A framework to obtain the formulas of the conductivity and aperture of rough fractures under thermohydromechanical conditions

In this investigation, a framework is proposed to find the equations to describe the fracture conductivity and fracture aperture as the functions of effective stress (the difference between geo-stress and fluid pressure), temperature difference (the difference between rock temperature and fluid temperature), and the rock mechanical properties. The framework consists of several lab experiments and a numerical model, which is time-saving to study the influences of the aforementioned influential factors on the fracture conductivity and aperture. After analyzing the lab experimental data, we find that it’s almost impossible to accurately measure the fracture aperture even with high-precision displacement sensors. Therefore, the numerical model coupling the fluid flow in the rough fracture, the solid deformation, and the heat transfer between the hot rock and the injected fluid is built. Three different distributions of the fracture surfaces are analyzed, and we find that the fracture surface roughness fits the normal distribution. After the data matching between the lab experimental data and the numerical results, a large number of numerical experiments using the numerical model are carried out to study the influences of the effective stress, temperature difference and the rock properties, including the elasticity and Poisson's ratio. When fitting the single variable analysis results, we find that the fracture conductivity and aperture are in different function forms of the aforementioned factors. But the reduction of fracture aperture and the natural logarithm of the normalized fracture conductivity can be described using the binary linear function of the effective stress and the temperature difference. Two key strengths of the research lie with the fact that it is time-saving to obtain the exact formulas of fracture conductivity and fracture aperture, and it can measure the dynamic fracture aperture accurately.