Density-dependent dispersion in heterogeneous porous media Part I: A numerical study

Advances in Water Resources

Volumn 30, Issue 12, 2007, Pages 2467-2480

  Landman, Anke Jannie ^a   Johannsen, K ^b   Schotting, Ruud ^c  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b IWR   (Germany)

^c UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Brine transport; Concentration variance; Density dependent flow; Heterogeneous porous media; High concentration gradient dispersion; Macrodispersion; Solute transport; Stochastic media

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DENSITY (SPECIFIC GRAVITY); DIFFUSION; MATHEMATICAL MODELS; POROUS MATERIALS; STATISTICAL METHODS; TRANSPORT PROPERTIES;

DENSITY-DEPENDENT FLOW; HETEROGENEOUS POROUS MEDIA; HIGH-CONCENTRATION-GRADIENT DISPERSION; MACRODISPERSION;

FLOW OF WATER;

CONVERGENCE OF NUMERICAL METHODS; DENSITY (SPECIFIC GRAVITY); DIFFUSION; FLOW OF WATER; MATHEMATICAL MODELS; POROUS MATERIALS; STATISTICAL METHODS; TRANSPORT PROPERTIES;

ACCURACY ASSESSMENT; BRINE; COMPUTER SIMULATION; CONCENTRATION (COMPOSITION); DENSITY DEPENDENCE; FRESHWATER; HETEROGENEOUS MEDIUM; PERMEABILITY; POROUS MEDIUM; SOLUTE TRANSPORT; TRACER; TWO-DIMENSIONAL MODELING; UNCERTAINTY ANALYSIS;

EID: 34748842610     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2007.05.016     Document Type: Article

References (40)

