Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 3. Single-fluid-phase flow
This work is the third in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach to modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works in thi...
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| Published in: | Advances in water resources Vol. 29; no. 11; pp. 1745 - 1765 |
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01.11.2006
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| Abstract | This work is the third in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach to modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works in this series, we demonstrate the TCAT approach for the case of single-fluid-phase flow. The formulated model is based upon conservation equations for mass, momentum, and energy and a general entropy inequality constraint, which is developed to guide model closure. A specific example of a closed model is derived under limiting assumptions using a linearization approach and these results are compared and contrasted with the traditional single-phase-flow model. Potential extensions to this work are discussed. Specific advancements in this work beyond previous averaging theory approaches to single-phase flow include use of macroscale thermodynamics that is averaged from the microscale, the use of derived equilibrium conditions to guide a flux–force pair approach to simplification, use of a general Lagrange multiplier approach to connect conservation equation constraints to the entropy inequality, and a focus on producing complete, closed models that are solvable. |
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| AbstractList | This work is the third in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach to modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works in this series, we demonstrate the TCAT approach for the case of single-fluid-phase flow. The formulated model is based upon conservation equations for mass, momentum, and energy and a general entropy inequality constraint, which is developed to guide model closure. A specific example of a closed model is derived under limiting assumptions using a linearization approach and these results are compared and contrasted with the traditional single-phase-flow model. Potential extensions to this work are discussed. Specific advancements in this work beyond previous averaging theory approaches to single-phase flow include use of macroscale thermodynamics that is averaged from the microscale, the use of derived equilibrium conditions to guide a flux–force pair approach to simplification, use of a general Lagrange multiplier approach to connect conservation equation constraints to the entropy inequality, and a focus on producing complete, closed models that are solvable. |
| Author | Miller, Cass T. Gray, William G. |
| Author_xml | – sequence: 1 givenname: William G. surname: Gray fullname: Gray, William G. email: GrayWG@unc.edu – sequence: 2 givenname: Cass T. surname: Miller fullname: Miller, Cass T. email: casey_miller@unc.edu |
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| Keywords | Porous medium models Single-phase flow TCAT Averaging theory models extension fluid phase foundations thermodynamics focus transport conservation entropy water resources buildings equilibrium theory energy |
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| SubjectTerms | Averaging theory Earth sciences Earth, ocean, space Exact sciences and technology groundwater flow Hydrology. Hydrogeology mathematical models porous media Porous medium models Single-phase flow solutes TCAT thermodynamics |
| Title | Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 3. Single-fluid-phase flow |
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