Transport in Porous Media

, Volume 18, Issue 3, pp 203–216 | Cite as

Effective hydraulic conductivities in unsaturated heterogeneous media by Monte Carlo simulation

  • Roger R. Eaton
  • James T. McCord


When modeling flow and transport through unsaturated heterogeneous geological deposits, it may be neither computationally nor technically feasible to account for the actual heterogeneity in the simulations. One would fall short in terms of technical feasibility because there is simply no way that the entire spatial domain could be characterized (e.g., you cannot measure hydraulic conductivity at every location at a site). With respect to computational feasibility, the non-linear nature of the Richards equation (which is used to model the flow process) makes simulation of most sites extremely computationally intensive. The computational roadblock is being dismantled as computer hardware advances, but our inability to precisely characterize geological heterogeneity is expected to remain with us for a very long time. To address this problem, the analyst typically uses average or ‘effective’ properties to model flow and transport behavior through heterogeneous media. In this paper, a variety of approaches for developing effective unsaturated flow properties are assessed. Computational results have been obtained which give the hydraulic conductivity ratios (K parallel/K nomal) for highly nonisotropic layered materials. These results are compared with analytical models. Good agreement was obtained for all soil saturation levels except for extremely dry conditions.

Key words

heterogeneity effective properties hydraulic conductivity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ababou, R., McLaughlin, D. and Gelhar, L. W., 1988, Three-Dimensional Groundwater Flow in Random Media,Ralph Parsons Lab. Report 318, Mass. Inst. of Technology.Google Scholar
  2. Ababou, R., McLaughlin, D., Gelhar, L. W. and Tompson, A. F. B., 1989, Numerical simulation of three-dimensional groundwater flow in randomly heterogeneous media,Transport in Porous Media 4, 549–565.CrossRefGoogle Scholar
  3. Ababou, R., 1991, Approaches to Large Scale Unsaturated Flow in Heterogeneous, Stratified, and Fractured Geologic Media,U.S. Nuclear Regulatory Commission, NUREG/CR-5743.Google Scholar
  4. Baker, A., Gelhar, L. W. and Gutjahr, A. L., 1978, Stochastic analysis of spatial variability in subsurface flows, 1: Comparison of one-dimensional flows,Water Resour. Res. 14(2), 263–271.CrossRefGoogle Scholar
  5. Bear, J., Braester, C. and Menier, P., 1987, Effective and relative permeabilities of anisotropic porous media,Transport in Porous Media 2, 301–316.Google Scholar
  6. Bowman, R. S., Grabka, D. P., Gibbens, J. F. and Stephens, D. B., 1990, Three-dimensional solute transport in a heterogeneous vadose zone,EOS Trans. Am. Geophys. Union 71, 514.Google Scholar
  7. Dagan, G., 1984, Solute transport in heterogeneous porous formations,J. Fluid Mech. 145, 151–177.CrossRefGoogle Scholar
  8. Eaton, R. R. and Hopkins, P. L., 1992, LLUVIA-II: A Program for Two-Dimensional, Transient Flow Through Partially Saturated Porous Media,SAND90-2416, Sandia National Laboratories, Albuquerque NM, August.Google Scholar
  9. Frederick, R. B., 1988, A Laboratory Experiment of Uniform Infiltration into a Sloping, Stratified and Uniform Sandy Soil, M.S. Thesis, NM Institute of Mining and Technology, Socorro, NM, 102 pp.Google Scholar
