Boundary Conditions: A Key Factor in Tubular-String Buckling

Abstract

Summary Boundary conditions for tubular-string buckling are divided into two kinds on the basis of the virtual work of the nonaxial force on the boundary conditions of the tubular string—namely, the first and the second kinds of boundary conditions. The first kind of boundary conditions means that the virtual work of no-axial force is zero, and both the conventional pinned and fixed ends belong to this kind. The second kind of boundary conditions means that the virtual work of no-axial force is not zero. Previous studies on tubular-string buckling mainly focus on the first kind but ignore the second kind of boundary conditions. In this paper, the effects of the two kinds of boundary conditions on tubular-string buckling are analyzed. The deflection of a long tubular string constrained in a wellbore is divided into the full helical-buckling section and transition section, whereas the transition section is divided further into the no-contact section and perturbed-helix section. The qualitative corresponding relation between boundary conditions and tubular-string buckling in transition and full helical-buckling sections is clarified. To clarify the quantitative relation between boundary conditions and tubular-string buckling, a general-packer model is proposed to depict the two categories of boundary conditions. With the general-packer model, the general potential energy of the tubular string is deduced. According to the minimum-potential-energy principle, the existence and stability of full helical-buckling solutions are given. The deflections of the tubular string in the no-contact and perturbed-helix sections are deduced with buckling differential equation and beam-column model. The bending moment, shear force, and contact force on the tubular string caused by buckling are also analyzed. The results show that boundary conditions, especially the second kind of boundary conditions, are an important factor that makes the tubular-string buckling problem complex, and this paper provides one source for a deeper understanding of boundary conditions.