Numerical simulation of three-dimensional saltwater-freshwater fingering instabilities observed in a porous medium

Advances in Water Resources

Volumn 29, Issue 11, 2006, Pages 1690-1704

  Johannsen, Klaus ^a   Oswald, Sascha ^b   Held, Rudolf ^c   Kinzelbach, Wolfgang ^d  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b HELMHOLTZ CENTRE FOR ENVIRONMENTAL RESEARCH UFZ   (Germany)

^c STATOIL   (Norway)

^d ETH ZURICH   (Switzerland)

Author keywords

Instability; Multigrid methods; NMR; Non invasive imaging; Porous media; Saltwater; Variable density flow

Indexed keywords

COMPUTER SIMULATION; FLOW OF WATER; IMAGING TECHNIQUES; MATHEMATICAL MODELS; POROUS MATERIALS; SALINE WATER;

MULTIGRID METHODS; NON-INVASIVE IMAGING; SALTWATER-FRESHWATER FINGERING INSTABILITY;

WATER RESOURCES;

COMPUTER SIMULATION; FLOW OF WATER; IMAGING TECHNIQUES; MATHEMATICAL MODELS; POROUS MATERIALS; SALINE WATER; WATER RESOURCES;

EXPERIMENTAL STUDY; FLOW STABILITY; FRESHWATER; IMAGING METHOD; POROUS MEDIUM; SIMULATION; WATER FLOW;

EID: 33748554494     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2005.12.008     Document Type: Article

References (57)

