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Effective Diffusivity Prediction of Radionuclides in Clay Formations Using an Integrated Upscaling Workflow

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Abstract

The effective diffusivity is a key parameter in the diffusive transport calculations, thus decisive for predicting the radionuclide migration in low-permeable clay-rich formations. Potential host rocks such as the Opalinus clay exhibit pore network heterogeneities, critically modified due to compositional variability in the sandy facies and owing to diagenetic minerals. Meaningful estimation of the effective diffusivity requires an understanding of transport mechanisms at the nanometer-scale as a starting point and a combination with upscaling strategies for considering compositional heterogeneities at the micrometer-scale. In this study, we propose an upscaling workflow that integrates transport simulations at both the nanometer-scale and the micrometer-scale to predict the effective diffusivities of radionuclides in the sandy facies of the Opalinus clay. The respective synthetic digital rocks provide conceptually two types of materials at the pore scale, in which the pore space and pore network in the clay matrix at the nanometer scale and mineral complexity in shales at the micrometer scale are considered. The numerical approach using the introduced digital rocks is validated with published experimental data that confirm the general applicability of the models. Sensitivity studies reveal the increase of effective diffusivity of shales as a function of increased pore space, reduced tortuosity, and an increased sheet silicate concentration compared to other rock components. Thus, such spatial variabilities at the pore scale of more complex sedimentary rocks are now addressed in the proposed approach and available for studying heterogeneous diffusion patterns compared to commonly assumed homogeneous behavior. Finally, and as a starting point for further upscaling strategies, we investigate anisotropic diffusion by studying the effect of lamination of the shales toward enhanced predictability of radionuclide migration.

Article Highlights

  • Upscaling workflow to predict effective diffusivity of radionuclides (RN) diffusion in shales showing compositional heterogeneity (sandy facies of Opalinus clay)

  • Sensitivity studies demonstrate and quantify the effect of the pore network geometry in the clay matrix as well as the effect of clay mineral concentration variability in shales on RN diffusion

  • Prediction of the heterogeneity of diffusivity based on multiple types of imaging data including compositional rock data

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

We thank our colleagues J. Kulenkampff, J. Schabernack, and T. Bollermann (HZDR) for fruitful discussions. We gratefully acknowledge funding by the German Federal Ministry of Education and Research (BMBF), grant 02NUK053B and the Helmholtz Association, grant SO-093 (iCross).

Funding

German Federal Ministry of Education and Research (BMBF), grant 02NUK053B and the Helmholtz Association, grant SO-093 (iCross).

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Authors and Affiliations

  1. Department of Reactive Transport, Institute of Resource Ecology, Helmholtz-Zentrum Dresden-Rossendorf, 04318, Leipzig, Germany

    Tao Yuan & Cornelius Fischer

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  1. Tao Yuan
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  2. Cornelius Fischer
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Contributions

The study was designed by CF and TY. TY performed numerical modeling and simulation. TY and CF performed data interpretation and discussed the results. TY drafted the manuscript and CF contributed to writing the paper.

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Correspondence to Tao Yuan.

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Yuan, T., Fischer, C. Effective Diffusivity Prediction of Radionuclides in Clay Formations Using an Integrated Upscaling Workflow. Transp Porous Med 138, 245–264 (2021). https://doi.org/10.1007/s11242-021-01596-0

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