Leakage of a packer may resUlt in costly failures of such operations as squeeze cementing, hydraulic fractur­ ing, 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. Investi­ gation 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.

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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. This compression decreases with the distance from
the bottom and becomes nil (neither compression nor tension) at the neutral point.
Above the neutral point, the string is in tension and remains straight.
The distance n from the bottom of the tubing to the neutral point is:
As proven in the Appendix, the pitch p (i.e., the distance between spirals, just
above the lower end of the tubing) is:

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Eq. 2 also gives pitch at any point below the neutral point, if F is understood as the
compression at that point. The pitch is the smallest at the lower end, where it may
be of the order of 20 ft, and increases as the neutral point is approached, where it
becomes infinite. In most situations occurring in oil well tubing, the neutral point is
located several thousand feet above the packer, and the number of .spirals may be of
the order of 1QO or 200. Consider now the same tubing, but sealed in a packer which
permits free motion of the tubing, as shown in Fig. 2. Consider that a pressure Pi is
applied inside the tubing at the packer level. This pressure P, subjects the bottom of
the tubing to a compressive force, and one would expect this compressive force to
buckle the tubing inside the casing. As proven in the Appendix, however, the tubing
will buckle more severely than could be expected from this actual compressive force
alone. It will buckle as if it were subjected to the following compressive force Fr.

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As part of this compressive force does not exist, the entire force Ff will be called
fictitious. If the packer configuration is as. shown in Fig. 3, the pressure P, subjects
the tubing to a tension one might think, therefore, that the string should remain
straight. Actually, however, the string will buckle although under tension. This
might be considered strange, but similar phenomena have been proven correct for
pumping· wells:" and other instances. It is proven in the Appendix that the tubing
buckles as if subjected to the compressive fictitious force Ff, given by Eq. 3.
Consider now a pressure Po applied outside the tubing at the packer level. In Fig. 3,
the pressure Po subjects the tubing to a compression and one might think, therefore,
that the string should buckle. Actually, however, the string will remain straight. It is
proven in the Appendix that, in the presence of both inside pressure P, and outside
pressure Po, the tubing behaves (as far as buckling or straightness is concerned) as
if it were subjected to the following fictitious force Ff.
The string will buckle if Ff is positive, i.e., a fictitious compression. It will remain
straight if Ff is either negative (i.e., a fictitious tension) or if Ff is zero. Eq. 4 holds
true for both the packer configurations of Figs. 2 and 3, and any other possible
configuration. It is also proven in the Appendix that in the presence of liquids the
weight per unit length, w, must be considered as:
The fictitious force Ff given by Eq. 4 and the weight per unit length, w, given by Eq.
5 must be used in Eq. 1 and 2 to obtain the location of the neutral point and the pitch.
With regard to Eq. 1, it should be well understood that, in the presence of liquids,
the neutral point is not the point at which there is neither' tension nor
compression!··'·' ~ Rather, it is the point below which the string is buckled and above
which the string is straight. Depending on conditions, this point may be either under
tension or compression, but its location in the string is always given by Eq. 1.
Reference:
Lubinski, A. & Althouse, W. (1962). Helical Buckling of Tubing Sealed in Packers.
Journal Of Petroleum Technology, 14(06), 655-670. http://dx.doi.org/10.2118/178-
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