Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 5. Single-fluid-phase transport

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...

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Published in:Advances in water resources Vol. 32; no. 5; pp. 681 - 711
Main Authors: Gray, William G., Miller, Cass T.
Format: Journal Article Conference Proceeding
Language:English
Published: Kidlington Elsevier Ltd 01.05.2009
Elsevier
Subjects:
Averaged thermodynamics
Averaging theory
Earth sciences
Earth, ocean, space
equations
Exact sciences and technology
groundwater flow
Hydrogeology
hydrologic models
Hydrology. Hydrogeology
Model formulation
Porous media
single fluid phase transport
Species transport
TCAT
thermodynamically constrained averaging theory
thermodynamics
Porous media
Model formulation
Averaged thermodynamics
TCAT
Species transport
Averaging theory
models
diffusion
interfaces
fluid phase
ground water
thermodynamics
hydrodynamics
transport
entropy
water resources
dispersion
porous media
flow
theory
ISSN:0309-1708, 1872-9657
Online Access:Get full text
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Summary: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.
Bibliography:http://dx.doi.org/10.1016/j.advwatres.2008.10.013
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ISSN:0309-1708
1872-9657
DOI:10.1016/j.advwatres.2008.10.013