One of the biggest challenges in flow and transport in geological porous media is that of scale. Frequently the resolution required to describe a pore structure comes at the expense of a field-of-view representative of rock heterogeneity. This challenge is particularly pronounced as the computational determination of effective flow and transport properties (e.g. permeability, diffusivity or effective conductivity) has required 3D imaging, imposing both technological and practical limitations on the scale of examination. 2D techniques allow for the examination of much larger length scales, but such data cannot easily be translated into effective properties. The past 10 years have seen an explosion in the availability of open source machine learning tools, allowing for an in-depth multivariant analysis of porous media structure and new approaches for the prediction of flow and transport properties.
Recent work has shown that machine learning based techniques can be used to predict permeability using only 2D data with a mean-square-fractional-error (MSFE) of <25%. We use this technique to analyze permeability predictions on 4 samples, two from micritic carbonate microporosity, and two from granular sandstones, imaged using a range of 2D and 3D imaging techniques, including micro-CT, nano-CT, Scanning Electron Microscopy (SEM) and automated optical petrography.
Micritic carbonate microporosity samples were extracted from a sample of Estaillades Limestone. A polished optical thin-section of the sample was scanned at 20X magnification using an automated petrographic microscope. The microporous grains were targeted for high (20nm) resolution scanning using an SEM. Two regions from microporous grains extracted using a femto-second laser, then scanned at high (65nm) resolution using a nano-CT. The top slice of the 3D CT data spatially correlated with the light and electron microscopy data from the same region. Granular sandstone samples were extracted from two samples of Berea Sandstone. Two 1” diameter cores were imaged at high (1.6µm) resolution using a X-ray microscope. Polished thin-sections were prepared for each sample and scanned using automated petrography.
Each sample therefore had a high-resolution 3D volume, spatially correlated with a scalable high resolution 2D image of the same region. For each sample permeability predictions were made from the 3D CT data using both multivariant prediction1 and Geodict software (Math2Market Gmbh.). Multivariant predictions were also made from the (2D) overlap region between the CT data and the SEM / optical petrography data. The multivariant predictions and the full-physics simulation predictions agreed to within the 25% MSFE shown across simulation benchmarks. The overlapping single-slice predictions from both CT data and SEM/optical petrography data agree extremely well (around 5% difference) for all samples. The single slice predictions agreed reasonably well with the full volume predictions, with better predictions made for sandstones (<25% error) than carbonates (around 50% error). This discrepancy is likely due to the greater level of heterogeneity within the carbonate microporosity. The validation of the use of 2D imaging techniques to predict flow properties allow for much larger spatial length-scales to be analyzed at the pore-scale, and potentially enabling direct upscaling from the pore to core scales.
