POREMAPS: A finite difference based Porous Media Anisotropic Permeability Solver for Stokes flow

Abstract: Porous materials are ubiquitous in various engineering and geological applications, where their permeability plays a critical role in viscous fluid flow and transport phenomena. Understanding and characterizing the microscale properties, the effective hydraulic parameters, and also the anisotropy of porous materials are essential for accurate modeling and predicting fluid flow behavior. The study pursues the Digital Rock Physics approach to retrieve intrinsic permeability and its evolution in anisotropic configurations of porous media, which are subjected to pore space alterations. Therefore, we discuss the development and implementation of a computational framework based on the finite difference method to solve the pseudo-unsteady Stokes equations for fluid flow on the pore scale. We present an efficient and highly parallelized implementation of this numerical method for large voxel-based data sets originating from different image-based experimental setups. A comprehensive variety of benchmarks has been conducted to assess and evaluate the performance of the proposed solver. The solver's compatibility with huge domain sizes generated by state-of-the-art imaging techniques is demonstrated. We investigate an open-cell foam undergoing deformation, observing that contrary to initial expectations, no anisotropy emerges. Further, we examine a microfluidic cell experiencing precipitation within its pore space, resulting in clear anisotropic development during the clogging process.