A mathematical model of nuclide migration and its parameters inversion in a two-dimension single fracture-porosity dual media

A mathematical model of nuclide (⁹⁰Sr) migration and its parameter inverse problem for the dual media consist of the two-dimension porosity and the single fracture media is studied. The nuclide migration model is a coupled parabolic system with initial and boundary conditions. If the variation of the nuclide concentration is known at the release point, a set of solution of the nuclide migration model can be obtained by the Fourier transform and the Saul' yev asymmetric difference scheme. On the contrary, the solution of the inverse problem of the nuclide migration model, i. e. hydrodynamic dispersion coefficient and average flow rate in fracture media, is reconstructed with the Genetic Algorithm derived from the measured data of nuclide concentration at a location. Finally, numerical simulations for the forward and inverse problems are given. Numerical results show that the solution of the forward problem can describe the variation of the nuclide migration, and the method proposed for the inverse problem is also effective to reconstruct the geological parameters of the nuclide migration model. (authors)