On the porous-continuum modeling of gravity-driven fingers in unsaturated materials: Extension of standard theory with a hold-back-pile-up effect

Water Resources Research

Volumn 38, Issue 11, 2002, Pages 16-1-16-11

  Eliassi, Mehdi ^a   Glass, Robert J ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Dynamic capillary pressure; Extended porous media theory; Gravity driven fingers; Hypodiffusive and hyperbolic flux relations; Nonmonotonicity; Wetting front instability

Indexed keywords

MULTIPHASE FLOW; POROUS MATERIALS; WETTING;

UNSATURATED MATERIALS;

WATER RESOURCES;

FINGERING; GRAVITY FLOW; POROUS MEDIUM; UNSATURATED MEDIUM; WETTING;

FINGERING; GRAVITY FLOW; RICHARDS EQUATION; UNSATURATED MEDIUM; WETTING FRONT;

EID: 0036880464     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2001wr001131     Document Type: Article

References (79)

1. Babel, M. S., A. Das Gupta, and R. Loof, Simulation of stable and unstable flows in unsaturated homogeneous coarse sand, Hydrol. Sci., 42, 49-65, 1997.
2. Babel, M. S., R. Loof, and A. Das Gupta, Fingered preferential flow in unsaturated homogeneous coarse sands, Hydrol. Sci., 40, 1-17, 1995.
3. Baker, R. S., and D. Hillel, Laboratory tests of a theory of fingering during infiltration into layered soils, Soil Sci. Soc. Am. J., 54, 20-30, 1990.
4. Benson, D. A., A model of water streaking down a wall, Water Resour. Res., 37, 427-430, 2001.
5. Chang, W. L., J. W. Biggar, and D. R. Nielsen, Fractal description of wetting front instability in layered soils, Water Resour. Res., 30, 125-132, 1994.
6. Chen, G., and S. P. Neuman, Wetting front instability in randomly stratified soils, Phys. Fluids, 8, 353-369, 1996.
7. del Rio, J. A., and M. Lopez de Haro, A generalization of the Richards equation within extended irreversible thermodynamics, Water Resour. Res., 27, 2141-2142, 1991.
8. Diment, G. A., and K. K. Watson, Stability analysis of water movement in unsaturated porous materials, 2, Numerical studies, Water Resour. Res., 19, 1002-1010, 1983.
9. Diment, G. A., and K. K. Watson, Stability analysis of water movement in unsaturated porous materials, 3, Experimental studies, Water Resour. Res., 21, 979-984, 1985.
10. Diment, G. A., K. K. Watson, and P. J. Blennerhassett, Stability analysis of water movement in unsaturated porous materials, 1, Theoretical considerations, Water Resour. Res., 18, 1248-1254, 1982.
11. Du, X., T. Yao, W. D. Stone, and J. M. H. Hendrickx, Stability analysis of the unsaturated water flow equation, 1, Mathematical derivation, Water Resour. Res., 37, 1869-1874, 2001.
12. Eliassi, M., On continuum-scale numerical simulations of gravity-driven fingers in unsaturated porous materials, Ph.D. dissertation, Univ. of N. M., Albuquerque, 2001.
13. Eliassi, M., and R. J. Glass, On the continuum-scale modeling of gravity-driven fingers in unsaturated porous media: The inadequacy of the Richards equation with standard monotonic constitutive relations and hysteretic equations of state, Water Resour. Res., 37, 2019-2035, 2001a.
14. Eliassi, M., and R. J. Glass, Porous continuum-scale modeling of gravity-driven fingers in unsaturated porous materials: Extended flux laws and numerical simulations, Eos Trans. AGU, 82(47), Fall Meet. Suppl., abstract H52A-0377, 2001b.
15. Geiger, S. L., and D. S. Durnford, Infiltration in homogenous sands and a mechanistic model of unstable flow, Soil Sci. Soc. Am. J., 64, 460-469, 2000.
