Skip to main content
Log in

Solute transport in aggregated porous media: Comparing model independent and dependent parameter estimation

  • Published:
Water, Air, and Soil Pollution Aims and scope Submit manuscript

Abstract

In many studies on solute transport soil column experiments arc used to obtain the transport characteristics for Convection-Dispersion-Models. Early breakthrough of the solute pulse has been attributed to a non-equilibrium in phase exchange. It is a standard procedure to determine several model parameter values from such breakthrough curves (BTC). This investigation is focused on the physical significance of simultaneously fitted parameter values used in the convection and diffusion-controlled mass transfer model (mobile — immobile phase concept). Saturated column experiments were conducted with solid phases consisting of porous and solid glass beads. One set of model parameter values was obtained from the breakthrough curves by simultaneous optimization and a second set was determined by independent measurements of individual parameter values. Both sets of parameter values described the BTCs equally well but deviated substantially from each other. These discrepancies were analysed in terms of local parameter sensitivities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Anamosa, P.R., Nkedi-Kizza, P., Blue, W.G. and Satain, J.B. (1990) ‘Water movement through an aggregated gravelly oxisol from Cameroon’, Geoderma 46, 263–281.

    Google Scholar 

  • Bear, J. and Bachmat, Y. (1991) ‘Introduction to modeling of transport phenomena in porous media’, Kluwer Academic Publishers., Dordrecht NL, 533p.

    Google Scholar 

  • Bond, W.J. and Wierenga, P.J. (1990) ‘Immobile water during solute transport in unsaturated sand columns’, Water Resour. Res. 26, 2475–2481.

    Google Scholar 

  • Cassel, D.K., Kruegar, T.H., Schroeer, F.W. and Norum, E.B. (1974) ‘Solute movement through disturbed and undisturbed soil cores’, Soil Sci. Soc. Am. J. 38, 36–40.

    Google Scholar 

  • Coats, K.H. and Smith, B.D. (1964) ‘Dead-end pore volume and dispersion in porous media’, Soc. Petr. Eng. J. 4, 73–84.

    Google Scholar 

  • De Smedt, F., Wauters, F. and Sevilla J. (1986) ‘Study of tracer movement through unsaturated soil’, J. Hydrol. 85, 169–181.

    Google Scholar 

  • Frank, P.M. (1978) ‘Introduction to system sensitivity theory’, Academic Press, New York, p. 9ff.

    Google Scholar 

  • Fried, J.J. (1975) ‘Groundwater pollution’, in Ven Te Chow (ed.), ‘Developments in Water Science 4’, Elsevier, p.31f.

  • Kissel, D.E., Ritchie, J.T. and Burnett, E. (1973) ‘Chloride movement in undisturbed clay soil’, Soil Sci. Soc. Am. Proc. 37, 21–24.

    Google Scholar 

  • Knopman, D.S. and Voss, C.I. (1987) ‘Behaviour of sensitivities in the one-dimensional advectiondispersion equation: Implications for parameter estimation and sampling design’, Water Resour. Res. 23, 253–272.

    Google Scholar 

  • Kool, J.B., Parker, J.C. and Zelazny, L.W. (1989) ‘On the estimation of cation exchange parameters from column displacement experiments’, Soil Sci. Soc. Am. J. 53, 1347–1355.

    Google Scholar 

  • Kreft, A. and Zuber, A. (1978) ‘On the physical meaning of the dispersion equation and its solution for different initial and boundary conditions’, Chem. Eng. Sci. 33, 1471–1480.

    Google Scholar 

  • Lapidus, L. and Amundson, N.R. (1952) ‘Mathematics of adsorption in beds. VI. The effect of longitudinal diffusion in ion exchange and chromatographic columns’, J. Phys. Chem. 56, 984–988.

    Google Scholar 

  • Nkedi-Kizza, P., Biggar, J.W., Selim, H.M., van Genuchten, M.Th., Wierenga, P.J., Davidson, J.M., and Nielson, D.R. (1984) ‘On the equivalence of two conceptual models for describing ion exchange during transport through an aggregated oxisol’, Water Resour. Res. 20, 1123–1130.

    Google Scholar 

  • Marquardt, D.W. (1963) ‘An algorithm for least squares estimation of non-linear parameters’, J. Soc. Ind. Appl. Math. 11, 431–441.

    Google Scholar 

  • Parker, J.C. and Valocchi, A.J. (1986) ‘Constraints on the validity of equilibrium and first-order kinetic transport models in structured soils’, Water Resour. Res. 22, 399–407.

    Google Scholar 

  • Parker, J.C. and Van Genuchten, M.Th. (1984a) ‘Flux-averaged and volume-averaged concentrations in continuum approaches to solute transport’, Water Resources. 20, 866–872.

    Google Scholar 

  • Parker, J.C. and van Genuchten, M.Th. (1984b) ‘Determining transport parameters from laboratory and field tracer experiments’, Virginia Agricultural Experimental Station, Blacksburg: Bulletin 84-3.

    Google Scholar 

  • Pfannkuch, H.O. (1963) ‘Contribution à l'étude des déplacement de fluides miscible dans un milieu poreux’, Rev. Inst. Fr. Petr. No.2, 18, 215–270.

    Google Scholar 

  • Press, W.H., Flannery, B.P., Teucholsky, S.A. and Vetterling, W.T. (1986) ‘Numerical recipies. The art of scientific computing’, Cambridge University Press. Cambridge,p 521.

    Google Scholar 

  • Rao, P.S.C., Rolston, D.E., and Jessup, R.E. (1980) ‘Experimental and mathematical description of nonadsorbed solute transfer by diffusion in spherical aggregates’, Soil Sci. Soc. Am. J. 44, 1139–1146.

    Google Scholar 

  • Van der Zee, S.E.A.T.M. (1991) ‘Reaction kinetics and transport in soil: Compatibility and differences between some simple models’, Transp. Porous Media 6, 703–737.

    Google Scholar 

  • Van Genuchten, M.Th. (1985) ‘A general approach for modeling solute transport in structured soil’, Hydrogeology of Rocks of Low Permeability, Proceedings of the 17th Int.Congr., Int.Association of Hydrogeologists, 513–524.

  • Van Genuchten, M.Th. and Wierenga, P.J. (1976) ‘Mass transfer studies in sorbing porous media I. Analytical solution’, Soil Sci. Soc. Am. J. 40, 473–480.

    Google Scholar 

  • Wilke, C.R. (1949) ‘Estimation of liquid diffusion coefficients’, Chem. Eng. Progr. 45, 218.

    Google Scholar 

  • Wilke, C.R. and Chang, P. (1955) ‘Correlation of diffusion coefficients in dilute solutions’, AIChE J. 1, 264–270.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koch, S., Flühler, H. Solute transport in aggregated porous media: Comparing model independent and dependent parameter estimation. Water Air Soil Pollut 68, 275–289 (1993). https://doi.org/10.1007/BF00479408

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00479408

Keywords

Navigation