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Abstract:
The thermal conductivity (TC) of a rock is, in collaboration with the temperature gradient, the basic parameter to determine the heat flow from the Earth interior. In addition, it forms the input into models targeted on temperature prognoses for geothermal reservoirs at those depths not reached by boreholes yet. Thus, the parameter is paramount in geothermal exploration and site selection.
Most commonly, TC of a rock is determined in the laboratory on samples that are either dry or water-saturated. In special situations (e.g. for mudstones/shales), preferred saturating fluids are isooctane or other alkanes. The saturation of rock samples gets increasingly important for those rocks exposing high porosity as the bulk TC (BTC) of a rock is positively correlated with its pore content. Because sample saturation is time-consuming, it is desirable, especially if large numbers of samples need to be assessed, to develop an approach that quickly converts dry-measured BTC into the respective saturated value without applying the saturation procedure.
Different petrophysical models can be applied to calculate the matrix TC (MTC) of a rock from the BTC and vice versa, if the effective porosity is known. (e.g. from well logging data) and the TC of the saturation fluid (e.g. gas, oil, water) is considered. We have investigated the performance of two-component (rock matrix, porosity) models that are widely used (arithmetic mean, geometric mean, harmonic mean, Hashin and Shtrikman mean, and effective medium theory mean) for a large suite of different sedimentary rocks. The sample set consisted of 1147 single data from three different sedimentary basins (North German Basin, Molasse Basin, Eastern Levantine Basin) encompassing four lithotypes with BTC in the range between 1.0 and
6.5 W m-1 K-1. The quality of fit between measured (laboratory) and calculated BTC values 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). The geometric mean model displays the best, however not satisfying correspondence between calculated and measured BTC. Correction equations are calculated based on the statistical data to improve the fit of the models. The application of the presented correction equations allow a significant improvement of the accuracy of BTC data calculated. However, the “corrected” geometric mean constitutes the only model universally applicable to different types of sedimentary rocks and, thus, is recommended for the calculation of BTC. The statistical analysis also resulted in lithotype-specific conversion equations, which permit a calculation of the water-saturated BTC from dry-measured TC. This approach has the advantage that the saturated BTC could be calculated quickly without application of any mixing model. The expected errors with this approach are in the range between 5 and 10 % (Fuchs et al., 2012).
Fuchs, S., Schütz, F., Förster, H.-J., Förster, A. (2012). Evaluation of mixing models for calculating bulk thermal conductivity of sedimentary rocks: correction charts and new conversion equations. Geothermics, under review.
