Local thermodynamic description of isothermal single-phase flow in porous media

TL;DR

This paper introduces a new thermodynamic framework for single-phase flow in porous media, linking microscopic molecular dynamics with macroscopic transport properties like permeability and hydraulic conductivity.

Contribution

It provides a local thermodynamic basis for Darcy's law using grand potential, and investigates transport coefficients across various porosities and densities.

Findings

Permeability varies with porosity and fluid density.

Transport coefficients depend differently on porosity and density.

Klinkenberg effect observed in permeability variation.

Abstract

Darcy's law for porous media transport is given a new local thermodynamic basis in terms of the grand potential of confined fluids. The local effective pressure gradient is determined using non-equilibrium molecular dynamics, and the hydraulic conductivity and permeability are investigated. The transport coefficients are determined for single-phase flow in face-centered cubic lattices of solid spheres. The porosity changed from that in the closest packing of spheres to near unity in a pure fluid, while the fluid mass density varied from that of a dilute gas to a dense liquid. The permeability varied between \SI{5.7e-20}{\meter^2} and \SI{5.5e-17}{\meter^2}, showing a porosity-dependent Klinkenberg effect. Both transport coefficients depended on the average fluid mass density and porosity but in different ways. These results set the stage for a non-equilibrium thermodynamic investigation of coupled transport of multi-phase fluids in complex media.