111(4):222-233.
[10]Kamel J M，Yigit A S.Modeling and analysis of stick-slip and bit bounce in oil well drillstrings equipped with drag bits［J］.Journal of Sound and Vibration，2014，333(25):6885-6899.
[11]Liang F，Gao A，Yang X D.Dynamical analysis of spinning functionally graded pipes conveying fluid with multiple spans［J］.Applied Mathematical Modelling，2020，83(3):454-469.
[12]Liang F，Yang X D，Qian Y J，et al.Transverse free vibration and stability analysis of spinning pipes conveying fluid［J］.International Journal of Mechanical Sciences，2018，137(1):195-204.
[13]Liang F，Yang X D，Zhang W，et al.Dynamical modeling and free vibration analysis of spinning pipes conveying fluid with axial deployment［J］.Journal of Sound and Vibration，2018，417:65-79.
[14]Zhang Y L，Chen L Q.External and internal resonances of the pipe conveying fluid in the supercritical regime［J］.Journal of Sound and Vibration，2013，332(9):2318-2337.
[15]Guzek A，Shufrin I，Pasternak E，et al.Influence of drilling mud rheology on the reduction of vertical vibrations in deep rotary drilling［J］.Journal of Petroleum Science and Engineering，2015，135(9):375-383 .
[16]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.
[17]Leonov G A，Kuznetsov N V，Kiseleva M A.et a1.Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor［J］.Nonlinear Dynamics，2014，77(1/2):277-288.
[18]Ritto T G，Aguiar R R，Hbaieb S.Validation of a drill string dynamical model and torsional stability［J］.Meccanica，2017，52(10):2959-2967.
[19]Hovda S.Semi-analytical model of the axial movements of an oil-well drillstring in vertical wellbores［J］.Journal of Sound and Vibration，2018，417(12):227-244.
[20]Zhao D P，Hovda S，Sangesland S.Abnormal down hole pressure variation by axial stick-slip of drillstring［J］.Journal of Petroleum Science and Engineering，2016，145:194-204.
[21]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 and Engineering，2014，116:36-49.
[22]Panda L N，Kar R C.Nonlinear dynamics of a pipe conveying pulsating fluid with parametric and internal resonances［J］.Nonlinear Dynamics，2007，49(1):9-30.
[23]Panda L N，Kar R C.Nonlinear dynamics of a pipe conveying pulsating fluid with combination，principal parametric and internal resonances［J］.Journal of Sound and Vibration，2008，309(5):375-406.
[24]Jin J D，Song Z Y.Parametric resonances of supported pipes conveying pulsating fluid［J］.Journal of Fluids and Structures，2005，20(6):763-783.
[25]Marcin K，Vahid V，Joseph P C，et al.Experimental studies of forward and backward whirls of drill-string［J］.Mechanical Systems and Signal Processing，2018，100(7):454-465.
[26]Wang L.A further study on the non-linear dynamic of simply supported pipes conveying pulsating fluid［J］.International Journal of Non-linear Mechanics，2009，44(1):115-121.
[27]Jin J D.Stability and chaotic motions of a restrained pipe conveying fluid［J］.Journal of Sound and Vibration，1997，208(3):427-439.(上接第55页)(Zhou Fan-hua，Wu Guang-qiang，Shen Hao，et al.Calculation of disc brake temperature in 15-cycle braking［J］.Automotive Engineering，2001，23(6):411-413.)
[7]张方宇，桂良进，范子杰.盘式制动器热-应力-磨损耦合行为的数值模拟［J］.汽车工程，2014，36(8):984-988.(Zhang Fang-yu，Gui Liang-jin，Fan Zi-jie.Numerical simulation on the coupling behavior between thermal load，contact stress and wear in a disc brake［J］.Automotive Engineering，2014，36(8):984-988.)
[8]初亮，马文涛，蔡健伟，等.基于车速的实时盘式制动器温度模型［J］.汽车工程，2016，38(1):61-64.(Chu Liang，Ma Wen-tao，Cai Jian-wei，et al.Realtime disc brake temperature model based on vehicle speed［J］.Automotive Engineering，2016，38(1):61-64.)
[9]孙冬野，刘升，郝允志，等.高强度制动轮边湿式制动器总成多场耦合下热可靠性分析［J］.汽车工程，2019，41(2):161-169.(Sun Dong-ye，Liu Sheng，Hao Yun-zhi，et al.Thermal reliability analysis of in-wheel wet brake assembly under high-intensity braking with multi-field coupling［J］.Automotive Engineering，2019，41(2):161-169.)
[10]Yuan K，Xiao N C，Wang Z L，et al.System reliability analysis by combining structure function and active learning Kriging model［J］.Reliability Engineering and System Safety，2020，195:106734.
[11]Cheng K，Lu Z Z.Structural reliability analysis based on ensemble learning of surrogate models［J］.Structural Safety，2020，83:101905.
[12]Xiao S，Oladyshkin S，Nowak W.Reliability analysis with stratified importance sampling based on adaptive Kriging［J］.Reliability Engineering and System Safety，2020，197:106852.
[13]Zhang X F，Wang L，Sorensen J D.AKOIS:an adaptive Kriging oriented importance sampling method for structural system reliability analysis［J］.Structural Safety，2020，82:101876.
[14]Guo Q，Liu Y S，Chen B Q，et al.An active learning Kriging model combined with directional importance sampling method for efficient reliability analysis［J］.Probabilistic Engineering Mechanics，2020，60:103054.
[15]Wang Q，Fang H.Reliability analysis of tunnels using an adaptive RBF and a first-order reliability method［J］.Computers and Geotechnics，2018，98:144-152.
[16]Yang Z，Pak U，Kwon C.Vibration reliability analysis of drum brake using the artificial neural network and important sampling method［J/OL］.Complexity，2021［2021-05-06］.https://doi.org/10.1155/2021/5517634.
[17]Zhang T，Zhou X P，Liu X F.Reliability analysis of slopes using the improved stochastic response surface methods with multicollinearity［J］.Engineering Geology，2020，271:105617.