Helical Buckling of Tubing Sealed in Packers
Authors: Lubinski Arthur , Althouse W.S. 
Published: December 2007

Abstract
Most gas wells and flowing oil wells are completed and treated through a string of tubing and a packer. Changes in temperature and in pressure inside or outside the tubing will:if free motion of the tubing inside the packer is permitted, increase or decrease the length of the tubing; orif free motion is prevented, induce forces in the tubing and on the packer.
If pressure inside the tubing is greater than outside, the tubing may buckle helically even in the presence of a packer-to-tubing tension. The tubing will always buckle, and much more severely, if free motion is permitted. The buckling may be prevented by pulling the tubing in sufficient tension. The prediction of these forces and tubing movement has heretofore been based upon calculations that did not include helical buckling. This paper presents means with which these length or force changes can be calculated while taking into account the effect of helical buckling. To avoid damaging formations, failure of remedial operations or damage to the tubing or packer, application is made to practical problems involving calculations of the required length of seals, amount of slackoff or tension, and prevention of permanent corkscrewing.

Introduction
Leakage of a packer may result in costly failures of such operations as squeeze cementing, hydraulic fracturing, etc. To avoid such failures, the authors are often asked questions pertaining to the length of necessary seals, the amount of necessary slackoff, etc. Published work does not take into account helical buckling of tubing. Investigation of helical buckling was prompted by the fact that allowance must be made for this phenomenon in order to provide relevant answers. In the past, theoretical work on helical buckling was confined to conditions for which such buckling does not occur. The mathematical treatment of behavior in a buckled condition, given in the Appendix, is novel. Assumptions upon which this investigation is based are listed and discussed in a special section.

FIELD APPLICATION
The following are a few of the many kinds of problems which may be solved with this paper.Consider a packer in which tubing may move. Such movement will occur after pressures and temperature are changed. The paper provides means for:calculating the amount of such movement and, therefore, the required length of seals; andcalculating the necessary amount of initial slackoff, for which there is no danger of unsealing the packer, if the length of seals is given.Such calculations, as well as those which follow, fully take into account the fact that part of the movement is due to elastic helical buckling of the lower part of the string. This buckling may occur even in tubing under tension. Insufficient initial slackoff for a given length of seals, or insufficient length of seals for a given slackoff, may result in costly failures. A field case of such a failure will be given further in this paper.In the case in which tubing cannot move in the packer, changes of pressure and temperature result in tubing-to-packer forces and forces in the tubing above the packer, both of which may be calculated. This knowledge is important because, if these forces are too large, they could damage the packer or the tubing.For wells in which wireline tools are to be run through the tubing, the paper provides means to keep the tubing from buckling, thereby permitting free passage of tools.In deep wells, mainly in the presence of large casing, tubing may become "corkscrewed", i.e., take a permanent helical set.
A field case is described further in the text. Using this paper, one may calculate in advance conditions under which permanent corkscrewing would occur, and then take preventive steps.

HELICAL BUCKLING
Consider a string of tubing, freely suspended in the absence of any fluid inside casing, as shown in Fig. 1(a). Now consider an upward force F applied at the lower end of this tubing. This force compresses the string; and if the compression is large enough (which is always the case in actual problems), the lower portion of the string will buckle into a helix, as shown in Fig. 1(b). The lower end of the tubing is subjected to a compression F.
JPT
P. 655^