Inter-helical and intra-helical buckling analyses of tubular strings with connectors in horizontal wellbores

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.