16. Glass, R. J., and M. J. Nicholl, Physics of gravity driven fingering of immiscible fluids within porous media: An overview of current understanding and selected complicating factors, Geoderma, 70, 133-163, 1996.
17. Glass, R. J., and L. Yarrington, Simulation of gravity fingering in porous media using a modified invasion percolation model, Geoderma, 70, 231-252, 1996.
18. Glass, R. J., T. S. Steenhuis, and J.-Y. Parlange, Wetting front instability as a rapid and far-reaching hydrologic process in the vadose zone, J. Contam. Hydrol., 3, 207-226, 1988.
19. Glass, R. J., G. H. Oosting, and T. S. Steenhuis, Preferential solute transport in layered homogeneous sands as a consequence of wetting front instability, J. Hydrol., 110, 87-105, 1989a.
20. Glass, R. J., J.-Y. Parlange, and T. S. Steenhuis, Wetting front instability, 1, Theoretical discussion and dimensional analysis, Water Resour. Res., 25, 1187-1194, 1989b.
21. Glass, R. J., T. S. Steenhuis, and J.-Y. Parlange, Mechanism for finger persistence in homogenous unsaturated, porous media: theory and verification, Soil Science, 148, 60-70, 1989c.
22. Glass, R. J., T. S. Steenhuis, and J.-Y. Parlange, Wetting front instability, 2, Experimental determination of relationships between system parameters and two-dimensional unstable flow field behavior in initially dry porous media, Water Resour. Res., 25, 1195-1207, 1989d.
23. Glass, R. J., J. King, S. Cann, and T. S. Steenhuis, Wetting front instability in unsaturated porous media: A three-dimensional study in initially dry sand, Transp. Porous Media, 5, 247-268, 1990.
24. Glass, R. J., J.-Y. Parlange, and T. M. Steenhuis, Immiscible displacement in porous media: Stability analysis Of three-dimensional, axisymmetric disturbances with application to gravity-driven wetting front instability, Water Resour. Res., 27, 1947-1956, 1991.
25. Gray, W. G., and S. M. Hassanizadeh, Paradoxes and realities in unsaturated flow theory, Water Resour. Res., 27, 1847-1854; 1991a.
26. Gray, W. G., and S. M. Hassanizadeh, Unsaturated flow theory including interfacial phenomena, Water Resour. Res., 27, 1855-1863, 1991b.
27. Gray, W. G., and K. O'Neill, On the general equations for flow in porous media and their reduction to Darcy's law, Water Resour. Res., 12, 148-154, 1976.
28. Gray, W. G., M. A. Celia, and P. C. Reeves, Incorporation of interfacial areas in models of two-phase flow, in Vadose Zone Hydrology Cutting Across Disciplines, edited by M. C. Parlange and J. W. Hopmans, pp; 58-85, Oxford univ. Press, New York, 1999.
29. Hassanizadeh, S. M., On the transient non-Fickian dispersion theory, Transp. Porous Media, 23, 107-124, 1996.
30. Hassanizadeh, S. M., and W. G. Gray, Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries, Adv. Water Resour., 13, 169-186, 1990.
31. Hassanizadeh, S. M., and W. G. Gray, Thermodynamic basis of capillary pressure in porous media, Water Resour. Res., 29, 3389-340,563, 1993a.
32. Hassanizadeh, S. M., and W. G. Gray, Toward an improved description of the physics of two phase flow, Adv. Water Resour., 16, 53-67, 1993b.
33. Hendrickx, J. M. H., and T.-M. Yao, Prediction of wetting front stability in dry field soils using soil and precipitation data, Geoderma, 70, 265-280, 1996.
34. Hilfer, R., Macroscopic equations of motion for two-phase flow in porous media, Phys. Rev. E, 58, 2090-2096, 1998.
