Response analysis of longitudinal vibration of sucker rod string considering rod buckling

Considering the limitation of simulation model of the deep well and ultra-deep well, an improved simulation model of sucker rod pumping system (SRPS) is presented. The main innovations of the simulation model are nonlinear longitudinal vibration model of sucker rod string (SRS) and numerical integral model of nonlinear system with pump time varying parameters. In the detail, the relationship of rod buckling and plunger load is analyzed using a finite element preprocessor module of ANSYS. Based on analysis results and experimental results, the change rule of equivalent stiffness is studied. Using parameters of oil well, the response of longitudinal vibration of SRS is analyzed. The new model is verified by comparing it with the available analytical solution, and good agreement is found. The simulation results show that the instantaneous equivalent stiffness of helical buckling section of SRS follows exponential distribution. The equivalent stiffness is affected by some parameters, among them, the values of water cut, density of crude oil and pump depth have a significant effect. With new model presented in this paper, the subharmonic resonance is found, which is characteristic of nonlinear vibration. Comparing with the steel rod, carbon fiber rod and fiberglass rod, the resonant phenomenon of single rod is more likely to happen for the wire rope sucker rod. However, when sucker rod is double stage rod, the resonant phenomenon of fiberglass rod is more likely to happen than other rods. The above results are significant to the optimization of SRS.