Grain reconstruction of porous media: application to a low-porosity Fontainebleau sandstone

Hierarchical reconstruction of three-dimensional porous media from a single two-dimensional image with multiscale entropy statistics

Despite the development of 3D imaging technology, the reconstruction of three-dimensional (3D) microstructure from a single two-dimensional (2D) image is still a prominent problem. In this paper, we propose a hierarchical reconstruction method based on simulated annealing, which is named hierarchical simulated annealing method (HSA), with the multiscale entropy statistics as the morphological information descriptor to reconstruct its corresponding three-dimensional (3D) microstructure from a single two-dimensional (2D) image. Both hierarchical simulated annealing (HSA) method and simulated annealing (SA) method are used to perform on the 2D and 3D microstructure reconstruction from a single 2D image, where the two-point cluster function and the standard two-point correlation function are used as the measurement metrics for the reconstructed 2D and 3D structures. From the 2D reconstructions, it can be seen that all the reconstructions of HSA method and SA method not only captures the similar morphological information with the original images, but also have a good agreement with the target microstructures in two-point cluster function. For the reconstructed 3D microstructures, the comparison of two-point correlation function shows that both HSA method and SA method can effectively reconstruct its 3D microstructure and the comparison of the reconstruction time between HSA method and SA method shows that the reconstruction speed of HSA method is an order of magnitude faster than that of SA method.

Composite material in the sea urchin Cidaris rugosa: ordered and disordered micrometre-scale bicontinuous geometries

The sponge-like biomineralized calcite materials found in echinoderm skeletons are of interest in terms of both structure formation and biological function. Despite their crystalline atomic structure, they exhibit curved interfaces that have been related to known triply periodic minimal surfaces. Here, we investigate the endoskeleton of the sea urchin Cidaris rugosa that has long been known to form a microstructure related to the Primitive surface. Using X-ray tomography, we find that the endoskeleton is organized as a composite material consisting of domains of bicontinuous microstructures with different structural properties. We describe, for the first time, the co-occurrence of ordered single Primitive and single Diamond structures and of a disordered structure within a single skeletal plate. We show that these structures can be distinguished by structural properties including solid volume fraction, trabeculae width and, to a lesser extent, interface area and mean curvature. In doing so, we present a robust method that extracts interface areas and curvature integrals from voxelized datasets using the Steiner polynomial for parallel body volumes. We discuss these very large-scale bicontinuous structures in the context of their function, formation and evolution.

Fast reconstruction of multiphase microstructures based on statistical descriptors

In this paper, we propose a hierarchical simulated annealing of erosion method (HSAE) to improve the computational efficiency of multiphase microstructure reconstruction, whose computational efficiency can be improved by an order of magnitude. Reconstruction of the two-dimensional (2D) and three-dimensional (3D) multiphase microstructures (pore, grain, and clay) based on simulated annealing (SA) and HSAE are performed. In the reconstruction of multiphase microstructure with HSAE and SA, three independent two-point correlation functions are chosen as the morphological information descriptors. The two-point cluster function which contains significant high-order statistical information is used to verify the reconstruction results. From the analysis of 2D reconstruction, it can find that the proposed HSAE technique not only improves the quality of reconstruction, but also improves the computational efficiency. The reconstructions of our proposed method are still imperfect. This is because the used two-point correlation functions contain insufficient information. For the 3D reconstruction, the two-point correlation functions of the 3D generation are in excellent agreement with those of the original 2D image, which illustrates that our proposed method is effective for the reconstruction of 3D microstructure. The comparison of the energy vs computational time between the SA and HSAE methods shows that our presented method is an order of magnitude faster than the SA method. That is because only some of the pixels in the overall hierarchy need to be considered for sampling.

Experimental study on the pore and solid structures of municipal solid waste under compression based on computed tomography (CT) scans

Municipal solid waste (MSW) is a highly heterogeneous porous medium that contains a variety of components and has complex pores and solid structures. Macroscale experiments are insufficient to describe the hydraulic and mechanical properties of MSW, especially for preferential flow in pores and the reinforcing effect of solids. For a deep understanding of the microscale structure of MSW, CT scanning tests were carried out on two kinds of samples prepared in the laboratory and drilled in landfills. MSW images were divided into pores and solids through dynamic threshold segmentation and morphological denoising methods. The distributions of pore size and structural solid angle were calculated by the maximum inscribed sphere (MIS) algorithm and angle statistical algorithm based on the surface model, respectively. According to the pore-size distribution, the pores were divided into large (diameter > 1 mm), medium (1 mm > diameter > 0.1 mm), and small (diameter < 0.1 mm) pores in MSW. Under a vertical stress of 50 kPa, the porosities of the large, medium, and small pores were 35%, 12%, and 26%, respectively. As the vertical stress increased to 400 kPa, the porosity of large pores decreased significantly to 15%, while the porosities of medium and small pores remained almost unchanged. In addition, the structural solid angle tended to be horizontal under compression, but its influence was limited. The structural solid angle was mainly concentrated at approximately 30-32°. The probability distribution of the structural solid angle could be well fitted using the Gauss function.

