Effect of viscosity, capillarity and grid spacing on thermal variable-density flow

Journal of Hydrology

Volumn 400, Issue 1-2, 2011, Pages 41-57

  Graf, Thomas ^a   Boufadel, Michel C ^b  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

^b TEMPLE UNIVERSITY   (United States)

Author keywords

Capillarity; Density; Elder problem; Heat flow; Unsaturated; Viscosity

Indexed keywords

CONVECTIVE FLOW; DENSITY; DENSITY FLOW; DOWN-WELLING; ELDER PROBLEM; ESTIMATED ERROR; FLOW DYNAMICS; GRID LEVELS; GRID-SPACINGS; HEAT FLOW; HIGHLY SENSITIVE; POROUS MEDIA; SPATIAL DISCRETIZATIONS; TEMPERATURE DEPENDENT; THERMAL VARIABLES; UNSATURATED; UNSATURATED FLOWS; UPWELLING REGION; WATER TABLES;

AQUIFERS; CAPILLARITY; HEAT TRANSFER; POROUS MATERIALS; SOIL MOISTURE;

VISCOSITY;

CAPILLARITY; DENSITY CURRENT; DOWNWELLING; ERROR ANALYSIS; FLUID FLOW; HEAT TRANSFER; NUMERICAL MODEL; POROUS MEDIUM; SENSITIVITY ANALYSIS; SOIL MOISTURE; SPATIAL ANALYSIS; TEMPERATURE EFFECT; UPWELLING; VISCOSITY; WATER TABLE;

CALLUNA VULGARIS;

EID: 79952487222     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jhydrol.2011.01.025     Document Type: Article

References (39)

