A stress-dependent fractal model for predicting the effective thermal conductivity of porous rocks with elliptical pore

Abstract

The diverse pore morphologies of porous rocks make it challenging to quantitatively characterize the intrinsic mechanisms of the effective thermal conductivity (ETC) under stress conditions. However, previous fractal theory studies on the transport properties of stress-dependent porous rocks with elliptical cross-sections of adjustable aspect ratios have mainly focused on the permeability, with less attention given to the effective thermal conductivity. Therefore, this paper establishes a novel fractal model for the stress-dependent ETC in porous rocks that employs elliptical cross-sections with adjustable aspect ratios. The model derives the relationship between the stress-dependent ETC and pore structure parameters. The model's validity is confirmed by the error of only 2.83 % between the theoretical predictions and the experimental data. The parameter sensitivity analysis indicates that the ETC of stress-sensitivity porous rocks is related to the capillary initial fractal dimension, capillary initial aspect ratio, initial porosity, Young's modulus, and Poisson's ratio. It is discovered that Young's modulus of the porous rocks has the greater impact on ETC, showing a negative correlation with it. The fractal model clarifies heat transfer mechanisms porous rocks with elliptical pore under effective stress, with each parameter physically defined and independent of empirical constants.