A Graph-Partitioning-Based Multiscale Preconditioner for Modeling Flow in Unstructured Pore Networks

Abstract Multiphase flow simulation in porous media is a challenging task with significant industrial implications. Pore Network Modeling (PNM) is an effective method that provides accurate results within a reasonable computational timeframe. However, as the complexity of these systems increases, particularly when simulating whole-core-sized pore networks (Digital Plugs) with millions of elements, there is a growing demand to improve the computational efficiency of PNM. The primary computational bottleneck is the pressure field update process, which involves solving a linear system of balance equations. To address this issue, our research focuses on evaluating the performance of a recently developed multiscale preconditioner for solving this system. We compare its performance against a state-of-the-art algebraic multigrid (AMG) method. Networks where the multiscale preconditioner outperforms AMG are identified, and a multilevel strategy is implemented to extend the capabilities of the method to networks with up to 200 million pore bodies. This shows the multiscale method is a promising alternative to accelerate multiphase simulations in Pore Network Modeling.