AN ANALYTICAL MODEL FOR PORE AND TORTUOSITY FRACTAL DIMENSIONS OF POROUS MEDIA

Accurate characterization of pore-scale structures of porous media is necessary for studying their transport mechanisms and properties. An analytical model for pore and capillary structures of porous media is developed based on fractal theory in this study. The pore and tortuosity fractal dimensions are introduced to characterize the pore size distribution and tortuous flow paths. A power law scaling between fractal probability function and pore diameter is proposed, which can be applied to determine the pore fractal dimension. The explicit expression for tortuosity fractal dimension is derived based on exactly self-similar fractal set and fractal capillary bundle model. The present fractal model has been validated by comparison with that of experiments and numerical simulations as well as theoretical models. The results show that the tortuosity fractal dimension decreases as porosity and pore fractal dimension increase, it increases with the increment of tortuosity. Both the particle shape and pore size range take important effect on the tortuosity fractal dimension under certain porosity. The proposed pore-scale model can present a conceptual tool to study the transport mechanisms of porous media and may provide useful guideline for oil and gas exploitation, hydraulic resource development, geotechnical engineering and chemical engineering.