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Considering the limitations of the static buckling theory on the eccentric wear of sucker rod and tubing, a new dynamic analysis method for the transverse vibration of sucker rod in the tubing is proposed. Taking the axial distribution load at the rod body and the dynamic load at the bottom into account, the dynamic model of transverse vibration is established based on the space buckling configuration of rod string which regarded as the deformation excitation during the down stroke. To solve the mathematical equations, the finite difference method is used to discretize the well depth, and the Newmark-beta method is used to discretize the time. Meanwhile, a restitution coefficient is introduced to depict the change of velocity and the momentum after the collision. The result shows the phenomenon of rod-tubing collision occurs mainly in the down stroke after the rod string post buckling; the collision force from the wellhead to the bottom increases gradually, of which distributed almost along the entire well depth; and the high frequency collision occurs below the neutral point where the collision force is also the biggest. Further, the collision frequency and the collision force decrease successively from the neutral point to the wellhead direction. But during the up stroke, few collisions occur, and the collision force is also very small. The simulation model is suitable for the eccentric wear analysis of rod-tubing, and provides a new theoretical basis for the optimal allocation of the centralizer.

journal of vibroengineering

The simulation model of sucker rod string transverse vibration under the space buckling deformation excitation and rod-tubing eccentric wear in vertical wells