Modeling density-driven flow in porous media by physics-informed neural networks for CO₂ sequestration

Accurate prediction of density-driven convection of CO₂ overlaying brine in porous media is crucial to the applications of geological carbon sequestration. In this paper, we introduce the physics-informed neural network (PINN) method to investigate the mass transfer of CO₂ injected into a homogeneous subsurface porous formation, where the concentration and the streamfunction are approximated by neural network representations. To mitigate the computational burden and training difficulties arising from learning the long-term diffusion and convection processes, we implement a time domain decomposition-based scheme so that the PINN solution can represent short-interval dynamics in a sequential manner. Furthermore, Fourier-type basis functions are encoded in the PINN architecture to map the spatial coordinates onto an embedding feature space characterized by various frequencies. The numerical results show that the use of Fourier feature embedding improves the training performance by handling the notorious spectral bias in deep neural networks and enhances the stability for long-term prediction of flow and transport. The proposed PINN method is applied to a benchmark problem to understand the effect of natural convection on the simulation performance. Compared to the high-fidelity stabilized FEM solution, the PINN approach presents agreeable statistical characteristics of CO₂-rich brine fingers, demonstrating the effectiveness of PINNs in modeling density-driven flow.