Spatial Transverse Vibration Simulation Model of Axially Moving Sucker Rod String under the Excitation of Curved Borehole

The mechanical model of transverse vibration of sucker rod string (SRS) in directional well is simplified to the transverse vibration model of longitudinal and transverse curved beam with initial bending under borehole constraints. In this paper, besides considering the excitation of alternating axial load on the transverse vibration of SRS, it is proposed for the first time that curved borehole is also the main excitation for the transverse vibration when the SRS moves reciprocating axially in the borehole. Based on the elastic body vibration theory, the transverse vibration mathematical model of SRS with initial bending under borehole constraints is established. In this model, the curved borehole excitation caused by the axial motion and the alternating axial load excitation is considered. Besides, the elastic collision theory is applied to describe the constraint of tube on the SRS transverse vibration in this model. Then the fourth-order Runge–Kutta method is used to calculate the transverse vibration of SRS in directional wells. The simulation results show the following: (1) The simulation results of the three simulation models in this paper are different. The results indicate that the curved borehole excitation caused by the axial motion and the alternating axial load excitation is the main excitation for the SRS transverse vibration. (2) In directional wells, the rod and tube contact along the well depth, and the dangerous sections locate at the deviation section of the borehole and the compression section of the rod. On the whole, the contact force between rod and tube in deviation section of borehole is larger. The transverse vibration of the compression section of the rod is the most violent