The calculation of gearbox torque components on sucker-rod pumping units using dynamometer card data

Power requirements and profitability of sucker-rod pumping are basically determined by the torque load on the pumping unit’s gearbox. Gearbox torques include the torque required to drive the polished rod and the torque used to rotate the counterweights. In addition to these, inertial torques arise in those parts of the pumping unit that turn at varying speeds. As shown in the paper, all torque components are functions of the crank angle; consequently, their exact calculation necessitates the knowledge of the crank angle versus time function. This circumstance, however, complicates torque calculations because contemporary dynamometers, used to acquire the necessary operating data, do not provide any information on the variation of the crank angle during the pumping cycle. The paper introduces a solution of the problem and presents an iterative calculation of the crank angle versus time function from dynamometer data. Based on this function crank velocity, crank acceleration, as well as beam acceleration can be calculated and all necessary gearbox torques can be evaluated. For calculating articulating inertial torque, the acceleration pattern of the walking beam during the pumping cycle is evaluated according to three different models and the accuracy of those is compared. The paper gives the details of the developed calculation models and presents a typical sample case.