A New Mechanistic Model for Oil-Water Emulsion Rheology and Boosting Pressure Prediction in Electrical Submersible Pumps ESP

Abstract As the second most widely used artificial lift method in petroleum industry, ESPs help maintain or increase flow rates by converting kinetic energy to hydraulic pressure. During the entire life of an oilfield, water is invariably produced with crude oil. As the field ages, the water cut in production increases. Due to high shear force inside rotating ESPs, the oil-water emulsions may form, which can be stabilized by natural surfactants or fine solids existing in the crude oil. The formation of emulsions during oil production create high viscous mixture, resulting in costly problems and flow assurance issues, such as pressure drop increase and production rate lost. This paper, for the first time, proposes a new mechanistic model for predicting oil-water emulsion rheology and its effect on the boosting pressure in ESPs. The model is validated with experimental measurements with an acceptable accuracy. The new mechanistic model starts from Euler equations for centrifugal pump, and introduces a conceptual best-match flowrate QBM, at which the outlet flow direction of ESP impeller matches the designed flow direction. The mismatch of velocity directions, resulted from varying liquid flow rates, is used to derive recirculation losses. Other losses due to flow direction change, friction, and leakage flow etc. are also incorporated in the new model. QBM is obtained by matching the predicted performance curve with the catalog curve for water. With the best match flow rate determined, the ESP hydraulic head under viscous fluid flow can be calculated. For oil-water emulsions, a new rheology model based on Brinkman (1952) correlation is developed, which accounts for ESP rotational speed, stage number, and interfacial properties etc. By incorporating the rheology prediction model into mechanistic model, the ESP boosting pressure under oil-water emulsion can be obtained. The mechanistic model-predicted ESP water performance curves are found to match the catalog curves perfectly. With high-viscosity fluid flow, the model predictions of ESP boosting pressure agree well with the experimental data. For most calculation results within medium to high flow rates, the prediction error is less than 15%. With oil-water two-phase flow, the proposed rheology model predicts the effective viscosities of emulsions match testing results with 10% prediction error. The inversion points, at which the continuous phase changes from oil to water as water cut increases, are also predicted. The predictions of ESP boosting pressure under oil-water emulsion flow by coupling the mechanistic model and emulsion rheology model are comparable with experimental results.

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