Abstract
Within the framework of stochastic theory and the spectral perturbation techniques, three-dimensional dispersion in partially saturated soils with fractal log hydraulic conductivity distribution is analyzed. Our analysis is focused on the impact of fractal dimension of log hydraulic conductivity distribution, local dispersivity, and unsaturated flow parameters, such as the soil poresize distribution parameter and the moisture distribution parameter, on the spreading behavior of solute plume and the concentration variance. Approximate analytical solutions to the stochastic partial differential equations are derived for the variance of asymptotic solute concentration and asymptotic macrodispersivities.
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References
Ababou, R.; Gelhar, L.W. 1990: Self-similar randomness and spectral conditioning: Analysis of scale effects in subsurface hydrology, in Dynamics of Fluids in Hierarchical Porous Formations, edited by J. H. Cushman, Academic Press Ltd., London
Burrough, P.A. 1983: Multiscale sources of spatial variation in soil. I: The application of fractal concepts to nested levels of soil variation, J. Soil Sci. 34, 577–597
Chang, C-M; Kemblowski, M.W. 1994: Unsaturated flow in soils with self-similar hydraulic conductivity distribution, Stochastic Hydrology and Hydraulics 8(4), 281–300
Freyberg, D.L. 1986: A natural gradient experiment on solute transport in a sand aquifer: 2. Spatial moments and the advection and dispersion of nonreactive tracers, Water Res. Res. 22(13), 2031–2046
Gelhar, L.W.; Axness, C.L. 1983: Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Res. Res. 19(1), 161–180
Gelhar, L.W. 1986: Stochastic subsurface hydrology from theory to applications, Water Res. Res. 22(9), 1355–1455
Hewett, T.A. 1986: Fractal distributions of reservoir heterogeneity and their influence on fluid transport, paper SPE15386 presented at the 61st Annual Technical Conference, Soc. of Pet. Eng., New Orleans, La., Oct. 5–8
Mandelbrot, B.B. 1983: The Fractal Geometry of Nature, 468 pp. W. H. Freeman, New York
Sudicky, E.A. 1986: A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process, Water Res. Res. 22(13), 2069–2082
Vomvoris, E.G.; Gelhar, L.W. 1990: Stochastic analysis of the concentration variability in a three-dimensional heterogeneous aquifer, Water Res. Res. 26(10), 2591–2602
Wheatcraft, S.W.; Tyler, S.W. 1988: An explanation of scale-dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry, Water Res. Res. 24(4), 566–578
Yeh, T-C, Gelhar, L.W.; Gutjahr, A.L. 1985: Stochastic analysis of unsaturated flow in heterogeneous soils, 1. Statistically isotropic media, Water Res. Res. 21 (4), 447–456
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Chang, C.M., Kemblowski, M.W. Stochastic analysis of unsaturated transport in soils with fractal log-conductivity distribution. Stochastic Hydrol Hydraul 9, 297–323 (1995). https://doi.org/10.1007/BF01581730
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DOI: https://doi.org/10.1007/BF01581730