Entropy-based measure of rock sample heterogeneity derived from micro-CT images

TL;DR

The paper tackles the challenge of quantifying rock sample heterogeneity from high-resolution micro-CT images without segmentation. It introduces an entropy-based measure that splits each image into subcubes, computes per-subcube attributes, and uses Shannon entropy to derive a heterogeneity score, further normalized by entropy quantiles; the entropy $H(I)$ is computed from the distribution of subcube attribute values, with discrete cases using $H(I) = -\sum p(k) \log_2 p(k)$ and continuous cases via kernel density estimation. Validation on 4,935 micro-CT images from 4,744 Brazilian reservoir samples shows that mean, standard deviation, and coefficient of variation attributes yield entropy-based ranks that align with expert heterogeneity assessments and outperform traditional GLCM texture attributes. The approach provides a scalable, automated, and cost-effective tool for reservoir characterization with potential to link textural heterogeneity measures to petrophysical properties.

Abstract

This study presents an automated method for objectively measuring rock heterogeneity via raw X-ray micro-computed tomography (micro-CT) images, thereby addressing the limitations of traditional methods, which are time-consuming, costly, and subjective. Unlike approaches that rely on image segmentation, the proposed method processes micro-CT images directly, identifying textural heterogeneity. The image is partitioned into subvolumes, where attributes are calculated for each one, with entropy serving as a measure of uncertainty. This method adapts to varying sample characteristics and enables meaningful comparisons across distinct sets of samples. It was applied to a dataset consisting of 4,935 images of cylindrical plug samples derived from Brazilian reservoirs. The results showed that the selected attributes play a key role in producing desirable outcomes, such as strong correlations with structural heterogeneity. To assess the effectiveness of our method, we used evaluations provided by four experts who classified 175 samples as either heterogeneous or homogeneous, where each expert assessed a different number of samples. One of the presented attributes demonstrated a statistically significant difference between the homogeneous and heterogeneous samples labelled by all the experts, whereas the other two attributes yielded nonsignificant differences for three out of the four experts. The method was shown to better align with the expert choices than traditional textural attributes known for extracting heterogeneous properties from images. This textural heterogeneity measure provides an additional parameter that can assist in rock characterization, and the automated approach ensures easy reproduction and high cost-effectiveness.

Figures (11)

• Figure 1: Illustration of the steps used to define the VOI.
• Figure 2: Illustration of the VOI division and subcube selection processes.
• Figure 3: Central slices of micro-CT images derived from different samples. The VOI is delimited by yellow rectangles in each view.
• Figure 4: Spearman correlation matrices produced for the entropy ranks of different attributes and division schemes with respect to the x and y coordinates. (a) 5 segments, (b) 10 segments, (c) Mean attribute, (d) Standard deviation attribute.
• Figure 5: Horizontal cross-section centre slices of the images with the highest and lowest entropy values for the selected attributes. The yellow boxes delimit the corresponding area within each VOI.