Abstract
In this paper the problem of solute transport through layered soil is modeled with a transfer function, representing the travel time to any depth in the soil as the sum of the travel times through the individual layers. The probability density function (pdf) of this travel time depends on the joint pdfs of the travel times through the individual layers, and hence on the correlation structure as well as the layer properties. Analytic expressions are derived for the flux and resident concentrations in layered soil for two limiting cases of correlation structure, for both convective-dispersive and stochastic-convective model representations of transport within the individual layers. These models are contrasted to the layered convection-dispersion model, which asumes continuous resident fluid concentration at the interface. Calculated concentrations are used to illustrate features of the different models, as well as to suggest experiments that might deduce the appropriate boundary condition to use at the interface between layers of different properties. The physical significance of various boundary condition assumptions is also discussed.
Similar content being viewed by others
References
Barry, D. A. and J. C. Parker, 1987, Approximations for solute transport through porous media with flow transverse to layering,Transport in Porous Media 2, 65–84.
Barry, D. A., Parlange, J-Y., Rand, R., and Parker, J. C., 1988, Addentum to: Approximations for solute transport through porous media with flow transverse to layering,Transport in Porous Media 2, 421–423.
Bruch, J. C., 1970, Two dimensional dispersion experiments in a porous medium,Water Resour. Res. 6, 791–800.
Butters, G. L. and Jury, W. A., 1989, Field scale transport of bromide in an unsaturated soil 2. Dispersion modeling,Water Resour. Res. 25, 1582–1588.
Butters, G. L., Jury, W. A., and Ernst, F. F., 1989, Field scale transport of bromide in an unsaturated soil. I. Experimental methodology and results.Water Resour. Res. 25, 1575–1581.
Dagan, G., 1984, Solute transport in heterogenous porous formations,J. Fluid Mech. 145, 151–177.
Dyson, J. S. and White R. E., 1986, A simple approach to solute transport in layered soils,J. Soil Sci. 40, 525–542.
Ellsworth, T. E., and Jury, W. A., 1991, A three dimensional field study of solute leaching through unsaturated soil II. Solute dispersion,Water Resour. Res. 27, 967–982.
Gardiner, C. W., 1985,Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences. 2nd edn, Springer-Verlag, New York.
Gelhar, L. W. and Axness, C., 1983, Three dimensional stochastic analysis of macrodispersion in aquifers,Water Resour. Res. 19, 161–180.
Jury, W. A., 1975, Solute travel-time estimates for tile-drained soils. I. Theory,Soil Sci. Soc. Amer. Proc 39, 1020–1024.
Jury, W. A., 1982, Simulation of solute transport using a transfer function model,Water Resour. Res. 18, 363–368.
Jury, W. A., 1985, Spatial variability of soil physical parameters in solute migration: A critical literature review. EPRI Topical Rep. EA 4228 Elect. Pow. Res. Inst., Palo Alto.
Jury, W. A. and Roth, K., 1990,Transfer Functions and Solute Movement through Soil: Theory and Applications, BirkhÄuser, Basel.
Jury, W. A., Sposito, G., and White, R. E., 1986, A transfer function model of solute movement through soil. I. Fundamental concepts,Water Resour, Res 22, 243–247.
Jury, W. A., Dyson, J. S., and Butters, G. L., 1990, A transfer function model of field scale solute transport under transient water flow.Soil Sci. Soc. Amer. J. 54, 327–332.
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. Soc. 33, 1471–1480.
Lumley, J. L. and Panofsky, H. A., 1964,The Structure of Atmospheric Turbulence, Wiley, New York.
Moranville, M. B., Kessler, D. P., and Greenkorn, R. A., 1977, Dispersion in layered porous media,A. I. Ch. Eng. J. 23, 786–794.
Shamir, U. Y. and Harliman, D. R. F., 1967, Dispersion in layered porous media,Proc. Am. Soc. Civ. Eng. Hyd. Div. 93, 236–260.
Simmons, C. S., 1982, A stochastic-convective transport representation of dispersion in one dimensional porous media systems,Water Resour. Res. 18, 1193–1214.
Stephens, D. B., Parsons, A. M., Mattson, E. D. Black, K., Flanigan, K., Bowman, R. S., and Cox, W. B., 1988, A field experiment of three dimensional flow and transport in a stratified soil. In: Wierenga, P. J. and Batchelet, D. (eds)Proc. International Conference and Workshop on the Validation of Flow and Transport Models for the Unsaturated Zone. Research Rep. 88-SS-04, New Mexico State University, Las Cruces.
Taylor, G. I., 1953, The dispersion of soluble matter flowing through a capillary tube,Proc. Lond. Math. Soc. Lond. 2, 196–212.
Utermann, J., Kladivko, E. J., and Jury, W. A., 1990, Evaluation of pesticide migration in tile-drained soils with a transfer function model,J. Environ. Qual. 19, 707–714.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jury, W.A., Utermann, J. Solute transport through layered soil profiles: Zero and perfect travel time correlation models. Transp Porous Med 8, 277–297 (1992). https://doi.org/10.1007/BF00618546
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00618546