直井中钻柱非线性屈曲的DQ法分析

Differential quadrature method for nonlinear buckling analysis of tubing in straight wells

采用微分求积法(DQ method)对直井中钻柱非线性屈曲控制微分方程进行了求解,在力学模型中考虑了钻柱重力和井壁切向摩擦的影响,摒弃了传统分析中的等螺距和小位移假设。分析表明:无摩擦时的DQ法计算结果与有限元的分析结果吻合,DQ法能对钻柱的非线性屈曲问题进行正确分析;井壁的切向摩擦能减缓钻柱的屈曲,井壁摩擦对钻柱屈曲的影响不可忽略。为直井中钻柱非线性屈曲的摩阻分析提供了一种新的算法,同时也将DQ法应用到石油机械工程领域当中。

The governing differential equilibrium equations of tubing buckling nonlinearly in straight wells with tangential friction effect were solved by the differential quadrature（DQ） method. The effects of tubing gravity and the friction between the tubing and the bore-hole were included. The assumptions of constant pitch and small angle displacement in traditional analysis were abandoned. It is shown that the results obtained from DQ method with no friction fit well with thoses obtained by finite element analysis, and the nonlinear buckling problem of tubing can be solved by DQ method. The tangential friction can weaken the buckling of tubing, thus can not be neglected. A new algorithm for the tubing buckling nonlinearly with friction was proposed, and the DQ method can be applied to petroleum engineering field.