title: Analytical solution to the diffusion, sorption and decay chain equation in a saturated porous medium between two reservoirs.
abstract: The diffusion and distribution coefficients are important parameters in the design of barrier systems used in radioactive repositories. These coefficients can be determined using a two-reservoir configuration, where a saturated porous medium is allocated between two reservoirs filled by stagnant water. One of the reservoirs contains a high concentration of radioisotopes. The goal of this work is to obtain an analytical solution for the concentration of all radioisotopes in the decay chain of a two-reservoir configuration. The analytical solution must be obtained by taking into account the diffusion and sorption processes. Concepts such as overvalued concentration, diffusion and decay factors are employed to this end. It is analytically proven that a factor of the solution is identical for all chains (considering a time scaling factor), if certain parameters do not change. In addition, it is proven that the concentration sensitivity, due to the distribution coefficient variation, depends of the porous medium thickness, which is practically insensitive for small porous medium thicknesses. The analytical solution for the radioisotope concentration is compared with experimental and numerical results available in literature.
authors.affiliation: Departamento de Energía, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo 180 Col. Reynosa Tamaulipas, México, D.F. 02200, Mexico. Electronic address: maestro_juan_rafael@hotmail.com.
authors.forename: Juan
authors.initials: J
authors.lastname: Guzman
authors.affiliation: Instituto Tecnológico de Morelia, Av. Tecnológico #1500, Lomas de Santiaguito, Morelia, Michoacán 58120, Mexico; On sabbatical leave, Universidad Autónoma Metropolitana, Azcapotzalco, México, D.F. 02200, Mexico.
authors.forename: Serguei
authors.initials: S
authors.lastname: Maximov
authors.affiliation: Departamento de Energía, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo 180 Col. Reynosa Tamaulipas, México, D.F. 02200, Mexico.
authors.forename: Rafael
authors.initials: R
authors.lastname: Escarela-Perez
authors.affiliation: Departamento de Energía, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo 180 Col. Reynosa Tamaulipas, México, D.F. 02200, Mexico.
authors.forename: Irvin
authors.initials: I
authors.lastname: López-García
authors.affiliation: Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Av. Instituto Politécnico Nacional s/n, U. P. Adolfo López Mateos, Col. San Pedro Zacatenco, México, D.F. 07738, Mexico.
authors.forename: Mario
authors.initials: M
authors.lastname: Moranchel
mesh_terms: D004058:Diffusion; D008962:Models, Theoretical; D016062:Porosity; D011868:Radioisotopes / Q000032:analysis*
chemical_list: D011868:Radioisotopes
keywords: Absorption; Chain; Decay; Diffusion; Isotope; Porous