An effective thermal conductivity model of rocks considering variable saturation and pore structure: Theoretical modelling and experimental validations

Abstract

The effective thermal conductivity (ETC) of rocks is crucial for many geological and engineering applications and projects. In this study, a three-component ETC model was proposed, which includes seven parameters, that are, the thermal conductivities of water (λw), gas (λg) and solid phase (λs), the porosity (φ), the coefficient of shape factor (n), the weighted harmonic parameter (η) and saturation degree (Sr). The methods to establish the parameters of the proposed model were described with validation carried out using several experiments including X-ray diffraction (XRD) test, porosity test and thermal conductivity test. Comparisons performed indicated that the new proposed model was flexible enough to reflect the variation of the ETC with saturation degree. Furthermore, the sensitivity analysis and grey correlation analysis were given in examining the effect of the parameters included in the model. The results showed that: 1) The parameter sensitivity analysis and grey correlation analysis of ETC show that the ETC is most sensitive to the thermal conductivity of solid phase (λs), followed by coefficient of shape factor (n), weighted harmonic parameter (η) and saturation degree (Sr), and less sensitive to the porosity (φ). 2) When the pore shape of the porous media is irregular or the thermal conductivity ratio of the continuous phase and discontinuous phase is larger than 100, n is a key parameter that can tremendously influence the value of ETC. 3) Although the change of η does not influence the maximum and minimum values of ETC, it can greatly affect the variation of ETC when 0 < Sr < 1.