# Estimation of Sedimentary Rock Porosity Using a Digital Image Analysis
## 3 Results and Discussion
### Scanning Electron Microscope (SEM) and Pore and Crack Analysis System (PCAS)
Experience shows that different magnifications can lead to different values of porosity [26], and thus caution needs to be taken while estimating the porosity from digital images. The PCAS analysis of the SEM images are given in Figure 9. PCAS first determines the void space and boundaries by examining the grey colour scale (0-255) of the original SEM images (Figure 9a-c). The next stage involves the segmentation quantification and noise removal, producing a set of images (Figure 9d-f) in which the void space can be clearly identified. Comparisons of the images of the three rock specimens suggest that the void distribution in the sandstone and siltstone appears to be more uniform compared to that of the coal. Further image processing (Figure 9g-i) reveals that there is less 'noise' in the sandstone than in the siltstone and coal, and the void space in the coal is more affected by the tensile rupture at the specimen surface. This can be accounted for by the different values of porosity (Table 3) obtained from the experimental procedure (MIP) and estimated by the digital analysis using the PCAS technique. This finding seems to agree with the existing literature [13; 44], which suggests that this discrepancy can be attributed to two main factors: (1) cracks and/or pores caused by the tensile damage at the surface of the specimen, and (2) different magnifications of the processed digital images. Figure 9: Pore and crack analysis system process and tensile damage of sandstone (**a**,**d**,**g**), siltstone (**b**,**e**,**h**), and coal (**c**,**f**,**i**). The results obtained from the experimental MIP procedure and digital analysis of SEM images by the PCAS technique are summarised in Table 3. Figure 10 demonstrates the correlation between the experimental (MIP) and PCAS data obtained for all three rock specimens. The upper and lower boundaries and the median value of multipliers obtained through the analysis of the existing literature (Table 1) are given in this figure as well. The data from this study seem to fit well within the range reported in the literature. The previous data on different types of sandstone and siltstone [24; 27; 31] give a relatively narrow range of multipliers (from 0.94 to 1.21) that can be used to estimate the rock porosity based on the digital image analysis. The results of this study suggest a value of 0.88, which seems to fit reasonably well with the previous research. These consistent results obtained for sandstone/siltstone by different researchers can be due to the mineral composition of these rocks (that is, quartz is the dominant mineral), which is associated with relatively uniform pore space in the micron range. However, there are still some limitations that need to be considered [15; 24; 27]. The first is related to the precision of MIP tests, as it may be challenging to accurately estimate  
Figure 10: Correlations between the porosity values obtained from the image analysis and laboratory experiments for the sandstone, siltstone, and coal. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Rock**} & \multicolumn{3}{c}{**Pore and Crack Analysis System**} & \multicolumn{3}{c}{**Mercury Intrusion Porosimetry**} \\ \cline{2-9}  & \multirow{2}{*}{**No.**} & **Mean** & **Sd** \(\pm\)**(\%)** & **Min** & **Max** \(\pm\)**(\%)** & **Porosity MIP** & **Porosity MIP** & **Porosity MIP Modify** \\ \hline Sandstone & 12 & 10.1 & 1.1 & 8.1 & 11.8 & 12.9 & 8.9 \\ \hline Silstone & 9 & 3.9 & 0.58 & 3.1 & 4.8 & 5.4 & 3.4 \\ \hline Coal & 9 & 7.6 & 2.15 & 5.7 & 10.9 & 19.9 & 9.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the porosity values obtained from the pore and crack analysis system and mercury intrusion porosimetry. the mercury intrusion in the pore space [37; 45]. Second, the pore space and microcracks observed in SEM images may be different from those in reality because the SEM images only identify 2D types of pore space, compared to the 3D pore space obtained from MIP experiments [15; 26].