Application of Physics-Informed Neural Networks to Immiscible Compositional Problems

Abstract

Carbon capture and storage is an essential technology to mitigate anthropogenic CO2 emissions from carbon-intensive industries. To model CO2 injection, physics-based numerical methods are computationally intensive due to the nonlinear nature of the governing equations. Therefore, several data-driven deep learning methods have been developed to serve as proxies and replace numerical simulations. These proxies have demonstrated significantly faster runtimes while maintaining comparable accuracy to numerical simulations. This makes them suitable for high-fidelity models and ensemble-based techniques that require a large number of forward runs. Our method utilizes physics-informed neural networks (PINNs) to parameterize the solution space of immiscible compositional problems. The PINN parameterizes the forward solution of the compositional problem based on the composition of the upstream grid block at the updated time step, the composition of the current grid block at the current time step and the total velocity at their interface. The neural network is trained in the entire solution space and is used in a sequential, cascading solver. In this approach, we obtain the pressure solution first before solving for transport by treating the reservoir as a series of two-cell problems. The resulting transport solver is applicable to all problems with different initial/injection conditions and different heterogeneous reservoirs. We demonstrate our approach for binary and multicomponent problems and furthermore use multilinear interpolation to compare and validate the solution method.