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.