New Buckling Solutions for Extended Reach Wells

Abstract

Abstract New exact buckling solutions have been found for horizontal wells. These solutions include critical axial buckling force, a variable pitch depending on pipe lateral weight, length change due to buckling, pipe wellbore contact force, and pipe bending moment. Previously, these results could only be obtained with non-linear computer solutions. Applications of these results include estimating lock-up conditions, determining loads that could cause permanent corkscrewing, and determining seal lengths for horizontal well completions. Several sample calculations are presented which illustrate the use of these new results to solve practical engineering problems. Introduction The most generally accepted method for the analysis of buckling, tubing movement, and packer selection is the method developed by Lubinski in reference 1. Henry Woods, in the appendix to Lubinski, developed a mechanical model of well buckling behavior that predicted the buckled configuration as a function of well loads. This model was based on slender beam theory, assumed the wellbore was straight and vertical, neglected friction, and assumed a helical shape with constant pitch. Mitchell developed a more general using the full set of beam-column equations constrained to be in contact with the casing2. Helical buckling in a deviated well, in this formulation, is described by a fourth order non-linear differential equation. The solution discovered by Lubinski and Woods was found to be an exact algebraic solution for a pipe with constant axial force and no lateral forces. An important observation is that this solution is not valid for horizontal wells because of the lateral gravity forces. The horizontal well equations were first solved by Mitchell, using numerical methods3. Recently, Mitchell has discovered analytic solutions to the horizontal well buckling problem4. The purpose of this paper is to develop applications of these analytic solutions to extended reach wells. Why is the accurate solution of the buckling equations important? Bending stresses due to tubing buckling will be overestimated for horizontal wells using Lubinski's formula. However, Lubinski's solution applied to horizontal wells will also overpredict tubing movement. Lubinski's solution will also overestimate tubing compliance, which may greatly underestimate axial loads, resulting in a non-conservative design. Lubinski will predict exaggerated tubing motion, which will require excessive seal length. Further, because tubing incremental motion will control the friction load direction, errors in overall tubing displacement will generate further errors in friction loads. This paper presents two new analytic solutions of the buckling differential equation. Results of interest are developed, including buckling length change, tubing contact forces and lock-up conditions, tubing bending moment, bending stresses and dogleg angle. At the end of this paper is a complete nomenclature and reference list.