The research of post-buckling about slender rod string in wellbore based on energy method and experiment

The buckling behavior of rod strings in wellbore is one of the most phenomena in petroleum engineering. The slender rod strings in wellbore were selected as research objects. Based on the energy method, the critical load of sinusoidal and helical buckling were derived for the string with the wellbore pressure at the bottom. According to the sinusoidal and helical buckling's geometry of the pressurized string, the contact friction state of post-buckling between rod strings and the wellbore was considered. In this paper, Lagrange multiplier method was adopted to describe the sliding displacement boundary conditions of wellbore and the gravitational potential energy and friction resistance dissipated energy were introduced in the energy method. The contact forces and friction resistances between rod string and wellbore were derived in the inclined and vertical wells. And the post buckling experimental apparatus was also developed in this paper. The results indicate that the sinusoidal and helical buckling critical loads and the 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 string, such as drilling, coiled tubing.