Routine well-wise injection/production data contain significant information which can be used for closed-loop reservoir management and rapid field decisions. Traditional physics-based numerical reservoir simulation can be computationally prohibitive for short-term decision cycles, and also requires 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. We propose a hybrid 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 it into a neural network as input. This physics-based input feature can reduce the model complexity and provide significant improvement in prediction performance. The second approach augments the residual terms in the neural network loss function with 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 superior prediction performance than pure machine learning models and reduced physics models in terms of multiphase production rates. Specifically, in the second method, the trained hybrid neural network model satisfies the reduced physics model, 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 excellent 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 preprocessing provide novel approaches to augment data-driven models with underlying physics to build interpretable models for understanding reservoir connectivity between wells and robust future production forecasting.

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