Kinematic analysis of solute mass flows in rock fractures with spatially random parameters

Field data of physical properties in heterogeneous crystalline bedrock, like porosity and fracture aperture, is associated with uncertainty that can have a significant impact on the analysis of solute transport in rock fractures. Solutions to the central temporal moments of the residence time probability density function (PDF) are derived in a closed form for a solute Dirac pulse. The solutions are based on a model that takes into account advection along the fracture plane, diffusion into the rock matrix and sorption kinetics in the rock matrix. The most relevant rock properties including fracture aperture and several matrix properties as well as flow velocity are assumed to be spatially random along transport pathways. The mass transport is first solved in a general form along one-dimensional pathways, but the results can be extended to multi-dimensional flows simply by substituting the expected travel time for inert water parcels. Based on data obtained with rock samples taken at Äspö Hard Rock Laboratory in Sweden, the solutions indicate that the heterogeneity of the rock properties contributes to increasing significantly both the variance and the skewness of the residence time probability density function for a pulse travelling in a fracture. The Äspö data suggests that the bias introduced in the variance of the residence time PDF by neglecting the effect of heterogeneity of the rock properties on the radionuclide migration is very large for fractures thinner than a few tenths of a millimetre.