Temperature dependence of the relationship of thermal diffusivity versus thermal conductivity for crystalline rocks

Abstract

Thermal diffusivity governs the transient heat transport equation. Thus, a realistic characterisation of this parameter and its temperature dependence is crucial for geothermal modelling. Due to sparse information from boreholes, lack of samples, and elaborate measurement procedures, there is often insufficient data on thermal diffusivity at elevated temperatures. We make use of existing data on crystalline (metamorphic and magmatic) rock samples from the Kola Peninsula and the Eastern Alps and develop a general relationship for the temperature dependence of thermal diffusivity up to 300°C. The temperature dependence of thermal conductivity is parameterised itself, using an empirical relationship which is set up for both data sets as well. Hence, only thermal conductivity at ambient temperatures is required for determining the temperature dependence of thermal diffusivity. We obtain different coefficients for both data sets which can be explained by different geological settings, and therefore different mineral compositions and internal structures. Comparisons with other expressions for these rock physical parameters show a good agreement at ambient conditions. General relations for thermal diffusivity at elevated temperatures are rare. A comparison of our results with data from two crystalline samples from the KTB and data from the Southern Indian Granulite Province highlights the need for further data, which will help to quantify uncertainties.