Slip Calculation of Rotational Speed of Electrical Submersible Progressive Cavity Pumps

Abstract Progressive cavity pumps (PCPs) are usually driven at surface through sucker rods. Due to the shear strength of sucker rods and the wear of the rod and tubing, the surface drive system limits its application in production rate and well depth, and in deviated and horizontal wells. Instead of using sucker rods to transmit driving torque from surface to pump, bottom driving PCP assembly sets electric submersible motors below PCP to drive the pump directly. Electric submersible motors for PCP are three phase, squirrel cage, induction motors. Motor speed is controlled by its winding poles. Nominal motor speeds widely used are 3500 RPM for two-pole motors and 1700 RPM for four-pole motors. This paper presents simplified correlations by using the nominal motor speeds in the design and analysis of bottom driving PCP wells. The simplified correlations do not account for the effect of motor speed slip. Actually, motor output speeds depend on loading power on the motor. Loading power is the power required by a PCP and its associated equipments to lift well fluid to surface. This paper presents the power consumption of each part in the bottom drive assembly, and the method of calculating motor slip from motor speed performance and calculated total required power. Also presented is the effect of frequency on motor speed. Finally presented are a model to design motor frequency with motor slip and an iteration algorithm to determine production rate at given frequency. This paper clarifies the concepts of volumetric, brake, mechanical, hydraulic, and slip powers associated with PCP pumping. It also differentiated motor output nominal, no-load, and full-load speeds, and the output speeds at load factors, at standard frequency, and at design frequencies.