Effects of Well Deviation on Helical Buckling
- R.F. Mitchell (Enertech Engineering and Research Co.)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling & Completion
- Publication Date
- March 1997
- Document Type
- Journal Paper
- 63 - 70
- 1997. Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 1.6 Drilling Operations
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- 1,104 since 2007
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Current helical buckling models are valid for vertical wells, but the validity of these solutions for deviated wells was not known. This paper describes the numerical solution of the non-linear buckling equations for arbitrary well deviation. Stability criteria are developed for lateral and helical buckling, and simple correlations are developed for buckling length change, maximum bending stress, and contact force.
The most generally accepted method for the analysis of buckling, tubing movement, and packer selection is the method developed by Lubinski et.a1. Analyses following Lubinski's basic approach have been developed for more complicated tubing configurations, e.g. tapered strings. Henry Woods, in the appendix to reference 1, developed a mechanical model of well buckling behavior that predicted the buckled configuration as a function of well loads. This model featured:
1. The slender beam theory is used to relate bending moment to curvature.
2. The tubing is assumed to buckle into a helical shape.
3. The wellbore is assumed to be straight and vertical.
4. The pitch of the helix is related to the buckling load through the principle of virtual work
5. Friction between the tubing and casing is neglected.
Mitchell developed a more general approach that replaces the virtual work relations with the full set of beam-column equations constrained to be in contact with the casing4. Helical buckling in a deviated well, in this formulation, is described by a second order non-linear differential equation. For a vertical well, the solution to this equation can be accurately approximated by the simple algebraic equation discovered by Lubinski and Woods. Because of the lateral gravity forces, it is not clear that this solution is valid for deviated or horizontal wells.
This paper presents a numerical solution to the buckling differential equation. The Galerkin technique is applied to the equation using cubic interpolation functions. The resulting non-linear algebraic equation is solved using Powell's method. Calculation of results, including buckling length change, tubing contact forces, and dogleg angle are developed. As a test, the solution technique duplicated Lubinski's solution for a vertical well, except near the neutral point, where the Lubinski solution does not satisfy the buckling equation. Several sample problems are solved and the effects of well deviation on stability are examined. Because of the intense numerical calculations needed to solve the deviated well buckling problem, the results of the analysis were used to develop simple analytical expressions for use in tubing analysis, e.g. buckled length change, maximum bending stress, and contact loads.
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