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Helical buckling of tubular strings with connectors is divided into two sub-problems: inter-helical buckling and intra-helical buckling. The suspended section of the tubular string is depicted by beam-column model and the continuous contact section is depicted by helix. Further introducing the continuous conditions, boundary conditions and periodic conditions, the deflection curves of tubular strings can be determined. On the basis of energy stability condition, the critical helical buckling loads are deduced by introducing the potential energy factor. The contact forces on contact points and continuous contact sections and maximum bending moments on tubular strings are calculated. The above studied are further applied into a case study. At last, the supporting effect and boundary effect caused by connectors are introduced and the relationship between inter-helical buckling and intra-helical buckling modes is clarified. The results indicate that for connectors of smaller diameters, the supporting effect plays the most important role and inter-helical buckling is easier to initiate. However, for connectors of larger diameters, the constraint effect is dominant and intra-helical buckling is more likely to occur. Increasing connector diameter and decreasing the length between adjacent connectors can increase critical helical buckling loads. Both the contact forces and maximum bending moments in the intra-helical buckling mode are larger than that in the inter-helical buckling mode, so intra-helical buckling should be avoided in the optimal design of connectors on tubular strings. [ABSTRACT FROM AUTHOR]

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. • A buckling model for a tubular string in a three-dimensional curved wellbore is established. • The critical buckling loads and the parameters (wavelength, amplitude, and helix pitch) can be obtained by the model. • The critical buckling loads calculated by the model are consistent with the values measured in published experiments. • Based on the buckling model, the contact force and bending moment of the tubular string can be determined. [ABSTRACT FROM AUTHOR]