Thermal conductivity of unconsolidated sediments with geophysical applications

A theoretical model for the prediction of the thermal conductivity of unconsolidated granular sediments, with application to sand shale mixtures, is presented. The sediment is modeled as an assemblage of grains of thermal conductivity 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 relationship between the effective thermal conductivity of the isotropic mixtures of grains saturated by the pore fluid, the porosity, and the thermal conductivities of the grains and pore fluid. The influence of the topology of the interconnected pore space is accounted for through the use of the electrical cementation exponent m, which is related to the electrical formation factor 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. This assumption holds well for unconsolidated sand shale mixture sediments as demonstrated by comparing the model to available experimental data. The model offers the possibility to derive thermal conductivity profiles from downholes measurements of natural radioactivity, electrical resistivity, and bulk density.