Modeling and simulation of temperature-density-driven flow and thermodiffusionin porous media

Journal of Porous Media

Volumn 14, Issue 8, 2011, Pages 671-690

  Grillo, Alfio ^a   Lampe, Michael ^a   Wittum, Gabriel ^a  

^a GOETHE UNIVERSITY   (Germany)

Author keywords

Hybrid mixture theory; Irreversible thermodynamics; Porous media; Thermodiffusion; Thermohaline flow

Indexed keywords

IRREVERSIBLE THERMODYNAMICS; MATHEMATICAL MODELING; MIXTURE THEORY; MODELING AND SIMULATION; SATURATED POROUS MEDIA; SINGLE-PHASE FLOW; TEST CASE; THERMODIFFUSION; THERMOHALINE;

COMPUTER SIMULATION; THERMAL DIFFUSION IN LIQUIDS; THERMODYNAMICS;

POROUS MATERIALS;

EID: 79953782343     PISSN: 1091028X     EISSN: None     Source Type: Journal    
DOI: 10.1615/JPorMedia.v14.i8.20     Document Type: Article

References (53)

1. Agar, J. N., Advances in Electrochemistry and Electrochemical Engineering, eds. Delahay, P. and Tobias, C. W., vol. 3, pp. 31-121, Interscience Publishers, New York, 1963.
2. Bader, S. and Kooi, J., Modeling of solute and water transport in semi-permeable clay membranes: Comparison with experiments, Adv. Water Resour., vol. 28, pp. 203-214, 2005. (Pubitemid 40251871)
3. Balmforth, N. J., Cast, A. R. R., and Julien, K. A., Thermohaline convection with nonlinear salt profiles, Phys. Fluids, vol. 10, no. (4), pp. 819-828, 1988.
4. Bastian, P., Birken, K., Eckstein, K., Johannsen, K., Lang, S., Neuss N., and Rentz-Reichert, H., UG-a flexible software toolbox for solving partial differential equations, Comput. Visualization Sci., vol. 1, no. (1), pp. 27-40, 1997.
5. Bear, J., Dynamics of Fluids in Porous Media, Dover, New York, 1972.
6. Bear, J., Hydraulics of Groundwater, Dover, Mineola, 1979.
7. Bear, J. and Bachmat, Y., Introduction to Modeling of Transport Phenomena in Porous Media, Kluwer, Dordrecht, 1990.
8. Benano-Melly, L. B., Caltagirone, J. P., Faissat, B., Montel, F., and Costeséques, P., Modeling Soret coefficient measurement experiments in porous media considering thermal and solutal convection, Int. J. Heat Mass Transfer, vol. 44, pp. 1285-1297, 2001.
9. Bennethum, L. S., Theory of flow and deformation of swelling porous materials at the macroscale, Comput. Geotech., vol. 34, pp. 267-278, 2007.
10. Bennethum, L., Murad, M. A., and Cushman, J. H., Macroscale thermodynamics and the chemical potential for swelling porous media, Transport Porous Media, vol. 39, pp. 187-225, 2000. (Pubitemid 30255025)
11. Boussinesq, J., Theorie analytique de la chaleur, Paris, 1903.
12. Celestino, A. and Leonardi, E., The effect of thermodiffusion on the stability of a salinity gradient solar pond, Int J. Heat Mass Transfer, vol. 48, pp. 4633-4639, 2005.
13. Celestino, A., Leonardi, E., and Maciocco, L., A computational study of salt diffusion and heat extraction in solar pond plants, Solar Energy, vol. 80, pp. 1498-1508, 2006. (Pubitemid 44794341)
14. Costeséques, P., Fargue, D., and Jamet, P., Thermodiffusion in porous media and its consequences, in Thermal Nonequilibrium Phenomena in Fluid Mixtures, eds. Köhler, W., and Wiegand, S., pp. 389-427, Springer, Berlin, 2002.
15. De Groot S. and Mazur P., Non-equilibrium Thermodynamics, 2nd reprint, North-Holland, Amsterdam, 1969.
