Buckling configurations of tubular strings constrained in three-dimensional curved wellbores

A new model depicting the buckling configuration of a tubular string in a three-dimensional curved wellbore is proposed. During modeling, the toolface angle is considered, and the sinusoidal buckling and helical buckling of the tubular string are considered on the basis of alignment with either the lower curved side or the outer curved side of the wellbore. After modeling, the energy method is used to solve the model, and the critical buckling load, which is related to the relationship between the buckling configuration and the axial load, can be obtained. The critical buckling loads calculated using the model presented in this paper are consistent with the measured data from published experiments and the trends of the He and Kyllingstad model. The results of the new model also show that with an increasing wellbore curvature, the influence of the toolface angle on the critical buckling load and the characteristic parameters of the buckling configuration (wavelength, amplitude, and pitch) decreases. Based on the expressions for the quantitative relationships between these characteristic parameters and the axial load, procedures for calculating the contact force and the bending moment are given. The results for the contact force show that the calculated values from the Johancsik et al. model and the Mitchell model are the average values calculated using the procedures presented in this paper for tubular strings under sinusoidal buckling and helical buckling, respectively. The calculation results show that the influence of the toolface angle on the bending moment of a tubular string under helical buckling is less than that under sinusoidal buckling. By using this model, not only can the critical buckling loads, contact forces and bending moments of tubular strings in three-dimensional curved wellbores be calculated, but the trends of these calculated values with the buckling configuration can also be identified to guide the selection of the control parameters for tubular strings in the field.