This paper discusses migration of radionuclides in the bedrock surrounding a repository. Currently available models use either a surface reaction or a bulk reaction concept to describe the retardation of migrating nuclides. The first model assumes that the nuclide reacts only with the surface of the fissures. This implies that the rock matrix is not utilized as a sink. The other model implies that the whole bulk of the rock is accessible to the nuclides. The paper analyzes the accessibility of the rock matrix to the radio‐nuclides. The transport mechanisms are shown to be flow of water and nuclides in the fissures and transport of nuclides from the water in the fissures into water in the microfissures of the rock by pore diffusion. The diffusion of the nuclides into the rock matrix and their sorption onto the surfaces of the microfissures are the main mechanisms retarding migration from a repository. The diffusivity of the nuclide may be as important as its sorption equilibrium constant. Diffusivities in the pores and microfissures in such dense rocks as granite under confining pressure of hundreds of bars can be expected to be 6–20% of the diffusivity in water. These data are obtained from electrical resistivity measurements of saltwater‐filled granites. Porosity of such granites varies from 0.4 to 0.9%. The apparent diffusivities in the granites will then vary between 0.25 · 10−12/Kdρp and 10 · 10−12/Kdρp m2/s, where Kdρp is the volume equilibrium constant. This varies from the porosity of the rock for nonsorbing species to up to and over 104. For a 100‐year contact time a nonsorbing nuclide can be expected to penetrate tens of meters of the rock matrix and a strongly sorbing nuclide with Kdρp larger than 104 will penetrate a few millimeters. The diffusion into the rock matrix can enhance the retardation by many orders of magnitude as compared to retardation by surface reaction in fissures only. The retardation may, on the other hand, be many orders of magnitude smaller than the maximum value that could be obtained if all the rock matrix were accessible. This depends very much on the fissure widths and spacings.

Abstract. Experimental observations and theoretical studies over the last 10 years or so have demonstrated that flow channeling or preferred flow paths is a common phenomenon in fractured rocks. The reason it has come to the forefront of scientific investigation is the recent interest in predicting solute transport in geological media as part of safety assessment of geologic isolation of nuclear or toxic wastes. Solute transport is much more sensitive to medium heterogeneity than is temperature or pressure. In this paper, experimental observations of tracer transport over distances ranging from centimeters to hundreds of meters are reviewed, and theoretical efforts to explain or model these observations are summarized. Processes that may explain some of the experimental observations without the use of flow-channeling models are discussed. The paper concludes with a discussion of the implications of flow channeling on the practical problems related to contaminant transport in geologic systems.

Calculations for the flow and solute transport through a single rough‐surfaced fracture were carried out. The fracture plane was discretized into a square mesh to which variable apertures were assigned. The spatially varying apertures of each single fracture were generated using geostatistical methods, based on a given aperture probability density distribution and a specified spatial correlation length. Constant head boundary conditions were assumed for the flow in the x direction of a single fracture with no flow boundaries in the y direction. The fluid potential at each node of the discretization mesh was computed and the steady state flow rates between all the nodes were obtained. Our calculations showed that fluid flow occurs predominantly in a few preferred paths. Hence, the large range of apertures in the single fracture gives rise to flow channeling. The solute transport was calculated using a particle tracking method. Both the spatial and time variations of tracer breakthrough results are presented. The spatial variation of tracer transport between a line of injection points and a line of observation points are displayed in contour plots which we labeled “transfer matrix.” Our results indicate that such plots can give information on the spatial correlation length of the heterogeneity in the fracture. The tracer breakthrough curve obtained from a line of point measurements is shown to be controlled by the aperture density distribution and is insensitive to statistical realization and spatial correlation length. These results suggest the importance of making line measurements in the laboratory and the field. Sensitivity of our results on parameter variations was also investigated.

