SENSITIVITY AND UNCERTAINTY ANALYSES APPLIED TO ONE-DIMENSIONAL RADIONUCLIDE TRANSPORT IN A LAYERED FRACTURED ROCK .1. ANALYTICAL SOLUTIONSAND LOCAL SENSITIVITIES

Exact analytical solutions based on Laplace transforms are derived for describing the one-dimensional space- and time-dependent advective tr ansport of a decaying species in a layered, fractured, saturated rock system. The rock layers are parallel and horizontal and of uniform thi ckness. Thefracture intersects normally to the rock layers and is of v arying aperture across its length. Thefracture network is serial in na ture and of uniform thickness within each layer. Fluid movement is ass umed to be exclusive to the fracture network. These solutions, which a ccount for advection in fracture, molecular diffusion into the rock ma trix, adsorption in both fracture and matrix, and radioactive decay, p redict the concentrations in both fracture and rock matrix and the cum ulative mass in the fracture. The solute migration domain in both frac ture and rock is assumed to be semi-infinite with nonzero initial cond itions. 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 n umerical examples related to the transport of Np-237 and Cm-245 in a f ive-layered system of fractured rock are used to verify these solution s with several well-established evaluation methods of Laplace inversio n integrals in the real and complex domain. In addition, with respect to the model parameters, a comparison of the analytically derived loca l sensitivities for the concentration and cumulative mass of Np-237 in thefracture with the ones obtained through a finite difference method of approximation is also reported. Both of these comparisons show exc ellent agreement. In spite of some limitations (i.e., assumptions of z ero dispersion in thefracture and infinite matrix diffusion), the new features embedded in the reported solutions allow one to deal with com monly witnessed layered media above the water table, when groundwater flow is under steady-state conditions. In addition the residual concen trations in both fracture and rock, coupled with the realistic option of periodically fluctuating decaying source, are considered. These sol utions are useful for verifying the accuracy of numerical codes design ed to solve similar problems and, above all, cost-effective for perfor ming sensitivity and uncertainty analyses of scenarios likely to be ad opted in performance assessment investigations of potential nuclear wa ste repositories.