Modeling thermal conductivity of clays: A review and evaluation of 28 predictive models
Introduction
Clays differ from other soils in many aspects including particle size and shape, specific surface area and mineralogy (Farrar and Coleman, 1967; Hepper et al., 2006; Maček et al., 2013; Paterson, 2018), which make it special in the thermal, hydraulic and mechanical characteristics (Kang et al., 2015; María and Villar, 2004; Mozumder and Laskar, 2015; Tang et al., 2011; Zhang et al., 2017a). With respect to this, clay has been widely used in disciplines such as environmental and earth science, agriculture and geotechnical/geological engineering. These applications include water treatment (Chang and Juang, 2004), backfilling material for buried high-voltage power cable and oil, gas or hot-water pipes (Newson et al., 2002; Reno and Winterkorn, 1967; Ye et al., 2010) or borehole heat exchanger (Luo et al., 2019; Yu et al., 2015), natural geological engineering barrier for hazardous waste disposal including radioactive nuclear waste (Gens et al., 2002; Madsen, 1998; Mügler et al., 2006; Tang and Cui, 2007; Villar et al., 2005; Yoon et al., 2018) and landfill (Ghorbel-Abid and Trabelsi-Ayadi, 2015; Kaya and Durukan, 2004).
Effective thermal conductivity of clay (λeff), reciprocal of thermal resistivity, is of critical importance and interest among these thermo-hydro-mechanical characteristics. Because λeff of clay is required to determines heat transmission through soil in order to optimize engineering design (He et al., 2021; Reno and Winterkorn, 1967; Wang et al., 2016; Xu et al., 2019b). Although great progress has been made in techniques of λeff measurement (Bristow et al., 1994; Campbell et al., 1991; He et al., 2018a; He et al., 2015; He et al., 2018b; Ren et al., 2003; Wang et al., 2020a; Zhang et al., 2017b), λeff data are still rare and sparse compared to that of soil hydraulic and mechanical properties. Therefore, many efforts have been made to model λeff of clays (Abuel-Naga et al., 2009; Akinyemi et al., 2011; Barry-Macaulay et al., 2011; Caridad et al., 2014; Dao et al., 2014; de Zárate et al., 2010; Garnier et al., 2010; Jougnot and Revil, 2010; Kang et al., 2015; Sun et al., 2020; Tang et al., 2008; Xu et al., 2019d). However, it is interesting to note that there is a lack of study that tends to collate and synthesize these works.
It is also noted that many of these thermal conductivity models for clay were commonly developed or tested on a small dataset composing 2 to less than 200 λeff measurements (Cai et al., 2015; de Zárate et al., 2010; Xu et al., 2019d). In addition, there is a lack of study assessing these models with a large dataset consisting of clays with wide range soil physic properties (e.g. water content, mineralogy, and bulk density). Previous studies (de Vries, 1952a; He et al., 2015; He et al., 2018b; Wang et al., 2020a) have shown that soil thermal conductivity measured with transient methods (e.g., heat pulse probe, thermal needle, and hot-wire method) is more accurate for soils from dryness to saturation compared to steady-state method (e.g., guarded hot plate, divided bar method, and heat flux meter). The steady-state methods result in phase change of ice for frozen soils or water redistribution in unfrozen soils under temperature gradient, especially in unsaturated soils. Therefore, λeff measured with the transient methods are recommended for development and calibration of predictive models for soil thermal conductivity (He et al., 2018b; Zhang et al., 2017b).
The objectives of this study, therefore, were threefold: (1) to conduct an extensive review of the predictive models for thermal conductivity of clay; (2) to compile a large dataset consisting of clays of various types from dry to full saturation states and at different bulk densities; (3) to evaluate the performance of the thermal conductivity models for clay with the compiled dataset. It is hoped that this work would provide the novice or expert alike information on the advantage and limitations on modeling thermal conductivity of clays for various purposes.
Section snippets
A review of thermal conductivity models for clays
The extensive literature search returned 28 thermal conductivity models for clays. These models were categorized into three groups: (1) theoretical/semi-theoretical models (N = 2) and mixing models (N = 4); (2) normalized models (N = 6); and (3) linear and non-linear regression models (N = 14). The initials and year of publication were used to represent the model for better science communications. It should note that only models developed for clays were presented and evaluated in this study.
Published datasets
To evaluate the various models to estimate λeff of clay, experimental data were collated by following several important criteria: (1) reliable and reproducible experimental techniques/setup. λeff were measured on soil samples with transient method (e.g., heat pulse method, hot-wire method and thermal probe) at room temperature under atmosphere pressure condition and thereby temperature effects on the λeff will not be considered in this study; (2) measurements were taken on pure clays or clay
Theoretical/semi-theoretical and mixing models
For the four theoretical/semi-theoretical models, the SK1998 model performed better than the JR2010 model (Fig. 1c and b, Table 2). Although the de Vries (1963) model has been widely applied, it cannot be used to well predict thermal conductivity of clay (Fig. 1a, Table 2). The performance of its simplified from proposed by Tian et al. (2016) is slightly better but still not satisfactory (Fig. 1b, Table 2). Theoretical models attract attention modeling soil physical properties including thermal
Conclusion
In this study, 28 thermal conductivity models for clays were reviewed and evaluated with a large compiled dataset from 21 studies. The resulted showed that the DF1979 model had the best performance on the whole compiled dataset but still not satisfactory. Performance of the thermal conductivity models may be dataset or soil dependent and cares should be taken when choosing the most appropriate model for prediction purpose in practice. Future efforts focusing on the development of more accurate
Declaration of Competing Interest
The author declares no conflict of interest.
Acknowledgements
Datasets used in this study were digitalized from the published literature.
