A Physics-Informed Neural Network Aided Venturi–Microwave Co-Sensing Method for Three-Phase Metering

Addressing the challenges of online measurement of oil-gas-water three-phase flow under high gas–liquid ratio (GVF > 90%) conditions (fire-driven mining, gas injection mining, natural gas mining), which rely heavily on radioactive sources, this study proposes an integrated, radiation-source-free three-phase measurement scheme utilizing a “Venturi tube-microwave resonator”. Additionally, a physics-informed neural network (PINN) is introduced to predict the volumetric flow rate of oil-gas-water three-phase flow. Methodologically, the main features are the Venturi differential pressure signal (ΔP) and microwave resonance amplitude (V). A PINN model is constructed by embedding an improved L-M model, a cross-sectional water content model, and physical constraint equations into the loss function, thereby maintaining physical consistency and generalization ability under small sample sizes and across different operating conditions. Through experiments on oil-gas-water three-phase flow, the PINN model is compared with an artificial neural network (ANN) and a support vector machine (SVM). The results showed that under high gas–liquid ratio conditions (GVF > 90%), the relative errors (REL) of PINN in predicting the volumetric flow rates of oil, gas, and water were 0.1865, 0.0397, and 0.0619, respectively, which were better than ANN and SVM, and the output met physical constraints. The results indicate that under current laboratory conditions and working conditions, the PINN model has good performance in predicting the flow rate of oil-gas-water three-phase flow. However, in order to apply it to the field in the future, experiments with a wider range of working conditions and long-term stability testing should be conducted. This study provides a new technological solution for developing three-phase measurement and machine learning models that are radiation-free, real-time, and engineering-feasible.