Heterogeneous matrix diffusion in crystalline rock — implications for geosphere retardation of migrating radionuclides

As a basis for an analysis of the effect of rock heterogeneity on radionuclide migration in a single fracture, the geostatistics of the main properties governing solute transport in crystalline rock have been determined experimentally for two granitic rock types. The rock samples were collected at the Äspö Hard Rock Laboratory, Sweden and used to deduce the auto-covariance functions for the porosity, effective diffusivity and partition coefficient, kd, and adsorption kinetics. One-dimensional analytical solutions for the mean values of the temporal moments of the residence time probability density function (PDF) show that the heterogeneity of the rock properties can have a substantial impact on the transport. A case study of the effect of heterogeneity in matrix diffusion for a single fracture could be performed by decomposing the transport problem into a one-dimensional mass transfer problem and a two-dimensional flow problem using a Lagrangian method of description. Monte Carlo simulations of the flow field indicate that the correlation length of the aperture is much longer along the trajectory paths than along an arbitrary direction. Increasing the correlation lengths and variances of the aperture and matrix diffusion increases significantly the variance of the travel time PDF.