Fractal Analysis of the Pore Space in Sandstones as Derived from Mercury Porosimetry and Image Analysis

Abstract

The pore space fractal dimension was measured using a model of a porous body based on the Menger sponge and mercury porosimetry data for selected samples of the reservoir sandstones of the Weglowka oil field (SE Poland) in a pore-throat diameter range between 91 and 0.0090 \(\upmu \)m. Based on the digital analyses of the two-dimensional images of thin sections impregnated with blue-dyed epoxy and taken under an optical microscope as well as the images of thin sections taken under a cold field emission gun scanning electron microscope (FEGSM) in the backscattered electron image mode, the current paper tries to quantify the pore space of sandstones by using the box counting method. The results derived from analysis of the pore-throat diameter distribution by mercury porosimetry revealed the multifractal structure of the pore space of sandstone in two separated ranges of the pore-throat size considerably lesser than the pore-throat diameters (10–50 \(\upmu \)m) corresponding to threshold pressures. This means that only the pore throats connecting wider parts of the pore network (pores) exhibit the fractal structure. The assumption that the fractal dimension monitoring the distribution of the pore-space volume within the smallest pore-throat diameters characterizes the overall pore-throat network in the rock sample provides a device to set apart the distribution of the pore-throat volume from the distribution of the pore volume. On the other hand, the fractal dimensions derived from the image analysis of thin sections describe the pore space as a whole.