井孔约束下水平井段钻柱的浑沌运动

CHAOTIC MOTION OF THE DRILLSTRING CONSTRAINED BY BOREHOLE IN HORIZONTAL SECTION

考虑了钻柱即时构形中轴向力对钻柱弯曲的影响 ,计及由于弯曲变形而产生的轴向附加力 ,得到了水平井段钻柱在周期性波动钻压激励下的非线性参数激励振动系统 ,导出了根据钻柱的物理和几何性质以及井孔尺寸计算系统参数的公式 .先通过Galerkin法对控制方程在空间域内加权消残 ,然后在时间域内用Melnikov Holmes方法得到了钻柱可能发生浑沌振动的参数激励的阈值 .文中结果可能对钻井轨迹的控制具有一定的指导意义 .

At the present time the controlling of trajectory of borehole is still a difficult problem for drilling engineers. Considering the effect of the axial force on the bending of the drillstring in horizontal section and taking the extra axial force caused by lateral deformation into account, this paper studies the nonlinear, parametrically excited system which can describe the vibration of the horizontal drillstring subjected to periodic weight on bit. The parameters of the dynamic system are formulated in terms of the physical and geometric character of the drillstring and the diameter of the well. After eliminating the residuals of the governing equation in space domain by Galerkin Method, the authors have got the threshold value of the parameter excitation that may trigger chaotic motion of the drillstring by means of Melnikov Holmes Method. The result obtained here may be helpful to improving the precision of controlling the trajectory of borehole.