Robert Sok

Direct and Stochastic Generation of Network Models from Tomographic Images: Effect of Topology on Residual Saturations

We generate the network model equivalents of four samples of Fontainebleau sandstone obtained from the analysis of microtomographic images. We present the measured distributions of flow-relevant geometric and topological properties of the pore space. We generate via bond dilution from a regular lattice, stochastic network models with identical geometric (pore-size, throat-size) and topological (coordination number distribution) properties. We then simulate the two-phase flow properties directly on the network model and the stochastic equivalent for each sample. The simulations on the stochastic networks are found to provide a poor representation of the results on the direct network equivalents. We find that the description of the network topology is particularly crucial in accurately predicting the residual phase saturations. We also find it necessary to introduce into the stochastic network geometry both extended pore-pore correlations and local pore-throat correlations to obtain good agreement with flow properties on the rock-equivalent network.

Digital Core Laboratory: Properties of reservoir core derived from 3D images

A facility for digital imaging, visualizing and calculation of reservoir rock properties in three dimensions (3D) is described. The facility includes a high resolution X-ray micro-computed tomography system capable of acquiring 3D images made up of 2000 voxels on core plugs up to 5 cm diameter with resolutions down to 2 μm. Subsets of four sandstone reservoir core plugs (5 mm in diameter) from a single well of a producing gas field are imaged in this study. The four cores exhibit a broad range of pore and grain sizes, porosity, permeability and mineralogy. Computational results made directly on the digitized tomographic images are presented for the pore size distribution, permeability, formation factor, NMR response and drainage capillary pressure. We show that data across a range of porosity can be computed from the suite of 5 mm plugs. Computations of permeability, formation factor and drainage capillary pressure are compared to data from a comprehensive SCAL laboratory study on 70 cores from the same well. The results are in good agreement. Empirical correlations between permeability and other petrophysical parameters are made and compared to common correlations. The results demonstrate the potential to predict petrophysical properties from core material not suited for laboratory testing (e.g., drill cuttings, sidewall core or damaged core) and the feasibility of combining digitized images with numerical calculations to predict properties and derive correlations for individual reservoir rock lithologies.

Developing a virtual materials laboratory

Tomographic imaging can now be routinely performed over three orders of magnitude in length scale with correspondingly high data fidelity. This capability, coupled with the development of advanced computational algorithms for image interpretation, three-dimensional visualization, and structural characterization and computation of physical properties on image data, allows for a new numerical laboratory approach to the study of real complex materials: the Virtual Materials Laboratory. Numerical measurements performed directly on images can, in many cases, be performed with similar accuracy to equivalent laboratory measurements, but also on traditionally intractable materials. These emerging capabilities and their impact on a range of scientific disciplines and industry are explored here.

Relative permeability from tomographic images; effect of correlated heterogeneity

Abstract We examine the calculation of relative permeability and residual saturation using networks derived from tomographic images of Fontainebleau sandstone previously used to successfully calculate single-phase transport properties. In contrast to electrical conductivity and permeability calculations, we find that that computed relative permeabilities and residual saturations for samples of the same sandstone display a high degree of variability. Randomizing pores and throats to remove all correlations almost completely eliminates the variability between samples and produces smooth numerical data sets. We conclude that correlations in rock microstructure, which appear to have little effect on the calculation of single fluid properties, have a major effect on computed relative permeability and residual saturation.

Elastic and transport properties of cellular solids derived from three-dimensional tomographic images

We describe a three-dimensional imaging and analysis study of eight industrial cellular foam morphologies. The foam morphologies were generated by differing industrial processing methods. Tomograms are acquired on an X-ray micro-computed tomography facility at scales of approximately equal to at resolutions down to 7 μm. The image quality is sufficient in all cases to measure local structure and connectivity of the foamed material, and the field of view large enough to calculate a range of material properties. Phase separation into solid and porous components is straightforward. Three-dimensional structural characteristics are measured directly on the porous and solid phases of the images. A number of morphological parameters are obtained, including pore volume-to-surface-area ratio, connectivity, the pore and solid phase size distributions defined by maximal sphere openings and chord length measurements. We further calculate the pore size distribution associated with capillary pressure via simulating of mercury drainage on the digital images. The binarized microstructures are used as a basis for calculations of transport properties (fluid permeability, diffusivity and thermal conductivity) and elastic moduli. From the data, we generate property–porosity relationships for the range of foam morphologies imaged and quantitatively analyse the effects of porosity and microstructure on the resultant properties of the foams. We compare our numerical data to commonly used theoretical and empirical property–porosity relationships. For thermal conductivity, we find that the numerical results agree extremely well with an empirical expression based on experimental data of various foams. The upper Hashin–Shtrikman bound also provides an excellent prediction of the data across all densities. From simulation of the diffusivity, we can define the tortuosity of the pore space within the cellular solid. We find that different processing methods lead to strong variations in the tortuosity of the pore space of the foams. For elastic properties, our results show that for the Young modulus, E, both the differential effective medium theory and the classical correlation give a good correlation. Assuming a constant Poissons ratio leads to reasonable agreement. The best correlation for is given by assuming a slight variation in as a linear function of porosity. The permeability of the foams varies over three orders of magnitude. Correlations for permeability based on the classical Kozeny–Carman equation lead to reasonable agreement, except at the lowest porosities. Permeability estimations based on mercury porosimetry give excellent agreement for all foams.