35. Hill, D. E., and J.-Y. Parlange, Wetting front instability in layered soils, Soil Sci. Soc. Am. Proc., 36, 697-702, 1972.
36. Hillel, D., Applications of Soil Physics, Academic, San Diego; Calif., 1980.
37. Hillel, D., and R. S. Baker, A descriptive theory of fingering during infiltration into layered soils, Soil Sci., 146, 51-56, 1988.
38. Joseph, D. D., and L. Preziosi, Heat waves, Rev. Modern Phys, 61, 41-73, 1989.
39. Kacimov, A. R-, and N. D. Yakimov, Nonmonotonic moisture profile as a solution of Richards' equation for soils with conductivity hysteresis, Adv. Water Resour., 21, 691-696, 1998.
40. Kalaydjian, F., A macroscopic description of multiphase flow in porous media involving spacetime evolution of fluid/fluid interface, Transp. Porous Media; 2, 537-552, 1987.
41. Kapoor, V., Criterion for instability of steady-state unsaturated flow, Transp. Porous Media, 25, 313-334, 1996.
42. Liu, Y., T. S. Steenhuis, J. S. Selker, and J.-Y. Parlange, Closed-form solution for finger width in sandy soils at different water contents, Water Resour. Res., 30, 949-952, 1994a.
43. Liu; Y., T. S. Steenhuis, J. S. Selker, and J.-Y. Parlange, Formation and persistence of fingered flow in coarse grained soils under different moisture contents, J. Hydrol., 159, 187-195, 1994b.
44. Lu, T. X., J. W. Biggar, and D. R. Nielsen, Water movement in glass bead porous media, 2, Experiments of infiltration and finger flow, Water Resour. Res., 30, 3283-3290, 1994.
45. Mandelis, A., Mandelis Replies, Phys. Today, 54, 100-102, 2001.
46. Marle, C.-M., On macroscopic equations governing multiphase flow with diffusion and Chemical reactions in porous media, Int. J. Eng. Sci., 20, 643-662, 1982.
47. Mualem, Y., A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res., 12, 513-522, 1976.
48. Neumann, S. P., and G. Chen, On instability during immiscible displacement in fractures and porous media, Water Resour. Res., 32, 1891-1894, 1996.
49. Nicholl, M. J., R. J. Glass, and S. W. Wheatcraft, Gravity-driven infiltration instability in initially dry nonhorizontal fractures, Water Resour. Res., 30, 2533-2546, 1994.
50. Nieber, J. L., Modeling finger development and persistence in initially dry porous media, Geoderma, 70, 207-229, 1996.
51. Nissen, H. H., P. Moldrup, L. W. de Jonge, and O. H. Jacobsen, Time domain reflectometry coil probe measurements of water content during fingered flow, Soil Sci. Soc. Am. J., 63, 493-500, 1999.
52. Palmquist, W. N., and A. I. Johnson, Model study of infiltration into layered materials, paper presented at American Society of Civil Engineering Annual Meeting, Boston, Mass., 10-14 Oct. 1960.
53. Palmquist, W. N., and A. I. Johnson, Vadose zone in layered non layered materials, Geol. Surv. Res., 119, 142-143, 1962.
54. Parlange, J.-Y., and E. D. Hill, Theoretical analysis of wetting front instability in soils, Soil Sci., 122, 236-239, 1976.
55. Pavone, D., Macroscopic equations derived from space averaging for immiscible two-phase flow in porous media, Rev. Inst. Fr. Petrole, 44, 29-41, 1989.
56. Peck, A. J., Moisture profile development and air compression during water uptake by bounded porous bodies, 3, Vertical columns, Soil Sci., 100, 44-51, 1965.
57. Philip, J. R., Stability analysis of infiltration, Soil Sci. Soc. Am: Proc., 39, 1042-1049, 1975.
