Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 6. Two-fluid-phase flow

This work is the sixth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works, the...

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Published in:Advances in water resources Vol. 32; no. 6; pp. 779 - 795
Main Authors: Jackson, Amber S., Miller, Cass T., Gray, William G.
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.06.2009
Elsevier
Subjects:
Averaged thermodynamics
Classical irreversible thermodynamics
Earth sciences
Earth, ocean, space
Exact sciences and technology
groundwater flow
Hydrogeology
hydrologic models
Hydrology. Hydrogeology
mathematical models
Model formulation
Multiphase flow
porous media
simplified entropy inequality
simulation models
TCAT
thermodynamically constrained averaging theory
thermodynamics
Model formulation
Averaged thermodynamics
Classical irreversible thermodynamics
Multiphase flow
TCAT
models
interfaces
fluid phase
ground water
thermodynamics
hydrodynamics
transport
entropy
water resources
multiphase flow
porous media
theory
ISSN:0309-1708, 1872-9657
Online Access:Get full text
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Summary:This work is the sixth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works, the limiting case of connected two-fluid-phase flow is considered. A constrained entropy inequality is developed based upon a set of primary restrictions. Formal approximations are introduced to deduce a general simplified entropy inequality (SEI). The SEI is used along with secondary restrictions and closure approximations consistent with the SEI to produce a general functional form of a two-phase-flow model. The general model is in turn simplified to yield a hierarchy of models by neglecting common curves and by neglecting both common curves and interfaces. The simplest case considered corresponds to a traditional two-phase-flow model. The more sophisticated models including interfaces and common curves are more physically realistic than traditional models. All models in the hierarchy are posed in terms of precisely defined variables that allow for a rigorous connection with the microscale. The explicit nature of the restrictions and approximations used in developing this hierarchy of models provides a clear means to both understand the limitations of traditional models and to build upon this work to produce more realistic models.
Bibliography:http://dx.doi.org/10.1016/j.advwatres.2008.11.010
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ISSN:0309-1708
1872-9657
DOI:10.1016/j.advwatres.2008.11.010