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

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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.