Numerical simulation of the transport of a radionuclide chain in a rock medium

For the safe disposal of High Level Waste (HLW), a common practice is to bury the sealed container called canister containing the concentrated and vitrified waste deep inside the earth surface within a rocky medium. In the event of an accidental breach of such a canister, the sealed waste may come in contact of pore water. If this happens, then the parent nuclides present in the HLW and their daughters generated by the radioactive decay reaction start migrating through the surrounding rock medium due to the combined effect of advection and diffusion. The accurate estimation of the transport of such a chain through a rock is important for radiological safety. Here, we report a finite difference based numerical simulation to address the issue. To simplify the problem, we consider the rock to be a collection of identical parallel fractures separated by porous matrices of equal width with a source at one end. A Forward Time and Centered Space (FTCS) finite difference scheme is implemented to solve the set of coupled partial differential equations that govern the transport mechanism. The scheme is validated using the methods available in the literature and subsequently it is applied to estimate the time dependent buildup of the active elements of a chain. Two independent chains each with three members are considered for simulation to address the safety related issues.