Previous theoretical formulations for sinusoidal and helical buckling of drill strings vary significantly and are mostly proposed for frictionless pipes without tool joints. Finite element analysis (FEA) methods have the ability to consider geometric details and large deflections. However, traditional FEA methods use shell or solid dimensional elements for this problem and are computationally expensive. In this paper, an explicit FEA based on beam and connector elements implemented in the Abaqus software is employed to study the buckling of drill strings in different wellbores. The wellbore geometry, stiffness, friction load, and friction induced torque are modeled using connector elements. A typical drill string in vertical, inclined, horizontal, and curved wellbores is simulated and the explicit FEA results for sinusoidal and helical buckling loads are compared to different theoretical formulations and experimental results in the literature. The effects of length, inclination angle and string effective weight due to buoyancy as well as the effect of tool joints in straight and curved wellbores is also studied and compared to present formulations and published experimental results. Overall, it is demonstrated that using explicit FEA can efficiently study drill strings buckling behavior in straight and curved wellbore conditions.
INTRODUCTIONIn order to increase the rate of drilling (rate of penetration), optimum weight should be put and maintained on the drilling bit. The weight on bit (WOB) is limited by the critical buckling load where the pipe loses elastic stability. Buckling can intensify the bending stress and lead to fatigue failure over time. More importantly, buckled shapes exert larger side forces than unbuckled which increases friction losses and can lead to the lockup of the string and potential loss of equipment and section of the well. Increases in the depth and deviation of wells have intensified this problem and led to the need for comprehensive models capable of analyzing and predicting different aspects of drill string buckling. Therefore, it is important to determine the maximum load permissible on the drill string. Critical buckling load depends on the pipe geometry, drill pipe elastic modulus and wellbore geometry. It is generally believed that the drill string will first change into a sinusoidal buckling shape and then to helical buckling. Lubinski (1952) performed a seminal analysis on buckling behavior of drill strings where he used classical theory of elasticity to study the instability of straight drill strings. The critical length of a pipe under its own weight with pinned boundary conditions was found according to the following formula.