Abstract: The dynamic equations of helically buckled pipe string in vertical wells are a group of high order nonlinear ordinary differential equations,which describe the axial force distribution and deformation behavior of pipe.This paper acquires the asymptical helix solutions of the nonlinear equations under a symmetric condition;presents the influence of frictional coefficient on the axial force distribution along the pipe,the locations of nutral point and lock-up point,and the lock-up force etc.,derives the formulae to determine the neutral point,the lock-up point and the lock-up force.The correlation of the frictional coefficients and the axial force distribution is presented in curves,neutral point and lock-up point varying with the axial force acting on the top or bottom end are also shown in the curves.The results in this paper can be practically used for pipe string design and operational parameter selection for HPHT deep well down hole operations.

Key words: oil well, pipe string, frictional force, deformation, force analysis

摘要： 描述垂直井中螺旋弯曲管柱轴力分布和变形行为的力学方程是一组高阶非线性常微分方程组.求得了这组非线性方程在对称性条件下的渐近螺线解;分析了摩擦系数对整个管柱上的轴力分布、“中性点”位置、“自锁点”位置以及“自锁力”等的影响;导出了“中性点”、“自锁点”以及“自锁力”的计算公式;并绘制出对应不同摩擦系数的轴力分布曲线以及“中性点”、“自锁点”随端部轴压变化的曲线.本文研究的结果对于高温、高压深井井下作业管柱的合理设计和作业参数的合理选择等具有较大的实用价值.

关键词: 油井, 管柱, 摩擦力, 变形, 受力分析