16. Denbigh, K., The Principles of Chemical Equilibrium, 4th edition, Cambridge University Press, Cambridge, 1968.
17. Diersch, H. J., Primitive variables finite element solutions of free convection flows in porous media, Zschr. Angew. Math. Mech., vol. 61, pp. 325-337, 1981.
18. Diersch, H. J. G. and Kolditz, O., Variable-density flow and transport in porous media: Approaches and challenges, Adv. Water Resour, vol. 25, no. (8), pp. 899-944, 2002. (Pubitemid 36000077)
19. Diersch, H. J. G. and Kolditz O., Variable-density flow and transport in porous media: Approaches and challenges, in Wasy Software FEFLOW© - Finite Element Subsurface flow and Transport Simulation System, vol. II, Wasy GmbH, Berlin, 2005.
20. Elder, J. W., Transient convection in a porous mediu, J. Fluid Mech., vol. 27, pp. 609-623, 1967.
21. Eringen, A. C, Mechanics of Continua, R. E. Krieger, 1980.
22. Fein, E., d3f, Ein Programmpaket zur Modellierung von Dichtestromungen, 39, GRS, Braunschweig, 1998.
23. Gajo, A. and Loret, B., Finite element simulations of chemomechanical coupling in elastic-plastic homoionic expansive clays, Comput. Methods Appl. Mech. Engrg., vol. 192, pp. 3489-3530, 2003. (Pubitemid 36967749)
24. Graf, T. and Therrien, R., Thermohaline groundwater flow and single-species reactive solute transport in fractured porous media, Adv. Water Resour, vol. 30, pp. 742-771, 2007.
25. Grillo, A., Wittum, G., Giaquinta, G., and Micunovic, M. V, A multiscale analysis of growth and diffusion dynamics in biological materials, Int. J. Eng. Sci., vol. 47, pp. 261-283, 2009.
26. Grillo, A., Federico, S., Wittum, G., Imatani, S., Giaquinta, G., and Mićunović, M. V, Evolution of a fibre-reinforced growing mixture, Nuovo Cimento C, vol. 32, no. (1), pp. 97-119, 2009.
27. Hassanizadeh, S. M., Derivation of basic equations of mass transport in porous media, Part 2, Generalized Darcy's and Fick's laws, Adv. Water Resour, vol. 9, pp. 207-222, 1986. (Pubitemid 17531039)
28. Hassanizadeh, S. M. and Gray, W. G., General conservation equations for multi-phase systems: 3. Constitutive theory for porous media flow, Adv. Water Resour, vol. 3, pp. 25-40, 1980. (Pubitemid 85211)
29. Holstad, A., Temperature-driven flow in porous media usind a mixed finite element method and finite volume method, Adv. Water Resour., vol. 24, pp. 843-862, 2001. (Pubitemid 32675895)
30. Ingle, S. E. and Horne, F. H., The Dufour Effect, J. Chem. Phys., vol. 59, no. (11), pp. 5882-5894, 1973.
31. Johannsen, K., Kinzelbach, W., Oswald, S., and Wittum, G., The saltpool benchmark problem-numerical simulation ofsaltwater upconing in a porous medium, Adv. Water Resour, vol. 25, no. (3), pp. 335-348, 2001. (Pubitemid 34416245)
32. Knaber, P. and Frolković, P., Consistent velocity approximation for finite volume or element discretizations of density driven flow in porous media, in: Computational Methods in Water Resources XI, Vol 1, Computational Methods in Subsurface Flow and Transport Problems, ed. Adama A. A. et al., pp. 93-100, Computational Mechanics Publications, Southampton, 1996.
33. Landau, L. D. and Liftschitz, E. M., Fluid Mechanics-Course of Theoretical Physics, 2nd edition, vol. 6, Pergamon, London, 1984.
