Fast Calculation Method of Two-Phase Flow in Horizontal Gas Wells Based on PI-DeepONet

With the deepening of unconventional oil and gas resource development, the gas–liquid two-phase flow phenomenon in horizontal gas wells is becoming increasingly complex. Accurate and efficient prediction of the flow state has become key to optimizing production. While traditional numerical simulation methods are highly accurate, their long calculation times make them unsuitable for real-time applications. Conversely, purely data-driven methods struggle with accuracy under sparse data conditions. This paper proposes a deep operator network method (PI-DeepONet) that integrates physical prior knowledge—specifically the drift-flux model—to rapidly predict two-phase flow parameters. By jointly training the network with both data loss and physical loss, the model’s accuracy and generalization are significantly enhanced. Comparing the results with the OLGA numerical simulator verifies the model’s high performance. The average relative error of the PI-DeepONet on the test set is less than 1%, with the error of some physical quantities controlled within 0.2%. Critically, the single prediction time is less than 0.1 s, achieving a calculation speed nearly 50,000 times higher than the traditional numerical simulation method. The model significantly improves prediction speed while ensuring accuracy, making it ideal for real-time simulation and rapid response requirements in horizontal wells. This study provides a new path for intelligent diagnosis and prediction of underground working conditions and demonstrates broad engineering application potential.