Sensitivity and Uncertainty Analyses Applied to One-Dimensional Radionuclide Transport in a Layered Fractured Rock. Part I: Analytical Solutions and Local Sensitivities

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Abstract
Exact analytical solutions based on Laplace transforms are derived for describing the one-dimensional space- and time-dependent advective transport of a decaying species in a layered, fractured, saturated rock system. The rock layers are parallel and horizontal and of uniform thickness. The fracture intersects normally to the rock layers and is of varying aperture across its length. The fracture network is serial in nature and of uniform thickness within each layer. Fluid movement is assumed to be exclusive to the fracture network. These solutions, which account for advection in fracture, molecular diffusion into the rock matrix, adsorption in both fracture and matrix, and radioactive decay, predict the concentrations in both fracture and rock matrix and the cumulative mass in the fracture. The solute migration domain in both fracture and rock is assumed to be semi-infinite with nonzero initial conditions. The concentration of each nuclide at the source is allowed to decay either continuously or a...