Entropy-mediated structure-permeability relations in skeletal porous materials
The aim of this paper is to formulate a new framework for characterisation of porous
materials and for obtaining first-principles structure-permeability relaions. The
formaslism is based on a representation of the porous medium in skeletal form and involves
several steps. First, the skeleton is characterised by a new fabric tensor that describes
the local pore structure. Second, the fabric tensor is used to construct a configurational
entropy of the porous medium, based on Edwards??? compactivity concept. Both the fabric
tensor and the entropic analysis are initially illustrated in two-dimensions and are then
extended to three-dimensional systems. Third, the local pore-scale permeability is expressed
in terms of the structure of the skeleton and the degrees of freedom that comprise the phase
space of configurational states. Fourth, the pore-scale permeability is calculated as an
expectation value over the partition function.
We propose that the same procedure can be used to find the conductivity of the porous medium
when it is filled with brine water. This makes it possible to derive a theoretical relation
between these two transport properties.