内外液压作用下套管柱屈曲载荷的级数解

Critical buckling load of casing string subjected to internal and external liquid pressure

关于油井套管柱的屈曲问题虽已经有一些研究文献 ,但深入系统地研究该问题的文献并不多 ,由于其微分方程求解困难 ,各文献并没有给出一致的套管临界屈曲载荷 ;并且给出的结果普遍偏高。文章首次将套管和内、外部液体一起考虑 ,建立其微分方程 ,并用无穷级数法求解 ,得到了比较准确的临界屈曲载荷。论述了管柱内、外壁侧向液压对管柱发生屈曲的影响 ,对于开口管柱 ,当其处于微弯状态时 ,内、外壁侧向压力引起管柱任一截面的弯矩等于作用于底端的轴向力和沿轴线均匀分布的液柱重力所产生的弯矩。

Although some research papers have been published on buckling of casing string in vertical oil well,there are few papers which give systematic and thorough study on this problem,and these papers generally give some larger critical buckling loads than the real result.This paper thoroughly and systematically studies the problem about casing string buckling,and the deflection differential equation of casing string with internal liquid pressure was built and solved by using infinite series method.The results obtained are lower than those in other papers.The influence of internal and external pressure on buckling of casing string was discussed.The moment on any cross section produced by internal and external pressure is equal to that created by a axial force and a liquid string weight force.The result can be used by the designers and constructors of oil well.