Advancing Gas Rate Estimation: Integrating Physics into Machine Learning Models

Abstract Accurate gas flow rate estimation plays a pivotal role in optimizing well performance and field operations. Traditional empirical models, such as the Gilbert equations and its modified forms, often fall short in capturing the complexity of multiphase flow and compositional effects under varying operational conditions. Pure data-driven machine learning (ML) models offer high accuracy but suffer from a lack of physical interpretability and poor extrapolation in edge cases. This study presents a Physics-Informed Machine Learning (PIML) framework that integrates a recalibrated Modified Gilbert equation into a hybrid ensemble ML model to enhance both predictive accuracy and physical consistency. Using a field dataset of 1,181 test records, the approach employs feature engineering, hybrid loss functions, and ensemble stacking (XGBoost, MLP, Ridge) to incorporate domain physics into the learning loop. The recalibrated choke equation is embedded into model training via a custom loss function to anchor predictions around physical expectations. The model achieves an R2 of 0.973 and an MSE of 0.393—matching the accuracy of pure ML models while gaining robustness in sparse data regions. Uncertainty quantification with bootstrapping and quantile regression validates prediction confidence, while SHAP analysis and feature importance plots offer transparency into the model’s decision-making process. The results demonstrate that physics-informed models can bridge the gap between analytical heuristics and black-box ML by offering scalable, accurate, and explainable gas rate estimation solutions. This work lays the foundation for intelligent virtual flow metering systems applicable in real-time production monitoring and optimization.