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.