Analytic and numerical studies are made to predict space-time-dependent normalized concentrations of radionuclides migrating through the water-saturated fractured porous rock with limited diffusion.
In this study, two extended migration models in a discrete fracture surrounded by porous rock matrix with limited diffusion are developed. Applicability and limitation of the models are investigated.
First model is the radionuclide migration system through a single, planar fracture with limited thickness, a, of surrounding porous rock matrix. We impose the impermeable boundary condition at the distance from the fracture surface. For smaller values of a, the distance from the fracture and rock interface to the boundary of the impermeable zone, the normalized concentrations deviate from those by the solution without the impermeable zone.
Second model, in general sense, includes the surface layer close to the fracture having different characteristics of matrix 1 from the intact rock matrix 2 based on the evident field studies. Although the full analytic solutions are developed for second model in zero dispersion case, numerical inversion of the Laplace Transform is employed to avoid the difficulties associated with the calculation of analytic solution. Higher physical space, which is explained by large porosity, for radionuclide to reside shows lower concentration in a fracture in water. The more radionuclide diffuses into the surrounding porous rock matrix 1, the less radionuclides remain in a fracture and move according to the assumed governing phenomena. As the retardation factors of surrounding porous rock matrix increase, the concentration front moves toward inlet boundary. The existence of difference characteristics of porous rock matrix accelerates the radionuclide migration depending on the thickness of porous rock matrix 1.
In spite of the intrinsic problem of numerical inversion, we used the Talbot method to obtain the normalized concentration in a fracture i...