Physics-informed deep learning for prediction of CO₂ storage site response

Accurate prediction of the CO₂ plume migration and pressure is imperative for safe operation and economic management of carbon storage projects. Numerical reservoir simulations of CO₂ flow could be used for this purpose allowing the operators and stakeholders to calculate the site response considering different operational scenarios and uncertainties in geological characterization. However, the computational toll of these high-fidelity simulations has motivated the recent development of data-driven models. Such models are less costly, but may overfit the data and produce predictions inconsistent with the underlying physical laws. Here, we propose a physics-informed deep learning method that uses deep neural networks but also incorporates flow equations to predict a carbon storage site response to CO₂ injection. A 3D synthetic dataset is used to show the effectiveness of this modeling approach. The model approximates the temporal and spatial evolution of pressure and CO₂ saturation and predicts water production rate over time (outputs), given the initial porosity, permeability and injection rate (inputs). First, we establish a baseline using data-driven deep learning models namely, Multilayer Perceptron (MLP) and Long Short-Term Memory (LSTM). To build a physics-informed model, the loss term is modified using the constraints defined by a simplified form of the governing partial differential equations (conservation of mass coupled with Darcy's law for a two-phase flow system). Our results indicate that incorporating the domain knowledge significantly improves the accuracy of predictions. The proposed modeling approach can be integrated in CO₂ storage management to accurately predict the critical site response indicators for a range of relevant input parameters, even when limited training data is available.