Figure 7: Side and front views of the 3D reconstruction of (A) and (D)
Berea Sandstone, (B) and (E) Indiana Limestone, and (C) and (F) and
Madison Limestone.
The Berea Sandstone sample was further analyzed using PCA. From the
calculations described earlier, a plot comparing porosity and number of
clusters is generated. In the porosity and number of clusters graph as
functions of threshold values (Figure 8A), a cluster peak (threshold
0.40) is observed, and no apparent cluster valleys are detected. The
cluster peak is observed when the corresponding threshold value
diminishes lower voxel values enough to disconnect the sample. At this
cluster peak the sample is the most disconnected. However, a calculated
porosity of 0.1946, similar to the measured gravimetric value of 0.1800
(Table 3) is found at this threshold value. Ideally, the Berea Sandstone
sample should be completely connected, however, it is possible that the
resolution achieved with MRI cannot account for the small (tens of
microns) throat connections between the pores that dominate this system.
This assessment is supported by the TD-NMR results.
In Figure 3(A-C), the black dotted lines represent the resolution of the
ZTE MRI technique achieved for image collection. As is clear from this
figure, not all the pore-size distributions can be resolved in the
collected images, therefore, the connectivity deduced through MRI will
not always be a true representation. Based on the TD-NMR results, MRI
should allow resolving some of the Berea Sandstone pores, but not the
pore throats. If we consider the Berea Sandstone sample exhibiting total
connectivity (only one cluster) (Figure 8A), as is true for threshold
values 0.05-0.25, then the porosity would be 1.0. However, the
gravimetric porosity of this sample is 0.180 (Table 3). Since the
calculated porosity is close to the gravimetric porosity a threshold
value 0.40, the Berea sample was analyzed at the threshold where the
peak is observed. The binary 3D reconstruction of sandstone was
transformed to the PCA form (Figure 8B). The PCA separates morphological
components based on their connectivity. The sandstone sample appears
homogenous with many, relatively, small clusters as seen in Figure 8B.
This is supported by the histogram in Figure 8C, where there are many
clusters with a range of sizes. Most of the clusters are in the range of
1-10 voxels in size, which is relatively small. Based on these results,
Berea Sandstone consists predominately of smaller pores (low pixel
count), with pore throats that cannot be resolved with the current MRI
method. Although the chosen threshold produces the gravimetric porosity
value, it does not produce proper connectivity of the sample, due to
resolution limitations, as indicated by the TD-NMR results.