Best thermal conductivity model for granitoids

Granitoid is an important part of the upper continental crust, and therefore its thermal conductivity (l) plays an important role in understanding the lithospheric thermal structure in a region and for geotechnical or geoengineering purposes. In above context, due to the lack of thermal conductivity data or absence of proper sample for its measurements, thermal conductivity values are assumed which can lead to erroneous results. In such scenario, when direct measurements are not possible, thermal conductivity can be estimated by indirect methods with proper precautions.


An attempt is made here first time in systematic way to arrive at the best mixing model for granitic rocks by comparing deviation between the measured values in the laboratory and calculated values from mineralogy of rocks. The considered mean models are: (i) arithmetic, (ii) geometric, (iii) harmonic, (iv) effective, (v) Voigt-Reuss-Hill and (vi) Hashin-Shtrikman along with its lower and upper bound. Thermal conductivity is calculated by using a percentage of various minerals in the rock and thermal conductivity of the individual minerals. Studied rocks are potassic granitoid (PG), biotite granitoid (BG), sodic granitoid (GG) and gneisses (BnG) from the Bundelkhand craton, central India.


Thermal conductivity is measured in the laboratory on 21 samples using the steady-state method. Data show wide variations in thermal conductivity values for granitoids (PG: 2.7−3.2, BG: 2.6−2.9, GG: 2.9−3.0 Wm1 K1) and gneisses (2.9−3.7 Wm1 K1). Mineralogical percentage of the rocks is determined using petrological and geochemical data through modal analysis and normative (CIPW-NORM) methods. Different mean model shows following order with measured thermal conductivity for both the methods:


λmea ∼ λHM < λLHS < λGM < λVRH < λEffMean < λHS < λUHS < λAM


Among all models, calculated thermal conductivity by Harmonic mean model shows satisfactory agreement (Figure 1). The deviation is −10.9 to 17.6% by using modal analysis method and −16.1 to 11.5% by using NORM method.


Therefore, we suggest that, in the case of non-availability of the proper sample for direct measurement, the thermal conductivity of very low porous granitoids could be satisfactorily determined by assessing their modal mineralogy and considering the harmonic mean model with mean mineral thermal conductivity (Figure 2).


Figure 1: Bivariate plots showing calculated thermal conductivity (λcal) versus measured thermal conductivity (λmea) with various mean models considering mean mineral thermal conductivity using modal analysis data.


Figure 2: Plot showing calculated harmonic mean thermal conductivity (λHM) versus measured thermal conductivity (λmea) for the studied rocks. λHM shown by three different symbols are determined by considering minimum, mean and maximum mineral thermal conductivity.



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Nishu Chopra, Labani Ray, Manavalan Satyanarayanan, R. Elangovan. Evaluate best-mixing model for estimating thermal conductivity for granitoids from mineralogy: A case study for the granitoids of the Bundelkhand craton, central India, Geothermics, 75, 1-14, 2018.