Thermal conductivity of unconsolidated sediments with geophysical applications

A theoretical model for the prediction of the thermal conductivity of uncon solidated granular sediments, with application to sand shale mixtures, is p resented. The sediment is modeled as an assemblage of grains of thermal con ductivity lambda(S) immersed in a pore fluid of thermal conductivity lambda (f). In order to take into account for the thermal interactions between the grains a differential effective medium approach is used to provide a relat ionship between the effective thermal conductivity of the isotropic mixture s of grains saturated by the pore fluid, the porosity, and the thermal cond uctivities of the grains and pore fluid. The influence of the topology of t he interconnected pore space is accounted for through the use of the electr ical cementation exponent m, which is related to the electrical formation f actor F by F = phi(-m), where phi is the interconnected porosity. The main assumption of the model lies in the small contiguity between the grains. Th is assumption holds well for unconsolidated sand shale mixture sediments as demonstrated by comparing the model to available experimental data. The mo del offers the possibility to derive thermal conductivity profiles from dow nholes measurements of natural radioactivity, electrical resistivity, and b ulk density.