Abstract: The problem of casing string stability was presented by Lubinski in 50's.Many papers have been published since then.In the view of theoretical reserch, this paper gets the numerical solution of critical force by considering the influence of full length and end constraints of casing string.The result is 15% larger than that given by Lubirski. With the influence of inside and outside pressure about critical force, this paper proves that the "Fititious Force" is equal to the minus of critical forces of open end tube and closed end tube, that is the end pressure force acting on the closed end of tube.

Key words: casing string, stability, force analvsis, Bessel function, critical value, fluid column pressure

摘要： 自鲁宾斯基50年代提出油井套管柱直立稳定性问题以来,国内外已发表许多论文[1～5],但从理论研究考虑,还应作进一步研究。本文以井口为坐标原点建立基本方程,明确考虑套管柱全长及上下两端约束条件,分析下端轴向力的失稳临界值。对确定临界值的超越方程进行了比较详细的数值研究,所得结果比鲁氏给出的约大15%.关于套管柱内外液压对临界力的影响问题,本文证明了所谓“虚拟力”就是开口管柱临界力与闭口管柱临界力之差,就是管柱下端的封头力。

关键词: 套管柱, 稳定性, 力分析, 贝塞尔函数, 临界值, 液柱压力