Geosciences Journal

, Volume 12, Issue 3, pp 285–297 | Cite as

A study of preferential flow in heterogeneous media using random walk particle tracking

  • Chan-Hee Park
  • Christof Beyer
  • Sebastian Bauer
  • Olaf Kolditz
Article

Abstract

We investigated the onset of preferential flow in heterogeneous porous media using the random walk particle tracking (RWPT) concept. The RWPT model is first used to analyze empirically the required number of particles to achieve accurate concentration distributions in two-dimensional homogeneous media and under uniform flow conditions. The analysis is then extended to randomly heterogeneous systems. By increasing the variance of log-normal hydraulic conductivity fields, the transition between homogeneous and preferential flows is observed. To analyze the degree of preferential flow in the porous media, we provide a diagram that consists of two dimensionless parameters: normalized travel time and distance. All the heterogeneous media synthetically generated show a linear relation in the diagram. The characteristic travel velocity increases with increasing heterogeneity. We found the diagram is a useful tool to analyze preferential flow.

Key words

random walk particle tracking particle resolution preferential flow travel time distribution heterogeneous porous media 

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References

  1. Bear, J., 1979, Hydraulics of groundwater. McGraw-Hill, New York.Google Scholar
  2. Berkowitz, B. and Scher, H., 1995, On characterization of anomalous dispersion in porous and fractured media, Water Resources Research, 31, 1461–1466.CrossRefGoogle Scholar
  3. Dagan, G., 1989, Flow and transport in porous formations, Springer-Verlag, New York.Google Scholar
  4. Gelhar, L.W., 1993, Stochastic subsurface hydrology, Prentice-Hall, Englewood Cliffs, New Jersey.Google Scholar
  5. Gerke, H. and van Genuchten, M. T., 1993, A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media, Water Resources Research, 29, 305–319.CrossRefGoogle Scholar
  6. Hassan, A.E. and Mohamed, M.M., 2003, On using particle tracking methods to simulate transport in single-continuum and dual continua porous media. Journal of Hydrology, 275, 242–260.CrossRefGoogle Scholar
  7. Janković, I., Fiori, A., and Dagan, G., 2006, Modeling flow and transport in highly heterogeneous three-dimensional aquifers: Ergodicity, gaussianity, and anomalous behavior-1. conceptual issues and numerical simulations, Water Resources Research, 42, doi:10.1029/2005WR004734.Google Scholar
  8. Kinzelbach, W., 1986, Groundwater modeling: an introduction with sample programs in BASIC. Elsevier, Amsterdam.CrossRefGoogle Scholar
  9. Knudby, C. and Carrera J., 2004, On the relationship between indicators of geostatistical, flow and transport connectivity, Advances in Water Resources, 28, 405–421.CrossRefGoogle Scholar
  10. Kolditz, O. and Bauer, S., 2004, A process-oriented approach to computing multi-field problems in porous media. Journal of Hydroinformatics 6, 225–244.Google Scholar
  11. Kolditz, O., Delfs, J.-O., Bürger, C., Beinhorn, M., and Park, C.-H., 2008, Numerical analysis of coupled hydrosystems based on an object-oriented compartment approach, Journal of Hydroinformatics, 10, doi:10.2166/hydro.2008.003.Google Scholar
  12. LaBolle, E.M., Fogg, G.E., and Tompson, A.F.B., 1996, Random-walk simulation of transport in heterogeneous porous media: Local mass-conservation problem and implementation methods. Water Resources Research, 32, 583–593.CrossRefGoogle Scholar
  13. Lou, J., Dentz, M., Cirpka, O.A., and Kitanidis, P.K., 2007, Break-through curve tailing in a dipole flow field, Water Resources Research, 43, doi:10.1029/2006WR005600.Google Scholar
