Porosity calculations and permeability simulations in a biolithite rock using x-ray tomography images

Engineering energy storage/extraction during geoenergy applications (e.g., geothermal energy extraction, CO₂ and/or Hydrogen storage) requires a very good knowledge of subsurface heterogeneities. One of the principal factors that influences the response of the underground system is the continuously evolving pore networks of the targeted rocks. This work aims to understand the pore network of a natural Biolithite, coming from a Greek outcrop, and predict the permeability of lab-scale systems (due to diagenesis and natural deformation) using digital images and stochastic model reconstructions.
X-ray images (50μm resolution) were acquired (at Lund University) from 3 cylindrical Biolithite samples, which were cored in three different directions (see Fig. 1e). No further lab-induced deformation took place in these rocks. The 3D digital volumes were initially pre-processed to reduce any noise and facilitate the segmentation that followed-up. During segmentation, the volumes were binarized to extract the pore-network of the volumes of interest. Machine learning algorithms were used for that purpose. Porosity was calculated along the height of the samples, using the binarized images. The anisotropy of the pores was investigated using Fiji; a structure tensor was calculated for each pixel in the image, by sliding a Gaussian analysis window - slice by slice throughout the whole stack (Clemons, et al., 2018), and crossplotted with the Feret X & Y parameters. The permeability tensor was calculated using the Pore Analysis Tools (PAT, Jiang et al., 2007) and the binarized images as input parameters. This calculation involves a) getting the 3D Euclidean distance map; b) clustering of voxels; c) extraction of the network pore space; d) partitioning of the pore space; e) computation of shape factors. PAT uses faster algorithms with higher efficiency to extract a representative network model. Pore Architecture Reconstruction (PAR) used stochastic network generation to rebuild arbitrary sized volume realizations based on 2D slices. Figure 1a shows a summary of the workflow adopted.
With multiple porosity systems contributing to the total porosity and potentially affecting the system's permeability, carbonates are fairly complex rocks. The classification and subsequent trends/cluster analysis of the pore-network within the samples were performed using the Trainable Weka segmentation, a Java-based repository of machine learning algorithms. Our findings show that this Biolithite typically has porosity between 18 and 30%. Permeability varies between 0.1 and 60 md. The pore geometry in samples B11 & B23 is elongated, unevenly distributed, and preferentially aligned. Lower permeabilities and micro-scale layering characterize sample B33. The Cretaceous laminate carbonate described by Buckman et al. in 2017 showed a comparable trend. The spatial relationship of interparticle and moldic porosities are inferred to be the main factor controlling permeability at this resolution. This is based on pore facies analogues from literature observations of similar pore characteristics (such as Folk, 1959; Choquette & Pray, 1970; Roels, et al., 2001, Ranjbar-Karami, et. al., 2021). Our results also show that the few larger-scale pores are poorly connected by the predominant smaller scale pores. Kz is higher than Kx and Ky in all our samples. This trend can be explained by the fact that some pores exhibit smaller voids at shallower depths that widen and become slightly more connected with increasing depth, as seen in a 3D projection within a smaller region of interest.
The ability to reconstruct pore network models from 3D x-ray computed tomography images with representative geometrical and topological characteristics at different scales is a key factor in modeling of some multiphase flow properties in porous media. This study describes the internal architecture of a Biolithite using 3D x-ray images, calculates porosity and permeability in different orientations, and attempts to reconstruct 3D image using stochastic models from 2D slices. It focuses on the importance of a reproducible, project specific workflow as an input to generating pore network models.