Well-log based prediction of thermal conductivity of sedimentary successions: a case study from the North German Basin

Data on rock thermal conductivity (TC) are important for the quantification of the subsurface temperature regime and for the determination of heat flow. If drill core is not retrieved from boreholes and thus no laboratory measurement of TC can be made, other methods are desired to determine TC. One of these methods is the prediction of TC from well logs. We have examined the relationships between TC and standard well-log data (gamma ray, density, sonic interval transit time, hydrogen index and photoelectric factor) by a theoretical analysis and by using real subsurface data from four boreholes of the North German Basin. The theoretical approach comprised the calculation of TC from well-log response values for artificial sets of mineral assemblages consisting of variable contents of 15 rock-forming minerals typical for sedimentary rocks. The analysis shows different correlation trends between TC and the theoretical well-log response in dependence on the mineral content, affecting the rock matrix TC, and on porosity. The analysis suggests the development of empirical equations for the prediction of matrix TC separately for different groups of sedimentary rocks. The most valuable input parameters are the volume fraction of shale, the matrix hydrogen index and the matrix density. The error of matrix TC prediction is on the order of 4.2 +/- 3.2 per cent (carbonates), 7.0 +/- 5.6 per cent (evaporites), and 11.4 +/- 9.1 per cent (clastic rocks). From the subsurface data, comprising measured TC values (n = 1755) and well-log data, four prediction equations for bulk TC were developed resembling different lithological compositions. The most valuable input parameters for these predictions are the volume fraction of shale, the hydrogen index and the sonic interval transit time. The equations predict TC with an average error between 5.5 +/- 4.1 per cent (clean sandstones of low porosity; Middle Buntsandstein), 8.9 +/- 5.4 per cent (interbedding of sandstone, silt- and claystones; Wealden), and 9.4 +/- 11 per cent (shaly sandstones; Stuttgart Fm.). An equation including all clastic rock data yields an average error of 11 +/- 10 per cent. The subsurface data set also was used to validate the prediction equation for matrix TC established for clastic rocks. Comparison of bulk TC, computed from the matrix TC values and well-log porosity according to the geometric-mean model, to measured bulk TC results in an accuracy <15 per cent. A validation of the TC prediction at borehole scale by comparison of measured temperature logs and modeled temperature logs (based on the site-specific surface heat flow and the predicted TC) shows an excellent agreement in temperature. Interval temperature gradients vary on average by <3 K km(-1) and predicted compared to measured absolute temperature fitted with an accuracy <5 per cent. Compared to previously published TC prediction approaches, the developed matrix and bulk TC prediction equations show significantly higher prediction accuracy. Bulk TC ranging from 1.5 to 5.5 W (m K)(-1) is always predicted with an average error <10 per cent relative to average errors between 15 and 35 per cent resulting from the application to our data set of the most suitable methods from literature.