Comparative measures of radionuclide containment in the crystalline geosphere

A probabilistic model for assessing the capacity of a fractured crystalline rock volume to contain radionuclides is developed. The rock volume is viewed as a network of discrete fractures through which radionuclides are transported by flowing water. Diffusive mass transfer between the open fractures and the stagnant water in the pore space of the rock matrix allow radionuclides access to mineral grains where physical and chemical processes-collectively known as sorption-can retain radionuclides. A stochastic Lagrangian framework is adopted to compute the probability that a radionuclide particle will be retained by the rock, i.e., the probability that it will decay before being released from the rock volume. A dimensionless quantity referred to as the "containment index" is related to this probability and proposed as a suitable measure for comparing different rock volumes; such as comparative measure may be needed, for example, in a site selection program for geological radioactive waste disposal. The probabilistic solution of the transport problem is based on the statistics of two Lagrangian variables: τ, the travel time of an imaginary tracer moving with the flowing water, and β, a suitably normalized surface area available for retention. Statistics of τ and β may be computed numerically using site-specific discrete fracture network simulations. Fracture data from the well-characterized Äspö Hard Rock Laboratory site in southern Sweden are used to illustrate the implementation of the proposed containment index for six radionuclides (¹²⁶Sn, ¹²⁹I, ¹³⁵Cs, ²³⁷Np, ²³⁹Pu, and ⁷⁹Se). It is found that fractures of small aperture imply prolonged travel times and hence long tails in both beta and tau. This, in turn, enhances retention and is favorable from a safety assessment perspective.