Buckling of Tubulars Inside Wellbores: A Review on Recent Theoretical and Experimental Works

Abstract

Abstract Buckling behavior of tubulars inside wellbores is the major subject of many articles. This paper presents a general overview on most of the material available in the literature on the subject and also comments on the different, and sometimes conflicting solutions presented in various works. Different aspects of the phenomenon are discussed including sinusoidal (lateral) and helical buckling and influence of torque. Introduction A good understanding of the buckling behavior of pipes in oilwell operations is very important for the petroleum industry. The significance of this matter can be measured by the great number of papers that have been presented on the subject in the last 50 years. Since Lubinski's1 first theoretical approach to sinusoidal buckling for vertical wells, buckling of tubing, drillpipe, casing and coil tubing has been studied by a number of authors. There are publications covering almost every particular case of the buckling problem like helical buckling, influence of wellbore inclination, influence of friction, torque effect, influence of wellbore curvature, etc. The differential equation representing the configuration of a rod buckled due to the action of an axial load F, was first presented by Euler in 17442. Solution of that differential equation indicated that a weightless rod will buckle provided that the following inequality is satisfied:Equation 1 In Eq. 1 n is a factor that depends on the end conditions. In 1881, Greenhill2 studied this problem considering the influence of the weight of the rod. Later, in 18832, he considered the influence of torque and produced the following inequality as a condition for the instability of long weightless rods:Equation 2 Last century the stability of long rods under various conditions of loading and support were investigated by many authors among whom it may be mentioned Goodier3,4 (1941, 1944), Hoff5 (1944), Timoshenko6 (1951) and Langhaar7 (1958). Those works, although fundamental for the understanding of the elastic stability theory, did not deal with the situation of tubulars confined within another circular cylinder. The problem of laterally constrained pipes presents different, and somehow, more complex characteristics than the unconstrained situation, mainly for cases where inclined or curved configurations are existent. Following, a summary of the most noted studies of buckling of pipes inside wellbores is presented. Literature Review In this section, comments on a number of papers published in the last 50 years are presented. Although not all papers available in the literature are mentioned in this review, the majority of the most important contributions on the subject of buckling of tubulars inside wellbores are referred here. As mentioned before, the first rigorous treatment of drill string stability was presented by Lubinski1. In that pioneer work an analysis of two dimensional buckling of drillpipes in vertical wells and its effects on bit inclination, shape of the string, wall contact force and bending moments were presented and thoroughly discussed. Lubinski's solution for the critical load of buckling used power series to solve the differential equation governing the instability problem. Use of Lubinski's method conducts to a very precise result expressed in form of power series. However, for long strings the terms of the series become very large and after a certain length the calculations may lead to inaccurate results.