Figure 14: Fractured Indiana Limestone cluster analysis at threshold values: (A) 0.30, (B) 0.60, (C) 0.70, and (D) 0.80 that correspond to cluster valleys found in Figure 14.
The fractured Madison Limestone does not behave significantly different from its counterpart shown in Figure 12. The non-fractured Madison Limestone sample has cluster valley thresholds of 0.35, and 0.55, compared to the fractured sample with cluster valley thresholds at 0.35 and 0.60 in Figure 13B. The threshold value of 0.35 is constant between the non-fractured and the fractured sample, meaning that the high connectivity that was previously observed held constant between the samples. The up shift from threshold 0.55 to 0.60 is significant because there is now more water in the fracture, which appears to be a part of the same threshold range and the vugs. The threshold value 0.60 (Figure 15B) indicates that this sample is more connected than its counterpart (threshold 0.55) in Figure 12B. Evidence of this is provided by the histograms associated with the images, since Figure 12B shows 9 clusters while Figure 15B has 7 clusters. The cluster sizes are also different. The biggest cluster in Figure 15B is significantly larger than the largest cluster in Figure 12B, by a four fold. This can be interpreted to mean that the fracture falls in the same threshold value range as the vugs, and connects not only the entire sample, but also specifically the vugs. This is anticipated, because water is closer to bulk behavior given similar feature sizes of vugs and fractures in this case.