Buckling of Tubulars Inside Wellbores: A Review on Recent Theoretical and Experimental Works
- J.C. Cunha (The U. of Alberta)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling & Completion
- Publication Date
- March 2004
- Document Type
- Journal Paper
- 13 - 19
- 2004. Society of Petroleum Engineers
- 1.14.1 Casing Design, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 1.10 Drilling Equipment, 4.1.2 Separation and Treating, 2 Well Completion, 1.6.1 Drilling Operation Management, 1.6 Drilling Operations, 4.3.4 Scale
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The buckling behavior of tubulars inside wellbores is the subject of many articles. This paper presents a general overview on most of the literature available 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 the influence of torque.
A good understanding of the buckling behavior of pipes in oilwell operations is very important in the petroleum industry. The significance of this matter can be measured by the great number of papers 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 coiled tubing has been studied by a number of authors.
There are publications covering almost every particular buckling case, such as helical buckling; torque effect; and the influence of wellbore inclination, friction, and wellbore curvature.
The differential equation representing the configuration of a rod buckled because of the action of an axial load, F, was first presented by Euler in 1744.2 The solution of that differential equation indicated that a weightless rod will buckle, provided the following inequality is satisfied.
In Eq. 1, n=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 1883,2 he considered the influence of torque and produced the following inequality as a condition for the instability of long, weightless rods.
Last century, the stability of long rods under various conditions of loading and support were investigated by many authors, among whom Goodier,3,4 Hoff,5 Timoshenko,6 and Langhaar7 should be mentioned.
Those works, although fundamental to understanding the elastic stability theory, did not deal with 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 in which inclined or curved configurations exist. A summary of the most noted studies of pipe buckling inside wellbores follows.
This section presents comments on a number of papers published in the last 50 years. Although not all papers available in the literature are mentioned in this review, the majority of the most important contributions on tubular buckling inside wellbores are referred to here.
As mentioned previously, the first rigorous treatment of drillstring stability was presented by Lubinski.1 In that pioneering work, an analysis of 2D drillpipe buckling in vertical wells and its effects on bit inclination, string shape, wall contact force, and bending moments were presented and discussed thoroughly.
Lubinski's solution for the critical buckling load used a power series to solve the differential equation governing the instability problem. Lubinski's method leads to a very precise result expressed in the form of a power series. However, the terms of the series become very large for long strings, and after a certain length, the calculations may lead to inaccurate results.
As an approximation for practical purposes, Lubinski proposed that the critical load for the first buckling mode of long strings should be calculated as:
Wang8 proposed that the exact factor in Eq. 3 to produce the critical load of buckling for an infinite pipe inside a vertical well should be 1.018793.
Later, with a nonlinear regression method, Guo9 combined Lubinski's results for short strings with the result for infinite columns to produce a function that gives approximated results for the critical buckling load of strings of any size.
During the 1950s, Lubinski10,11 published other important papers analyzing tubular buckling in oilwell operations. Among other interesting features, those papers have derivations showing the influence of fluid density (inside and outside the pipe) on the buckling process and also how buckling could affect operations in pumping wells.
In 1962, Lubinski et al.12 published another fundamental paper, in which the helical buckling of production tubing was studied for the first time. Also for the first time, the effect of fluid flow on buckling was presented. In that paper, the equation for the force-pitch relationship was derived as:
In addition, expressions for displacement length, bending moments, and the strain energy of bending and compression were developed. Note that for the first time, this paper observed a differentiation between the beginning of the buckling process, normally called sinusoidal buckling (also known as lateral or 2D buckling), and the more severe case of helical buckling. The differences between these two situations are analyzed in the next section.
The interested reader can find the most important works of Arthur Lubinski in Ref. 13.
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