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Stochastic Analysis of Solute Transport in Saturated and Unsaturated Porous Media
Abstract The application of stochastic methods to the analysis and prediction of the large-scale behavior of heterogeneous natural porous earth materials is reviewed emphasizing recent results for solute transport in saturated and unsaturated media. A stochastic methodology based on the representation of natural heterogeneity as a three dimensional statistically anisotropic homogeneous random field is developed. This approach makes use of spectral representation and a pertubation approximation to solve the stochastic partial differential equations governing flow and solute transport under the assumption of local statistical homogeneity. This approach leads to solutions for the large-scale mean behavior in terms of effective parameters such as hydraulic conductivities and macrodispersivities, and for the variance of the dependent variables, head and concentration. Results for the case of saturated solute transport demonstrate especially the near source developing dispersion characteristics that are reflected by the mean behavior, as well as the concentration variance as a measure of the reliability of predictions from the classical transport equation. It is found that the concentration variance is very large near sources of contamination, indicating the large uncertainty that is to be anticipated in classical transport models under those conditions. Field observations of large-scale solute transport in aquifers are also discussed. In the case of unsaturated flow the occurrence of large-scale tension-dependent hydraulic anisotropy and large-scale hysteresis is illustrated, and predictions of macrodispersivity under unsaturated conditions are also presented. Discussions focus on research needs and future directions, emphasizing the need for carefully designed numerical experimentation and large-scale controlled field experiments.
Stochastic Analysis of Solute Transport in Saturated and Unsaturated Porous Media
Abstract The application of stochastic methods to the analysis and prediction of the large-scale behavior of heterogeneous natural porous earth materials is reviewed emphasizing recent results for solute transport in saturated and unsaturated media. A stochastic methodology based on the representation of natural heterogeneity as a three dimensional statistically anisotropic homogeneous random field is developed. This approach makes use of spectral representation and a pertubation approximation to solve the stochastic partial differential equations governing flow and solute transport under the assumption of local statistical homogeneity. This approach leads to solutions for the large-scale mean behavior in terms of effective parameters such as hydraulic conductivities and macrodispersivities, and for the variance of the dependent variables, head and concentration. Results for the case of saturated solute transport demonstrate especially the near source developing dispersion characteristics that are reflected by the mean behavior, as well as the concentration variance as a measure of the reliability of predictions from the classical transport equation. It is found that the concentration variance is very large near sources of contamination, indicating the large uncertainty that is to be anticipated in classical transport models under those conditions. Field observations of large-scale solute transport in aquifers are also discussed. In the case of unsaturated flow the occurrence of large-scale tension-dependent hydraulic anisotropy and large-scale hysteresis is illustrated, and predictions of macrodispersivity under unsaturated conditions are also presented. Discussions focus on research needs and future directions, emphasizing the need for carefully designed numerical experimentation and large-scale controlled field experiments.
Stochastic Analysis of Solute Transport in Saturated and Unsaturated Porous Media
Gelhar, Lynn W. (author)
1987-01-01
44 pages
Article/Chapter (Book)
Electronic Resource
English
Numerical modeling of one-dimensional solute transport in an unsaturated porous media
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Micromechanics of saturated and unsaturated porous media
| British Library Online Contents | 2002