MODELING OF TWO-PHASE DARCY FLOW WITH PHYSICS-INFORMED NEURAL NETWORKS

Abstract

Recent breakthroughs in deep learning have greatly enhanced the ability to solve complex computational physics problems. In this paper, we introduce Physics-Informed Neural Networks (PINNs) that incorporate a spatially-dependent diffusion function to model two-phase flow in porous media, with a focus on the Buckley-Leverett problem. Our study explores various approaches, including the incorporation of a diffusion term and the modification of the flux function into a convex hull, using both Multi-Layer Perceptron (MLP) and Attention-based neural network architectures. Furthermore, we evaluate the performance of PINNs in modeling laboratory experimental data, specifically examining their ability to capture the dynamics of the saturation front. Our findings reveal that while the attention-based model achieves marginally higher accuracy, it is significantly more time-intensive to train. Conversely, the MLP architecture demonstrates superior efficiency in terms of training time, offering a speedup ranging from 7 to 13 times. A sensitivity analysis conducted on the constant diffusion coefficient shows that PINNs can effectively approximate the pattern of the saturation front. Our investigation has also demonstrated that utilizing a spatially-dependent diffusion function leads to improved accuracy when compared to a constant diffusion coefficient, particularly in aligning with experimental data. This highlights the potential of adapting the diffusion function to better fit experimental observations, enabling PINNs to achieve more precise results.