Physics-Aware Deep-Learning-Based Proxy Reservoir Simulation Model Equipped with State and Well Output Prediction
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AbstractPhysics-aware machine learning (ML) techniques have been used to endow data-driven proxy models with features closely related to the ones encountered in nature. Examples span from material balance and conservation laws. Physics-based and data-driven reduced-order models or a combination thereof (hybrid-based models) can lead to fast, reliable, and interpretable simulations used in many reservoir management workflows. We built on a recently developed deep-learning-based reduced-order modeling framework by adding a new step related to information of the input-output behavior (e.g., well rates) of the reservoir and not only the states (e.g., pressure and saturation) matching. A Combination of data-driven model reduction strategies and machine learning (deep- neural networks NN) will be used here to achieve state and input-output matching simultaneously. In Jin, Liu and Durlofsky (2020), the authors use a NN architecture where it is possible to predict the state variables evolution after training an autoencoder coupled with a control system approach (Embed to Control - E2C) and adding some physical components (Loss functions) to the neural network training procedure. In this paper, we extend this idea by adding the simulation model output, e.g., well bottom-hole pressure and well flowrates, as data to be used in the training procedure. Additionally, we added a new neural network to the E2C transition model to handle the connections between state variables and model outputs. By doing this, it is possible to estimate the evolution in time of both the state variables as well as the output variables simultaneously. The method proposed provides a fast and reliable proxy for the simulation output, which can be applied to a well-control optimization problem. Such a non-intrusive method, like data-driven models, does not need to have access to reservoir simulation internal structure. So it can be easily applied to commercial reservoir simulations. We view this as an analogous step to system identification whereby mappings related to state dynamics, inputs (controls), and measurements (output) are obtained. The proposed method is applied to an oil-water model with heterogeneous permeability, 4 injectors, and 5 producer wells. We used 300 sampled well control sets to train the autoencoder and another set to validate the obtained autoencoder parameters.
