Evidence of Heterogeneous Matrix Diffusion in Fractured Crystalline Rock in Laboratory Migration Experiments
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Evidence of Heterogeneous Matrix Diffusion in Fractured Crystalline Rock in Laboratory Migration Experiments Shulan Xu and Anders Wörman Department of Earth Sciences, Uppsala University, Villavägen 16, S-75236 Uppsala, Sweden ABSTRACT The geostatistics of the main properties of transport in crystalline rock at Äspö Hard Rock Laboratory, Sweden have been determined experimentally, using a large number of samples, as a basis for the analysis of the effect of the uncertainty in rock heterogeneity on radionuclide migration in a single fracture. The auto-covariance functions were estimated for the porosity, effective diffusivity and adsorption characteristics, such as partition coefficient, kd and adsorption kinetics. The one-dimensional analytical solutions for the mean values of the temporal moments of the residence time probability density function (PDF) were derived by using the spectral method. The solutions were applied to the evaluation of migration experiments on granitic drill cores from the Äspö Hard Rock Laboratory. Fractures were created in drill cores by sawing and tritium was used as a non-sorbing tracer in several experiments in each drill core. By systematically varying the flow velocity, u, we could verify the non-linear influence of 1/u on the variance of the residence time PDF according to the theory. The effect of the uncertainty in the heterogeneous rock properties on the solute transport observed in the migration experiments corresponds fairly well to the theoretical effect using the auto-covariance functions. INTRODUCTION Performance assessments (PA) of repositories for spent nuclear fuel include estimates of the transport of radionuclides that accidentally escape through the engineered (local) barriers. An important issue is how the interaction of various physical and geochemical processes and their spatial variability (uncertainty) can be accounted for on a geometrical scale relevant to the PA analysis. During the past decades many laboratory migration experiments with sorbing or nonsorbing tracers have been conducted to verify the models and improve the understanding of the transport mechanisms (e.g. [1], [2] and [3]). In addition to generally recognized mechanisms such as advection, dispersion, matrix diffusion and sorption, radionuclide migration can depend significantly on both sorption kinetics and the heterogeneity of matrix diffusion. In this study one-dimensional analytical solutions for the mean values of the temporal moments of the residence time PDF have been derived by using the spectral method ([4], [5] and [6]). The analyses included adsorption kinetics and the heterogeneity in both rock properties and advection velocity. Auto-covariance functions of the rock transport properties are required as a basis for the analyses and are thus determined experimentally in this study. Application of the solutions can be extended to a two-dimensional transport problem by using a Lagrangian method of description (e.g. [7] and [8]). Further, we use the developed solutions to evaluate laboratory mi
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