Digital rock physics benchmarks—Part I: Imaging and segmentation
Highlights
► We propose four rock microstructure images as benchmark geometries for digital rock tools. ► The digital samples are Fontainebleau and Berea sandstone, a vuggy carbonate and a pack of spherical beads. ► Sample porosities range from 14.7% and 18.3% for the sandstones to 24.3% for the sphere pack.
Introduction
The fundamental aim of rock physics is to discover, understand and model relations between remotely-sensed geophysical observables and in-situ rock properties. Conventional rock-physics models are based on either empirical relations from laboratory measurements or theoretical models based on idealized microstructures and calibrated with available measurements. These models have given important insights to understanding cross-property relations. However, these models are almost always over-simplified, with regard to the geometry they represent and, at times, with the physical interactions within the geometry. Moreover, different rock property models represent or characterize rock microstructure differently, thereby lacking commonality and making cross-property analyses difficult.
Using high resolution representations of the complex pore geometry, digital rock physics has rapidly emerged as a potential source of valuable rock property relations (e.g., elastic, transport, and electrical properties) and fundamental understanding of pore-scale processes governing these properties. Its main principle is “image-and-compute” aimed at imaging 3D geometry of the mineral phase and the pore-space of a rock and then computationally simulating physical processes in this digital object: fluid flow to quantify permeability, electrical current flow to quantify resistivity, and elastic deformation to quantify elastic moduli and the elastic-wave velocity. With the advent of robust fine-resolution 3D imaging capability and software and hardware availability, digital rock physics is set to be a game-changer.
A modern method to acquire images of pore geometries is the micro-scale x-ray computed tomography (μxCT). The method enables the measurement of the local x-ray absorption within a small, cylindrical rock sample, with a typical diameter of a few millimeters or less. Three-dimensional images are reconstructed from a large number radiographs, i.e. projections of the imaged object, obtained at different projection angles. The result of the reconstruction is a grayscale image, where the brightness is proportional to the CT-number of the material within the object (Mees et al., 2003). A source of x-rays is available at synchrotron research facilities. Commercial μxCT scanners use x-ray tubes as a light source.
A cornerstone of the digital rock physics workflow is the segmentation of the scanned 3-D rock object. Segmentation refers to the identification and labeling of pore and mineral phases within the image. Due to the size of the 3-D data sets, manual segmentation is usually not feasible and image processing algorithms are required to automatically perform this task. Common image processing tools for 3-D segmentation are spatial filtering, noise and artifact removal, thresholding, morphological operations and cluster analysis. The segmentation of a grayscale image is not unique and segmentation algorithms therefore require manual interaction and quality control. For a review of image segmentation methods applied to porous media, we refer to Sezgin and Sankur (2004) or Iassonov et al. (2009).
An alternative way of obtaining three-dimensional images of rock microstructures is based on stochastic methods and is sometimes referred to as 2D-to-3D reconstruction (e.g. Liang et al., 2000, Keehm et al., 2003). The idea of this method is to estimate statistical properties of a rock sample from a two-dimensional image, such as obtained from scanning electron microscopy. The advantage of this approach is the possibility to generate a large number of digital samples with similar microstructural properties. The images thus produced, however, do not capture the complexity of natural rock samples, which limits their range of applications. In an attempt to generate pore geometries that more closely represent the fabrics of sedimentary rocks, so-called process-based methods have been developed. Those methods simulate or mimic the physical and geological processes that are acting during the rock genesis (Øren and Bakke, 2002).
As digital rock physics becomes more adopted in the geosciences and engineering, there is a critical need to establish benchmark datasets that researchers can use for testing and validating property-estimation algorithms and codes. In this paper, we describe four benchmark digital datasets: a Fontainebleau sandstone image, a Berea sandstone image, a Grosmont carbonate image, and a pack of spherical beads. The first three datasets consist of high resolution CT-scans, examples of segmentation and thresholding of the intensity data. The fourth dataset, the bead pack, was prepared by discretizing a random close pack on a regular 3D lattice. The initial random close pack was constructed using a granular dynamics simulation. We believe these datasets provide important benchmark model geometries for the digital rock physics community.
