3D Digital Rock Modeling of the Fractal Properties of Pore Structures

Fractal parameters of porous media have been a focus of study in petroleum engineering and hydrogeology for several decades because they provide an effective way to describe the complexity of pore structure across a wide range of scales. This paper combines 3D process-driven digital rock modeling with fractal analysis in order to understand the effect of varying sorting, compaction, cementation, and the fine grain fraction of binary models on the fractal parameters and specific surface area of porous media. Digital rock models (DRMs) were constructed to simulate sandstone using a process-driven modeling technique which simulates sedimentation. The fractal parameters of the resulting pore geometry were calculated using the box-counting method on 2D and 3D representations of the DRMs. Our simulations indicate that increasing compaction or cementation lead to significant decreases in fractal dimension, specific surface area (SSp) and porosity, showing that these two diagenetic processes can affect the pore microstructure of the rock significantly. While interface fractal dimension (Di) and SSp both increase slightly with decreases in sorting (grain size variety), and porosity decreases slightly. Examining the behavior of binary models, the porosity of our digital models shows a V-shaped curve as fine grain fraction increases from 0 to 1, consistent with, but higher than the theoretical values, which we attribute to incomplete packing of the grains arising from the simplified packing algorithm and finite boundary of models. The value of both SSp and Di increase as the fine grain fraction increases. However, we must notice that the porosity may be underestimated, and the fractal dimension may be overestimated when we use models consisting of very fine spherical grains due to the effect of image resolution.