A model is developed to describe the transport of an N-member radionuclide decay chain along a discrete fracture situated in a porous matrix. An analytical solution is presented and a series of simulations are performed to study the relative significance of diffusion process into rock matrix, stagnant water, chain decay and hydrodynamic dispersion. The results show that a simplified model that ignores the effect of stagnant water zone can lead to significant error in the estimated time of arrival and peak value of the nuclides. The results demonstrate that for a two-member decay chain, neglecting the parent and modeling its daughter as a single species can result in significant overestimation of peak value of the nuclide. Moreover, it is found that as the dispersion increases, the arrival time and peak time of daughter decrease, while the peak value increases.
Water flow and solute transport in fractured rocks are studied over very long times to gain a firm understanding of fundamental mechanisms affecting contaminant transport from radioactive waste repositories. Flow in such rocks takes place mostly in fractures that form complex networks of conducting paths. An overview can be found in Tsang & Neretnieks (1998).
In fractured rocks, because of the low permeability usually associated with the rock matrix, nearly all of the groundwater flows within the fractures. Thus, the fractures act as principal pathways for direct transport of contaminant in these systems, whereas the porous rock matrix containing immobile groundwater and sorbing micropore surfaces serves as the main reservoir for storing contaminants.
It has been found that dissolved contaminants in the water flowing in the fractures can also diffuse into the micropores of the porous rock matrix where they will access a larger water volume than that of the flowing water; Sorbing nuclides will sorb on the micropore surfaces in the rock matrix and will be even more retarded.
In addition, the solutes can diffuse into stagnant water in the fractures themselves and from this water further into the rock matrix. For simplicity, however, many of the models ignored the existence of the stagnant water zone in the fracture plane (Dershowitz et al. & Hartley 1998, Poteri & Laitinen 1999). That is, it is assumed that for flow and transport in fracture networks the entire fracture surface is in contact with flowing water. This implies that the entire fracture surface is available for reaction with solutes carried by the water and that diffusion into stagnant water zones in the fractures is not accounted for, in contradiction to field observations that groundwater is flowing only in a small part of a conductive fracture to form one or more flowing channels (Tsang & Neretnieks 1998).