There are some numerical solutions(4,5) for pipe buckling problems in vertical and horizontal wells, but, we need exact analytic solutions for precise analysis of pipe buckling problems. The first analytic solution for pipe buckling in a vertical well was presented by Lubinski and Woods in 1962(2) . When the non-linear differential equation describing buckling behavior of pipes in vertical and horizontal wells was developed by R.F. Mitchell(6) , this solution was found to be an exact analytic solution for this differential equation. No other analytic solution has been discovered until 2002(8) , when, Mitchell himself developed three new analytic solutions for the vertical well buckling problems and two new analytic solutions for the horizontal well problems.

In this paper, these five solutions are described and modified to some extent, and the development and evaluation technique are presented. Some results of interest such as buckling contact force and critical force limits for pipe buckling also are developed. These analytic solutions are valuable both for predicting previously unanticipated buckling behavior and for providing guidance in further numerical evaluations of this problem.

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