Physics-Guided Deep Learning for Prediction of Energy Production from Geothermal Reservoirs

Predictive models are traditionally used for the development and management of geothermal reservoirs. While field operation optimization based on physics-based simulations offers dependable strategies, simulation models require detailed descriptions of reservoir conditions and properties and entail extensive computational efforts. As efficient alternatives to traditional physics-based simulation, data-driven predictive models such as deep learning-based models can provide fast predictions to facilitate complex iterative tasks that otherwise entail high computation time. However, purely data-driven models that are trained using limited data often provide physically inconsistent predictions and fail to generalize beyond the training data. This has important consequences in optimization applications where, during optimization, the well control strategies are likely to fall beyond the training data. These limitations undermine the suitability and strength of data-driven models in scientific and engineering applications, where the amount of data is typically limited but physical laws are well-established and frequently used. To address the above challenges, we propose a novel physics-guided machine learning model by incorporating the general structure of the physics-based equations into deep learning models. A typical approach for incorporating physics is adding physics-based constraints in the loss function to regularize the trainable parameters. However, this approach does not exploit or adapt the architecture of the neural network. In this work, the architecture of the proposed recurrent neural networks (RNN) is designed to represent the differential equations of the subsurface flow system. We present the physics-guided RNN models in detail and demonstrate their connection to the underlying differential equations describing the fluid flow physics. We investigate the prediction performance of the proposed models by first applying them to controlled example to evaluate their extrapolation power, before using them with simulated and field datasets.