Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 7. Single-phase megascale flow models

Advances in Water Resources

Volumn 32, Issue 8, 2009, Pages 1121-1142

  Gray, William G ^a   Miller, Cass T ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

Averaging theory; Model formulation; System scale; TCAT

Indexed keywords

AVERAGING THEORY; CONSERVATION EQUATIONS; ENTIRE SYSTEM; ENTROPY BALANCE; FLOW AND TRANSPORT; FLOW MODEL; IRREVERSIBLE THERMODYNAMICS; LOCAL EQUILIBRIUM ASSUMPTION; MICRO-SCALE; MODEL FORMULATION; MULTISCALE; POROUS MEDIUM SYSTEMS; SPATIAL VARIATIONS; SYSTEM SCALE; TCAT; THERMODYNAMICALLY CONSTRAINED AVERAGING THEORIES; TIME VARIATIONS;

POROUS MATERIALS;

ENERGY BALANCE; FLOW MODELING; NUMERICAL MODEL; POROUS MEDIUM; SPATIAL VARIATION; THERMODYNAMICS; TRANSPORT PROCESS;

EID: 67650484112     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2009.05.010     Document Type: Article

References (28)

1. Bailyn M. A survey of thermodynamics (1994), American Institute of Physics Press, New York
2. Barenblatt G.E., Zheltov I.P., and Kochina I.N. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. J Appl Math (USSR) 24 5 (1960) 1286-1303
3. Bear J. Hydraulics of groundwater (1979), McGraw-Hill, New York
4. Callen H.B. Thermodynamics and an introduction to thermostatistics (1985), Wiley, New York
5. Cermelli P., Fried E., and Gurtin M.E. Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces. J Fluid Mech 544 (2005) 339-351
6. Darcy H. Determination of the laws of flow of water through sand. In: Freeze R.A., and Back W. (Eds). Physical hydrology (1983), Hutchinson Ross, Stroudsburg, PA
7. De Groot S.R., and Mazur P. Non-equilibrium thermodynamics (1984), Dover, New York
8. Eringen A.C. Mechanics of continua. 2nd ed. (1980), Krieger, Huntington, NY
9. Fosdick R, Tang H. Surface transport in continuum mechanics. Math Mech Solids, 2008. doi:10.1177/1081286507087316.
10. Gray W.G. On the definition of derivatives of macroscale energy for the description of multiphase systems. Adv Water Resour 25 8-12 (2002) 1091-1104
11. Gray WG, Ghidaoui MS. Thermodynamic analysis of stream flow hydrodynamics. J Hydraul Res, in press.
12. Gray W.G., and Hassanizadeh S.M. Averaging theorems and averaged equations for transport of interface properties in multiphase systems. Int J Multiphase Flow 15 1 (1989) 81-95
13. Gray W.G., and Miller C.T. Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 1. Motivation and overview. Adv Water Resour 28 2 (2005) 161-180
14. Gray W.G., and Miller C.T. Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 3. Single-fluid-phase flow. Adv Water Resour 29 11 (2006) 1745-1765
15. Gray W.G., and Miller C.T. Consistent thermodynamic formulations for multiscale hydrologic systems: fluid pressures. Water Resour Res 43 9 (2007)
16. Gray W.G., and Miller C.T. Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 5. Single-fluid-phase transport. Adv Water Resour 32 5 (2009) 681-711
17. Gray W.G., and Schrefler B.A. Analysis of the solid phase stress tensor in multiphase porous media. Int J Numer Anal Methods Geomech 31 (2007) 541-581
18. Gray W.G., Leijnse A., Kolar R.L., and Blain C.A. Mathematical tools for changing scales in the analysis of physical systems (1993), CRC Press, Inc., Boca Raton, FL
19. Jackson A.B.S., Miller C.T., and Gray W.G. Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 6. Two-fluid-phase flow. Adv Water Resour 32 6 (2009) 779-795
20. Jou D., and Casas-Vazquez J. Extended irreversible thermodynamics and its relation with other continuum approaches. J Non-Newtonian Fluid Mech 96 1-2 (2001) 77-104
21. Marle C.M. On macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous media. Int J Eng Sci 20 5 (1982) 643-662
22. Maugin G.A. The thermomechanics of nonlinear irreversible behaviors: an introduction (1999), World Scientific Press, Singapore
23. Miller C.T., and Gray W.G. Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 2. Foundation. Adv Water Resour 28 2 (2005) 181-202
24. Miller C.T., and Gray W.G. Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 4. Species transport fundamentals. Adv Water Resour 31 3 (2008) 577-597
25. Murad M.A., and Cushman J.H. Multiscale flow and deformation in hydrophilic swelling porous media. Int J Eng Sci 34 3 (1996) 313-338
26. Pinder G.F., and Gray W.G. Essentials of multiphase flow and transport in porous media (2008), John Wiley & Sons, Inc., Hoboken, NJ
27. Reggiani P, Rientjes THM. Flux parameterization in the representative elementary watershed approach: application to a natural basin. Water Resour Res 2005;41:W04013. doi:10.1029/2004WR003693.
28. Whitaker S. Introduction to fluid mechanics (1968), Prentice-Hall, Inc., Englewood Cliffs, NJ