Macro-scale effective constitutive relationships for two-phase flow processes in heterogeneous porous media with emphasis on the relative permeability-saturation relationship

Journal of Contaminant Hydrology

Volumn 76, Issue 1-2, 2005, Pages 47-85

  Braun, Christopherus ^a   Helmig, Rainer ^b   Manthey, Sabine ^b  

^a Technologieberatung Grundwasser U   (Germany)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Averaging effective conductivity; Macroscopic residual saturation; Saturation dependent anisotropy; Two phase flow; Upscaling

Indexed keywords

DENSE NON-AQUEOUS PHASE LIQUIDS (DNAPL); DISCRETIZATION; PERMEABILITY-SATURATION RELATIONSHIPS; PRESSURE-SATURATION RELATIONSHIPS;

ANISOTROPY; CAPILLARY FLOW; COMPUTER SIMULATION; MATHEMATICAL MODELS; PARAMETER ESTIMATION; POROUS MATERIALS;

TWO PHASE FLOW;

PERMEABILITY; POROUS MEDIUM; SATURATION; TWO-PHASE FLOW;

PERMEABILITY; POROUS MEDIUM; SATURATION; TWO PHASE FLOW;

ANISOTROPY; ARTICLE; FLOW; PERMEABILITY; POROSITY; PRIORITY JOURNAL;

CHEMISTRY, PHYSICAL; MODELS, THEORETICAL; PERMEABILITY; POROSITY; SOIL POLLUTANTS; WATER POLLUTANTS;

EID: 9944234486     PISSN: 01697722     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jconhyd.2004.07.009     Document Type: Article

References (47)

