Helical buckling of coiled tubing with initial bending curvature in three-dimensional curved wellbores

In this paper, a new buckling model of coiled tubing (CT) in a three-dimensional curved wellbore is established, considering the influence of the curvature and toolface angle of the wellbore and the initial CT bending curvature. First, with the wellbore curvature and toolface angle, the CT buckling configuration is based on the lower or outer curved side of the wellbore. When the initial CT bending curvature is less than the critical bending curvature, the initial CT configuration in the wellbore undergoes sinusoidal buckling; otherwise, the CT undergoes helical buckling. Second, the buckling model is solved by the energy method. After solving this buckling model, the critical CT helical buckling load, the critical bending curvature, and the quantitative relationship between the axial load and pitch can be obtained. Third, the CT contact force calculation method under a helical buckling configuration in a three-dimensional curved wellbore is given by combining the buckling model and the beam-column model. The influence of the initial bending curvature is also considered. Finally, the calculated values of the buckling model and contact force calculation method were compared with existing experimental data and published models to validate the proposed model. Therefore, the methods presented in this paper can be used to not only predict helical CT buckling but also optimize downhole engineering design parameters considering the influence of the initial bending curvature in more realistic drilling wellbore conditions.