A new mechanistic model on boosting pressure of Electrical Submersible Pumps (ESPs) under gas-liquid two-phase flow

Electrical Submersible Pumps (ESPs) are widely used in offshore and unconventional oil/gas fields to increase production and efficiency since 20^th century. It is a revaluation oil production method, which is particularly used in wells with less sufficient natural pressure and energy. The submerged centrifugal pump was firstly developed to pump water in mines, and Armais Arutunoff developed the first ESP that used in oil wells, which later became popular and well-known in the industry. However, the ESP is very sensitive to flow conditions, and it has undergone significant technological advancements to improve their tolerance, efficiency, reliability, and adaptability to hash and complex downhole flow conditions. ESPs are usually comprised with an electric motor, seal, and a series of centrifugal pump stages, and are widely adept at handling high-volume fluid lifting in deep and deviated wells. Nowadays. ESPs are also commonly used in unconventional wells, like shale-oil wells. Therefore, the gas tolerance ability, viscosity effect, and long-term exploitation capability of ESPs have drawn significant attention. Due to the compact assembly and high-shear flow field in a rotating impeller, the gas-liquid two-phase flow inside ESPs is complicated, bringing in high risks for two-phase transportation and difficulties for safety control. Thus, the applications of ESP-based artificial lift technology in offshore and unconventional oil/gas fields for safe and efficient production is restricted considerably. In this work, aiming at the difficulties of performance prediction for ESPs under multiphase flow, a novel mechanistic model to predict the boosting pressure in ESPs is proposed. The new model starts form from Euler equations and introduces a best-match flowrate at which the flow direction at ESP impeller outlet matches the designed flow direction. The mismatch of velocity triangle in a rotating impeller is result from the varying liquid flow rates. Losses due to flow direction change, friction, and leakage etc., were incorporated in the model. Based on the force balance on a stable gas bubble in a centrifugal flow field, the in-situ gas void fraction inside a rotating ESP impeller can be estimated, from which the gas-liquid mixture density is calculated. The predicted ESP boosting pressures match the corresponding experimental measurements with acceptable accuracy. The proposed method can be used to accurately predict the the oil viscosity, water-cut emulsion, and gas-liquid flow effect on pump performance. The model can be used to help pump engineer to develop new pump geometries, as well as help artificial lift engineer to improve well completion design.