Matrix Diffusion of Radionuclides from a Finite Porous Rock Matrix to a Fracture: Importance of Back-Diffusion with a Constant Inlet Boundary Condition

Matrix diffusion into a rock matrix has been regarded to retard radionuclide migration in a fracture. Recent field findings on a fractured system indicate that only a small portion of the rock in a fractured porous medium contributes to holding a radionuclide by matrix diffusion. To understand this effect, radionuclide migration in a fracture and diffusion from a finite rock matrix to a fracture are discussed with limited matrix diffusion under solubility-limited boundary conditions of a target radionuclide for the band-type release. Numerical inversion of the Laplace transform method is applied to estimate concentrations in a fracture and a finite rock matrix and fluxes at the fracture surface. Matrix diffusion into a finite rock matrix shows enhanced radionuclide migration and a higher concentration profile in a fracture. Diffusive flux from a finite rock matrix into a fracture after the end of leaching time shows higher peak values than flux from an infinite rock matrix because of (a) higher saturation of a radionuclide in a finite rock matrix and (b) increase of a radionuclide concentration in a fracture. Therefore, it is more realistic and conservative to apply the finite matrix diffusion for the overall assessment in a potential repository embedded in a fractured porous medium.