Analysis of sinusoidal post-buckling deformation of horizontal coiled tubing with initial residual bending

In the process of horizontal well construction, the working environment in the well is very complicated. It is difficult to determine the actual deformation and force of the coiled tubing in the wellbore from the load change at the wellhead along. In addition, the coiled tubing wrapped around the reel and entering the wellbore through the injection head may cause an initial residual bending. In this paper, the mathematical model of the coiled tubing under axial load during buckling deformation is established, and the analytical solution with the time term is derived by reasonable simplification of the model. The effect of residual bending on the post-sinusoidal buckling of the coiled tubing in the horizontal well was investigated using the separation variable method. The effect of residual bending variations on the well wall contact forces is analyzed. The research shows that the initial parameter Г is the main factor influencing the post-sinusoidal buckling of the coiled tubing with residual bending. The larger the parameter value Г, the greater the effect of the residual bending on the post-sinusoidal buckling deformation of the coiled tubing, and the earlier the critical point of the mixed sinusoidal-helical buckling of the coiled tubing appears. The compression velocity of the coiled tubing has a significant effect on the well wall contact force. The faster the compression, the greater the contact force. By introducing the time term and the separation variable, this paper provides a new method and theoretical basis for further study of the process of entering sinusoidal-helical buckling of the coiled tubing with initial residual bending.