Defining the pressures of a fluid in a nanoporous, heterogeneous medium

Abstract

We describe the thermodynamic state of a single-phase fluid confined to a porous medium with Hill's thermodynamics of small systems, also known as nanothermodynamics. This way of defining small system thermodynamics, with a separate set of control variables, may be useful for the study of transport in nondeformable porous media, where presently no consensus exists on pressure computations. For a confined fluid, we observe that there are two pressures, the integral and the differential pressures. We use molecular simulations to investigate and confirm the nanothermodynamic relations for a representative elementary volume (REV). For a model system of a single-phase fluid in a face-centered cubic lattice of solid spheres of varying porosity, we calculate the fluid density, fluid-solid surface tension, replica energy, integral pressure, entropy, and internal energy.

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

“…We start with a single-phase flow, to document the use of new concepts on porous media pressure in a simple way. We have reported equilibrium studies with this coarsegraining procedure previously (Galteland et al 2019(Galteland et al , 2022Erdős et al 2020;Rauter et al 2020). We expand these results to non-equilibrium conditions in this work.…”

“…there is equilibrium at the boundary between the porous medium and the bulk phase surrounding the porous medium, we have the condition This condition was recently used to determine the solid integral pressure ps (Galteland et al 2022). We shall here use the relation 8 to determine the REV integral pressure in the equation of state (Eq.…”

“…With this procedure, we were able to determine the transport coefficients l and k. The procedure has been used earlier by us to establish the same gradient in integral pressure (Galteland et al 2022); however, the permeability calculations are done for the first time here.…”

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

“…We start with a single-phase flow, to document the use of new concepts on porous media pressure in a simple way. We have reported equilibrium studies with this coarse-graining procedure previously [8,21,9,22,23,24]. We expand these results to non-equilibrium conditions in this work.…”

“…With this procedure, we were able to determine the transport coefficients l and k. The procedure has been used earlier by us to establish the same gradient in integral pressure [24], however, the permeability calculations are done for the first time here.…”