Figure 8. PCA analysis of Berea Sandstone. (A) Porosity and number of cluster graph vs. threshold value plot, (B) PCA image, (C) Histogram of cluster-size distribution, and (D) photograph of sample (blue line indicates the FOV).
Cluster analysis was also performed on the non-fractured Indiana limestone sample. Figure 9 shows a porosity and number of clustervs . threshold plot. The valleys are present at the threshold values of 0.60 and 0.80, indicating where the sample is the most connected. In this analysis, a porosity of 0.1477 was calculated at a threshold value of 0.60. This porosity is similar to the measured gravimetric porosity of 0.173 with a deviation of 14.8% (Table 3). The cluster valley at the threshold value 0.60 (Figure 10A) is indicative of the entire pore system, including small pores, and vugs (dissolution pores). Whereas, the secondary valley (threshold 0.80, Figure 10B) represents higher proton density areas, such as vugs, which do not include the smaller pores. As seen in Figure 10B, the vugs have been isolated, not only from the smaller pores, but also from one another, as the threshold values for the bulk of the small pores have been put outside of the range of interest. These vugs are the connection between groups of smaller pores. Because the vugs have larger water volumes and tend to be space apart through the sample, compared to the small pores and throats in the Berea sample, they fall within the threshold limits and are discernable from one another. Higher connectivity is observed in spite of some of the pores and pore throats being below the resolution limits, as seen by Figure 3B, leading to the conclusion that this sample is dominated by the vug system. Figure 3B also shows that a majority of the porosity is contained in the larger vugs, therefore confirming that this sample is dominated by the vugs. Therefore, this sample is reliably characterized with this workflow, showing relatively higher connectivity when compared to other samples.