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Saturation Dependence of Thermal Conductivity of Soils: Classification and Estimations

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Abstract

Thermal conductivity is a key parameter governing heat transfer in rocks and soils with applications to geothermal systems and groundwater studies. Its accurate measurement is crucial to understand energy exchange in the Earth's subsurface. This study explores the application of the percolation-based effective-medium approximation (P-EMA) model to a broad range of soil types using a database including 158 soil samples. The P-EMA model for soil thermal conductivity, introduced by Ghanbarian and Daigle, is validated through robust optimization of its parameters and by comparing with the laboratory measurements where we find an excellent match between the theory and the experiments. A regression-based model is developed to estimate the P-EMA model parameters directly from other soil properties, such as sand, clay, bulk density, and thermal conductivities at completely dry and full saturation. The proposed regression-based relationships are evaluated using unseen data from two databases: one from Kansas containing 19 soil samples and another from Canada containing 40 soil samples. These regression-based relationships offer an approximation for the P-EMA model parameters, providing a practical approach to estimate the thermal conductivity of soils. Furthermore, a curve-clustering approach is proposed to classify soil thermal conductivity curves based on their similarities, providing insights into the heterogeneity of samples. We find seven clusters for each of which the average P-EMA model parameters are reported. The classification and regression models generally extend the seamless applicability of the P-EMA model.

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Data Availability

The data used in this study is available upon request from the corresponding author.

Abbreviations

P-EMA:

Percolation-based Effective-Medium Approximation

\({t}_{s}\) :

Scaling exponent

\(\lambda\) :

Thermal conductivity, W·m−1·°C−1

\(\Phi\) :

Porosity, cm3·cm−3

\({\rho }_{b}\) :

Bulk density, g·cm−3

\({\theta }_{c}\) :

Critical water content, cm3·cm−3

\(\theta\) :

Water content, cm3·cm−3

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Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Department of Geology and Geography, West Virginia University, Morgantown, WV, USA

    Tobi Ore

  2. Porous Media Research Lab, Department of Geology, Kansas State University, Manhattan, KS, USA

    Behzad Ghanbarian

  3. Institute of Soil Science, Universität Rostock, Rostock, Germany

    Klaus Bohne

  4. Institute of Ecology, Technische Universität Berlin, Berlin, Germany

    Gerd Wessolek

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  1. Tobi Ore
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  2. Behzad Ghanbarian
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  3. Klaus Bohne
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  4. Gerd Wessolek
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Contributions

Tobi Ore—Methodology, Formal Analysis, Investigation, Validation, Writing—Original Draft, Review and Editing, Visualization; Behzad Ghanbarian—Conceptualization, Methodology, Investigation, Validation, Resources, Supervision, Writing – Review and Editing; Klaus Bohne—Resources, Writing—Review and Editing; and Gerd Wessolek—Resources, Writing—Review and Editing.

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Correspondence to Tobi Ore.

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Ore, T., Ghanbarian, B., Bohne, K. et al. Saturation Dependence of Thermal Conductivity of Soils: Classification and Estimations. Int J Thermophys 45, 81 (2024). https://doi.org/10.1007/s10765-024-03375-7

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