An x-ray tomography facility for quantitative prediction of mechanical and transport properties in geological, biological, and synthetic systems

A fully integrated X-ray tomography facility with the ability to generate tomograms with 20483 voxels at 2 micron spatial resolution was built to satisfy the requirements of a virtual materials testing laboratory. The instrument comprises of a continuously pumped micro-focus X-ray gun, a milli-degree rotation stage and a high resolution and large field X-ray camera, configured in a cone beam geometry with a circular trajectory. The purpose of this facility is to routinely analyse and investigate real world biological, geological and synthetic materials at a scale in which the traditional domains of physics, chemistry, biology and geology merge. During the first 2 years of operation, approximately 4 Terabytes of data have been collected, processed and analysed, both as static and in some cases as composite dynamic data sets. This incorporates over 300 tomograms with 10243 voxels and 50 tomograms with 20483 voxels for a wide range of research fields. Specimens analysed include sedimentary rocks, soils, bone, soft tissue, ceramics, fibre-reinforced composites, foams, wood, paper, fossils, sphere packs, bio-morphs and small animals. In this paper, the flexibility of the facility is highlighted with some prime examples.

Micro-CT Facility for Imaging Reservoir Rocks at Pore Scales

A micro-CT facility for imaging, visualizing and calculating sedimentary rock properties in three dimensions (3D) is described. The facility is capable of acquiring 3D Xray CT images made up of 2000 voxels on core plugs up to 5 cm diameter with resolutions down to 2 μm. This allows the 3D pore-space of a rock to be imaged across several orders of magnitude. In parallel with standard microscopic techniques, the spatial distributions of different mineralogies can be identified. We demonstrate the capabilities by imaging a reservoir carbonate core at different resolutions. First, an image of a 4 cm diameter plug is analysed at a resolution of 42 μm. This allows one to deduce the size, shape and spatial distribution of the disconnected vug porosity. Within the imaged volume over 30000 separate vugs are identified and a broad vug size distribution is measured. From higher resolution images (2.5-20 μm) on a 5 mm diameter subset of the core one can measure characteristic (intergranular) pore sizes. The apparent porosity of the core increases with enhanced image resolution. This behaviour implies a continuum of pore sizes exist within the core at these resolutions. Carbonate sediments have been conventionally described by a discrete bior tri-modal pore size distribution; in contrast our analysis exhibits no distinct pore sizes but a broad distribution of pore size spanning over more than two orders of magnitude.

Quantitative properties of complex porous materials calculated from X-ray μCT images

A microcomputed tomography (μCT) facility and computational infrastructure developed at the Department of Applied Mathematics at the Australian National University is described. The current experimental facility is capable of acquiring 3D images made up of 20003 voxels on porous specimens up to 60 mm diameter with resolutions down to 2 μm. This allows the three-dimensional (3D) pore-space of porous specimens to be imaged over several orders of magnitude. The computational infrastructure includes the establishment of optimised and distributed memory parallel algorithms for image reconstruction, novel phase identification, 3D visualisation, structural characterisation and prediction of mechanical and transport properties directly from digitised tomographic images. To date over 300 porous specimens exhibiting a wide variety of microstructure have been imaged and analysed. In this paper, analysis of a small set of porous rock specimens with structure ranging from unconsolidated sands to complex carbonates are illustrated. Computations made directly on the digitised tomographic images have been compared to laboratory measurements. The results are in excellent agreement. Additionally, local flow, diffusive and mechanical properties can be numerically derived from solutions of the relevant physical equations on the complex geometries; an experimentally intractable problem. Structural analysis of data sets includes grain and pore partitioning of the images. Local granular partitioning yields over 70,000 grains from a single image. Conventional grain size, shape and connectivity parameters are derived. The 3D organisation of grains can help in correlating grain size, shape and orientation to resultant physical properties. Pore network models generated from 3D images yield over 100000 pores and 200000 throats; comparing the pore structure for the different specimens illustrates the varied topology and geometry observed in porous rocks. This development foreshadows a new numerical laboratory approach to the study of complex porous materials.

Experimental Verification of Effect of Size on Drainage Capillary Pressure Computed from Digitized Tomographic Images

This paper presents comparisons between drainage capillary pressure curves computed directly from 3D micro-tomographic images (micro-CT) and laboratory measurements conducted on the same core samples. It is now possible to calculate a wide range of petrophysical and transport properties directly from micro-CT images or from equivalent network models extracted from these images. Capillary pressure is sensitive to rock microstructure and the comparisons presented are the first direct validation of image based computations. The measured data include centrifuge and mercury injection drainage capillary pressure for fired Berea, Bentheimer and Obernkirchner sandstones and unfired Mount Gambier carbonate. The measurements cover a wide range of porosities and permeabilities. The measurements were made on core samples with different diameters (2.5 cm, 1.5 cm, 1 cm and 0.5 cm) to assess the effect of up-scaling on capillary pressure measurements. The smallest diameter samples were also used to obtain the 3D micro-CT images. Good agreement was obtained between the experimental measurements and direct computations on 3D micro-CT images.

Virtual Core Laboratory: Properties of Reservoir Rock Derived From X-ray CT Images.

We demonstrate that accurate predictions of petrophysical properties can be made directly from digitized tomographic images. Computations of both transport (formation factor and permeability) and elastic properties from micro-tomographic images of a suite of Fontainebleau sandstone are shown to be in excellent agreement with experimental measurements over a wide range of porosities (5% < φ < 25%). Four small (5 mm i.d.) plugs from a producing gas field have also been analysed. Unlike Fontainebleau, these four cores exhibit a broad range of pore and grain sizes, porosity and mineralogy. Computations of permeability and capillary pressure are made directly on the digitized tomographic images and compared to laboratory core measurements. The results are in excellent agreement. The very small sample size required for imaging may allow representative petrophysical data to be obtained from sidewall cores and drill cuttings.