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

Abstract

Different numerical models can be deployed to calculate the matrix thermal conductivity of a rock from the bulk thermal conductivity (BTC), if the effective porosity of the rock is known. 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 1.0–6.5Wm−1K−1. 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%.