An improved model for permeability estimation in low permeable porous media based on fractal geometry and modified Hagen-Poiseuille flow

Permeability is a crucial macroscopic parameter in characterizing fluid flow and mass transfer behavior in porous media. A great theoretical basis for permeability estimation has been provided by many traditional and recently presented fractal models. However, since the influence of overlying sediments, the low-permeability porous media such as natural rock and coal generally have lower permeability and porosity with abundant pores which have more complex structure and rougher surface. The fluid located at surface tends to be bound to form irreducible state. Generally, this natural phenomenon is often ignored in the conventional fractal permeability model. In this study, the improved model was theoretically deduced based on the fractal geometry theory with considering the irreducible water saturation. 133 total sandstone samples from a gas reservoir were used to verify the validity of the developed model. The mercury injection experiment and the conventional physical property test were carried out, and the thin section image of each sample was crafted. The pores were segmented by the proposed color extracted algorithm for calculating pore fractal dimension. The results show that the available fractal model overestimates permeability values. A new form of the classical Kozeny-Carman equation was also developed to accurately estimate permeability. In the low permeable porous media, the empirical Kozeny-Carman constant needs to take 3.5, instead of 5. However, no longer is typical superiority found at very low permeability (< 0.5 mD) in the improved fractal model and corresponding reasons are analyzed and discussed.