Funding for this research was provided in part by the National Natural Science Foundation of China [Grant No. 41877015, 42077135], Natural Science Foundation of Shaanxi Province [2020JM-169], Young science and technology star of Shaanxi Province, China Postdoctoral Science Foundation [Grant No. 2018M641024], the Training Program Foundation for the Young Talents of Northwest A&F University, and the 111 project [Grant No.
References (154)
- et al.
Thermal conductivity of soft Bangkok clay from laboratory and field measurements
Eng. Geol.
(2009) Effect of tillage treatments on soil thermal conductivity for some Jordanian clay loam and loam soils
Soil Tillage Res.
(2000)- et al.
Revisiting the block method for evaluating thermal conductivities of clay and granite
Int. Commun. Heat Mass Transf.
(2011) - et al.
Thermal conductivity of soils and rocks from the Melbourne (Australia) region
Eng. Geol.
(2013) - et al.
Development of correlations for soil thermal conductivity
Int. Commun. Heat Mass Transf.
(1992) - et al.
Measurements of the thermal conductivity of clay-sand and clay-graphite mixtures used as engineered barriers for high-level radioactive waste disposal
Appl. Clay Sci.
(1992) - et al.
Thermal characterization and prediction model of typical soils in Nanjing area of China
Eng. Geol.
(2015) - et al.
Thermal conductivity and density of clay pastes at various water contents for pelotherapy use
Appl. Clay Sci.
(2014) - et al.
Adsorption of tannic acid, humic acid, and dyes from water using the composite of chitosan and activated clay
J. Colloid Interface Sci.
(2004) - et al.
Anisotropic thermal conductivity of natural Boom Clay
Appl. Clay Sci.
(2014)
Measurement of the thermal conductivity of clays used in pelotherapy by the multi-current hot-wire technique
Appl. Clay Sci.
Factors controlling rock–clay buffer interaction in a radioactive waste repository
Eng. Geol.
Competitive adsorption of heavy metals on local landfill clay
Arab. J. Chem.
Soil–Litter–Iso: A one-dimensional model for coupled transport of heat, water and stable isotopes in soil with a litter layer and root extraction
J. Hydrol.
Evaluation of five composite dielectric mixing models for understanding relationships between effective permittivity and unfrozen water content
Cold Reg. Sci. Technol.
Distributed temperature sensing for soil physical measurements and its similarity to heat pulse method
A new model for predicting soil thermal conductivity from matric potential
J. Hydrol.
Room for improvement: A review and evaluation of 24 soil thermal conductivity parameterization schemes commonly used in land-surface, hydrological, and soil-vegetation-atmosphere transfer models
Earth Sci. Rev.
Modelling of soil solid thermal conductivity
Int. Commun. Heat Mass Transf.
A review and evaluation of 39 thermal conductivity models for frozen soils
Geoderma
Clay mineralogy, cation exchange capacity and specific surface area of loess soils with different volcanic ash contents
Geoderma
Utilization of bentonite-embedded zeolite as clay liner
Appl. Clay Sci.
Thermal conductivity of compacted bentonite as a buffer material for a high-level radioactive waste repository
Ann. Nucl. Energy
Thermo-hydro-mechanical properties of bentonite-sand-graphite-polypropylene fiber mixtures as buffer materials for a high-level radioactive waste repository
Int. J. Heat Mass Transf.
A comparison of methods used to characterize the soil specific surface area of clays
Appl. Clay Sci.
Prediction of unconfined compressive strength of geopolymer stabilized clayey soil using Artificial Neural Network
Comput. Geotech.
Determination of the thermal conductivity of opalinus clay via simulations of experiments performed at the Mont Terri underground laboratory
J. Appl. Geophys.
River flow forecasting through conceptual models part I - A discussion of principles
J. Hydrol.
Thermal properties of two organic (peat, pine bark) and two inorganic (perlite, clay) horticultural substrates
Catena
Measurement of thermal conductivity of buffer materials and evaluation of existing correlations predicting it
Nucl. Eng. Des.
How to evaluate models: Observed vs. predicted or predicted vs. observed?
Ecol. Model.
Study of thermal properties of a basaltic clay
Geo-Frontiers
Effect of compaction pressure and water content on the thermal conductivity of some natural clays
Clay Clay Miner.
Heat Conductivity of Buffer Materials
Mineralogy, porosity and fluid control on thermal conductivity of sedimentary rocks
Geophys. J. Int.
Measurement of soil thermal properties with a dual-probe heat-pulse technique
Soil Sci. Soc. Am. J.
Soil Physics with BASIC: Transport Models for Soil-Plant Systems
Probe for measuring soil specific heat using a heat-pulse method
Soil Sci. Soc. Am. J.
The effective stagnant thermal conductivity of porous media with periodic structures
J. Porous Media
An empirical model for the thermal conductivity of compacted bentonite and a bentonite–sand mixture
Heat Mass Transf.
Emerging trends in expansive soil stabilisation: A review
J. Rock Mech. Geotech. Eng.
Measurement and Modeling for Thermal Conductivity of Geomaterials
Soil heat and water flow with a partial surface mulch
Water Resour. Res.
A generalized thermal conductivity model for soils and construction materials
Can. Geotech. J.
A global high-resolution data set of soil hydraulic and thermal properties for land surface modeling
J. Adv. Model. Earth Syst.
A nonstationary method for determining thermal conductivity of soil in situ
Soil Sci.
The Thermal Conductivity of Soil
Thermal properties of soil
Thermal properties of peaty soils: Effects of liquid-phase impedance factor and shrinkage
Vadose Zone J.
Soil thermal and hydrological characteristics in designing underground cables
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