钻井液与钻柱的耦合纵向振动分析
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摘要
考虑钻井液与钻柱的泊松耦合,基于管内外钻井液与钻柱间的耦合纵向波动方程组,应用特征矢量法,研究地层切变模量和钻柱泊松比边界对钻柱内纵向应力波和钻井液纵向压力波传输的影响。在此基础上推导钻柱纵向振动的频率方程,引入等效质量分析管内外液动压力下的钻柱固有频率。理论求解表明,钻柱的泊松效应造成应力波与压力波耦合,且管内外不同介质间的波速耦合对压力波的影响明显,而对应力波的影响较弱,故耦合对泥浆脉冲传输的影响远大于钻柱声遥测。钻井液的液动压力增加纵振的惯性质量,导致固有频率与不考虑钻井液相比有较大下降。综合等效粘惯性质量、粘性阻尼系数和钻井液惯性力,建立多因素影响下的钻柱纵向耦合振动模型。
Considering the Possion coupling mechanism bet- ween them,the equations of motion for the drillstring and drilling fluids inside and outside the drillstring are developed. The eigenvector method is used to study the effects of shear modulus of formation and Possion ratio of drillstring on stress wave and pressure wave propagations.The frequency equation of drillstring axial vibration is deduced.The theoretical results show that the strong coupling occurs between the inner and outer fluids because of approximately the same wave speed, while the coupling effect between the fluid modes and the pipes mode is much weaker.Thus the coupling has more effect on mud pulse telemetry than drillstring acoustic telemetry. Furthermore,since the inner and outer drilling fluid pressure adds the inertial mass of drillstring,the natural frequency of drillstring axial vibration drops compared with inexistence of drilling fluids.The coupling equation of axial motion for the drillstring is expressed in terms of viscous inertial mass, viscous damping coefficient,drilling fluid pressure and inertial force.
Considering the Possion coupling mechanism bet- ween them,the equations of motion for the drillstring and drilling fluids inside and outside the drillstring are developed. The eigenvector method is used to study the effects of shear modulus of formation and Possion ratio of drillstring on stress wave and pressure wave propagations.The frequency equation of drillstring axial vibration is deduced.The theoretical results show that the strong coupling occurs between the inner and outer fluids because of approximately the same wave speed, while the coupling effect between the fluid modes and the pipes mode is much weaker.Thus the coupling has more effect on mud pulse telemetry than drillstring acoustic telemetry. Furthermore,since the inner and outer drilling fluid pressure adds the inertial mass of drillstring,the natural frequency of drillstring axial vibration drops compared with inexistence of drilling fluids.The coupling equation of axial motion for the drillstring is expressed in terms of viscous inertial mass, viscous damping coefficient,drilling fluid pressure and inertial force.
引文
[1]PLACIDO J C R,SANTOS H M R,GALEANO Y D. Drillstring vibration and wellbore instability[J].Journal of Energy Resources Technology,2002,124(4):217-222.
[2]ZHANG Q,MISKA S.Effects of flow-pipe interaction on drill pipe buckling and dynamics[J].Journal of Pressure Vessel Technology,2005,127(2):129-136.
[3]RICHTER U.Effect of mud pulses to drill string vibrations [M].Kleinwalsertal:German Polish Workshop,1999.
[4]BERND S,EBERHAND B,ANDREAS B,et al.Drilling dynamics in the presence of mud flow[C]//SPE59236, 2000.
[5]MITCHELL R F.Dynamic surge/swab pressure predictions [J].SPE Drilling Engineering,1988:325-333.
[6]LEE H Y.Drillstring axial vibration and wave propagation in boreholes[D].Gambridge:Massachusetts Institute of Technology,1991.
[7]屈展．钻井液液动压力对钻柱纵向振动的影响[J]．石油机械，1993，21(6)：21-24，50．
[8]LEA S H,KYLLINGSTAD A.Propagation of coupled pressure waves in borehole with drillstring[C]//SPE37156, 1996:963-972.
[9]居荣初，曾心传．弹性结构与液体的耦联振动理论[M]．北京：地震出版社，1983．
[10]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．
[2]ZHANG Q,MISKA S.Effects of flow-pipe interaction on drill pipe buckling and dynamics[J].Journal of Pressure Vessel Technology,2005,127(2):129-136.
[3]RICHTER U.Effect of mud pulses to drill string vibrations [M].Kleinwalsertal:German Polish Workshop,1999.
[4]BERND S,EBERHAND B,ANDREAS B,et al.Drilling dynamics in the presence of mud flow[C]//SPE59236, 2000.
[5]MITCHELL R F.Dynamic surge/swab pressure predictions [J].SPE Drilling Engineering,1988:325-333.
[6]LEE H Y.Drillstring axial vibration and wave propagation in boreholes[D].Gambridge:Massachusetts Institute of Technology,1991.
[7]屈展．钻井液液动压力对钻柱纵向振动的影响[J]．石油机械，1993，21(6)：21-24，50．
[8]LEA S H,KYLLINGSTAD A.Propagation of coupled pressure waves in borehole with drillstring[C]//SPE37156, 1996:963-972.
[9]居荣初，曾心传．弹性结构与液体的耦联振动理论[M]．北京：地震出版社，1983．
[10]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．
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