ABSTRACT
The constrained buckling of a tube in a slanted well under gravity and the compressive force has been analysed by several authors over the last three decades. This study of force analysis in the setting stage was motivated by an interest in the packer’s initial conditions and boundary conditions. The buckling behavior of the pipe string influences the design of the well and the production operations. For example, an axial displacement influences the setting length design, and the bending stress may influence weight and grade. The problem with a sinusoidal buckling of the pipe string was first studied by Paslay and Bogy (1964). In their work, the end of the pipe string was supported by hinges. The critical force at the bottom of the tube for sinusoidal buckling was found to be a function of the length of the pipe. Since the pressure in the pipe increases with depth, the amplitude of the sinusoidal buckling also increases with depth so Paslay and Bogy found that the number of sinusoids in the buckling multiplied with the length of the pipe.An asymptotic solution to the sinusoidal buckling of an extremely long pipe was analysed by Dawson (1984) based on a sinusoidal buckling with a constant amplitude. In their work, simple descriptions for the buckling force and wave numbers were derived. The most generally accepted method for the analysis of buckling, tubular movement, and
packer selectionwas developed byLubinski andAlthouse (1962), which considered only a vertical well with no friction. Some further analysis using Lubinski’s approach has been done for more complicated tubular configurations such as tapered pipe strings (Cheatham, 1984). HenryWoods, in the appendix to Lubinski and Althouse (1962), developed a mechanical model to predict the buckling configuration for tubular buckling behavior. Mitchell developed amore general approach that replaced the virtual work relations with a full set of beam-column equations constrained to be in contact with the casing (He and Kyllingstad, 1995). In this formation, helical buckling in a deviated well, was described using a fourth order non-linear differential equation. For a vertical well, the solution to this equation can be accurately approximated using the simple algebraic equation discovered by Lubinski and Woods. This solution, however, is not valid for deviated or horizontal wells because of the lateral gravitational forces. Using the Galerkin technique Miska and Cunha (1995) sought numerical solutions, which confirmed the thought that under a general load the deformed shape of the pipe is a combination of helices and sinusoids, while helical deformation occurs only under special values for the applied load. For more research on the pipe string buckling deformation, readers can refer to McCann and Suryanarayana (1994), Mitchell (1988; 1997), (Xu et al., 2012b) and Wu and Juvkam-Wold (1995).
