CO2-Brine Gravity-Driven Displacement Estimation Using Numerical Methods and Deep Learning

Abstract In the context of carbon geological sequestration, CO2 injection into saline aquifers induces a dynamic multiphase flow regime, characterized by a sharp interface between the displacing fluid (CO2) and the displaced fluid (brine) driven by their density contrast (CO2 is less dense than brine). This sharp interface is mathematically described by a nonlinear ordinary differential equation (ODE), posing significant computational challenges due to its stiffness and sensitivity to parameter variations. Although this complex ODE has been addressed in prior research studies, such as Nordbotten and Celia (2006) and Okwen et al. (2010), no explicit solution for the entire CO2-brine interface has been presented. This gap motivates a deeper investigation to find the best solution strategy. In this study, we develop two numerical approaches: (1) a finite difference, (2) a physics-informed deep learning framework. The latter leverages Physics-Informed Neural Networks (PINNs) to approximate solutions while intrinsically embedding the governing physics, offering a computationally efficient alternative to conventional methods. Our work rigorously compares these approaches against Okwen's correlation for χmax. Our findings demonstrate physics-informed machine learning to be a more rigorous solution method, outperforming traditional numerical methods in accuracy.