Reconstruction of elastic properties and thermal conductivity of solid materials from their small fragments

Abstract

The absence of direct measurement of physical properties on the rock cuttings necessitates the use of theoretical approaches. One of the most promising is the use of methods of effective medium theory. In this work we apply the generalized singular approximation of effective medium theory to solve this problem. We construct a parametric mathematical model of effective physical properties of a composite material made from rock cuttings to link the effective properties of the composite material with its compositional and microstructure parameters. The list of unknown parameters includes those characterizing the elastic and thermal properties of rocks. We develop a technique for manufacturing the composite samples that are compacted mixtures of fine-grained wax and rock cuttings. We propose a method to restore the velocities of elastic waves (compressional and shear) and thermal conductivity of rocks from experimental data on the respective physical properties of composites based on the constructed model. This method is tested on fifteen composite samples made from four rocks of different types (two sandstones, quartz glass and white marble). The theoretical values characterizing the elastic and thermal properties of rocks are compared with respective experimental data obtained in independent experiments performed for these rocks. The average difference in the elastic wave velocities and thermal conductivity does not exceed 10%, whereas the maximum difference in the respective properties varies from 14 to 23%.