1. A. Ahmadi, and M. Quintard Large-scale properties for two-phase flow in random porous media J. Hydrol. 183 1996 69 99
2. J. Allan, J. Ewing, J. Braun, and R. Helmig Scale effects in multiphase flow modeling First International Conference on Remediation of Chlorinated and Recalcitrant Compounds, Monterey, CA, USA 1998
3. T. Arbogast, S.E. Minkoff, and P.T. Keenan An operator-based approach to upscaling the pressure equation V.N. Burganos G.P. Karatzas A.C. Payatakes C.A. Brebbia W.G. Gray G.F. Pinder Computational Methods in Water Resources XII, Band I 1998 Computational Mechanics Publication Southhampton, UK 405 412
4. J.W. Barker, and S. Thibeau A critical review of the use of pseudorelative permeabilities for upscaling Soc. Pet. Eng., RE 12 1997 138 143
5. J. Bear Dynamics of Fluids in Porous Media 1972 Dover Publications New York
6. J. Bear, and J.J. Nitao On equilibrium and the number of degrees of freedom in modelling transport in porous media Transport and Reactive Processes in Aquifers 1994 431 436
7. J. Bear, and J.J. Nitao On equilibrium and primary variables in transport in porous media Transp. Porous Media 18 1995 151 184
8. Braun, C., 2000. Ein Upscaling-Verfahren für Mehrphasenströ mungen in porösen Medien. Forschungsbericht 103, Dissertation, Mitteilungen Institut für Wasserbau, Universität Stuttgart, Stuttgart.
9. C. Braun, S.M. Hassanizadeh, and R. Helmig Two-phase flow in stratified porous media-effective parameters and constitutive relationships V.N. Burganos G.P. Karatzas A.C. Payatakes C.A. Brebbia W.G. Gray G.F. Pinder Computational Methods in Water Resources XII, Band I 1998 Computational Mechanics Publication Southhampton, UK 43 50
10. R.H. Brooks, and A.T. Corey Hydraulic Properties of Porous Media Hydrol. Pap. vol. 3 1964 Colorado State University Fort Collins
11. Burdine, N.T., 1953. Relative Permeability Calculations from Pore-Size Distribution Data. Research Report, Petroleum Transactions, AIME.
12. W.T. Cardwell, and R.L. Parsons Average permeabilities of heterogeneous oil sands AIMME 160 1945 34 40
13. M.A. Celia, P.C. Reeves, and H.K. Dahle On the use of porescale computational models for two-phase porous-media flow V.N. Burganos G.P. Karatzas A.C. Payatakes C.A. Brebbia W.G. Gray G.F. Pinder Computational Methods in Water Resources XII, Band I 1998 Computational Mechanics Publication Southhampton, UK 397 404
14. Y.C. Chang, and K.K. Mohanty Scale-up of two-phase flow in heterogeneous porous media J. Pet. Sci. Eng. 18 1997 21 34
15. A.T. Corey, and C.H. Rathjens Effect of stratification on relative permeability J. Pet. Technol. 1956 69 71
16. A.J. Desbarats Upscaling capillary pressure-saturation curves in heterogeneous porous media Water Resour. Res. 31 2 1995 281 288
17. L.J. Durlofsky Numerical calculation of equivalent grid block permeability tensors for heterogenous porous media Water Resour. Res. 27 5 1991 699 708
18. B.B. Dykaar, and P.K. Kitanidis Determination of the effective hydraulic conductivity for heterogeneous porous media using a numerical spectral approach: 1. Method Water Resour. Res. 28 4 1992 1155 1166
19. R.E. Ewing, M. Espedal, and M. Celia Solution methods for multiscale porous media flow A. Peters G. Wittum B. Herrling U. Meissner Computational Methods in Water Resources X, Band I 1994 Kluwer Academic Publishers 449 456
20. T.R. Green, J.E. Constanz, and D.L. Freyberg Upscaled soil-water retention using van Genuchten's function J. Hydrol. Eng. 1 3 1996
21. S.M. Hassanizadeh, M.A. Celia, and H.K. Dahle Dynamic effects in the capillary pressure-saturation relationship and its impact on unsaturated flow Vadose Zone Hydrol. 1 2002 38 57
22. T.H. Illangasekare, J.L. Ramsey, K.H. Jensen, and M.B. Butts Experimental study of movement and distribution of dense organic contaminants in heterogenous aquifers J. Contam. Hydrol. 20 1995 1 25
23. E. Kasap, and L.W. Lake An analytical method to calculate the effective permeability tensor of a grid block and its application in an outcrop study Soc. Pet. Eng., SPE 1989 18434
24. P.R. King Upscaling permeability: error analysis for renormalisation Transp. Porous Media 23 1996 337 354
25. B.H. Kueper, and E.O. Frind Two-phase flow in heterogeneous porous media: 1. Model development Water Resour. Res. 27 6 1991 1049 1057
26. B.H. Kueper, and E.O. Frind Two-phase flow in heterogeneous porous media: 2. Model application Water Resour. Res. 27 6 1991 1059 1070
27. B.H. Kueper, and B. Girgrah Effective large-scale parameters for two-phase flow in heterogenous porous media T. Stauffer R. Draco Transport and Reactive Processes in Aquifers 1994
28. B.H. Kueper, W. Abbott, and G. Farquhar Experimental observations of multiphase flow in heterogeneous porous media J. Contam. Hydrol. 5 1989 83 95
29. L.W. Lake Enhanced Oil Recovery 1989 Prentice Hall New Jersey
30. A. Mantoglou, and L.Q. Gelhar Stochastic modelling of large-scale transient unsaturated flow systems Water Resour. Res. 23 1 1987 37 46
31. Y. Mualem A new model for predicting the hydraulic conductivity of unsaturated porous media Water Resour. Res. 10 1976 514 520
32. K. Pruess On the validity of a Fickian diffusion model for the spreading of liquid infiltration plumes in partially saturated heterogeneous media Comput. Methods Water Resour. 10 1994 537 544
33. K. Pruess A Fickian diffusion model for the spreading of liquid plumes infiltrating in heterogeneous media Transp. Porous Media 24 1996 1 33
34. M. Quintard, and S. Whitaker Two-phase flow in heterogenous porous media: the method of large-scale averaging Transp. Porous Media 3 1988 357 413
35. A.E. Sáez, C.J. Otero, and I. Rusinek The effective homogenous behaviour of heterogenous porous media Transp. Porous Media 1989 213 238
36. A.E. Scheidegger The Physics of Flow Through Porous Media 3rd ed. 1974 University of Toronto Press Toronto
37. D. Stauffer Introduction to Percolation Theory 1985 Taylor and Francis
38. M.T. Van Genuchten A closed-form equation for predicting the hydraulic conductivity of unsaturated soils Soil Sci. Soc. Am. J. 44 1980 892 898
39. Van Lent, T., 1992, Numerical Spectral Methods Applied to Flow in Highly Heterogenous Aquifers. Dissertation, Stanford University.
40. J.E. Warren, and H.S. Price Flow in Heterogenous Porous Media J. Soc. Pet. Eng. 1961 153 169 (September)
41. X.H. Wen, and J.J. Gómez-Hernández Upscaling hydraulic conductivities in heterogenous media: an overview J. Hydrol. 183 1996 9 32
42. J.K. Williams Simple renormalisation schemes for calculating effective properties of heterogeneous reservoirs 1st European Conference on the Mathematics of Oil Recovery, Cambridge, UK 1989 (July)
43. Y.S. Wu A multiple-porosity method for simulation of naturally fractured petroleum reservoirs Soc. Pet. Eng., SPE 1996 15129
44. T.C.J. Yeh, L.W. Gelhar, and A.L. Gutjahr Stochastic analysis of unsaturated flow in heterogeneous soils: 1. Statistically isotropic media Water Resour. Res. 21 4 1985 447 456
45. T.C.J. Yeh, L.W. Gelhar, and A.L. Gutjahr Stochastic analysis of unsaturated flow in heterogeneous soils: 2. Statistically anisotropic media with variable α Water Resour. Res. 21 4 1985 457 464
46. T.C.J. Yeh, L.W. Gelhar, and A.L. Gutjahr Stochastic analysis of unsaturated flow in heterogeneous soils: 3. Observations and applications Water Resour. Res. 21 4 1985 465 471
47. Y.C. Yortsos, C. Satik, J.C. Bacri, and D. Salin Large-scale percolation theory of drainage Transp. Porous Media 10 1993 171 195