Upscaled Soil-Water Retention Using van Genuchten's Function
Publication: Journal of Hydrologic Engineering
Volume 1, Issue 3
Abstract
Soils are often layered at scales smaller than the block size used in numerical and conceptual models of variably saturated flow. Consequently, the small-scale variability in water content within each block must be homogenized (upscaled). Laboratory results have shown that a linear volume average (LVA) of water content at a uniform suction is a good approximation to measured water contents in heterogeneous cores. Here, we upscale water contents using van Genuchten's function for both the local and upscaled soil-water-retention characteristics. The van Genuchten (vG) function compares favorably with LVA results, laboratory experiments under hydrostatic conditions in 3-cm cores, and numerical simulations of large-scale gravity drainage. Our method yields upscaled vG parameter values by fitting the vG curve to the LVA of water contents at various suction values. In practice, it is more efficient to compute direct averages of the local vG parameter values. Nonlinear power averages quantify a feasible range of values for each upscaled vG shape parameter; upscaled values of N are consistently less than the harmonic means, reflecting broad pore-size distributions of the upscaled soils. The vG function is useful for modeling soil-water retention at large scales, and these results provide guidance for its application.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Carsel, R. F., and Parrish, R. S. (1988). “Developing joint probability distributions of soil water retention characteristics.”Water Resour. Res. 24(5), 755–769.
2.
Chen, Z. Q., Govindaraju, R. S., and Kavvas, M. L.(1994). “Spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields. 1: Development of models.”Water Resour. Res., 30(2), 523–533.
3.
Constantz, J. E.(1995). “Determination of water retention in stratified porous materials.”Transport in Porous Media, 18(3), 217–229.
4.
Constantz, J. E., and Herkelrath, N. W.(1984). “Submersible pressure outflow cell for measurement of soil water retention and diffusivity from 5 to 95°C.”Soil Sci. Soc. Am. J., 48(1), 7–10.
5.
Desbarats, A. J.(1995). “Upscaling capillary pressure-saturation curves in heterogeneous porous media.”Water Resour. Res., 31(2), 281–288.
6.
Deutsch, C.(1989). “Calculating effective absolute permeability in sandstone/shale sequences.”SPE Formation Evaluation, 26(4), 343–348.
7.
Ferrand, L. A., and Celia, M. C.(1992). “The effects of heterogeneity on the drainage capillary pressure-saturation relation.”Water Resour. Res., 28(3), 859–870.
8.
Green, T. R. (1994). “The roles of moisture-dependent anisotropy and landscape topography in soil-water flow and groundwater recharge,” PhD thesis, Stanford Univ., Stanford, Calif.
9.
Green, T. R., and Freyberg, D. L.(1995). “State-dependent anisotropy: comparisons between quasi-analytical solutions and stochastic results for steady gravity drainage.”Water Resour. Res., 31(9), 2201–2211.
10.
Hills, R., Hudson, D. B., Porro, I., and Wierenga, P. J.(1989). “Modeling one-dimensional infiltration into very dry soils. 2: Estimation of the soil water parameters and model predictions.”Water Resour. Res., 25(6), 1271–1282.
11.
Korvin, G. (1981). “Axiomatic characterization of the general mixture rule.”Geoexploration, Vol. 19, 267–276.
12.
Leverett, M. C. (1941). “Capillary behavior in porous solids.”Trans. Am. Inst. Min. Metal. Pet. Engrg., Vol. 142, 152–169.
13.
Mantoglou, A., and Gelhar, L. W.(1987). “Capillary tension head variance, mean soil moisture content, and effective specific soil moisture capacity of transient unsaturated flow in stratified soils.”Water Resour. Res., 23(1), 47–56.
14.
Mehta, B., Shiozawa, S., and Nakano, M.(1994). “Hydraulic properties of a sandy soil at low water contents.”Soil Sci., 157(4), 208–214.
15.
Michiels, P., Hartmann, R., and Strooper, E. D.(1989). “Comparisons of the unsaturated hydraulic conductivity of a coarse-textured soil as determined in the field, in the laboratory, and with mathematical models.”Soil Sci., 47(4), 299–304.
16.
Mualem, Y.(1976). “A new model for predicting the hydraulic conductivity of unsaturated porous media.”Water Resour. Res., 12(3), 513–522.
17.
Nash, M. S., and Flint, A. L. (1993). “Determination of water retention characteristics of a skeletal soil at Yucca Mountain.”Agronomy Abstracts, Am. Soc. of Agronomy, Inc., Madison, Wis., 214.
18.
Nielsen, D. R., van Genuchten, M. T., and Biggar, J. W. (1986). “Water flow and solute transport processes in the unsaturated zone.”Water Resour. Res., 22(9), 89S–108S.
19.
Nimmo, J. R.(1991). “Comment on the treatment of residual water content in `A consistent set of parametric models for the two-phase flow of immiscible fluids in the subsurface,' by L. Luckner et al.”Water Resour. Res., 27(4), 661–662.
20.
Quintard, M., Bertin, H., and Whitaker, S. (1989). “Two-phase flow in heterogeneous porous media: the method of large-scale averaging applied to laboratory experiments in a stratified system.”Proc., SPE89: Annu. Tech. Conf. and Exhibition, Soc. of Pet. Engrs.
21.
Richards, L. A.(1931). “Capillary conduction of liquids through porous mediums.”Phys., 1(5), 318–333.
22.
Rossi, C., and Nimmo, J. R.(1994). “Modeling of soil water retention from saturation to oven dryness.”Water Resour. Res., 30(3), 701–708.
23.
Russo, D.(1988). “Determining soil hydraulic properties by parameter estimation: on the selection of a model for the hydraulic properties.”Water Resour. Res., 24(3), 453–459.
24.
Russo, D.(1992). “Upscaling of hydraulic conductivity in partially saturated heterogeneous porous formations.”Water Resour. Res., 28(2), 397–410.
25.
Russo, D., and Bouton, M.(1992). “Statistical analysis of spatial variability in unsaturated flow parameters.”Water Resour. Res., 28(7), 1911–1925.
26.
van Genuchten, M. T.(1980). “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.”Soil Sci. Soc. Am. J., 44(5), 892–898.
27.
van Genuchten, M. T. (1985). “RETC.F77: a program to analyze observed soil water tension and hydraulic conductivity data.”Tech. Rep., U.S. Salinity Lab., Riverside, Calif.
28.
Vereecken, H., Maes, J., Feyen, J., and Darius, P.(1989). “Estimating the soil moisture retention characteristic from texture, bulk density, carbon content.”Soil Sci., 148(6), 389–403.
29.
Yabusaki, S. B., and Scheibe, T. D.(1993). “Scaling of flow and transport behavior in heterogeneous groundwater systems.”EOS, Trans., Am. Geophys. Union, 74(43), 251.
30.
Yeh, G. T. (1987). “3DFEMWATER: three-dimensional finite element model of water flow through saturated-unsaturated media.” Rep. No. ORNL-6386, Oak Ridge Nat. Lab., Oak Ridge, Tenn.
31.
Yeh, T.-C. J., and Harvey, D. J.(1990). “Effective unsaturated hydraulic conductivity of layered sands.”Water Resour. Res., 26(6), 1271–1279.
32.
Yeh, T.-C. J., Gelhar, L. W., and Gutjahr, A. L.(1985). “Stochastic analysis of unsaturated flow in heterogeneous soils. 2: Statistically anisotropic media with variable α.”Water Resour. Res., 21(4), 457–464.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 1 • Issue 3 • July 1996
Pages: 123 - 130
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Jul 1, 1996
Published in print: Jul 1996
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.