  10. Freeze, R. A., 1975, A stochastic-conceptual analysis of one-dimensional groundwater flow in non-uniform homogeneous media,Water Resour. Res. 9(5), 725–741.CrossRefGoogle Scholar
  11. Freeze, R. A. and Cherry, J., 1979,Groundwater, Prentice-Hall Publishers.Google Scholar
  12. Gelhar, L. W. and Axness, C. L., 1983, Three-dimensional stochastic analysis of macrodispersion in aquifers,Water Resour. Res. 19, 161–180.CrossRefGoogle Scholar
  13. Hills, R. G. and Wierenga, P. J., 1991, Model validation at the Las Cruces Trench Site,U.S. Nuclear Regulatory Comm., NUREG/CR-5716.Google Scholar
  14. Hopmans, J., Schukking, H. and Torfs, P. J. J. F., 1988, Two-dimensional steady state unsaturated water flow in heterogeneous soils with autocorrelated soil properties,Water Resour. Res. 24(12), 2005–2018.CrossRefGoogle Scholar
  15. Mantoglou, A. and Gelhar, L. W., 1987, Stochastic modeling of large-scale transient unsaturated flow systems,Water Resour. Res. 23(1), 37–46.CrossRefGoogle Scholar
  16. McCord, J. T., 1991, Application of Second-Type Boundaries in Unsaturated Flow Modeling,Water Resour. Res. 27(12), 3257–3260.CrossRefGoogle Scholar
  17. McCord, J. T., Stephens, D. B. and Wilson, J. L., 1991, The importance of hysteresis and state-dependent anisotropy in modeling variably saturated flow,Water Resour. Res. 27(7), 1501–1517.CrossRefGoogle Scholar
  18. Mualem, Y., 1984, Anisotropy of unsaturated soils,Soil Sci. Soc. Am. J. 48, 505–509.CrossRefGoogle Scholar
  19. Polmann, D., 1990, Application of Stochastic Methods to Transient Flow and Transport in Heterogeneous Unsaturated Soils, Doctoral Dissertation, Dept. of Civil Engineering, Massachusetts Institute of Technology, 476 pp.Google Scholar
  20. Russo, D., 1991, Stochastic analysis of simulated vadose zone solute transport in a vertical cross-section of heterogeneous soil during nonsteady water flow,Water Resour. Res. 27(3), 267–283.CrossRefGoogle Scholar
  21. Russo, D., Zaidel, J. and Laufer, A., 1994, Stochastic-analysis of solute transport in partially saturated heterogeneous soil. 1. numerical experiments,Water Resour. Res. 30(3), 769–779.CrossRefGoogle Scholar
  22. Smith, L. and Schwartz, F. W., 1980, Mass transport, 1. A stochastic analysis of macroscopic dispersion,Water Resour. Res. 16, 303–313.CrossRefGoogle Scholar
  23. Stephens, D. B., and Heermann, S. H., 1988, Dependence of anisotropy on saturation in a stratified sand,Water Resour. Res. 24(5), 770–778.CrossRefGoogle Scholar
  24. Yeh, T.-C., Gelhar, L. W. and Gutjahr, A. L., 1985a, Stochastic analysis of unsaturated flow in heterogeneous soils, 2: Statistically anisotropic media with variable,Water Resour. Res. 21(4), 457–464.CrossRefGoogle Scholar
  25. Yeh, T.-C., Gelhar, L. W. and Gutjahr, A. L., 1985b, Stochastic analysis of unsaturated flow in heterogeneous soils, 3: Applications,Water Resour. Res. 21(4), 465–473.CrossRefGoogle Scholar
  26. Yeh, T.-C., 1989, One-Dimensional steady state infiltration in heterogeneous soils,Water Resour. Res. 25(10), 2149–2148.CrossRefGoogle Scholar
  27. Zimmerman and Wilson, 1990, Description of and User's Manual for TUBA: A Computer Code for Generating Two-Dimensional Random Fields via the Turning Bands Method,Scientific and Engineering Analysis Software, Albuquerque New Mexico.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Roger R. Eaton
    • 1
  • James T. McCord
    • 2
  1. 1.Thermal and Fluid Engineering Dept.Sandia National LaboratoriesAlbuquerqueUSA
  2. 2.Environmental Risk Assessment Dept.Sandia National LaboratoriesAlbuquerqueUSA

Personalised recommendations