Development of an Advanced Mechanistic Heat Transfer Model to Predict Motor Skin Temperatures in Scale-Prone Electrical Submersible Pump Applications

Summary Persistent radioactive contamination in Kuwait’s northern oil fields, linked to electrical submersible pumps (ESPs), necessitates urgent scientific inquiry. ESP-lifted wells in oil-producing formations rich in barium (Ba), combined with high sulfate (SO4) seawater injection, create conditions conducive to radioactive contamination of subsurface completions. In this study, we hypothesize that temperature gradients caused by ESP heat fluxes in wellbores contribute to barite (BaSO4) precipitation and radium (Ra) uptake (either through adsorption or coprecipitation), introducing a previously overlooked source of radioactivity in oil and gas production. In this work, we develop a mechanistic model to estimate temperature distribution along the entire axial length of the ESP motor skin, addressing gaps between reported and calculated temperatures outside the ESP string, particularly around the motor. Motor skin temperature is estimated based on heat generation from the pump’s power demands and heat dissipation resistance, influenced by production flow characteristics surrounding the motor. The model’s underlying physics considers the conservation of energy, convective heat forces, and Newton’s cooling law. The proposed model uniquely accounts for several key factors often simplified in previous models that influence thermal behavior, including the turbulent flow thermal boundary layer, the transitional flow regime, and multiphase flow slippage and patterns. This advancement enhances precision and applicability, making the model a more effective tool for predicting motor skin temperature across diverse operational conditions. Model validation shows strong alignment with experimental and field data, maintaining an average error of ±3%, confirming its precision and reliability for practical applications. Simulated temperatures from North Kuwait ESP-lifted wells are integrated with barite (BaSO4) solubility values, revealing a complex interaction that inhibits precipitation and, in some cases, triggers dissolution-reprecipitation, ultimately creating conditions that enhance Ra uptake.