Study on Sinusoidal Post-Buckling Deformation of Coiled Tubing in Horizontal Wells Based on the Separation Constant Method

Abstract

In this paper, a set of partial differential equations considering the dynamic effects of the coiled tubing (CT) is established based on the bending theory of slender beams considering the axial loads. The analytical solution of sinusoidal deformation with the time term is obtained. The critical load of coiled tubing during sinusoidal buckling and the change of half-wave number during sinusoidal post-buckling are studied through the introduction of the necessary conditions, solution and the separation constant. The contact force of coiled tubing with sinusoidal post-buckling on the horizontal well wall is analyzed. The results show that the critical load for sinusoidal buckling of fixed-size CT is related to the section angular acceleration coefficient. The half-wave number produced by the sinusoidal post-buckling bending of the CT gradually decreases during compression. The contact force of the deformed CT to the borehole wall is related to the compression speed of the CT. By introducing the dynamic term and the separation constant, this research model can provide a theoretical basis for studying the transformation of the CT from sinusoidal buckling to helical buckling.