A STUDY OF THE THERMAL EVOLUTION OF PERMEABILITY AND POROSITY OF POROUS ROCKS BASED ON FRACTAL GEOMETRY THEORY

Abstract

The temperature effect on the permeability of porous rocks continues to be a considerable controversy in the area of reservoirs since the thermal expansion of mineral grains exhibits complicated influence on pore geometries in them. To investigate the degree of effect of pore structures on the hydro-thermal coupling process, a study of the thermal evolution of permeability and porosity of porous rocks is performed based on fractal theory and on thermal as well as stress effects. This work can provide a general physical explanation on some arguments in this area. The proposed models for permeability and porosity can be associated with temperature and the pore-structural parameters as well as physical parameters of porous rocks, such as the initial porosity (${\varphi }_0)$, the initial fractal dimension ($D_{f,0})$, the fractal dimension for tortuosity ($D_{T,T})$ and the thermal expansion coefficient of pore volume (${\alpha }_T)$. The validity of the proposed models for temperature-dependent permeability and temperature-dependent porosity is validated by comparing them with the available experimental results. The investigations are performed in detail considering the essential effects of pore-structural parameters and physical parameters of porous rock on the dimensionless temperature-dependent permeability and temperature-dependent porosity as well as the fractal dimensions for pore areas and tortuosity. It is found that the pore distribution scale range ratio (${\lambda }_{min,T}/{\lambda }_{max,T})$, and pore thermal expansion coefficient (${\alpha }_T)$ have significant effects on the dimensionless temperature-dependent permeability and temperature-dependent porosity of porous rock as well as the fractal dimensions for pore areas and tortuosity. The proposed models may provide a fundamental understanding of the coupled hydro-thermal process of rocks.