The Multiscale Pore Connectivity Network via Scaling Relationship Derived from a Sandstone Image

Abstract

This paper presents a study on a multiscale pore connectivity network derived from a sandstone image. We first convert a grayscale sandstone image into pore and grain regions. The binary pore-grain image is transformed into multiscale pore by performing morphological opening operations with increasing structuring element size. A pore connectivity network (PCN), which is a skeleton network that describes the structure of pore space from multiscale pore-grain images, is extracted. The PCN can be computed by using morphological transformations with reference to three different probing rules (in the form of octagon, square, and rhombus). It is observed that the length of multiscale PCN varies with the number of opening transformations. This is due to the fact that the intricacy of the pore image is reduced with the increasing cycle of opening transformations. Next, we estimate the fractal dimensions of these multiscale PCNs using box-counting method. The values obtained follow universal power-law relationships. We further analyze the relationship of multidimensional opening in quantitative manner. A rescaled formula based on the linearity of decreasing fractal dimension values of pore space is proposed. This technique is applied to estimate the fractal dimensions of a sequence of multi-dimensional sandstone image generated by morphological opening.