Stochastic analysis of contaminant transport in porous media: analysis of a two-member radionuclide chain

In this study the authors extend previous stochastic analyses of contaminant transport in geologic media for a single species to a chain of two species. The authors particular application is the quantification of uncertainties due to lack of characterization of the spatial variability of hydrologic parameters on transport of radionuclides from a high-level waste repository to the biosphere. Radionuclide chains can have a significant impact on demonstrating compliance (or violation) of standards regulating the release to the environment accessible to humans. Two approaches for determining the cross-covariance terms in the mean concentration equations are presented. One uses a Taylor expansion to obtain the cross-covariance between the velocity and concentration fluctuations, while the other is based on a Fourier-Laplace double transform method. For the conditions of interest here, the difference between these two approaches are expected to be small. In addition, the variances are calculated in a unique way by solving another associated partial differential equation. A parametric study is carried out to examine the sensitivity of the mean concentration of the two species and their corresponding variances and cross-covariance on the parameters associated with the structure of the stochastic velocity field. It is found that the dependent variables are most sensitive to the intensity and correlation length of the velocity fluctuations. The magnitude of the variances and cross-covariance of the concentrations are proportional to the magnitude of the mean concentrations which depend on inlet concentration boundary conditions