Correspondence of max-flow to the absolute permeability of porous systems

Abstract

The absolute permeability of porous media is an important parameter for various technological applications ranging from ground water hydrology to hydrocarbon recovery to microfluidics. There are scaling relationships between the geometric structure of a porous domain and its absolute permeability within a given class of structure. However, there exists no universal relationship between permeability and structure. We use network models of porous domains and apply the max-flow min-cut theorem to extract insights into the structures that most influence absolute permeability. The max-flow min-cut theorem states that the maximum flow through any network is exactly the sum of the edge weights that define the minimum cut. We hypothesize that the min-cut can be related to network permeability. We demonstrate that flow in porous media can be modeled as described by the max-flow min-cut theorem, which provides an approach to measure the absolute permeability of three-dimensional digital images of porous media. The max-flow of a network is found to correspond to its absolute permeability for over four orders of magnitude and identifies structural regions that result in significant energy dissipation. The findings are beneficial for the design of porous materials, as a subroutine for digital rock studies, the simplification of large network models, and further fundamental studies on the structure and flow properties of porous media.