Analytical solutions for reactive transport of N-member radionuclide chains in a single fracture

Several numerical codes have been used to simulate radionuclide transport in fractured rock systems. The validation of such numerical codes can be accomplished by comparison of numerical simulations against appropriate analytical solutions. In this paper, we present analytical solutions for the reactive transport of N-member radionuclide chains (i.e., multiple species of radionuclides and their daughter species) through a discrete fracture in a porous rock matrix applying a system decomposition approach. We consider the transport of N-member radionuclide chains in a single-fracture–matrix system as a starting point to simulate more realistic and complex systems. The processes considered are advection along the fracture, lateral diffusion in the matrix, radioactive decay of multiple radionuclides, and adsorption in both the fracture and matrix. Different retardation factors can be specified for the fracture and matrix. However, all species are assumed to share the same retardation factors for the fracture and matrix, respectively. Although a daughter species may penetrate farther along the fracture than its parent species when a constant-concentration boundary condition is applied, our results indicate that all species retain the same transport speed in the fracture if a pulse of the first species is released into the fracture. This solution scheme provides a way to validate numerical computer codes of radionuclide transport in fractured rock, such as those being used to assess the performance of a potential nuclear-waste repository at Yucca Mountain.