Investigations On Stress-Dependent Thermal Conductivity Of Fractured Rock By Fractal Theory

Stress field is a key external factor affecting the thermodynamic properties of rock in many scientific and engineering fields ranging from geoscience to practical problems in geothermal resources, oil and gas exploitation, mineral exploitation, etc. In this work, the stress-dependent models for the effective thermal conductivity of fractured rock are proposed by combining the fractal geometry theory and the two-part Hooke’s model. The proposed model for the effective thermal conductivity is a function of the effective stress and structure-parameters and physical parameters of fractured rock, such as porosity (ϕσ), fracture orientations (𠜃 and φ) as well as ks and kf. The results show that thermal conductivity increases nonlinearly with increasing stress at low stress range due to the closure of fractures, then, it exhibits an almost linear behavior of pressure dependence at high stress range for most fractures closing completely. The proposed thermal conductivity model coupled with stress is evaluated by comparison with the available experimental data. The model predictions show a good agreement with the available experimental data. A more detailed investigation of the essential influence of structures parameters of a set of fractures on the dimensionless stress-dependent thermal conductivity is performed. The proposed model may provide a good quantitative understanding of the stress effect on thermal conductivity of fractured rock.