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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| Veröffentlicht in: | Advances in water resources Jg. 32; H. 6; S. 779 - 795 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Miller, Cass T. Jackson, Amber S. Gray, William G. |
| Author_xml | – sequence: 1 givenname: Amber S. surname: Jackson fullname: Jackson, Amber S. email: asalle1@email.unc.edu organization: Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3205, USA – sequence: 2 givenname: Cass T. surname: Miller fullname: Miller, Cass T. email: casey_miller@unc.edu organization: Department of Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, NC 27599-7431, USA – sequence: 3 givenname: William G. surname: Gray fullname: Gray, William G. email: GrayWG@unc.edu organization: Department of Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, NC 27599-7431, USA |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 6. Two-fluid-phase flow |
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