Radionuclide migration was studied in a natural fissure in a granite core. The fissure was oriented parallel to the axis in a cylindrical core 30 cm long and 20 cm in diameter. The traced solution was injected at one end of the core and collected at the other. Breakthrough curves were obtained for the nonsorbing tracers, tritiated water, and a large-molecular-weight lignosulphonate molecule and for the sorbing tracers, cesium and strontium. From the breakthrough curves for the nonsorbing tracers it could be concluded that channeling occurs in the single fissure. A 'dispersion' model based on channeling is presented. The results from the sorbing tracers indicate that there is substantial diffusion into and sorption in the rock matrix. Sorption on the surface of the fissure also accounts for a part of the retardation effect of the sorbing species. A model which includes the mechanisms of channeling, surface sorption, matrix diffusion, and matrix sorption is presented. The experimental breakthrough curves can be fitted fairly well by this model by use of independently obtained data on diffusivities and matrix sorption. BACKGROUND The migration of radionuclides in various kinds of rocks has become an area of large interest in the last decade because of various national and international efforts in studying the final disposal of radioactive wastes from nuclear power plants. In the Swedish studies [KBS Nuclear Fuel Safety Project, 1977; 1978], crystalline rock has been selected as the most suitable bedrock in which to build a repository. In crystalline rock the water moves in fissures which may be fairly far apart at larger depths. The radionuclides, carried by the water, will interact in various ways with the rock. They may be strongly retarded by sorption on the surface of the fissures and, given time, may also penetrate the intercrystalline microfissures of the matrix of the rock. The present study aims at obtaining experimental results from radionuclide migration in a single fissure under well defined conditions. Such results should be useful in understanding and possibly predicting radionuclide migration in fissured crystalline rock. THE EXPERIMENT Flow SystemThe rock used in this study was a 30-cm-long granitic drill core (20-cm diameter) taken from the Stripa mine at a depth of 360 m below ground level. The core has a natural fissure which runs parallel to the axis. The cylindrical surface of the drill core was sealed with a coat of urethane lacquer to prevent any water leaving the rock except through the outlet end of the fissure. The granite cylinder was thereafter mounted between two plexiglas end plates containing inlet and outlet channels slightly wider than the fissure (Figure 1).Artificial groundwater with a tracer was fed to the upper channel by means of a four-channel peristaltic pump (Istma-

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The diffusion of nonsorbing species in different rock materials and fissure coating materials has been studied on a laboratory scale. The nonsorbing species were iodide, Uranine, and Cr-EDTA. The results show that the effective diffusivity of iodide in rock materials with fissure coating material is of the same magnitude as or higher than the effective diffusivity of iodide in rock materials without fissure coating material. The results also show that the variations in the rock material are too large to give one value of the diffusivity in a rock material from a certain area. The estimated effective diffusivity of iodide in rock materials without fissure coating material was found to be in the range 1 x 10 -•'• m2/s to 70 x 10 -•'• m:•/s.

Tracer tests in natural fissures performed in the laboratory are analyzed by means of fitting two different models. In the experiments, sorbing and nonsorbing tracers were injected into a natural fissure running parallel to the axis of a drill core. The models take into account advection, dispersion, diffusion into the rock matrix, and sorption onto the surface of the fissure and on the microfissures inside the matrix. For the second mechanism, one of the models considers hydrodynamic dispersion, while the other model assumes channeling dispersion. The models take into account time delays in the inlet and outlet channels. The dispersion characteristics and water residence time were determined from the experiments with nonsorbing tracers. Surface and volume sorption coefficients and data on diffusion into the rock matrix were determined for the sorbing tracers. The results are compared with values independently determined in the laboratory. Good agreement was obtained using either model. When these models are used for prediction of tracer transport over larger distances, the results will depend on the model. The model with channeling dispersion will show a greater dispersion than the model with hydrodynamic dispersion, assuming constant dispersivity.

Within the framework of density functional theory, a weighted correlation approach is developed in order to obtain the density distributions of an inhomogeneous fluid. It results in a formally exact expression, by means of the concept of a weighted pair correlation function, used to evaluate the change of the single-particle direct correlation function of the system relative to that of a reference state. When applying the approach for practical use, however, an approximation of the pair correlation function has to be made, along with an appropriate definition of a weight function. Noticeably, combining this approach with fundamental measure theory gives rise to a new method, which we call the FMT/WCA-k(2) approach, for studying the structural and thermodynamic properties of a charged hard-sphere fluid subjected to a spatially varying external potential. Application of the FMT/WCA-k(2) approach in a range of electrolyte concentrations and surface charge densities, against the Monte Carlo simulations, shows that it is superior to the typical approaches of density functional theory in predicting the ionic density profiles of both counter-ions and co-ions near a highly charged surface. It is capable of capturing the fine features of the structural properties of the electric double layers, to well reproduce the layering effect and the charge inversion phenomenon, also in strongly coupled cases where divalent counter-ions are involved. In addition, it is found that the FMT/WCA-k(2) approach even has an advantage over the anisotropic, hyper-netted chain approaches in giving better agreement with the Monte Carlo results.