34. Liu, I. S., Method of lagrange multipliers for exploitation of the entropy principle, Arch. Rational Mech. Anal., vol. 46, pp. 131-148, 1972.
35. Mazur, P. and De Groot S., Extension of onsager's oheory of reciprocal relations, Phys. Rev., vol. 94, pp. 224-226, 1954.
36. Mićunović, M. V., Thermodynamics of viscoplasticity- fundamentals and Applications, Springer, New York, 2009.
37. Oberbeck, A., Über die Wärmeleitung der Flüssigkeiten bei Berücksichtigung der Strömungen infolge von Temperaturdifferenzen, Ann. Phys. Chem., pp. 271-292., vol. 7, 1879.
38. Oldenburg, C. M. and Pruess, K., Layered thermohaline convection in hypersaline geothermal systems, Transport Porous Media, vol. 33, pp. 29-63, 1998.
39. Oldenburg, C. M. and Pruess, K., Plume separation by transient thermohaline convection in porous media, Geophys. Res. Lett., vol. 26, no. (19), pp. 2997-3000, 1999. (Pubitemid 30045071)
40. Oldenburg, C. M. and Pruess, K., Thermohaline convective mixing at a brine interface, in Proceedings of the 25th Workshop on Geothermal Reservoir Engineering, Stanford University, January 24-26, 2000.
41. Onsager, L., Reciprocal relations in irreversible processes, I, Phys. Rev., vol. 38, pp. 2265-2279, 1931.
42. Parvathy, C. P. and Prabhamani, R. P., Thermohaline instability with thermal diffusion and horizontal gradients, Appl. Sci. Res., vol. 45, pp. 163-178, 1988. (Pubitemid 18617805)
43. Peppin, S. S. L., Spannuth, M. J., and Wettlaufer, J. S., Onsager reciprocity in premelting solids, J. Stat. Phys., 2009.
44. Petit, C. J., Hwang, M. H., and Lin, J. L., The soret effect in dilute acqueous alkaline earth and nickel chloride solutions at 25C, Int. J. Thermophys., vol. 7, no. (3), pp. 687-697, 1986. (Pubitemid 16615172)
45. Rauch, J., Diffusion and thermal diffusion in polymer solutions, in German PhD thesis, Universität Bayreuth, Germany, 2006.
46. Rempel, A. W., Wettlaufer, J. S., and Worster, M. G., Interfacial premelting and the thermomolecular force: Thermodynamic buoyancy, Phys. Rev. Lett., vol. 87, no. (8), 088501-1, 2001.
47. Rowley, R. L. and Horne, F. H., The Dufour Effect. III. Direct experimental determination of the heat of transport of carbon tetrachloride-cyclohexane liquid mixtures, J. Chem. Phys., vol. 72, no. (1), pp. 131-139, 1980.
48. Ruggeri, T. and Simić S., On the hyperbolic system of a mixture of Eulerian Fluids: A comparison between single-and multi-temperature models, Math. Mech. Appl. Sci., vol. 30, pp. 335-849, 2007.
49. Sanyal, S. K. and Mukherjee, A. K., Heat of transport and heat capacity of transport of some acqueous electrolytes, J. Chem., vol. 66, pp. 435-438, 1988.
50. Sugisaki, M., Soret coefficients and heat of transport of polyvalent electrolytes in an acqueous solution, Bull. Chem. Soc. J., vol. 40, no. (10), pp. 2751-2754, 1975.
51. Tyrrell, H. J. V., The calculation of diffusion coefficients and Soret coefficients from optical measurements on pure Soret effect cells, Trans. Faraday Soc., vol. 52, pp. 940-948, 1956.
52. Voss, C. I. and Souza, W. R., Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater transition zone, Water Resour. Res., vol. 26, pp. 2097-2106, 1987.
53. Wilmanski, K., On thermodynamics of nonlinear poroelastic materials, J. Elasticity, vol. 71, pp. 247-261, 2003.