Prediction of porous media fluid flow using physics informed neural networks

Due to the explosion of the digital age of data, deep learning applications for different physical sciences have gained momentum. In this paper, we implement a physics informed neural network (PINN) technique that incorporates information from the fluid flow physics as well as observed data to model the Buckley-Leverett problem. The classical problem of drainage of gas into a water-filled porous medium is used to validate our implementation. Several cases are tested that signify the importance of the coupling between observed data and physics-informed neural networks for different parameter space. Our results indicate that PINNs are capable of capturing the overall trend of the solution even without observed data but the resolution and accuracy of the solution are improved tremendously with observed data. Adding a small amount of diffusion to the PDE-constrained loss function improved the solution slightly only when observed data were used. Moreover, the PINN is used to solve the inverse problem and infer the most optimal multiphase flow parameters. The performance of the PINN is compared to that of an artificial neural network (ANN) without any physics. We show that the ANN performs comparably well to the PINN when the observed data used to train the ANN include times that span the early- and late-time behavior. As opposed to the PINN, the ANN is not able to predict the solution when only early-time saturation profiles are provided as observed data and extrapolation are needed.