A fractional differential scheme for the effective transport properties of multiscale reactive porous media: Applications to clayey geomaterials

Cosenza, Philippe; Giot, Richard; Giraud, Albert; Hedan, Stéphen

doi:10.1002/nag.3259

Cited by 3 publications

(1 citation statement)

References 75 publications

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“…Nevertheless, as a starting point, we focus on neutral species (e.g., HTO). Thus Archie's law can be applied as a first approximation to correlate porosity and diffusivity (Cosenza et al., 2021).…”

Section: Methodsmentioning

confidence: 99%

A Comparative Study on Heterogeneity of Clay Rocks Using Pore‐Scale Diffusion Simulations and Experiments

et al. 2022

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Clay rocks such as the Opalinus Clay (OPA) in Switzerland are considered as potential host rocks for deep geological disposal of nuclear wastes. Radionuclide migration in clay rocks is dominated by molecular diffusion highly dependent on the pore network geometries. In the sandy facies of OPA (SF-OPA), this pore network is critically modified due to compositional variability and owing to diagenetic reaction products, for example, carbonate and sulfide minerals (Philipp et al., 2017). Such spatial variability is responsible for heterogeneous diffusion patterns (Kulenkampff et al., 2015). At the continuum scale, the representative elementary volume (REV) is an important parameter for understanding and modeling the reactive transport (RT) of contaminants and radionuclides. An accurate estimation of the REV for diffusion is decisive for a meaningful continuum-scale simulation of radionuclide migration in heterogeneous clay rocks like SF-OPA, thus playing an important role in the safety analysis of deep geological repositories for nuclear waste.In continuum mechanics for a heterogeneous material, the REV is the smallest volume over which a measurement can be made to produce a representative value of the macroscopic property in three-dimensional space (3D) (Bear Abstract Accurate modeling and simulation of radionuclide migration in clay rocks such as the Opalinus Clay (OPA) play a key role in the safety assessment of deep geological repositories for nuclear wastes. At the continuum scale, the representative elementary volume (REV) is a fundamental constraint to quantify the effective diffusivity, which is a key parameter in reactive transport (RT) models. Therefore, an accurate estimation of the REV is essential for a meaningful continuum-scale RT simulation in heterogeneous clay rocks. This study presents a comprehensive analysis of the heterogeneities of porosity and effective diffusivity in clay rocks by using the classical sampling theory and pore-scale simulations. First, in this study, the two-dimensional representative elementary area is correlated with the REV for porosity via a characteristic length. Next, it is shown that the REV for diffusivity is larger than the REV for porosity. Moreover, these two REVs can be correlated using Archie's law. In such a way, the REV for diffusivity can be determined by the developed correlations through analyzing two-dimensional microstructures, thus significantly reducing the computational cost. Finally, the applicability of our approach for clay rocks is validated by experimental data on the diffusion of tritiated water in the heterogeneous sandy facies of OPA. From both the experimental data and the modeling prediction, the REV for diffusivity in the sandy facies of OPA is in the order of cubic centimeters. This study provides critical insights into the diffusion in heterogeneous clay rocks toward an enhanced predictability of radionuclide migration.Plain Language Summary Contaminant migration in clay rocks is dominated by molecular diffusion due to their low permeability....

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Section: Methodsmentioning

confidence: 99%

A Comparative Study on Heterogeneity of Clay Rocks Using Pore‐Scale Diffusion Simulations and Experiments

et al. 2022

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Effective medium approximation for the electromagnetic properties of rocks with surface conductivity

Markova,

Markov,

Jarillo

2024

Journal of Applied Geophysics

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A connectivity dependent model for electrical properties of multiphase media

Zhang,

Chen,

Yang

et al. 2024

Applied Physics Letters

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Determining the effective electrical properties of a multiphase medium is essential for understanding its performance. However, accurately characterizing the internal structure and calculating the effective electrical properties of complex multiphase media can be challenging, often resulting in divergent results from different models. In this study, we propose a connectivity dependent model for mixed media based on the effective medium approximation, which incorporates structural influences. This model simplifies itself to analytical forms in specific scenarios, such as simple series and parallel configurations. Our model demonstrates two key advantages: First, the model parameters depend solely on the shape distribution of each phase within the medium, making it applicable to multiphase systems (≥3) without requiring additional corrections. Second, it can predict the percolation threshold and provide insights into permeability and connectivity analyses of the medium. We demonstrate the effectiveness and versatility of our model through a series of parameter analyses and comparisons with experimental data.

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A fractional differential scheme for the effective transport properties of multiscale reactive porous media: Applications to clayey geomaterials

Cited by 3 publications

References 75 publications

A Comparative Study on Heterogeneity of Clay Rocks Using Pore‐Scale Diffusion Simulations and Experiments

A Comparative Study on Heterogeneity of Clay Rocks Using Pore‐Scale Diffusion Simulations and Experiments

Effective medium approximation for the electromagnetic properties of rocks with surface conductivity

A connectivity dependent model for electrical properties of multiphase media

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