广义边界下含双相流水平井钻柱频率特性分析

钻柱在内流作用和旋转因素的影响下容易产生耦合振动，发生疲劳失效。本文基于微分求积法（DQM）对含双相流水平井钻柱耦合动力学特性进行了研究。利用扩展的Hamilton变分原理建立了计入内流、轴向压力及旋转等因素影响的水平井钻柱动力学方程。在振动问题中考虑了广义边界条件，通过改变边界等效弹簧刚度将模型简化为简支、悬臂等简单边界条件模型进行研究。通过分析旋转角速度、轴向压力、液相流速、气体体积分数等因素对模型频率特性的影响，得到了无量纲固有频率随不同参数变化的特征曲线。分析结果表明：不同边界条件下模型的频率特性曲线有很大的差别；气体体积分数对临界流速的影响在悬臂管系统中表现的更为明显；在简支管模型中，随着轴力的增大会产生模态耦合颤振。此外，通过液相流速和旋转角速度的频率云图展示了两种因素对钻柱频率特性的影响。

Analysis of Frequency Characteristics of Horizontal Well Drill String with Two-phase Flow Under Generalized Boundary Conditions

Under the influence of internal fluid and Coriolis force generated by rotation, the drilling string easily brings about coupled vibration, causing serious accidents such as fatigue failure. Based on the differential quadrature method (DQM), this paperstudiedthe dynamic characteristics of the drilling string in a horizontal well with two-phase flow affected by multiple factors. Using the extended Hamilton variational principle, the dynamics equation for thedrill stringis established that takes into account the influence factors such as internal fluid, axial pressure and rotation. The generalized boundary condition is used to solve the vibration problem. The boundary condition model is simplified, and the cantilever is supported by changing the stiffness of the boundary equivalent spring. By analyzing the influence factors such as rotational angular velocity, axial pressure, fluid velocity, gas volume fraction and other factors on the frequency characteristics of the model, the characteristic curve of the dimensionless natural frequency with different parameters are obtained. The analysis results show that: the frequency characteristic curve of the model under different boundary conditions is very different; the influence of gas volume fraction on critical flow velocity is more obvious in the cantilever pipe system; with the simply supported pipe system, as the axial pressure increases, the cantilever pipe system may exhibit modal coupling flutter. In addition, the frequency cloud diagram of the fluid velocity and the rotational angular velocity demonstrates the influence of the two factors on the frequency characteristics of the drilling string.