Equilibrium equations for nonlinear buckling analysis of drill-strings in 3D curved well-bores

Abstract

With the development of drilling technology, the oil/gas well has evolved from its early vertical straight form to the inclined, horizontal, plane curved, or even 3D curved well-bore. Understanding of the buckling behavior of a drill-string in a well-bore is crucial for the success of a drilling operation. Therefore, equilibrium equations for analyzing the buckling behavior of a drill-string in a 3D curved well-bore are required. Based on Love’s equilibrium equations for a curved and twisted rod in space, a set of equilibrium equations for the nonlinear buckling analysis of a drill-string in a 3D curved well-bore are derived by introducing a radial constraint of the well-bore. The proposed formulae can account for the well curvature and tortuosity. Thus, it can be used to analyze the buckling behaviors of a drill-string constrained in a well-bore and subjected to axial compression, torsion at its upper end, and gravity simultaneously. It is worth noting that the existing equations in the literature for a drill-string in a straight and plane curved well-bore with a constant curvature are a special case of the proposed model. Thus, the present model can provide a theoretical basis for the nonlinear buckling analysis of a drill-string constrained in a 3D curved well-bore.