An Integrated Approach to Virtual Flow Metering of Wells with ESP Based on a Combined Hydraulic and Electric Model

Accurate real-time flow rate estimation for ESP-lifted wells remains challenging due to limited direct measurements, high water cut, gas-oil ratio variations, and pump degradation. This paper presents an integrated virtual flow metering (VFM) approach that combines hydraulic and electrical models of ESP systems within a single physically consistent framework. The algorithm performs multi-stage adaptation — first to hydraulic parameters (intake pressure) and then to electrical telemetry (motor power, amperage, voltage, and load) — followed by optimized weighting of calibration coefficients for production rate recovery. The method was validated on a large set of wells in Western Siberia. The integrated VFM achieved a mean absolute percentage error (MAPE) of 4,866%, improving accuracy by 1,549% relative to purely hydraulic models. These results demonstrate that accounting for both hydraulic and electrical subsystems enable reliable, high-resolution flow estimation without installing additional downhole metering devices, providing an efficient tool for production optimization and ESP performance management. Flow rate restoration is performed using multi-parameter optimization of a function that considers intake pressure, power, current, voltage, and submersible motor load.