1. Alvarez-Lacalle E., Ortin J., and Casademunt J. Nonlinear Saffman-Taylor instability. Phys Rev Lett 92 5 (2004) Art. no. 054501
2. Bacri J.-C., Salin D., and Yortsos Y.C. Analyse linéaire de la stabilité de l'écoulement de fluides miscibles en milieux poreux. C R Acad Sci Paris 314 II (1992) 139-144
3. Bank R.E., Sherman A.H., and Weiser A. Refinement algorithms and data structures for regular local mesh refinement. Scientific Computing IMACS (1983), North-Holland, Amsterdam
4. Bastian P., Birken K., Johannsen K., Lang S., Neuss N., Rentz-Reichert H., et al. UG - a flexible software toolbox for solving partial differential equations. Comput Visual Sci 1 (1997) 27-40
5. Bear J., and Bachmat Y. Introduction to modeling of transport phenomena in porous media (1991), Kluwer Academic Publishers
6. Beck J.L. Convection in a box of porous material saturated with fluid. Phys Fluids 15 (1972) 1377-1383
7. Callaghan P.T. Principles of nuclear magnetic resonance microscopy (1991), Clarendon Press, Oxford
8. Casademunt J. Viscous fingering as a paradigm of interfacial pattern formation: recent results and new challenges. Chaos 14 3 (2004) 809-824
9. Chuoke R.L., van Meurs P., and van der Poel C. The instability of slow, immiscible, viscous liquid-liquid displacements in permeable media. Trans Inst Min Metall Pet Eng 216 (1959) 188-194
10. Coskuner G., and Bentsen R.G. An extended theory to predict the onset of viscous instabilities for miscible displacements in porous media. Transp Porous Media 5 (1990) 473-490
11. Diersch H.-J.G., and Kolditz O. Variable-density flow and transport in porous media: approaches and challenges. Adv Water Resour 25 (2002) 899-944
12. Fein E, editor. d3f - Ein Programmpaket zur Modellierung von Dichteströmungen. GRS, Braunschweig, GRS-139, 1998. ISBN 3-923875-97-5.
13. Elder J.W. Steady free convection in a porous medium heated from below. J Fluid Mech 27 (1967) 29-48
14. Fernandez J., Kurowski P., Petitjeans P., and Meiburg E. Density-driven unstable flows of miscible fluids in a Hele-Shaw cell. J Fluid Mech 451 (2002) 239-260
15. Frolkovic P. Consistent velocity approximation for density driven flow and transport. In: van Keer R, et al., editors. Advanced computational methods in engineering, 1998. p. 603-11.
16. Graf F., Meiburg E., and Härtel C. Density-driven instabilities of miscible fluids in a Hele-Shaw cell: linear stability analysis of the three-dimensional Stokes equations. J Fluid Mech 451 (2002) 261-282
17. Hassanizadeh S.M., and Leijnse A. On the modelling of brine transport in porous media. Water Resour Res 24 (1988) 321-330
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. Herbert A.W., Jackson C.P., and Lever D.A. Coupled groundwater flow and solute transport with fluid density strongly dependent upon concentration. Water Resour Res 24 (1988) 1781-1795
20. Herrmann K.-H., Pohlmeier A., Wiese S., Shah N.J., Nitzsche O., and Vereecken H. Three-dimensional nickel ion transport through porous media using magnetic resonance imaging. J Environ Qual 31 (2002) 506-514
21. Hill M.A. Channeling in packed columns. Chem Eng Sci 1 (1952) 247-253
22. Hoffman F., Ronen D., and Pearl Z. Evaluation of flow characteristics of a sand column using magnetic resonance imaging. J Contam Hydrol 22 (1996) 95-107
23. Holzbecher E.O. Modeling density-driven flow in porous media (1998), Springer-Verlag, Berlin, Heidelberg
24. Johannsen K. Numerische Aspekte dichtegetriebener Stroemung in poroesen Medien (2004), Habilitationsschrift, Heidelberg University
25. Johannsen K., Kinzelbach W., Oswald S.E., and Wittum G. The saltpool benchmark problem - numerical simulation of saltwater upconing in a porous medium. Adv Water Resour 25 (2002) 335-348
26. Leijnse A. Three-dimensional modeling of coupled flow and transport in porous media. PhD thesis. University of Notre Dame, Indiana, 1992.
27. Martin J., Rakotomalala N., and Salin D. Gravitational instability of miscible fluids in a Hele-Shaw cell. Phys Fluids 14 2 (2002) 902-905
28. Meiburg E., and Chen C.-Y. High-accuracy implicit finite-difference simulations of homogeneous and heterogeneous miscible porous media flows. SPE J 5 2 (2000) 129-137
29. Menand T., and Woods A.W. Dispersion, scale and time dependence of mixing zones under gravitationally stable and unstable displacements in porous media. Water Resour Res 41 (2005) W05014 10.1029/2004WR003701
30. Oswald S. Available from: http://www.ihw.ethz.ch/url/connect?ihw=fingering_EN.
31. Oswald S. Dichteströmungen in porösen Medien: Dreidimensionale Experimente und Modellierung. PhD thesis. Institut für Hydromechanik und Wasserwirtschaft, ETH Zürich, Switzerland, no. 12812, 1998.
32. Oswald S., Kinzelbach W., Greiner A., and Brix G. Observation of flow and transport processes in artificial porous media via magnetic resonance imaging in three dimensions. Geoderma 80 3-4 (1997) 417-429
33. Oswald S.E., and Kinzelbach W. Three-dimensional physical benchmark experiments to test variable-density flow models. J Hydrol 290 1-2 (2004) 22-42
34. Oswald S.E., Scheidegger M.B., and Kinzelbach W. Time-dependent measurement of strongly density-dependent flow in a porous medium via nuclear magnetic resonance imaging. Transp Porous Media 47 1-2 (2002) 169-193
35. Pearl Z., Magaritz M., and Bendel P. Nuclear magnetic resonance imaging of miscible fingering in porous media. Transp Porous Media 12 (1993) 107-123
36. Petitjeans P., Chen C.-Y., Meiburg E., and Maxworthy T. Miscible quarter five-spot displacements in a Hele-Shaw cell and the role of flow induced dispersion. Phys Fluids 11 7 (1999) 1705-1716
37. Rannacher R. Numerical analysis of nonstationary fluid flow. Technical Report SFB 123, Preprint 492, University of Heidelberg, Germany, November 1988.
38. Riaz A., and Meiburg E. Three-dimensional miscible displacement simulations in homogeneous porous media with gravity override. J Fluid Mech 494 (2003) 95-117
39. Rumpf M., and Wierse A. GRAPE, eine objektorientierte Visualisierungs- und Numerikplattform. Informatik Forschung und Entwicklung 7 (1992) 145-151
40. Saffman P.G., and Taylor G.I. The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous fluid. Proc Royal Soc Lond A 245 (1958) 312-329
41. Scheidegger A.E. General theory of dispersion in porous media. J Geophys Res 66 (1961) 3273
42. Schincariol R.A., and Schwartz F.W. An experimental investigation of variable density flow and mixing in homogenous and heterogeneous porous media. Water Resour Res 26 10 (1990) 2317-2329
43. Schneider KJ. Investigation of the influence of free thermal convection on heat transfer through granular material. In: Proceedings of the 11th international congress on refrigeration. Oxford: Pergamon Press; 1963. p. 247-53.
44. 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
45. Simmons C.T. Variable-density groundwater flow: from current challenges to future possibilities. Hydrogeol J 13 (2005) 116-119
46. Simmons C.T., Fenstemaker T.R., and Sharp Jr. J.M. Variable-density groundwater flow and solute transport in heterogeneous porous media: approaches and challenges. J Contam Hydrol 52 1-4 (2001) 245-275
47. Simmons C.T., Narayan K.A., and Wooding R.A. On a test case for density-dependent groundwater flow and solute transport models: the salt lake problem. Water Resour Res 35 12 (1999) 3607-3620
48. Tan C.T., and Homsy G.M. Stability of miscible displacement in porous media: rectilinear flow. Phys Fluids 29 (1986) 3549-3556
49. Tchelepi H.A., and Orr F.M.J. Interaction of viscous fingering, permeability heterogeneity, and gravity segregation in three dimensions. SPE Res Eng 9 4 (1994) 266-271
50. van As H., and van Dusschoten D. NMR methods for imaging of transport processes in micro-porous systems. Geoderma 80 3-4 (1997) 389-403
51. van der Vorst H. Bi-CGSTAB: a fast and smoothly converging variant of big for the solution of nonsymmetric linear systems. SIAM J Sci Stat Comp 13 (1992) 631-644
52. Weatherill D., Simmons C.T., Voss C.I., and Robinson N.I. Testing density-dependent groundwater models: two-dimensional steady state unstable convection in infinite, finite and inclined porous layers. Adv Water Resour 27 5 (2004) 547-562
53. Wooding R.A. The stability of a viscous liquid in a vertical tube containing porous material. Proc R Soc Lond, Ser A 252 (1959) 120-134
54. Wooding R.A. Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell. J Fluid Mech 39 3 (1969) 477-495
55. Wooding R.A., Tyler S.W., and White I. Convection in groundwater below an evaporating salt lake. 1. Onset of instability. Water Resour Res 33 6 (1997) 1199-1217
56. Wooding R.A., Tyler S.W., White I., and Anderson P.A. Convection in groundwater below an evaporating salt lake. 2. Evolution of fingers or plumes. Water Resour Res 33 6 (1997) 1219-1228
57. Zimmerman W.B., and Homsy G.M. Three-dimensional viscous fingering: a numerical study. Phys Fluids 4 9 (1992) 1901-1914