Transition-Set Morphometry for Inter-Scale Contacts in Digital Sandstones

This paper introduces a transition-set morphometry for quantifying inter-scale contacts in digital sandstones. Pore volume, a medial pore-throat subsystem, and fracture porosity are treated as distinct geometric subsystems. Their finite-neighborhood contacts are represented by transition sets such as $T_{VL}$, $T_{VF}$, and, when a residual skeleton is resolved, $T_{LF}$. The method measures the density, finite-scale dimension, and weighted contact measures of these sets. A matrix-mode test was performed on 21 digital sandstone samples from the Imperial College micro-CT collection and Digital Porous Media Portal dataset DRP-317. Permeability, expressed as $\log_{10}K$, served as an external response for assessing how much structural information the descriptors carry. The transition dimension $d_{VL}$ alone produced little independent predictive gain, whereas contact measures combining transition-set density with local pore radius were more informative. The adaptive measure $\widehat C_{VL}^{(d+1)}=\mu_{VL}(\overline D_{VL}/D_*)^{d_{VL}+1}$ increased leave-one-out $R^2$ from 0.752 to 0.881 in the combined sample and from 0.287 to 0.807 within DRP-317. Fractured datasets DRP-5, DRP-31, and DRP-285 were then used to test the transfer of the same transition-set construction to fracture-related contacts. The results support transition sets as reproducible morphometric descriptors of inter-scale contact.