Algebraic multiscale grid coarsening using unsupervised machine learning for subsurface flow simulation

Subsurface flow simulation is vital for many geoscience applications, including geoenergy extraction and gas (energy) storage. Reservoirs are often highly heterogeneous and naturally fractured. Therefore, scalable simulation strategies are crucial to enable efficient and reliable operational strategies. One of these scalable methods, which has also been recently deployed in commercial reservoir simulators, is algebraic multiscale (AMS) solvers. AMS, like all multilevel schemes, is found to be highly sensitive to the types (geometries and size) of coarse grids and local basis functions. Commercial simulators benefit from a graph-based partitioner; e.g., METIS to generate the multiscale coarse grids. METIS minimizes the amount of interfaces between coarse partitions, while keeping them of similar size which may not be the requirement to create a coarse grid. In this work, we employ a novel approach to generate the multiscale coarse grids, using unsupervised learning methods which is based on optimizing different parameter. We specifically use the Louvain algorithm and Multi-level Markov clustering. The Louvain algorithm optimizes modularity, a measure of the strength of network division while Markov clustering simulates random walks between the cells to find clusters. It is found that the AMS performance is improved when compared with the existing METIS-based partitioner on several field-scale test cases. This development has the potential to enable reservoir engineers to run ensembles of thousands of detailed models at a much faster rate.