1. Anderson SJ. An experimental investigation of high concentration displacements in saturated porous media. Ph.D. Thesis, The University of Western Australia; 1997.
2. Andričević R. Effects of local dispersion and sampling volume on the evolution of concentration fluctuations in aquifers. Water Res Res 34 5 (1998) 1115-1129
3. Bastian P., et al. UG - a flexible software toolbox for solving partial differential equations. Comput Visual Sci 1 (1997) 27-40
4. Bear J. Dynamics of fluids in porous media (1988), Dover, New York
5. Bellin A., Salandin P., and Rinaldo A. Simulation of dispersion in heterogeneous porous formations: statistics, first-order theories, convergence of computations. Water Resour Res 28 9 (1992) 2211-2227
6. Black T.C., and Freyberg D.L. Stochastic modeling of vertically averaged concentration uncertainty in a perfectly stratified aquifer. Water Resour Res 23 6 (1987) 997-1004
7. Bouhroum A. Einfluß der Viskositäts - und Dichteunterschiede zweier mischbarer Flüssigkeiten auf den Koeffizienten der longitudinalen hydrodynamischen Dispersion. Teil II Dichteunterschiede. Deutsche Gewässerkundliche Mitteilungen 33 (1989) 9-13
8. Burr D.T., Sudicky E.A., and Naff R.L. Nonreactive and reactive solute transport in three-dimensional heterogeneous porous media: Mean displacement, plume spreading, and uncertainty. Water Resour Res 30 3 (1994) 791-815
9. Cvetkovic V., Shapiro A.M., and Dagan G. A solute flux approach to transport in heterogeneous formations 2. Uncertainty analysis. Water Resour Res 28 5 (1992) 1377-1388
10. Dagan G. Solute transport in heterogeneous porous formations. J Fluid Mech 145 (1984) 151-177
11. Dagan G. Transport in heterogeneous porous formations: spatial moments, ergodicity, and effective dispersion. Water Resour Res 26 6 (1990) 1281-1290
12. Dagan G., and Fiori A. The influence of pore-scale dispersion on concentration statistical moments in transport through heterogeneous aquifers. Water Resour Res 33 7 (1997) 1595-1605
13. van Duijn C.J., and Schotting R.J. Brine transport in porous media: on the use of Von Mises and similarity transformations. Comput Geosci 2 (1998) 125-149
14. Fein E. D3f - Ein Programmpaket zur Modellierung von Dichteströmungen. GRS-139 (1998), Braunschweig, Germany
15. Ferziger H., and Perić M. Computational methods for fluid dynamics (1999), Springer
16. Gelhar L.W., and Axness C.L. Three dimensional stochastic analysis of macrodispersion in aquifers. Water Resour Res 19 1 (1983) 161-180
17. Graham W., and McLaughlin D. Stochastic analysis of nonstationary subsurface solute transport 1. Unconditional moments. Water Resour Res 25 2 (1989) 215-232
18. Hassanizadeh S.M., and Leijnse A. A non-linear theory of high-concentration-gradient dispersion in porous media. Adv Water Resour 18 4 (1995) 203-215
19. Hassanizadeh SM, Leijnse A, de Vries WJ, Stapper RAM. Experimental study of brine transport in porous media. RIVM Report 728514005, Bilthoven, The Netherlands; 1990.
20. Hassanizadeh S.M., and Leijnse T. On the modeling of brine transport in porous media. Water Resour Res 24 3 (1988) 321-330
21. Holzbecher E. The mixed convection number for porous media flow. In: Ingham DB., et al. (Ed). Emerging technologies and techniques in porous media, NATO Science Series II vol. 134 (2004), Kluwer Academic Publishers 169-181
22. Hsu K.C. The influence of the log-conductivity autovariance structure on macrodispersion coefficients. J Contamin Hydrol 65 (2003) 65-77
23. Jiao C.-Y., and Hötzl H. An experimental study of miscible displacements in porous media with variation of fluid density and viscosity. Trans Porous Media 54 (2004) 125-144
24. Johannsen K. On the validity of the Boussinesq approximation for the Elder problem. Comput Geosci 7 3 (2003) 169-182
25. Johannsen K., Kinzelbach W., Oswald S., and Wittum G. The saltpool benchmark problem - numerical simulation of saltwater upconing in a porous medium. Adv Water Resour 25 3 (2002) 335-348
26. Kapoor V., and Gelhar L.W. Transport in heterogeneous aquifers 1. Dynamics of concentration fluctuations. Water Resour Res 30 6 (1994) 1775-1788
27. Kapoor V., and Gelhar L.W. Transport in heterogeneous aquifers 2. Predictions and observations of concentration fluctuations. Water Resour Res 30 6 (1994) 1789-1801
28. Kretz V., Berest P., Hulin J.P., and Salin D. An experimental study of the effects of density and viscosity contrasts on macrodispersion in porous media. Water Resour Res 39 2 (2003) 1032-1040
29. Landman AJ. Analysis of physical mechanisms underlying density-dependent transport in porous media, Ph.D. Thesis, Delft University of Technology; 2005.
30. Landman A.J., and Schotting R.J. Heat and brine transport in porous media: the Oberbeck-Boussinesq approximation revisited. Trans Porous Media (2007) 10.1007/s11242-007-9104-9
31. Lessoff S.C., Indelman P., and Dagan G. A note on the influence of a constant velocity boundary condition on flow and transport in heterogeneous formations. Water Resour Res 63 10 (2000) 3095-3101
32. Moser H. Einfluß der Salzkonzentration auf die hydrodynamische Dispersion im porösen Medium. Ph.D. thesis, Mitteilung nr. 128, Technische Universität Berlin; 1995.
33. Rannacher R. Numerical analysis of nonstationary fluid flow, Technical Report SFB 123 Preprint 492, University of Heidelberg, Germany; 1988.
34. Robin M.J.L., Gutjar A.L., Sudicky E.A., and Wilson J.L. Cross-correlated random field generation with the direct fourier transform method. Water Resour Res 29 7 (1993) 2385-2397
35. Schotting R., and Landman A.J. Towards a physically based theory of high-concentration-gradient dispersion in porous media. Experimental, theoretical and numerical studies. In: Ingham DB., et al. (Ed). Emerging technologies and techniques in porous media, NATO Science Series II vol. 134 (2004), Kluwer Academic Publishers 321-336
36. Schotting R.J., Moser H., and Hassanizadeh S.M. High-concentration-gradient dispersion in porous media: experiments, analysis and approximations. Adv Water Resour 22 7 (1999) 665-680
37. Smith L., and Schwartz F. Mass transport 2. Analysis of uncertainty in prediction. Water Resour Res 17 2 (1981) 351-369
38. Trefry M.G., Ruan F.P., and McLaughlin D. Numerical simulations of preasymptotic transport in heterogeneous porous media: departures from the gaussian limit. Water Resour Res 39 3 (2003) 1063-1077
39. Vanderborght J. Concentration variance and spatial covariance in second-order stationary heterogeneous conductivity fields. Water Resour Res 37 7 (2001) 1893-1912
40. Vomvoris E.G., and Gelhar L.W. Stochastic analysis of the concentration variability in a three-dimensional heterogeneous aquifer. Water Resour Res 26 10 (1990) 2591-2602