A Computationally Efficient Method for Determining Permeability in Rocks with Dynamically Varying Pore Topology

Permeability is a key rock property important for scientific applications that require simulation of fluid flow. Although permeability is determined using core flooding experiments, recent advancements in micro-CT imaging and pore scale fluid flow simulations have made it possible to constrain permeability honoring pore scale rock structure. However, due to high computational and experimental costs, it might be difficult to determine permeability for systems which might undergo a dynamic variation in the underlying pore topology caused by a range of geological processes. This study presents a graph theory-based approach to determine permeability for such systems. The method involves transforming a given micro-CT rock image to a graph network map followed by the identification of the least resistance path to fluid flow between the inlet and the outlet faces. The method was tested on a variety of micro-CT images. Our analysis suggested a strong correlation of flow resistance determined from graph theory and numerically determined permeability. This indicates that the graph theory method can be used as a proxy for full physics simulations for determining effective permeability for samples with changing pore structure while improving computational efficiency by a factor of 250.