Dynamics of pump jacks with theories and experiments

In this paper, we revisit the issues related to dynamics and mechanisms of the pump jack as a surface unit of the sucker rod pumping systems. In particular, we employ both the traditional study methods based on trigonometric relationships and current Newton-Raphson iteration based general solution techniques for the sets of nonlinear governing equations of angles within the four-bar linkages. The nonlinear computational methods enable the study of transient behaviors of pump jacks with non-uniform motor speeds and further analytical studies of the positions, velocities, and accelerations as well as the polish rod force and motor torque in comparison with the actual experimental measures documented in Echometer TAM software and other case studies. These current nonlinear approaches have paved a way for more in-depth studies of the entire downhole system as a specific viscoelastic dynamical system with respective stiffness and damping coefficients for individual wells. In this study, we also identify a common misunderstanding about the structural unbalance B as illustrated in API Specification 11E Page 47 which must be multiplied by the sine function of the polar angle of the Walking beam measured from its horizontal position. This key finding has been confirmed and validated with the comparison between results from both traditional and proposed nonlinear approaches and experimentally measured data collected by Echometer equipment and TAM software.