A new model to find optimum counterbalancing of sucker-rod pumping units including a rigorous procedure for gearbox torque calculations

Abstract

The profitability of sucker-rod pumping depends mainly on the prime mover's power use because the dominant part of the operational cost is the power bill. The required prime mover power, however, is defined by the torque loading of the pumping unit's gearbox. The paper analyzes the different kinds of gearbox torque components, their possible calculation methods, and introduces a novel calculation procedure that utilizes the data of a dynamometer survey. Traditional counterbalancing methods normally assume that the combined center of gravity of the crank plus counterweights system falls on the centerline of the crank arm. This assumption greatly simplifies the calculation of counterbalance torque, but at the same time it seriously reduces the possible number of counterbalance arrangements. The paper eliminates this simplification and allows the selection of unrestricted variations of counterweights and their respective positions. In such cases, the counterbalance's combined center of gravity does not fall on the centerline of the crank and an offset angle is created between the crank angle and the phase of the counterbalance torque vs crank angle function. Formulas for these parameters are introduced that can handle any combination of counterweights at any positions on the cranks' edges. When comparing the available models for optimum counterbalancing, the authors show that the traditional procedure of equalizing the peak torques during the up-, and the downstroke does not produce the smoothest possible net gearbox torque. Net torque fluctuations are lower if the objective of optimization is changed to find the minimum of CLF (Cyclic Load Factor). Additional benefits of this recommended optimization procedure are that it requires the minimum of motor nameplate power and the minimum power cost. The authors describe the development of a new model for counterbalance optimization that changes both the magnitude and the phase angle of the maximum counterbalance moment during optimization. This solution is a major improvement over previous models because those did not change the phase angle of the counterbalance moment. The new model offers a better match to the variation of the rod torque and can produce a smoother net torque and lower prime mover powers. The developed optimization procedure uses PSO (Particle Swarm Optimization) principles, an AI iterative optimization scheme. The developed computer program incorporates a rigorous procedure to calculate gearbox torque components and can follow both the traditional model and the recommended model seeking the minimum of CLF. All statements and conclusions are supported by results of example problems. • A procedure is proposed to find the counterbalance system’s CG that can handle any combinations/positions of CWs on the cranks. • traditional formulas of CB torque vs crank angle are modified to include the effects of the lead/lag of the CB torque function. • The traditional way of CB optimization is proved to not produce the smoothest possible net gearbox torque. • The proposed optimization provides a better match to the variation of the rod torque and can produce a smoother net torque. • The PSO (Particle Swarm Optimization) AI method was used to optimize counterbalance conditions of pumping unit gearboxes.