Migration of radionuclides from a deep geological repository: analytical model with radial diffusion in host matrix

A mathematical model has been developed to study the migration of radionuclides through a single fracture from a high-level radioactive waste repository located in deep geological granite formations. The model utilizes two coupled equations; one for the fracture and the other for the host rock. The processes considered include advection, surface sorption, diffusive loss to the host rock and radioactive decay for transport in the fracture and radial diffusion, adsorption and radioactive decay for transport in the host rock. The source term to the model is provided as a two-component leach flux from the virtified waste form stored in the repository. The inlet concentration is derived using material balance for the amount of radioactivity that has entered into the fracture and host rock. Results indicate steep gradients in the radionuclide concentrations within the first 50 m along the fracture axis. It is observed that about 99% of the radioactivity is retained by the host rock. The radionuclide concentration in the fracture water increases as the fracture radius increases until a critical fracture radius is reached. Thereafter the concentration decreases due to the increase in the volumetric flux of water. The magnitude of the critical fracture radius mainly depends on the fracture water velocity