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Homogenization of Solute Transport in Unsaturated Double-Porosity Media: Model and Numerical Validation

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The development of a macroscopic model for solute transport coupled with unsaturated water flow in double-porosity media is presented in this work, by using the asymptotic homogenization method. The model was derived for the case in which the medium exhibits a strong contrast of transport properties by upscaling rigorously the transport mechanisms from micro-scale to macro-scale. It consists of two coupled equations for dispersion–convection processes at macroscopic level and diffusion intervention from local scale that can be described by a non-Fickian behaviour of solute concentration breakthrough. The proposed model was numerically implemented in the environment of a finite element code (commercial software) and applied to 2D examples with different boundary conditions. To validate, a comparative analysis between the results obtained from the homogenized model and the fine scale model (reference solution obtained from explicit heterogeneous representation of the medium structure) was carried out. The obtained numerical tool for the two-scale implementation enables treating various types of two-equation models to study the macroscopic non-Fickian transport and also non-equilibrium evolution of concentration fields inside the micro-porous medium.

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 107.01-2015.25. The first author is greatly indebted to Prof. Jolanta Lewandowska, Université de Montpellier for supervising his Ph.D. thesis in which the method of homogenization has been comprehended. We would like to thank the anonymous reviewers for their valuable suggestions and comments. Funding was provided by NAFOSTED (Grant No. 107.01-2015.25).

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  1. Centre Asiatique de Recherche sur l’Eau (CARE)/Faculty of Environment and Natural Resources, Ho Chi Minh City University of Technology, VNU-HCM, 268 Ly Thuong Kiet St., Dist. 10, Ho Chi Minh City, Viet Nam

    T. D. Tran Ngoc

  2. CARE/Faculty of Geology and Petroleum Engineering, Ho Chi Minh City University of Technology, VNU-HCM, 268 Ly Thuong Kiet St., Dist. 10, Ho Chi Minh City, Viet Nam

    Nam H. N. Le

  3. Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, 1 Vo Van Ngan St., Thu Duc Dist., Ho Chi Minh City, Viet Nam

    Tieng V. Tran

  4. Arts et Métiers ParisTech, CNRS, I2M Bordeaux, Esplanade des Arts et Métiers, 33405, Talence, France

    Azita Ahmadi

  5. I2M, UMR CNRS 5295, Université de Bordeaux, Esplanade des Arts et Métiers, 33405, Talence, France

    Henri Bertin

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Tran Ngoc, T.D., Le, N.H.N., Tran, T.V. et al. Homogenization of Solute Transport in Unsaturated Double-Porosity Media: Model and Numerical Validation. Transp Porous Med 132, 53–81 (2020). https://doi.org/10.1007/s11242-020-01380-6

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