Physics Informed Machine Learning for Reservoir Connectivity Identification and Production Forecastingfor CO2-EOR
Authors: Nagao Masahiro , Datta-Gupta Akhil 
Published: September 2024

Abstract
Routine well-wise injection/production data contain significant information which 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 detailed geologic model which can be time-consuming to build. As an alternative, reduced physics models provide an efficient simulator free workflow, but often have a limited range of applicability. Pure machine learning models often lack physical interpretability and can have limited predictive power. To address these challenges, we propose hybrid models, combining machine learning and 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 input and multiphase production rates as output. 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 pre-processing to obtain approximate solutions that feed 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, physics-informed neural network (PINN) is applied. The residual terms are augmented in the neural network loss function using 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 improved predictive performance.
Our proposed hybrid models are first validated using a benchmark reservoir simulation case and then applied to a field case to show the robustness and efficacy of the method. The hybrid models are shown to provide superior prediction performance than pure machine learning 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 inter-well 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 for both benchmark case and field case. 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.