Scale dependency of anisotropic thermal conductivity of heterogeneous geomaterials

Abstract

The precise determination of subsurface thermal properties is critical for ground-source heating systems. The geomaterials are inherently heterogeneous, and their thermal conductivity measured in laboratory and field tests often exhibits anisotropic behaviours. However, the accurate measurement of thermal responses in geomaterials presents a challenging task due to the anisotropy’s variation with the observed scale. Hence, a numerical method is developed in this work and illustrated by taking a typical anisotropic structure of geomaterials with the porosity of 0.5 as an example. The differences in data from laboratory measurements and field tests are discussed to explore the scale effect on anisotropic thermal properties. A series of simulation tests are conducted on specimens with varying dimensions using the finite element method. Results indicate that the thermal properties show a substantial sensitivity to the observation scale, the variation of which decreases with the sample dimensions. By comparing in situ data and laboratory results, the values of average thermal conductivity and corresponding anisotropy ratio are lower than those at small scales, indicating that careful consideration should be given to the thermal properties to account for heterogeneity and anisotropy. In addition, four upscaling schemes based on the averaging method are discussed. This study sheds light on the gap between the laboratory results and the field’s inherent properties and provides guidelines for upscaling small-scale results to field-scale applications.