A mathematical model of nuclide migration and its inverse analysis in dual media

A mathematical model of nuclide migration and its inverse analysis for the dual media consisting of the porosity and the single fracture media, are explored. The nuclide migration model is a coupled parabolic equations with initial and boundary conditions. If the variation of the nuclide concentration has been known at the release point, an analytical solution of the nuclide migration model is obtained by the Laplace transform and its inverse analysis. On the contrary, the solution of the inverse problem of the nuclide migration model, namely the nuclide concentration at the release point, is reconstructed by the principle of superposition of partial differential equations and the quasi-solution method of inverse problems from the measured data of nuclide concentration at one downstream point. Finally, numerical simulations for the forward and inverse problems are given. Numerical results show that the analytical solution of the forward problem can describe the variation of the nuclide migration, and the method proposed for the inverse analysis is also effective to reconstruct the nuclide pollution source.