<p>The overall objective of the current study is to develop a quantitative understanding of the effects of spatial variability in physical and geochemical properties of crystalline rock on the migration of radionuclides along a single fracture in bedrock. A stochastic model was developed to describe the transport of solutes in fractured rock. The model describes the migration of radionuclides along a one-dimensional path and includes the transversal diffusion into the rock matrix and sorption kinetics. By using a Lagrangian method of description we can extend the model to the description of a two-dimensional transport problem in single fractures. </p><p>This study presents the first analysis of the impact of heterogeneous mass transfer on the transport of radionuclides in rock fractures, where most of the relevant rock properties such as aperture, porosity, effective diffusivity, sorption capacity and maximum diffusion depth are defined as being spatially random. The stochastic analysis performed here reflects the uncertainty in our knowledge of the properties associated with a discrete sampling technique in site investigations.</p><p>Geostatistics of the main parameters was determined experimentally on a large number of rock samples taken from the Swedish crystalline basement. The knowledge of the covariance functions of the main rock properties is then used as a basis for a stochastic analysis. By combining the small perturbation approach with the spectral method the problem could be solved in terms of closed form solutions for the central temporal moments of the residence time probability density function. </p><p>In order to be able to distinguish between the effects of various mechanisms from the effects of heterogeneity on the migration of radionuclides, it was necessary to perform independent studies of the effect of the variation of the dispersion coefficient on the aspect ratio of a rectangular flow section and the effect of adsorption kinetics on the migration. </p><p>Finally, the effect of the heterogeneous rock properties on the solute transport observed in a limited number of migration experiments corresponds fairly well to the theoretical effect expected on the basis of the experimentally determined auto-covariance functions. </p>

The overall objective of the current study is to develop a quantitative understanding of the effects of spatial variability in physical and geochemical properties of crystalline rock on the migration of radionuclides along a single fracture in bedrock. A stochastic model was developed to describe the transport of solutes in fractured rock. The model describes the migration of radionuclides along a one-dimensional path and includes the transversal diffusion into the rock matrix and sorption kinetics. By using a Lagrangian method of description we can extend the model to the description of a two-dimensional transport problem in single fractures. This study presents the first analysis of the impact of heterogeneous mass transfer on the transport of radionuclides in rock fractures, where most of the relevant rock properties such as aperture, porosity, effective diffusivity, sorption capacity and maximum diffusion depth are defined as being spatially random. The stochastic analysis performed here reflects the uncertainty in our knowledge of the properties associated with a discrete sampling technique in site investigations. Geostatistics of the main parameters was determined experimentally on a large number of rock samples taken from the Swedish crystalline basement. The knowledge of the covariance functions of the main rock properties is then used as a basis for a stochastic analysis. By combining the small perturbation approach with the spectral method the problem could be solved in terms of closed form solutions for the central temporal moments of the residence time probability density function. In order to be able to distinguish between the effects of various mechanisms from the effects of heterogeneity on the migration of radionuclides, it was necessary to perform independent studies of the effect of the variation of the dispersion coefficient on the aspect ratio of a rectangular flow section and the effect of adsorption kinetics on the migration. Finally, the effect of the heterogeneous rock properties on the solute transport observed in a limited number of migration experiments corresponds fairly well to the theoretical effect expected on the basis of the experimentally determined auto-covariance functions.

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