Impact of Porosity Heterogeneity in the Diffusion of Some Alkali- and Alkaline Earth-Metals in Crystalline Rock

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ABSTRACT Data from diffusion experiments using Na+, Ca 2+, Sr 2+, Cs+ and Ba2+ as tracers in a crystalline rock type (Asp6 diorite, originating from the Asp6 Hard Rock Laboratory) have been evaluated using a heterogeneity model. The model concept consists of diffusion in a variety of different channels with different porosities. The porosity distribution used has been obtained from independently performed measurements of porosity distributions using the 14Cpolymethylmethacrylate impregnation method. Breakthrough curves in through-diffusion experiments as well as penetration profiles in the matrix have been evaluated using the porosity distributions. In the calculations only two parameters, the pore diffusivity (Dp) and the sorption distribution coefficient (Kd) have been varied in order to fit the experimental data to the proposed model. For the penetration profile of more strongly sorbing tracers, i.e., Cs+ and Ba 2+, a significantly better explanation of the data is obtained using a heterogeneity model compared to using a uniform porosity distribution model. The data from the through-diffusion experiments gives a better explanation of the shape at the beginning of the breakthrough curve. The implication of the proposed diffusion model is discussed, both from an in situ sorption experiment application and a performance assessment application.

INTRODUCTION For a repository for spent nuclear fuel in deep bedrock, as proposed in many countries, the role of the surrounding rock acting as a barrier in retarding released radionuclides is an important parameter. The retardation process in fractured rock is due to the sorption of radionuclides on the fracture walls combined with diffusion into the fracture coatings and further into micropores of the rock, i.e., matrix diffusion [1]. By assuming a homogeneous distribution of the porosity and combining this with the distribution coefficients (Kd) determined from static batch experiments with crushed rock material, performance assessment has shown that the matrix diffusion is the far major retardation process for transport in the geosphere [2]. A parameter that has focused some interest during the recent years is the heterogeneity of the diffusion pathways. Haggerty et al. [3] has shown that the results obtained in in situ experiments performed in Culebra dolomite can be explained by a heterogeneous mass transfer, applying a log-normal distribution of the diffusion rates. By impregnation of samples of crystalline generic rock types with 14C labelled methylmethacrylate (14C-MMA) followed by polymerisation, it has been shown that the porosity of the rock is strongly heterogeneously distributed [4,5]. Bradbury and Green [6] applied a dead end pore model in order to interpret the early part of the breakthrough curve in a through-diffusion experiment. However, a general problem is that involving heterogeneity in the interpretation of experiments gives more parameters to use in the calculations. Doubts can therefore be raised whether the obtained better fitting of the results are