Predicting Resistivity and Permeability of Porous Media Using Minkowski Functionals

Abstract

Permeability and formation factor are important properties of a porous medium that only depend on pore space geometry, and it has been proposed that these transport properties may be predicted in terms of a set of geometric measures known as Minkowski functionals. The well-known Kozeny-Carman and Archie equations depend on porosity and surface area, which are closely related to two of these measures. The possibility of generalizations including the remaining Minkowski functionals is investigated in this paper. To this end, twodimensional computer-generated pore spaces covering a wide range of Minkowski functional value combinations are generated. In general, due to Hadwiger's theorem, any correlation based on any additive measurements cannot be expected to have more predictive power than those based on the Minkowski functionals. We conclude that the permeability and formation factor are not uniquely determined by the Minkowski functionals. Good correlations in terms of appropriately evaluated Minkowski functionals, where microporosity and surface roughness are ignored, can, however, be found. For a large class of random systems, these correlations predict permeability and formation factor with an accuracy of 40% and 20%, respectively.

Percolativity of Porous Media

“…Other suggestions include n-connectedness (Ohser and Schladitz 2009) or the Euler characteristic (Schlüter and Vogel 2011;Chiu et al 2013;Jiang and Arns 2020). Recently (Berg 2012;Hauskrecht 2018;Slotte et al 2020), tortuosity (Krüger 1918;Scheidegger 1957;Bear 1972) and constrictivity (Owen 1952;Boyack and Giddings 1963) have found some attention. Except for nonintersecting capillaries however, the latter quantities cannot be computed from the geometry alone (Ghanbarian et al 2012;Hauskrecht 2018).…”

Nanothermodynamic Description and Molecular Simulation of a Single-Phase Fluid in a Slit Pore

“…The central problem is to understand how to integrate properties on the pore scale to the macroscale where Darcy’s law applies. In order to account for shape and size effects, it was recently proposed to use the four Minkowski functionals [ 10 , 11 , 12 ]. This simplifies the description of a representative elementary volume (REV).…”

Pore‐Scale MultiResolution Rock‐Typing of Layered Sandstones via Minkowski Maps

“…A recently introduced rock‐typing and upscaling scheme (Jiang & Arns, 2020b) using the Minkowski functionals consisting of volume, surface area, integral of mean curvature and integral of total curvature (Hyde et al., 1990; Mecke, 1998, 2000; Vogel et al., 2011)—see Armstrong et al. (2018) for a recent review—and corresponding regional averages or Minkowski maps (C. H. Arns et al., 2005; Jiang & Arns, 2020a; Slotte et al., 2020) as regional morphological descriptors on laminated sandstone led to a robust homogenization of the underlying micro‐structure and upscaling of transport properties. A multivariate Gaussian mixture model (GMM) (Huang & Chau, 2008; Kim & Kang, 2007; A. Sheppard et al., 2014) was applied to the Minkowski maps, leading to compact rock‐types, which were sampled and characterized for their respective physical properties.…”