Abstract: The buckling equation of pipe string in horizontal boreholes is a fourth non-linear ordinary differential equation with a small parameter.There are two critical points for the equation.One is related to sinusoidal buckling,another is to helical buckling.The two critical buckling loads are solved with linearization method and perturbation method in this paper,the results obtained by this paper well coincide with those given by others with energy method or experimental data.In this paper,the normal contact force between the borehole wall and buckled pipe string,bending moment and stress are analyzed as well.

Key words: pipe string, horizontal well, stability, differential equation, force analysis

摘要： 管柱在水平井眼中的屈曲方程是一个含有小参数的四阶非线性常微分方程.屈曲方程有两个临界点,一个对应于正弦屈曲,另一个对应于螺旋屈曲.本文利用线性化分析方法和小参数摄动分析方法,求得了两个相应的临界屈曲载荷.其结果与他人用能量法导出的结果和用实际数据拟合的结果非常吻合.本文还对管柱屈曲后与井壁之间的法向接触力、弯矩及应力等进行了分析.

关键词: 管柱, 水平井, 稳定性, 微分方程, 受力分析