Single-Phase Model for Electric Submersible Pump (ESP) Head Performance
Summary This paper presents a new incompressible single-phase model for ESP head performance. Sachdeva (1988, 1994) and Cooper and Bosch (1966) developed models for ESP channels and for inducers, respectively. The model presented in this paper is based on 1D approximation along an ESP channel. The new derived pressure ordinary differential equation (ODE) for frictionless incompressible flow (Bird 1960) is consistent with the pump Euler equation. New models for pump frictional and shock losses have been proposed. Finally, a comparison between the predicted pump performance and the pump performances derived from the affinity law for different rotational speeds is presented. The single-phase model can predict ESP performance under different fluid viscosities and also is the basis of a gas/liquid model for ESP head performance. Introduction ESPs are dynamic multistage devices that use kinetic energy to increase liquid pressure. The relationship between the head developed by the pump and the flow rate through the pump for a certain rotational speed is usually known as the pumphead performance curve. This curve is experimentally determined by the pump manufacturer using water as the working fluid. As a consequence, published pumphead performance curves can be used for any other low-viscosity, single-phase liquid, independent of its density. Pump performance, however, is significantly affected by the presence of free gas or high-viscosity fluids. The U. of Tulsa Artificial Lift Projects (TUALP) is currently conducting experimental as well as theoretical research to improve the understanding of pump performance when handling viscous fluids and two-phase flow mixtures at different pump rotational speeds. A better understanding of the pump performance under those conditions will certainly contribute to a reduction in the uncertainty of engineering tools for the selection, design, and operation of ESPs in more challenging applications. This paper presents the new single-phase model developed for the prediction of an ESP's performance. The model consists of the mass and momentum equations, based on the streamline approach or 1D assumption. In the momentum equations, the calculation of the friction factor proposed by Sachdeva is improved by incorporating the channel curvature, channel rotation, and channel cross-sectional effects. A new shock loss model, including rotational speeds, has been proposed. The new single-phase model is capable of predicting the pump performance for different pump rotational speeds and for different fluid viscosities.