Local Thermodynamic Description of Isothermal Single-Phase Flow in Simple Porous Media

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 $$5.7 \times {10^{-20}} \hbox {m}^2$$ 5.7 × 10 - 20 m 2 and $$5.5 \times {10^{-17}} \hbox {m}^2$$ 5.5 × 10 - 17 m 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.

Rayleigh–Schrödinger Perturbation Theory and Nonadditive Thermodynamics

“…This did not satisfy the prolific physical chemist Terrell L. Hill, who generalized standard Gibbsian thermodynamics to propose a purely thermodynamic framework for nonadditive systems. , The general idea in Hill’s extended thermodynamic framework is fairly intuitive, and it facilitates the use of thermodynamics’ powerful tools in environments otherwise not accessible to classical thermodynamics (see e.g. refs − , , and and refs therein). However, Hill’s powerful framework does not reconcile with the standard thermostatistical treatment based on purely mechanical energy levels.…”

“… 4 , 5 The general idea in Hill’s extended thermodynamic framework is fairly intuitive, and it facilitates the use of thermodynamics’ powerful tools in environments otherwise not accessible to classical thermodynamics (see e.g. refs ( 9 − 11 , 34 , and 35 ) and refs therein). However, Hill’s powerful framework does not reconcile with the standard thermostatistical treatment based on purely mechanical energy levels.…”

“…This creates the need for an additional phenomenological term, a subdivision potential that accounts for the interaction between a small subsystem and its surroundings. Far from being a mere curiosity, Hill's small-system method (later termed nanothermodynamics 6−8 ) has found applications in different domains, such as transport in porous media, 9 drug delivery, 10 and materials science. Yet, when it comes to undergraduate thermodynamics, Hill's generalized theory has a distinct disadvantage with respect to classical extensive thermodynamics.…”

Commentaries on Nanothermodynamics

“…In order to later deal with transport in porous media, we first define in the book the properties of a representative elementary volume (REV) of such media (11,25). In a face-centered cubic-type lattice with confined fluids the REV is a unit cell, and the driving force across a series of such REVs becomes minus the gradient of the so-called integral pressure.…”