Estimating porosity and permeability using Digital Image Analysis (DIA) technique for highly porous sandstones

Abstract

In the present study, 12 theoretical models have been introduced for studying the effect of the grain size and shape on the intergranular porosity, ∅. From the first eight models, it is stated that the grain size has no effect on the intergranular porosity, but it is declared that the smaller the grain size means the smaller the interstitial pore spaces and therefore, the less the ability of the pore spaces to receive finer sediments, then the higher the porosity. On the other hand, studying the present models revealed that the total intergranular porosity decreases when increasing the grain elongation ‘E’ (the length of the grain/the diameter of the grain) as a shape anisotropy parameter. A new equation has been introduced relating the total pore volume to the grain shape/elongation.

$$ \emptyset = 26.188\ {E^{-1 }} + 21.431 $$

The grain sorting of the present models has been studied by adding another group of grains of the critical grain size of occupation inside the pore spaces; the pore volume decreases by about 41.0 % of the total porosity. To check the applicability of the proposed equation, 46 samples of highly porous sandstone have been selected from different places in Egypt and studied petrographically, and their total pore volume have been measured using Digital Image Analysis (DIA) ‘∅ _Im’ and helium injection technique ‘∅ _He.’ Petrographically, the studied samples are quartz arenite and ferruginous quartz arenite. The pore types are mostly characterized mostly as (1) intergranular porosity and rarely as (2) intragranular porosity, (3) vuggy porosity, and (4) fracture porosity. The grain elongation ‘E’ for the present samples has been measured using the DIA technique; it varies from 1.34 to 1.73. Porosity ‘∅ _He’ varies between 25.8 and 34.7 %, gas permeability ‘k’ varies from 0.14 to 6.92 μm² (very good to excellent rank), and the mean pore diameter ‘D’ varies between 3.9 and 25.7 μm (macro to mega pores). The study stated the applicability of the present equation and introduced a number of equations that could be used to calculate porosity, permeability, and pore radius in terms of grain elongation. The applicability of the present study has some limitations due to (1) cementation, (2) microporosity, and (3) fracturing. The effect of cementation can be minimized by processing the grains and the surrounding cement statistically as a bulk ellipsoid unit, whereas the micropores/fractures can be measured by helium injection.