The Analytic Technique and Experimental Research Methods of Post-buckling about Slender Rod Strings in Wellbore

Document Type: Research Paper


College Mechanical Science Engineering, Northeast Petroleum University, Hei Long-Jiang, Daqing,China


The buckling behavior of rod strings in wellbore is one of the key issues in petroleum engineering. The slender rod strings in vertical wellbore were selected as research objects. Based on the energy method, the critical load formulas of sinusoidal and helical buckling were derived for the string with the bottom of the wellbore pressure. According to the sinusoidal and helical buckling’s geometry of the pressurized column, the contact friction state of post-buckling between the rod strings and the wellbore was considered. This paper adopted Lagrange multiplier method to describe sliding displacement boundary conditions of wellbore and introduced gravitational potential energy and friction resistance dissipated energy in the energy method. The contact forces and friction resistances between the rod string and wellbore were derived in vertical wells. The post buckling experimental apparatus was also developed in this paper. The sinusoidal and helical buckling critical loads and friction resistances were derived under different loads. The experimental results are consistent with the theoretical results. Therefore, this article would provide an effective method for buckling column such as drilling and coiled tubing.


      [1]     Tan M. L., Gan L. F., and Wang X. W., “Nonlinear Helical Buckling of Drill- Strings in Inclined Wellbore,” Engineering Mechanics, 2007, 24, 199-202.

      [2]     Mitchell R. F., “Buckling of tubing inside casing,” SPE 150613, IADC/SPE Drilling Conference and Exhibition, San Diego, California, USA, 2012, 1-13.

      [3]     Xiu-gen W., Bai-lin Z., and Peng-fei H., “Study on Post-buckling of Constrained Bar,” Journal of Tongji University (Natural Science), 2009, 37, 26-31.

      [4]     Gao G. and Miska S., “Effects of Friction on Post-buckling Behavior and Axial Load Transfer in a Horizontal Well,” SPF Journal, SPE 120084, 2010, 15, 1104-1118.

      [5]     Gao G. and Di Q., Miska S., “Stability Analysis of Pipe with Connectors in Horizontal Wells,” SPF Journal SPE 146959, 2012, 17, 931-941.

      [6]     Jubao L., Xiuwen W., and Qianbei Y., “The Buckling Deformation and Contact with Inner Rod and Outer Casing for Compressional Tubing,” Mechanics in Engineering, 2011, 33, 25-29.

      [7]     Tan M. and Gan L., “Equilibrium Equations for Nonlinear Buckling Analysis of Drill-strings in 3D Curved Wellbores,” Science in China Series E: Technological Sciences, 2009, 52, 590-595.

      [8]     Mitchell R. F., “Tubing Buckling: the State of The Art,” SPE Drilling & Completion, SPE 104267, 2008,23, 361 - 370.

      [9]     Mitchell R. F. and Weltzin T., “Lateral Buckling: the Key to Lockup,” SPE 139824, SPE Drilling & Completion, 2011, 26, 436-450.