Evaluation of thermal conductivity temperature corrections applied in terrestrial heat flow studies

Abstract

We collated 117 sets of temperature-dependent thermal conductivity measurements on minerals and rocks for the purpose of evaluating the comparative accuracy of different types of temperature corrections commonly applied in terrestrial heat flow studies. Data used consisted of measurements on 10 minerals, 59 igneous rocks, 19 sedimentary rocks, and 29 metamorphic rocks with a thermal conductivity range from 1.4 to 9.0 W/m-K at room temperature (20-25°C). The data set included thermal conductivites measured at temperatures from 0 to 500°C. When accuracy was bench-marked against the entire data set, corrections proposed by Sekiguchi [1984], Somerton [1992], Sass et al. [1992], Funnell et al. [1996], and Chapman et al. [1984] were found to have mean absolute relative errors of 6.9%, 7.7%, 8.5%, 14.2%, and 17.6%, respectively. The correction proposed by Somerton [1992] was found to have the lowest mean absolute relative error for minerals (11.3%) and sedimentary rocks (6.5%), while the correction proposed by Sekiguchi [1984] was-found to have the lowest mean absolute relative error for igneous (5.4%) and metamorphic rocks (4.9%). The correction schemes were also found to differ in their systematic errors. Corrections proposed by Sekiguchi [1984], Somerton [1992], Sass et al. [1992], Funnell et al. [1996], and Chapman et al. [1984] were found to have mean relative errors of -3.3%, +2.6%, -5.8%, -11.0%, and +15.5%, respectively. Most of the temperature-dependent thermal conductivity data used to evaluate correction schemes were measurements on air-saturated rocks; however, the invariance of the relative rankings with respect to rock porosity suggests the rankings may be valid with respect to in situ conditions.