Christoph H. Arns

Computation of linear elastic properties from microtomographic images: Methodology and agreement between theory and experiment

Elastic property‐porosity relationships are derived directly from microtomographic images. This is illustrated for a suite of four samples of Fontainebleau sandstone with porosities ranging from 7.5% to 22%. A finite‐element method is used to derive the elastic properties of digitized images. By estimating and minimizing several sources of numerical error, very accurate predictions of properties are derived in excellent agreement with experimental measurements over a wide range of the porosity. We consider the elastic properties of the digitized images under dry, water‐saturated, and oil‐saturated conditions. The observed change in the elastic properties due to fluid substitution is in excellent agreement with the exact Gassmanns equations. This shows both the accuracy and the feasibility of combining microtomographic images with elastic calculations to accurately predict petrophysical properties of individual rock morphologies. We compare the numerical predictions to various empirical, effective medium ...

Accurate estimation of transport properties from microtomographic images

Estimating and minimizing several sources of numerical error result in very accurate predictions of transport properties directly from digitized images. Simulation of electrical conductivity on microtomographic images of Fontainebleau sandstone are in excellent agreement with experimental measurements over a wide range of porosity. The results show the feasibility of combining digitized images with transport calculations to accurately predict petrophysical properties of individual rock morphologies.

Minimal surface scaffold designs for tissue engineering

Triply-periodic minimal surfaces are shown to be a more versatile source of biomorphic scaffold designs than currently reported in the tissue engineering literature. A scaffold architecture with sheetlike morphology based on minimal surfaces is discussed, with significant structural and mechanical advantages over conventional designs. These sheet solids are porous solids obtained by inflation of cubic minimal surfaces to sheets of finite thickness, as opposed to the conventional network solids where the minimal surface forms the solid/void interface. Using a finite-element approach, the mechanical stiffness of sheet solids is shown to exceed that of conventional network solids for a wide range of volume fractions and material parameters. We further discuss structure-property relationships for mechanical properties useful for custom-designed fabrication by rapid prototyping. Transport properties of the scaffolds are analyzed using Lattice-Boltzmann computations of the fluid permeability. The large number of different minimal surfaces, each of which can be realized as sheet or network solids and at different volume fractions, provides design flexibility essential for the optimization of competing design targets.

Digital rock physics: 3D imaging of core material and correlations to acoustic and flow properties

3D X-ray microtomographic imaging and visualization of core material at the pore scale and subsequent analysis of petrophysical properties can give important insight to understanding properties of reservoir core material. 3D images allow one to map in detail the pore and grain structure and interconnectivity of core material. Numerical calculations on image data are in agreement with experimental data for flow and elastic properties on simple core material. This development forms the basis for developing more meaningful structure-property correlations in rock.

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.

3D Imaging and Simulation of Elastic Properties of Porous Materials

Obtaining accurate estimates of elastic properties of disordered materials has been a problem of interest for decades. Recent advances in 3D computed tomography and numerical simulations have led to a new digital approach.

Permeability Upscaling for Carbonates from the Pore-Scale Using Multi-Scale Xray-CT Images

bility due to large permeability contrasts. The most accurate upscaling technique is employing Darcy’s law. A key part of the study is the establishment of porosity transforms between highresolution and low-resolution images to arrive at a calibrated porosity map to constraint permeability estimates for the whole core.