Application of multi-group diffusion theory to mechanistic modeling of leaching behavior of solidified low-level radioactive waste forms

The application of multi-concentration group mathematical modeling to the leaching of radionuclide waste-forms which have continuous porous matrix such as cemented waste form is described. The modeling is illustrated analyzing a hypothetical of some transport mechanisms such as molecular diffusion, ionic migration and convective flow for release of interest radionuclide from a solidified waste form which contains discrete particles of radioactive Sr-85 nuclides into the aqueous environment. The group parameters are derived from the classical electrochemistry concept of ion transport in dilute electrolytic solution. The numerical analysis is based on the Crank-Nicolson Implicit Methods which assures the stability of the solution at a practical time step. The results show that, for a short-time period of leaching in demineralized water the leaching behavior follows the predominating diffusion mechanism. After this point, the role of other processes apparent and continue until all radionuclides in the cement waste are leached out when compared to the Semi-Infinite Diffusion model which is based on pure diffusion mechanism. The multi-concentration group model can also be applied to long-term prediction of complicated release mechanisms of the radionuclides in the waste form of a particular disposal environment, unless the variables of interest such as the corrosion rate, the chemical reaction, erosion rate and etc. are determined by experiment or theoretical hypothesis. The appropriate differential equation then can be solved by the same general numerical approach