58. Raats, P. A. C., Unstable wetting fronts in uniform and non-uniform soils, Soil Sci. Soc. Am. J., 37, 681-685, 1973.
59. Raats, P. A. C., and A. Klute, Transport in soils: Balance of momentum, Soil Sci. Soc. Am. Proc., 32, 452-456, 1968.
60. Selker, J. S., and M. H. Schroth, Evaluation of hydrodynamic scaling in porous media using finger dimensions, Water Resour. Res.; 34, 1935-1940, 1998.
61. Selker, J. S., P. Leclerq, J.-Y. Parlange, and T. S. Steenhuis, Fingered flow in two dimensions, 1, Measurements of matric potential, Water Resour. Res., 28, 2513-2521, 1992a.
62. Selker, J. S., J.-Y. Parlange, and T. S. Steenhuis, Fingered flow in two dimensions, 2, Predicting finger moisture profile, Water Resour. Res., 28, 2523-2528; 1992b.
63. Selker, J. S., T. S. Steenhuis, and J.-Y. Parlange, Wetting front instability in homogenous sandy soil under continuous infiltration, Soil Sci. Soc. Am. J., 56, 1346-1350, 1992c.
64. Sililo, O. T. N., and J. H. Tellam, Fingering in unsaturated zone flow: A qualitative review with laboratory experiments in heterogeneous systems, Ground Water, 38, 864-871, 2000.
65. Sobolev, S. L., Rapid solidification under local nonequilibrium conditions, Phys. Rev. E, 55, 6845-6854, 1997.
66. Sposito, G., The statistical mechanical theory of water transport through unsaturated soil, 1, The conservation laws, Water Resour. Res., 14, 474-478, 1978.
67. Sposito, G., The "physics" of soil water physics, Water Resour. Res., 22, 83S-88S, 1986.
68. Tabuchi, T., Infiltration and ensuing percolation in columns of layered glass particles packed in laboratory, Trans. Agric. Eng. Soc. Jpn., 1, 13-19, 1961.
69. Tamai, N., T. Asaeda, and C. G. Jeevaraj, Fingering in two-dimensional, homogeneous, unsaturated porous media, Soil Sci., 144, 107-112, 1987.
70. Ursino, N., Linear stability analysis of infiltration, analytical and numerical solution, Transp. Porous Media, 38, 261-271, 2000.
71. van Genuchten, M. T., A closed-form equation for predicting the hydraulic properties of unsaturated soils, Soil Sci. Soc. Am. J., 44, 892-898, 1980.
72. Vazquez, F., J. A. del Rio, and M. Lopez de Haro, Fluctuations far from equilibrium: Hyperbolic transport, Phys. Rev. E, 55, 5033-5043, 1997.
73. Wang, Z., J. Feyen, M. T. van Genuchten, and D. R. Nielsen, Air entrapment effects on infiltration rate and flow instability, Water Resour. Res., 34, 213-222, 1998a.
74. Wang, Z., J. Feyen, and C. J. Ritsema, Susceptibility and predictability of conditions for preferential flow, Water Resour. Res., 34, 2169-2182, 1998b.
75. Wang, z., J. Feyen, and D. E. Elrick, Prediction of fingering in porous media, Water Resour. Res., 34, 2183-2190, 1998c.
76. White, I., P. M. Colombera, and J. R. Philip, Experimental study of wetting front instability induced by sudden change of pressure gradient, Soil Sci. Soc. Am. J., 40, 824-829, 1976.
77. White, I., P. M. Colombera, and J. R. Philip, Experimental study of wetting front instability induced by gradual change of pressure gradient and by heterogeneous porous media; Soil Sci., Soc. Am. J., 41, 483-489, 1977.
78. Yao, T. M., and J. M. H. Hendrickx, Stability of wetting fronts in dry homogenous soils under low infiltration rates, Soil Sci. Soc. Am. J., 60, 20-28, 1996.
79. Yao, T. M., and J. M. H. Hendrickx, Stability analysis of the unsaturated water flow equation, 2, Experimental verification, Water Resour. Res., 37, 1875-1881, 2001.