受压旋转钻柱非线性动力学与分叉研究

STUDY ON NONLINEAR DYNAMICS AND BIFURCATIONS IN ROTATING COMPRESSIVE-DRILL STRING

在水平井钻井过程中,钻柱由于受压很容易发生横向振动,引发钻柱失效、井眼扩径等严重事故。该文将受压柔性旋转钻柱简化为柔性旋转梁,将钻柱受到的复杂载荷简化到柔性旋转梁系统中,基于von Karman理论建立了柔性钻柱的动力学方程,再利用Galerkin法离散偏微分方程,得到了钻柱的非线性控制方程,并且利用多尺度法得到了平均方程。运用非线性动力学的方法分析柔性旋转梁在共振情况下的复杂动力学响应,得出系统中钻柱旋转角速度对非线性动力学响应的变化规律。研究结果可为水平井钻井过程中减少钻柱失效、提高钻速和降低钻井成本提供参考。

In drilling process of horizontal wells, the transverse vibration of drill string likely occur due to axial compression, which may cause serious accidents such as drill string failure and hole expanding etc. In this paper, the compressive-drill string is simplified as a revolving flexible beam subjected to a load condition simplified from complicated excitations of drill string. Thus, the nonlinear dynamic model of flexible drill string is established based on the von Karman theory, where the partial differential equation is discreted by Galerkin method, and then the nonlinear control equation of drill string is acquired, and the average equation is obtained by multiscale method. The complex behaviour of flexible drilling string in resonance is analyzed by nonlinear dynamic method, and the dependence of nonlinear dynamics responses on rotating speed is investigated. The research results will provide a theoretical basis for the practical efforts of decreasing failure rate, improving drilling rate and reducing drilling cost during the drilling process of horizontal well.