Statistical representative elementary volumes of porous media determined using greyscale analysis of 3D tomograms

Digital rock physics carries the dogmatic concept of having to segment volume images for quantitative analysis but segmentation rejects huge amounts of signal information. Information that is essential for the analysis of difficult and marginally resolved samples, such as materials with very small features, is lost during segmentation. In X-ray nanotomography reconstructions of Hod chalk we observed partial volume voxels with an abundance that limits segmentation based analysis. Therefore, we investigated the suitability of greyscale analysis for establishing statistical representative elementary volumes (sREV) for the important petrophysical parameters of this type of chalk, namely porosity, specific surface area and diffusive tortuosity, by using volume images without segmenting the datasets. Instead, grey level intensities were transformed to a voxel level porosity estimate using a Gaussian mixture model. A simple model assumption was made that allowed formulating a two point correlation function for surface area estimates using Bayes' theory. The same assumption enables random walk simulations in the presence of severe partial volume effects. The established sREVs illustrate that in compacted chalk, these simulations cannot be performed in binary representations without increasing the resolution of the imaging system to a point where the spatial restrictions of the represented sample volume render the precision of the measurement unacceptable. We illustrate this by analyzing the origins of variance in the quantitative analysis of volume images, i.e. resolution dependence and intersample and intrasample variance. Although we cannot make any claims on the accuracy of the approach, eliminating the segmentation step from the analysis enables comparative studies with higher precision and repeatability.