Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 5. Single-Fluid-Phase Transport.

Advances in Water Resources
W G Gray, Cass T Miller

Abstract

This work is the fifth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are used to develop models that describe species transport and single-fluid-phase flow through a porous medium system in varying physical regimes. Classical irreversible thermodynamics formulations for species in fluids, solids, and interfaces are developed. Two different approaches are presented, one that makes use of a momentum equation for each entity along with constitutive relations for species diffusion and dispersion, and a second approach that makes use of a momentum equation for each species in an entity. The alternative models are developed by relying upon different approaches to constrain an entropy inequality using mass, momentum, and energy conservation equations. The resultant constrained entropy inequality is simplified and used to guide the development of closed models. Specific instances of dilute and non-dilute systems are examined and compared to alternative formulation approaches.

Citations

May 7, 2010·Journal of Contaminant Hydrology·D Johnson WrightC T Miller
Feb 9, 2013·Advances in Water Resources·William G GrayBernhard A Schrefler
Dec 15, 2017·Journal of the Royal Society, Interface·B Rita AlevriadouMuniswamy Madesh
Sep 1, 2017·Journal of the Royal Society, Interface·Javier Buceta
Oct 6, 2017·Journal of the Royal Society, Interface·Altug OzcelikkaleBumsoo Han
Feb 21, 2014·New Journal of Physics·G SciumèBa Schrefler
Nov 27, 2014·Physical Biology·G SciumèB A Schrefler
May 24, 2017·Frontiers in Cell and Developmental Biology·Alan R Kay
Oct 21, 2020·Physical Review. E·Timothy M Weigand, Cass T Miller

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