水平井造斜段弯曲钻柱振动方程的建立及求解

Establishment and solution of the vibration equation on the bending drill string in horizontal wells' whipstocking section

以定向造斜井段中的弯曲钻柱为研究对象,分析其钻进过程中轴向振动和扭转振动,考虑钻井液阻尼、自重和与井壁摩擦对振动特性的耦合作用,建立系统动力学模型,推导出振动微分方程并确定约束条件。对求解方法和过程进行研究探讨,在给定初始条件和边界条件下,采用假设模态法求解钻柱振动模型,得出轴向振动和扭转振动特性的近似表达式。其建模理论、思路和对振动方程的求解讨论可推广应用于不同轨迹井段中的钻柱。

Taking the bending drill string in the horizontal wells' whipstocking section as the research object,the paper analyzes its axial and torsional vibration.Considering the coupling effect on the vibration characteristics of the drilling fluid friction,dead weight and its friction on the well wall,the model of systematic dynamics was established,the vibration differential equation was derived and the constraints were determined.The method and process of solution were studied.Given the initial and boundary conditions,the assumed mode method was adopted to solve the drill string vibration model to obtain the approximate expressions of axial and torsional vibration characteristics.Its modelling theory,line of thought and solution and discussion of the vibration equation can be widely applied to the drill strings in different-track sections.