The numerical simulation of entire sucker rod string buckling with couplings in vertical wells

A new model is built to study the buckling of a rod string with couplings in the vertical well considering two important loads: the axial distribution load along the rod and the concentrated load at the bottom. Firstly, the calculation method for the axial distribution load of the sucker rod string is established based on a wave equation of longitudinal vibration. And, the simulation results show that the axial distribution load of sucker rod string has an obvious non-uniform distribution characteristic. The friction force between the plunger and the pump barrel (FFPPB), which is an important part of the concentrated load at the bottom, is improved based on both the Newtonian fluid (NF) and the non-Newtonian power law fluid (NNPLF) by using the Flunent software. In view of the above improvement of the computational method, a simulation model of the entire rod string buckling with couplings is established. Under the assumption that the coupling is taken as a radial constraint boundary, the two-point boundary value problem (BVP) algorithm is used to solve the differential equation, and the least square method is used to establish the continuity conditions on the supporting point of coupling. The simulation results show that the eccentric state of the plunger (eccentricity ratio \(\upvarepsilon =0\sim 1\)) has a significant influence on the eccentric wear area between the rod-tubings, which should be taken into account in the practical calculation. And compared without couplings, the contact pressure between the sucker rod string and the tubing is transferred to the couplings, which fits the engineering reality. Further, the simulation result implies the centralizers should be installed firstly near the couplings in order to protect the couplings better. The new method lays the theoretical foundation for the further studying the rod wear life and the design of the eccentric wear prevention.