A Mineralogical Model for Thermal Transport Properties of Rocks: Verification for Low-Porosity, Crystalline Rocks at Ambient Conditions. (20th February 2023) - Merriman, Jesse D; Whittington, Alan G; Hofmeister, Anne M
Abstract: Thermal conductivity ( K ) describes the response of matter to temporal or spatial variations in temperature ( T ). To quantify the effect of varying mineralogy on heat transport of rocks, an accurate (±2%) contact-free heat transfer method was applied at ambient T to multiple sections from 33 different low porosity, continental, igneous and metamorphic rocks. Thermal diffusivity ( D heat ) was measured using laser-flash analysis, which was previously used to construct our large mineralogical database and which mitigates spurious radiative transfer found in other techniques. These measurements constrain K, because K is the product of D heat with the known (or calculable) properties of density and specific heat measured at constant pressure ( P ). Compositions, proportions, and orientations of minerals, plus rock density, average grain-size ( L ), and porosity were characterized for 61 sections from 29 silicate rocks plus 5 sections from 3 marbles. Our database was used to evaluate component summation (averaging) formulae that were recently developed by considering Fourier's laws, and to quantify the dependence of K and/or D heat on key rock descriptors. We found that: (1) phase proportions and compositions are the main cause of variations; (2) minor porosity and foliation have minor effects; and (3) within ~5%, isotropic rocks follow D heat  = ½{[Σ( f i / D i )] −1  + Σ (f i D i )} where f i is volumetric mineral fraction, analogous to the Voigt-Reuss-Hill average for elastic moduli. Using this formula predictively depends on the accuracy of f i and D i . Quartzo-feldspathic rocks can be described by a new formula that uses only quartz fraction and plagioclase composition. Combining our mineralogical model with a universal formula for D heat ( T ) and a thermodynamic identity for K ( P ) accurately constrains conductive thermal transport for Earth's low porosity, crystalline rock layers.