Evaluation of common mixing models for calculating bulk thermal conductivity of sedimentary rocks: Correction charts and new conversion equations

Abstract

Vice versa, using these parameters, the BTC can be determined for saturation fluids of different thermal conductivity (TC). In this paper, the goodness-of-fit between measured and calculated BTC values of sedimentary rocks has been evaluated for two-component (rock matrix and pores) models that are used widely in geothermics: arithmetic mean, geometric mean, harmonic mean, Hashin and Shtrikman mean, and effective-medium theory mean. The examined set of samples consisted of 1147 TC data in the interval 1.0 to 6.5 W/(mK). The quality of fit was studied separately for the influence of lithotype (sandstone, mudstone, limestone, dolomite), saturation fluid (water and isooctane), and rock anisotropy (parallel and perpendicular to bedding). From the studied models, the geometric mean displays the best, however not satisfying correspondence between calculated and measured BTC. To improve the fit of all models, respective correction equations are calculated. The "corrected" geometric mean provides the most satisfying results and constitutes a universally applicable model for sedimentary rocks. In addition, the application of the herein presented correction equations allows a significant improvement of the accuracy of existing BTC data calculated on the basis of the other mean models. Finally, lithotype-specific conversion equations are provided permitting a calculation of the water-saturated BTC from data of dry-measured BTC and porosity (e.g., well log derived porosity) with no use of any mixing model. For all studied lithotypes, these correction and conversion equations usually reproduce the BTC with an uncertainty < 10%.

Geothermal investigations in western Anatolia using equilibrium temperatures from shallow boreholes

“…Measurements were made on surface outcrops under dry conditions, so they had to be corrected for wet conditions. The geometric mixing model was applied for the porosity correction (Fuchs et al, 2013). For porosities of sedimentary rocks, the values reported by Fuchs et al (2013) were used.…”

“…The geometric mixing model was applied for the porosity correction (Fuchs et al, 2013). For porosities of sedimentary rocks, the values reported by Fuchs et al (2013) were used. For volcanic and metamorphic rocks, porosity values of 5 and 4 % were used, respectively (JICA, 1987).…”

Tracking the thermal properties of the lower continental crust: Measured versus calculated thermal conductivity of high-grade metamorphic rocks (Southern Granulite Province, India)

“…Several attempts have been made in the past to calculate the TC of rocks indirectly from its mineral composition (e.g., Birch and Clark, 1940;Beck and Beck, 1965;Horai and Baldridge, 1972;Brigaud and Vasseur, 1989;Pribnow and Umsonst, 1993;Jessop, 2013;Fuchs et al, 2013). All these approaches, however, were confronted with various shortcomings.…”

Surface heat flow and lithosphere thermal structure of the Rhenohercynian Zone in the greater Luxembourg region

“…Isooctane saturation was applied to claystone and marlstone, to avoid clay swelling (Fuchs et al, 2013).…”

“…The TC of saturating fluids ( = 0.025 W m -1 K -1 for air, 0.095 W m -1 K -1 for isooctane and 0.604 W m -1 K -1 for water at room temperature) was taken according to Fuchs et al (2013). The median, mean and range of TC for the different Palaeozoic and Mesozoic lithotypes are given in Table 4.…”