On the numerical solution of radioactivity migration in a porous medium

The deep burial of vitrified radioactive waste in rock and the storage of spent fuel rods in storage tanks at sufficient depths call for the modeling of the migration of radioactivity in rock. Rock is considered as a system of connected parallel fractures. The two coupled partial differential equations which govern the transport in the fracture and in the porous matrix need to be solved by an efficient numerical procedure. Here, we indicate an accurate scheme that has the following two components. The first is the use of a very high order derivative approximation for the concentration gradient at the interface of the waste-matrix and the fracture. The second is the use of Crank-Nicolson finite difference scheme and this gives numerical values which are second order accurate both in space and time variables. With this prescription, reliable estimates of the concentration can be obtained at a distance of 500 m from the source for both long lived and short lived species. Typical concentration plots for few important species are provided.