Physics Informed Machine Learning for Reservoir Connectivity Identification and Robust Production Forecasting

Routine well-wise injection/production data contain significant information that can be used for closed-loop reservoir management and rapid field decision-making. Traditional physics-based numerical reservoir simulation can be computationally prohibitive for short-term decision cycles, and it requires a detailed geologic model. Reduced physics models provide an efficient simulator-free workflow but often have a limited range of applicability. Pure machine learning models lack physical interpretability and can have limited predictive power. To address these challenges, we propose hybrid models, combining machine learning and a physics-based approach, for rapid production forecasting and reservoir connectivity characterization using routine injection/production and pressure data. Our framework takes routine measurements, such as injection rate and pressure data, as inputs and multiphase production rates as outputs. We combine reduced physics models into a neural network architecture by utilizing two different approaches. In the first approach, the reduced physics model is used for preprocessing to obtain approximate solutions that feed it into a neural network as input. This physics-based input feature can reduce the model complexity and provide significant improvement in prediction performance. In the second approach, a physics-informed neural network (PINN) is applied. The residual terms are augmented in the neural network loss function as physics-based regularization that relies on the governing partial differential equations (PDE). Reduced physics models are used for the governing PDE to enable efficient neural network training. The regularization allows the model to avoid overfitting and provides better predictive performance. Our proposed hybrid models are first validated using a 2D benchmark reservoir simulation case and then applied to a field-scale reservoir case to show the robustness and efficiency of the method. The hybrid models are shown to provide prediction performance that is superior to pure machine learning models and reduced physics models in terms of multiphase production rates. Specifically, in the second method with PINN, the trained hybrid neural network model satisfies the reduced physics system, making it physically interpretable, and provides interwell connectivity in terms of well flux allocation. The flux allocation estimated from the hybrid model was compared with streamline-based flux allocation, and reasonable agreement was obtained. By combining the reduced physics model with the efficacy of deep learning, model calibration can be done very efficiently without constructing a geologic model. The proposed hybrid models with physics-based regularization and physics-based preprocessing provide novel approaches to augment data-driven models with underlying physics to build interpretable models for understanding reservoir connectivity between wells and for robust future production forecasting.