Physics-Informed Neural Networks for Multi-Phase Flow in Porous Media Considering Dual Shocks and Interphase Solubility

TL;DR

This paper advances physics-informed neural networks (PINNs) to accurately solve complex multi-phase flow equations in porous media, effectively handling discontinuities and inverse problems with limited data.

Contribution

It introduces a novel PINN approach combined with Welge's Construction to better solve hyperbolic PDEs with shocks and rarefactions in porous media flows.

Findings

PINNs outperform traditional methods in modeling shock and rarefaction waves.

The approach effectively estimates PDE parameters from limited and noisy data.

Applications include water flooding, polymer flooding, and CO2 injection simulations.

Abstract

Physics-Informed Neural Networks (PINNs) integrate physical principles into machine learning, finding wide applications in various science and engineering fields. However, solving nonlinear hyperbolic partial differential equations (PDEs) with PINNs presents challenges due to inherent discontinuities in the solutions. This is particularly true for the Buckley-Leverett (B-L) equation, a key model for multi-phase fluid flow in porous media. In this paper, we demonstrate that PINNs, in conjunction with Welge's Construction, can achieve superior precision in handling the B-L equations in different scenarios including one shock and one rarefaction wave, two shocks connected by a rarefaction wave traveling in the same direction, and two shocks connected by a rarefaction wave traveling in opposite directions. Our approach accounts for variations in fluid mobility, fluid solubility, and gravity effects, with applications in modeling 1D water flooding, polymer flooding, gravitational flow, and CO$_2$ injection into saline aquifers. Additionally, we applied PINNs to inverse problems to estimate multiple PDE parameters from observed data, demonstrating robustness under conditions of slight scarcity and up to 5% impurity of labeled data, as well as shortages in collocation data.