Abstract
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.
Highlights
Pumping unit lifting is the main way of artificial lifting [1]. e study of rod string mechanics is the basis of pumping unit lifting design and optimization [2,3,4,5,6]
The maximum value of the rod-tube contact force and the position and time of the maximum value are not the same. e standard deviation of the difference between contact force simulation results obtained by model 2, model 3, and model 1 can reach 17.72 N/m and 56.10 N/m, respectively, which indicates that the simulation results of the instantaneous contact force obtained by the three models are quite different. e rod-tube contact force is related to the vibration law of sucker rod string (SRS), so the simulation results of the three models are different
According to the above researches, the following conclusions can be obtained: (1) e transverse vibration of SRS is one of the main factors leading to eccentric wear between SRS and tube string, so the research on SRS transverse vibration has always been the focus in oil field
Summary
Pumping unit lifting is the main way of artificial lifting [1]. e study of rod string mechanics is the basis of pumping unit lifting design and optimization [2,3,4,5,6]. In Ghasemloonia et al.’s work [15], considering the mud damping, driving torque, and space alternating axial load excitation, Galerkin’s method was used to establish the nonlinear axial-transverse coupling vibration simulation model of rotary drill string. Lukasiewicz [18] established an axialtransverse coupling vibration model of SRS in deviation plane based on elastomer theory, considering the initial bending of borehole and the constraint of tube on rod string. Wang and Dong [22] considered the nonlinear excitation of the SRS’s geometric bending stiffness and established the coupled axial-transverse vibration simulation model; the nonlinear phenomenon of SRS is analyzed on this basis. The essence of the mechanical model adopted by the above researches can be summarized as follows: e SRS (longitudinal and transverse bending beam) with or without initial bending generates transverse vibration under the excitation of alternating axial load.
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