Simulation model of the sucker rod string buckling configuration in vertical well tubing

A new model based on the entire rod string buckling configuration in vertical well tubing is proposed. The buckling configuration for the rod string constrained in vertical wellbores is divided into four sections: the bottom and second suspended sections, the middle helical section and the top suspended section. The mathematical model not only includes the bending differential equations above the four sections, the boundary conditions at two ends, but also the continuity conditions at contact points whose positions are variable. The numerical simulation of the entire rod string buckling configuration is realized through transforming the mathematical model into non-linear algebraic equations solved by a genetic algorithm. The simulation results show that the boundary conditions at the two ends have little effect on the helical buckling configuration, but, however, the boundary condition, especially at the bottom, has a considerable effect on the configurations of the suspended sections. Compared to the previous results, the new model provides a more accurate description of rod string buckling and can simulate a more genuine buckling configuration of the rod string in the downhole.