关键词: 水平井, 管柱, 稳定性, 变形, 非线性微分方程

Abstract: In this paper,a four order nonlinear differential equation with a parameter β, which describes the buckling deformation of pipes inhorizontal wells,is derived by using the principle of minimum potential energy and the variational method. Two bifurcation points (β₁=1,β₂=1.47) as well as the two critical buckling loads Fcrsand Fcrhare obtained and the three different types of bifurcation solutions are also analysized. When β<β₁, the nonlinear equation has a zero solution,which is related to the stable state of the pipes. When β₁≤β<β₂, the equation has a peoriodic solution,which is related to the sinusoidal buckling state. And when β≥β₂, it has a helix solution,which is related to the helical buckling state. The results obtained here are very important for correctly designing pipes and reasonably selecting working parameters in horizontal well drilling,completing and stimulating operations.

Key words: horizontal well, pipe, stability, deformation, non-linear differential equation