Analytical and Experimental Study of Oil/water Emulsion in Multi Stage Electric Submersible Pump

Abstract

The non-Newtonian behavior of oil/water emulsion in the ESP stage is still not well understood. The industry relies on existing empirical correlations, which only valid for production pipelines without considering the effect of shear force acting on the system. This paper will present the analytical modeling of emulsion rheology in the ESP stage and its effect on ESP boosting pressure. An extensive experimental data set validates the analytical model accuracy. The Brinkman empirical correlation is the baseline of the analytical model development. Emulsion rheology in the ESP stage depends on many factors. Dimensionless analysis by the Buckingham-Phi theorem indicates that at least three parameters play an essential role in the emulsion rheology at the pump stage. Those parameters are concatenated and applied as the modified function of Brinkman empirical correlation. In addition, the pump boosting pressure performance observed experimentally to study the emulsion rheology effect at the ESP. More than a thousand experiment data points employed to test the proposed model, and its comparison is studied statistically. The dimensional analysis prevails that the turbulence effect at the stage condition reflected by the Reynolds number, the droplet size effect represented by the Weber number and the Strouhal numbers relates to the shearing effect due to impeller rotation. The analytical model and experiment perform with two different oil viscosity, 45 cp and 70 cp. The results reveal that the higher oil viscosity reaches the inversion point at a lower water fraction since the turbulence decreases with higher oil viscosity. The emulsion rheology from the experiment result shows a significant increase of emulsion viscosity at water fraction close to the inversion point since the increase of hydrodynamic forces due to a higher number of water droplets. The emulsion rheology model aligns with the experiment results for the inversion point at around 35% and 32% water-fraction, respectively. The emulsion rheology model shows a good agreement with the experimental data with a 15% standard deviation of relative error. Increasing water fraction up to the inversion point deteriorates pump boosting pressure since the high friction loss occurs due to higher emulsion viscosity. Nevertheless, as the water fraction passes theinversion point, the boosting pressure starts to rebound as the water turns into the continuous phase. The formation of oil/water emulsion in the ESP is inevitable during production operation and consequently affects the pump boosting pressure. The inversion point phenomena occur at a different range of water fractions for different oil viscosity. A better understanding of emulsion rheology at the pump stage will lead to an accurate artificial lift design and eventually avoid operation failure during production well operation.