Transport with a very low density contrast in Hele-Shaw cell and porous medium: Evolution of the mixing zone

Transport in Porous Media

Volumn 55, Issue 3, 2004, Pages 339-360

  Oltean, C ^a   Felder, Ch ^a   Panfilov, M ^a   Bues M A ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Generalized dispersion tensor; Hele Shaw cell; Homogenization; Low density contrast; Numerical and experimental data; Tracer

Indexed keywords

COMPUTER SIMULATION; LIGHT ABSORPTION; MIXTURES; POROUS MATERIALS; TENSORS; TRANSPORT PROPERTIES;

HELE-SHAW CELL; OPTIMAL CONCENTRATION;

DYES;

DISPERSION; FLOW MODELING; GROUNDWATER; MIXING; POLLUTANT TRANSPORT; STOKES FLOW; TRACER;

DISPERSION; FLOW MODELING; GROUNDWATER POLLUTION; MIXING; POLLUTANT TRANSPORT; POROUS MEDIUM; STOKES FORMULA; TRACER;

EID: 1542572702     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:TIPM.0000013332.08029.af     Document Type: Article

References (38)

1. Adler, P. M. and Thovert, J.-F.: 1999, Fractures and fracture networks, in: J. Bear (ed.), Theory and Applications of Transport in Porous Media, Kluwer Academic Publishers, Dordrecht.
2. Auriault, J. L. and Adler, P. M.: 1995, Taylor dispersion in porous media: analysis by multiple scale expansions, Adv. Water Res. 18, 217-226.
3. Boggs, J. M., Young, S. C., Beard, L. M., Gelhar, L. W., Rehfeldt, K. R. and Adams, E. E.: 1992, Field study of dispersion in a heterogeneous aquifer. 1. Overview and site description, Water Resour. Res. 28, 3281-3291.
4. Brenner, H. and Edwards, D. A.: 1993, Macrotransport Processes, Butterworths Heinemann, London.
5. Buès, M. A. and Oltean, C.: 2000, Numerical simulations for saltwater intrusion by the mixed hybrid finite element method and discontinuous finite element method, Transport in Porous Media 40, 171-200.
6. Detwiler, R. L., Rajaram, H. and Glass, R. J.: 2000, Solute transport in variable-aperture fractures: an investigation of the relative importance of Taylor dispersion and macrodispersion, Water Resour. Res. 36, 1611-1625.
7. Elder, J. W.: 1967, Transient convection in a porous medium, J. Fluid Mech. 27, 609-623.
8. Galeati, G., Gombolati, G. and Neuman, S. P.: 1992, Coupled and partially coupled Eulerian-Lagrangian model of freshwater-seawater mixing, Water Resour. Res. 28, 149-165.
9. Gowda, V. and Jaffre, J.: 1993, A discontinuous finite element method for scalar nonlinear conservation laws, Rapport de recherche INRIA 1848.
10. Herbert, A. W., Jackson, C. P. and Lever, D. A.: 1988, Coupled groundwater flow and solute transport with fluid density strongly dependant upon concentration, Water Resour. Res. 24, 1781-1795.
11. Homsy, G. M.: 1987, Viscous fingering in porous media, Ann. Rev. Fluid Mech. 19, 271-311.
12. Horne, R. N. and Rodriguez, F.: 1983, Dispersion in tracer flow in fractured geothermal systems, Geophys. Res. Lett. 10, 289-292.
13. Huyakorn, P. S., Andersen, P. F., Mercer, J. W. and White Jr., H. O.: 1987, Saltwater intrusion in aquifers: development and testing of a three-dimensional finite element model, Water Resour. Res. 23, 293-312.
14. Istok, J. D. and Humphrey, M. D.: 1995, Laboratory investigation of buoyancy-induced flow (plume sinking) during two-well tracer tests, Ground Water 33, 597-604.
15. Kolditz, O., Ratke, R., Diersch, H. J. and Zielke, W.: 1997, Coupled groundwater flow and transport. I. Verification of variable density flow and transport models, Adv. Water Res. 21, 27-46.
16. Konikow, L. F., Sanford, W. E. and Campbell, P. J.: 1997, Constant-concentration boundary condition; lessons from the HYDROCOIN variable-density groundwater benchmark problem, Water Resour. Res. 33, 2253-2261.
17. Liu, H. H. and Dane, J. H.: 1997, A numerical study on gravitational instabilities of dense aqueous phase plumes in three-dimensional porous media, J. Hydrol. 194, 126-142.
