Fractal dimension, lacunarity and succolarity analyses on CT images of reservoir rocks for permeability prediction

An explicit relationship between seepage properties and microscopic structure of porous media is being sought for the development of oil and gas resources. An effective method to accurately characterize and quantify the microscopic structure of porous media is a key issue. Fractal geometry can take advantage of several physically-based parameters to analyze microstructures of reservoir rocks. In this study, three fractal structural parameters, fractal dimension, lacunarity and succolarity, were employed to characterize scale-invariant complexity, heterogeneity, and anisotropy of rock microstructures, respectively. Twelve three-dimensional digital cores of sandstone reservoir rocks were used to evaluate permeability in terms of fractal dimension, lacunarity and succolarity. The parameters were utilized to quantitatively characterize differences in core micro-structure and predict their effects on permeability. Due to the confounding influence of porosity, the fractal dimension was not an accurate predictor of the variation in permeability on its own. Instead, the results reveal that lacunarity and succolarity were better able to predict differences in structure and permeability. Succolarity, in particular, showed an exponential relationship with permeability, yielding a coefficient of determination of 0.940. Using a combination of fractal structural parameters in the place of pore-size distribution, can provide a better explanation of the relationship between fluid flow, and the heterogeneous structure and anisotropic physical properties of reservoir rocks.