Section snippets
Fontainebleau sandstone
The Fontainebleau sandstone dataset was acquired using the synchrotron source at Brookhaven National Laboratory by ExxonMobil and has been used in pioneering digital rock studies (e.g. Olson and Rothman, 1997, Lindquist et al., 2000). Fontainebleau sandstone consists mainly of monodisperse quartz sand grains. We provide the image segmented binary data (288×288×300) with grain and pore voxels (Fig. 1), unlike our other benchmark datasets which are available as raw images. The laboratory measured
Image processing and segmentation
The second step in the digital rock physics workflow is the segmentation of the raw images. The purpose of this step is to remove artifacts of imaging, such as concentric shadows in the CT image and to delineate pores and minerals. Simple brightness thresholding is often not adequate for this purpose and, in this case, advanced image processing, such as noise reduction, artifact removal and multiband thresholding need to be utilized (Iassonov et al., 2009). This step is key to the success of
Discussion
The goal of segmentation is to identify all phases in an image correctly and distinctly. In most cases, the segmentation involves grayscale thresholding as a key step to distinguish between pore space and solid grains. The choice of segmentation algorithms, filtering parameters, and specifically the grayscale threshold, introduce an ambiguity to the process. Several methods exist that help choosing optimal thresholds (Sezgin and Sankur, 2004), but even if the image histograms reveal clearly
Summary
We provide four digital images of porous rock microstructures as benchmark datasets for digital rock simulations. The imaged rock samples are Fontainebleau and Berea sandstone, a vuggy carbonate rock, and a computer-generated sphere pack.
For the Berea sandstone and for the carbonate sample, we provide different segmentations of the original grayscale image. Both images have a significant amount of sub-resolution porosity, and the porosity cannot be uniquely determined by the segmentation
Acknowledgments
The Fontainebleau sandstone image is courtesy of Brent Lindquist in collaboration with ExxonMobil. This work was supported by the Energy Resources R&D program of the KETEP grant funded by the Ministry of Knowledge Economy of Korea (No. 2009201030001A). E.H. Saenger thanks the DFG (Deutsche Forschungsgemeinschaft) for supporting him through a Heisenberg scholarship (SA 996/1-2). We acknowledge the sponsors of the Stanford Rock Physics Project, the Stanford Center for Reservoir Forecasting and
References (30)
- et al.
Pore geometry and transport properties of Fontainebleau sandstone
International Journal of Rock Mechanics and Mineral Sciences
(1993) - et al.
Measurement of the deformation and adhesion of solids in contact
Journal of Colloid and Interface Science
(1987) - et al.
Acquisition, optimization and interpretation of X-ray computed tomographic imagery: applications to the geosciences
Computer and Geosciences
(2001) - et al.
Permeability and electrical conductivity of porousmedia from 3D stochastic replicas of the microstructure
Chemical Engineering Science
(2000) - et al.
Investigating 3D geometry of porous media images
Physics and Chemistry of the Earth
(1999) - et al.
Pore space morphology analysis using maximal inscribed spheres
Physica A: Statistical Mechanics and its Applications
(2006) - et al.
The morphological approach to segmentation: the watershed transformation
The velocity of compressional waves in rocks to 10 kilobars. Part 1
Journal of Geophysical Research
(1960)- Buades, A., Coll, B., Morel, J.M., 2005. A non local algorithm for image denoising. In: Proceeding of the International...
- et al.
An overview of the geology of the Upper Devonian Grosmont carbonate bitumen deposit, Northern Alberta, Canada
Natural Resources Research
(2007)
Compressional wave velocities in metamorphic rocks at pressures to 10 kilobars
Journal of Geophysical Research
Mercury porosimetry: a general (practical) overview
Particle & Particle Systems Characterization
Constructing discrete medial axis of 3-D objects
International Journal of Computational Geometry & Applications
Effect of porosity and clay content on wave velocity in sandstones
Geophysics
Über den Kontakt elastischer Körper
Journal für die reine und angewandte Mathematik
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