  14. Moreno, L., Tsang, C.F., Tsang, Y., and Neretnieks, I., 1990, Some anomalous features of flow and solute transport arising from fracture aperture variability, Water Resources Research, 26, 2377–2391.Google Scholar
  15. Moreno, L. and Tsang, C.F., 1994, Flow channeling in strongly heterogeneous porous media: A numerical study, Water Resources Research, 30, 1421–1430.CrossRefGoogle Scholar
  16. Nichol, C., Smith, L., and Beckie, R., 2005, Field-scale experiments of unsaturated flow and solute transport in a heterogeneous porous medium, Water Resources Research, 41, doi:10.1029/ 2004WR003035.Google Scholar
  17. Nordqvist, A.W., Tsang, Y.W., and Tsang, C.F., 1992, A variable aperture fracture network model for flow and transport in fractured rocks, Water Resources Research, 28, 1703–1713.CrossRefGoogle Scholar
  18. Nordqvist, A.W., Tsang, Y.W., Tsang, C.F., Dverstorp, B., and Andersson, J., 1996, Effects of high variance of fracture transmissivity on transport and sorption at different scales in a discrete model for fractured rocks, Journal of Contaminant Hydrology, 22, 39–66.CrossRefGoogle Scholar
  19. Ogata, A. and Banks, R.B., 1961, A solution of the differential equation of longitudinal dispersion in porous media, Professional paper No. 411-A, USGS, Washington, DC.Google Scholar
  20. Ohman, J., Niemi, A., and Tsang, C.F., 2005, A regional-scale particle-tracking method for nonstationary fractured media, Water Resources Research, 41, doi:10.1029/2004WR003498.Google Scholar
  21. Park, C.-H. and Aral, M.M., 2007, Sensitivity of the solution of the Elder problem to density, velocity, and numerical perturbations. Journal of Contaminant Hydrology, 92, 33–49.CrossRefGoogle Scholar
  22. Park, C.-H, Beyer, C., Bauer, S. And Kolditz, O., 2007, Benchmark test for random walk particle tracking methods. Center for Applied Geoscience, University of Tübingen, GeoSys (Preprint), Tübingen.Google Scholar
  23. Park, C.-H, Beyer, C., Bauer, S. And Kolditz, O., 2008, Using global node-based velocity in random walk particle tracking in variably saturated porous media: Application to contaminant leaching from road construction. Environmental Geology, doi: 10.1007/ s00254-007-1126-7.Google Scholar
  24. Rosqvist, N.H., Dollar, L.H., and Fourie, A.B., 2005, Preferential flow in municipal solid waste and implication for long-term leachate quality valuation of laboratory-scale experiments, Waste Management & Research, 23, 367–380.CrossRefGoogle Scholar
  25. Schultze-Mankuch, D., 2005, Longitudinal dispersivity data and implications for scaling behavior, Ground Water, 43, 443–456.CrossRefGoogle Scholar
  26. Tsang, C.F. and Neretnieks, I., 1998, Flow channeling in heterogeneous fractured rocks, Review of Geophysics, 36, 275–298.CrossRefGoogle Scholar
  27. Tompson, A.F.B. and Gelhar, L.W., 1990, Numerical simulation of solute transport in three-dimensional randomly heterogeneous porous media. Water Resources Research 26, 2451–2562.CrossRefGoogle Scholar
  28. Wang, W. and Kolditz, O., 2007, Object-oriented finite element analysis of thermo-hydromechanical (thm) problems in porous media. Int. J. Numerical Methods in Engineering 68, doi:10.1002/ nme.1770.Google Scholar
  29. Yeh, G.T., 1981, On the computation of Darcian velocity and mass balance in the finite-element modeling of groundwater-flow. Water Resources Research 17, 1529–1534.CrossRefGoogle Scholar

Copyright information

© The Association of Korean Geoscience Societies 2008

Authors and Affiliations

  • Chan-Hee Park
    • 1
  • Christof Beyer
    • 2
  • Sebastian Bauer
    • 2
  • Olaf Kolditz
    • 1
  1. 1.Department of Environmental Informatics, Helmholtz Centre for Environmental ResearchUFZLeipzigGermany
  2. 2.Institute of Geosciences, GeohydromodellingChristian Albrechts University of KielKielGermany

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