1. Bataillé A., Genthon P., Rabinowicz M., Fritz B. Modeling the coupling between free and forced convection in a vertical permeable slot: implications for the heat production of an Enhanced Geothermal System. Geothermics 2006, 35:654-682.
2. Bear J. Dynamics of Fluids in Porous Media 1988, Elsevier, New York.
3. Bear J., Gilman A. Migration of salts in the unsaturated zone caused by heating. Lett. Math. Phys. 1995, 19:139-156.
4. Bolton E.W., Lasaga A.C., Rye D.M. A model for the kinetic control of quartz dissolution and precipitation in porous media flow with spatially variable permeability: formulation and examples of thermal convection. J. Geophys. Res. 1996, 101(B10):22157-22187.
5. Boufadel M.C., Suidan M.T., Venosa A.D. A numerical model for density-and-viscosity-dependent flows in two-dimensional variably-saturated media. J. Contam. Hydrol. 1999, 37:1-20.
6. Boufadel M.C., Suidan M.T., Venosa A.D. Numerical modeling of water flow below dry salt lakes - effect of capillarity and viscosity. J. Hydrol. 1999, 221(12):55-74.
7. Boufadel M.C. A mechanistic study of nonlinear solute transport in a groundwatersurface water system under steady state and transient hydraulic conditions. Water Resour. Res. 2000, 36(9):2549-2565.
8. Boussinesq V.J. Théorie analytique de la chaleur 1903, Gauthier-Villars, Paris, (Chapter 2.3).
9. Clift, S.S., D'Azevedo, F., Forsyth, P.A., Knightly, J.R., 1996. WATSIT-1 and WATSIT-B Waterloo sparse iterative matrix solvers, users guide with developer notes for version 2.0.0, (8). University of Waterloo, Waterloo.
10. Diersch H.-J.G. Primitive variables finite element solutions of free convection flows in porous media. Zschr. Angew. Math. Mech. 1981, 61:325-337.
11. Diersch H.-J.G., Kolditz O. Variable-density flow and transport in porous media: approaches and challenges. Adv. Water Resour. 2002, 25(8-12):899-944.
12. Elder J.W. Transient convection in a porous medium. J. Fluid Mech. 1967, 27(3):609623.
13. Finsterle S., Doughty C., Kowalsky M.B., Moridis G.J., Pan L., Xu T., Zhang Y., Pruess K. Advanced vadose zone simulations using TOUGH. Vadose Zone J. 2008, 7(2):601-609.
14. Forkel, C., Celia, M.A., 1992. Numerical simulation of unsaturated flow and contaminant transport with density and viscosity dependence. Computational methods in water resources IX. Mathematical Modeling in Water Resources, vol. 2, Computational Mechanics Publications, 351359.
15. Forsyth P.A., Sammon P.H. Practical considerations for adaptive implicit methods in reservoir simulation. J. Comput. Phys. 1986, 62:265-281.
16. Freeze R.A., Cherry J.A. Ground water 1979, Prentice-Hall, Englewood Cliffs.
17. Frolkovič P., De Schepper H. Numerical modelling of convection dominated transport coupled with density driven flow in porous media. Adv. Water Resour. 2001, 24:6372.
18. Graf T., Therrien R. Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures. Adv. Water Resour. 2005, 28(12):1351-1367.
19. Graf T., Therrien R. Coupled thermohaline groundwater flow and single-species reactive solute transport in fractured porous media. Adv. Water Resour. 2007, 30:742-771.
20. Grifoll J., Gastó J.M., Cohen Y. Non-isothermal soil water transport and evaporation. Adv. Water Resour. 2005, 28:12541266.
21. Johannsen K., Kinzelbach W., Oswald S.E., Wittum G. The saltpool benchmark problem - numerical simulation of saltwater upconing in a porous medium. Adv. Water Resour. 2002, 25(3):335-348.
22. Kolditz O., Ratke R., Diersch H.-J.G., Zielke W. Coupled groundwater flow and transport: 1. Verification of variable-density flow and transport models. Adv. Water Resour. 1998, 21(1):27-46.
23. Molson J.W., Frind E.O., Palmer C. Thermal energy storage in an unconfined aquifer 2: model development, validation and application. Water Resour. Res. 1992, 28(10):2857-2867.
24. Mualem Y. A new model to predict the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 1976, 12:513-522.
25. Nield D.A., Bejan A. Convection in Porous Media 1999, Springer, New York.
26. Oberbeck A. Ueber die Wärmeleitung der Flüssigkeiten bei Berücksichtigung der Strömung infolge von Temperaturdifferenzen. Ann. Phys. Chem. 1879, 7:27192.
27. Ogata, A., Banks, R.B., 1961. A solution of the differential equation of longitudinal dispersion in porous media. US Geological Survey, Technical Report 411-A, Professional Paper.
28. Oldenburg, C.M., Hinkins, R.L., Moridis, G.J., Pruess, K., 1995. On the development of MP-TOUGH2. In: Proceedings of TOUGH Workshop 1995, Lawrence Berkeley Laboratory, Berkeley.
29. Oldenburg C.M., Pruess K. Dispersive transport dynamics in a strongly coupled groundwater-brine flow system. Water Resour. Res. 1995, 31(2):289302.
30. Prasad A., Simmons C.T. Unstable density-driven flow in heterogeneous porous media: a stochastic study of the Elder [1967b] " short heater" problem. Water Resour. Res. 2003, 39(1):1007. 10.1029/2002WR001290.
31. Prasad A., Simmons C.T. Using quantitative indicators to evaluate results from variable-density groundwater flow models. Hydrogeol. J. 2005, 13(5-6):905-914.
32. Rausch R., Schäfer W., Therrien R., Wagner C. Introduction to Solute Transport Modelling 2005, Gebrüder Borntraeger, Berlin.
33. Simpson M.J., Clement T.P. Theoretical analysis of the worthiness of Henry and Elder problems as benchmarks of density-dependent groundwater flow models. Adv. Water Resour. 2003, 26(1):17-31.
34. Therrien R., Sudicky E.A. Three-dimensional analysis of variably saturated flow and solute transport in discretely-fractured porous media. J. Contam. Hydrol. 1996, 23(6):1-44.
35. Therrien R., McLaren R.G., Sudicky E.A., Panday S.M. Hydrogeosphere - A Three-dimensional Numerical Model Describing Fully-integrated Subsurface and Surface Flow and Solute Transport 2009, University of Waterloo, Waterloo.
36. Thiesen M., Scheel K., Diesselhorst H. Untersuchungen über die thermische Ausdehnung von festen und tropfbar flüssigen Körpern - Bestimmung der Ausdehnung des Wassers für die zwischen 0° und 40° liegenden Temperaturen [Investigations on the thermal expansion of solid and liquid materials - Determination of the expansion of water for temperatures between 0° und 40°]. Wiss. Abhandlungen der Physik.-Techn. Reichsanst. 1900, 3:1-70.
37. van Genuchten M.T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 1980, 44:892-898.
38. Voss C.I., Souza W.R. Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transition zone. Water Resour. Res. 1987, 26:2097-2106.
39. Weatherill D., Graf T., Simmons C.T., Cook P.G., Therrien R., Reynolds D.A. Discretizing the fracture-matrix interface to simulate solute transport. Ground Water 2008, 46(4):606-615.