Diffusion and decay chain of radioisotopes in stagnant water in saturated porous media

• The dispersion of radioisotopes in stagnant water in porous media is modeled.
• The dispersion equation is decoupled in two equations.
• The first equation is described by diffusion without decay.
• The second equation is described by decay chain without diffusion.
• The decay chain equation is determined using the Laplace transform.

The analysis of the diffusion of radioisotopes in stagnant water in saturated porous media is important to validate the performance of barrier systems used in radioactive repositories. In this work a methodology is developed to determine the radioisotope concentration in a two-reservoir configuration: a saturated porous medium with stagnant water is surrounded by two reservoirs. The concentrations are obtained for all the radioisotopes of the decay chain using the concept of overvalued concentration. A methodology, based on the variable separation method, is proposed for the solution of the transport equation. The novelty of the proposed methodology involves the factorization of the overvalued concentration in two factors: one that describes the diffusion without decay and another one that describes the decay without diffusion. It is possible with the proposed methodology to determine the required time to obtain equal injective and diffusive concentrations in reservoirs. In fact, this time is inversely proportional to the diffusion coefficient. In addition, the proposed methodology allows finding the required time to get a linear and constant space distribution of the concentration in porous mediums. This time is inversely proportional to the diffusion coefficient. In order to validate the proposed methodology, the distributions in the radioisotope concentrations are compared with other experimental and numerical works.