INFLUENCE OF TEMPERATURE ON THERMAL CONDUCTIVITY, THERMAL CAPACITY AND THERMAL DIFFUSIVITY FOR DIFFERENT TYPES OF ROCK

Abstract

Thermal modeling down to great depth, e.g. down to the Mohorovicic discontinuity, requires representative values of thermal conductivity and thermal capacity at an appropriate depth. Often there is a lack of data, especially concerning temperature and pressure dependence of thermal conductivity and thermal capacity, due to missing or questionable data from boreholes. Studies of the temperature and pressure dependence of thermal conductivity and thermal capacity showed that temperature is dominating. Thus measurements on a set of magmatic, metamorphic and sedimentary rocks sampled from different depth levels of the Eastern Alpine crust were used to obtain an estimate of the temperature dependence of both properties––at least for the area of investigation––and to give a review of the temperature dependence of thermal conductivity (λ), thermal capacity (ρ×cp) and thermal diffusivity (κ) for different types of rock.The temperature dependence of thermal conductivity for crystalline (magmatitic and metamorphic) rocks is different to that of sedimentary rocks. Using the approach that the thermal resistivity (1/λ) is a linear function of temperature whose slope increases with λ(0), the conductivity at a temperature of 0 °C, two general equations were determined. The equation for crystalline rocks was verified in the temperature range of 0–500 °C and the equation for sedimentary rocks was tested in the temperature range from 0 to 300 °C. A general equation for the temperature dependence of λ for Eastern Alpine rocks can thus be formulated:with empirical constants and corresponding uncertainties a=0.0030±0.0015 and b=0.0042±0.0006 for crystalline rocks. The constants for corresponding sedimentary rocks are a=0.0034±0.0006 and b=0.0039±0.0014. λ is given in W m−1 K−1, T in °C.At ambient conditions thermal diffusivity (κ) and thermal conductivity (λ) for Eastern Alpine crystalline rocks show the relationship:κ=0.45×λ.