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

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 according to some periodical fluctuations where both are subjected to either a step or band release mode. Two numerical examples related to the transport of ²³⁷Np and ²⁴⁵Cm in a five-layered system of fractured rock are used to verify these solutions with several well-established evaluation methods of Laplace inversion integrals in the real and complex domain. In addition, with respect to the model parameters, a comparison of the analytically derived local sensitivities for the concentration and cumulative mass of ²³⁷Np in the fracture with the ones obtained through a finite difference method of approximation is also reported. Both of these comparisons show excellent agreement. In spite of some limitations (i.e., assumptions of zero dispersion in the fracture and infinite matrix diffusion), the new features embedded in the reported solutions allow one to deal with commonly witnessed layered media above the water table, when groundwater flow is under steady-state conditions. In addition the residual concentrations in both fracture and rock, coupled with the realistic option of periodically fluctuating decaying source, are considered. These solutions are useful for verifying the accuracy of numerical codes designed to solve similar problems and, above all, cost-effective for performing sensitivity and uncertainty analyses of scenarios likely to be adopted in performance assessment investigations of potential nuclear waste repositories.