The purpose of this paper is to present theoretical solutions based on an improved energy method for predicting the helical buckling (HB) behavior of pipes in vertical, inclined, and horizontal wells.
The energy method has been applied to solve the pipe-in-pipe’s (PIP) helical buckling behavior since Lubinski, et al  in the 1950’s. However, in the preceding studies, the energy methods are not yet completely correct because the pipe’s potential energy of the distributed contact normal force induced by the helical buckling was considered to be negligible. This deficiency caused improper deductive procedures.
In this paper, the energy method is improved by adding the term of the potential energy of the distributed contact normal force. With this improvement, not only can the PIP’s critical helical buckling forces be successfully derived, but it also provides a deeper insight on the PIP’s helical buckling onset, as well as the post helical buckling behavior.
For inclined and horizontal wells, equations are provided to determine the critical forces required to initiate the helical buckling mode for both “long” and “short” pipes. In addition, the post buckling behavior is also described, and a new concept of helical buckling zone (HBZ) for “short” pipes is introduced based on the force-pitch plots as an area in-between the helical buckling’s onset curve and the classical Lubinski curve.
Finite element ABAQUS models have also been utilized to confirm the analysis using the improved energy method. And the ABAQUS results show remarkable agreement with the theoretical solutions.