A Fractal Pore-Scale Model Of Stress-Dependent Thermal Conductivity In A Rectangular Cross-Section Tree-Like Microfracture Network

Stress is an important external element influencing effective thermal conductivity (ETC). However, previous theoretical investigations of stress-dependent effective thermal conductivity have used a simplified parallel plate model, overlooking the complex structure of rock fracture networks. Therefore, this paper establishes a new fractal model for the stress-dependent ETC of a rectangular cross-section tree-like microfracture network. The model derives a constitutive equation between the stress-dependent ETC and the microscopic geometry structural parameters of the microfracture network. The model’s validity is confirmed by the error of less than 0.291% between the theoretical predictions and the experimental data. The influence of geometry structural parameters of the microfracture network (length ratio, width ratio, height ratio, angle, total number of branches and ratios of soft part, hard part, etc.) on the ETC under the low-stress state has been analyzed. It was discovered that the soft part of the rock microfracture network has the most impact on ETC. The fractal pore-scale model clarifies heat transfer mechanism in rock microfracture network under effective stress, with each parameter physically defined and independent of empirical constants.