18. Nakamura, I., Miyata, M. and Sakai, Y.: 1983, On a method of the concentration measurement by the use of light absorption law, Bull. JSME 26, 1357-1365.
19. Oldenburg, M. C. and Pruess, K.: 1995, Dispersive transport dynamics in a strongly coupled groundwater-brine flow system, Water Resour. Res. 31, 289-302.
20. Oltean, C. and Buès, M. A.: 2001, Coupled groundwater flow and transport in porous media. A conservative or non-conservative form? Transport in Porous Media 44, 219-246.
21. Oltean, C. and Buès, M. A.: 2002, Infiltration of salt solute in homogeneous and saturated porous media - an analytical solution evaluated by numerical simulations, Transport in Porous Media 48, 61-78.
22. Oltean, C., Felder, Ch. and Buès, M. A.: 2000, Density-driven flow and transport in porous media - infiltration with high permeability ratio, in: L. R. Bentley et al. (eds), Computational Methods in Water Resources XIII, Computational Methods for Subsurface Flow and Transport, Vol. 1, A.A. Balkema, Rotterdam, pp. 67-74.
23. Paschke, N. W. and Hoopes, J. A.: 1984, Buoyant contaminant plumes in groundwater, Water Resour. Res. 20, 1183-1192.
24. Schincariol, R. A. and Schwartz, F. W.: 1990, An experimental investigation of variable density flow and mixing in homogeneous and heterogeneous media, Water Resour. Res. 26, 2317-2329.
25. Schincariol, R. A., Schwartz, F. W. and Mendoza, C. A.: 1997, Instabilities in variable density flows: stability and sensitivity analyses for homogeneous and heterogeneous media, Water Resour. Res. 33, 31-41.
26. Sudicky, E. A., Cherry, J. A. and Frind, E. O.: 1983, Migration of contaminants in groundwater at a landfill: a case study. 4. A natural-gradient dispersion test, J. Hydrol. 63, 81-108.
27. Swartz, C. H. and Schwartz, F. W.: 1998, An experimental study of mixing and instability development in variable-density systems, J. Contam. Hydrol. 34, 169-189.
28. Taylor, G. I.: 1953, Dispersion of a soluble matter in solvent flowing slowly through a tube, Proc. R. Soc. Lond. A 219, 186-203.
29. Triboix, A., Trinh Thieu, B. and Zilliox, L.: 1975, Théorie de la dispersion sous l'effet d'un contraste de densité: infiltration d'un liquide miscible dans un milieux poreux saturé d'eau en repos, CR Acad. Sci. Paris 280, 1713-1716.
30. Voss, C. I. and Souza, R. W.: 1987, Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transition zone, Water Resour. Res. 23, 1851-1866.
31. Wooding, R. A.: 1960, Instability of a viscous liquid of variable density in a vertical Hele-Shaw cell, J. Fluid Mech. 7, 501-515.
32. Wooding, R. A.: 1963, Convection in a saturated porous medium at large Rayleigh number or Peclet number, J. Fluid Mech. 15, 527-544.
33. Wooding, R. A., Tyler, S. W. and White, I.: 1997a, Convection in groundwater below an evaporating salt lake. 1. Onset of instability, Water Resour. Res. 33, 1199-1217.
34. Wooding, R. A., Tyler, S. W., White, I. and Anderson, P. A.: 1997b, Convection in groundwater below an evaporating salt lake. 2. Evolution of fingers or plumes, Water Resour. Res. 33, 1219-1228.
35. Yang, Z. and Yortsos, Y. C., 1997, Asymptotic solutions of miscible displacements in geometries of large aspect ratio, Phys. Fluids 9, 286-298.
36. Zimmerman, R. W. and Bodvarsson, G. S.: 1996, Hydraulic conductivity of rock fractures, Transport in Porous Media 23, 1-30.
37. Zimmerman, W. B. and Homsy, G. M.: 1991, Nonlinear viscous fingering in miscible displacement with anisotropic dispersion, Phys. Fluids A 3, 1859-1872.
38. Zimmerman, W. B. and Homsy, G. M.: 1992, Viscous fingering in miscible displacements: unification of effects of viscosity contrast, anisotropic dispersion, and velocity dependence of dispersion on nonlinear finger propagation, Phys. Fluids A 4, 1859-1872.