Fractal characteristics based on different statistical objects of process-based digital rock models

Abstract

Fractal characteristics of porous media have been a focus of research in geosciences for several decades and measuring fractal dimensions has become a common method to describe the structural properties of porous media. In this paper, the fractal dimensions of solid phase, pore phase and interface between them are studied by box counting method based on digital rocks. The process-based modeling technique is utilized to construct models with different pore structure firstly, which includes four kinds: grain-size contrast, grain-size variety, compaction and cementation. Then the fractal dimensions of solid, pore and interface of these models are calculated and analyzed using box counting method through different statistical objects. Finally, the fractal dimensions of real digital rocks are calculated, and the relationship between fractal dimensions and rock properties such as pore structure, porosity and permeability is qualitatively analyzed. The research results indicate that only the interface fractal dimension can better distinguish and characterize the pore structure of process-based digital rock models with slight variation in porosity. On the other hand, if porosity of these models varies significantly, both pore fractal dimension and interface fractal dimension are available to distinguish and represent pore structure well, and pore fractal dimension is more sensitive and active to the change of pore structure and porosity. When using fractal dimensions to represent and analyze pore structure of real rocks, the fractal dimensions of pore and interface should be considered comprehensively. Furthermore, the interface fractal dimension is better than the pore fractal dimension in characterizing the pore structure of some sandstone digital rocks.