Descriptor-based method combined with partition to reconstruct three-dimensional complex microstructures

A descriptor-based method combined with a partition approach is proposed to reconstruct three-dimensional (3D) microstructures based on a set of two-dimensional (2D) scanning electron microscopy (SEM) images. The features in the SEM images are identified and partitioned into small features using the watershed algorithm. The watershed algorithm first finds the local gray-level maxima, and partitions the features through the gray-level local minima. The 3D size distribution and radial distribution of the small spherical elements are inferred, respectively, based on the 2D size distribution and radial distribution using stereological analysis. The 3D microstructures are reconstructed by matching the inferred size distribution and radial distribution through a simulated annealing-based procedure. Combining with the proposed partition approach, the descriptor-based method can be applied to complex microstructures and the computational efficiency of the reconstruction can be largely improved. A case study is presented using a set of 2D SEM images with nanoscale pore structure from the low-density CSH (calcium silicate hydrate) phase of a hardened cement paste. Cross sections were randomly selected from the reconstructed 3D microstructure and compared with the original SEM images using the pore descriptors and the two-point correlation function with satisfactory agreement. Using the 3D reconstructed model, the properties of the sample material can be investigated on such a small scale as demonstrated in this paper on quantifying the absolute permeability.

Cardiolipin Remodeling Defects Impair Mitochondrial Architecture and Function in a Murine Model of Barth Syndrome Cardiomyopathy

BACKGROUND

Cardiomyopathy is a major clinical feature in Barth syndrome (BTHS), an X-linked mitochondrial lipid disorder caused by mutations in Tafazzin (TAZ), encoding a mitochondrial acyltransferase required for cardiolipin remodeling. Despite recent description of a mouse model of BTHS cardiomyopathy, an in-depth analysis of specific lipid abnormalities and mitochondrial form and function in an in vivo BTHS cardiomyopathy model is lacking.

METHODS

We performed in-depth assessment of cardiac function, cardiolipin species profiles, and mitochondrial structure and function in our newly generated Taz cardiomyocyte-specific knockout mice and Cre-negative control mice (n≥3 per group).

RESULTS

Taz cardiomyocyte-specific knockout mice recapitulate typical features of BTHS and mitochondrial cardiomyopathy. Fewer than 5% of cardiomyocyte-specific knockout mice exhibited lethality before 2 months of age, with significantly enlarged hearts. More than 80% of cardiomyocyte-specific knockout displayed ventricular dilation at 16 weeks of age and survived until 50 weeks of age. Full parameter analysis of cardiac cardiolipin profiles demonstrated lower total cardiolipin concentration, abnormal cardiolipin fatty acyl composition, and elevated monolysocardiolipin to cardiolipin ratios in Taz cardiomyocyte-specific knockout, relative to controls. Mitochondrial contact site and cristae organizing system and F1F0-ATP synthase complexes, required for cristae morphogenesis, were abnormal, resulting in onion-shaped mitochondria. Organization of high molecular weight respiratory chain supercomplexes was also impaired. In keeping with observed mitochondrial abnormalities, seahorse experiments demonstrated impaired mitochondrial respiration capacity.

CONCLUSIONS

Our mouse model mirrors multiple physiological and biochemical aspects of BTHS cardiomyopathy. Our results give important insights into the underlying cause of BTHS cardiomyopathy and provide a framework for testing therapeutic approaches to BTHS cardiomyopathy, or other mitochondrial-related cardiomyopathies.

Evolutive Models for the Geometry and Heat Conductivity of an Intumescent EVA-ATH Composite during Its Thermal Degradation

Reliable predictions from numerical simulations in fire safety applications require knowledge of the combustible materials’ properties in their initial and thermally degraded states. The thermal conductivity of the sheath material of electrical cables, present in massive amounts in industrial plants, is addressed here. An evolutive conceptual model is proposed for the morphology of this intumescent polymer composite during its thermal degradation. It accounts for the multiscale structure and anisotropy observed during a thorough characterization based on tomographic images of samples at representative stages of the degradation. The evolution of the geometrical characteristics during the process is linked to chemical advancement parameters according to a reasoned scenario based on physical arguments and balance considerations. The anisotropic thermal conductivity tensor can be deduced from the geometry by a nested application of classical models. Ultimately, the conductivity is obtained as an analytic function of the chemical advancement and temperature. The model predictions were validated by comparisons with direct numerical solutions of thermal problems in the fully described geometry provided by the tomographies, and with measurements from the literature. The methodology and conceptual tools can be of interest for the treatment of other materials and in other contexts of application.

Efficient uncertainty quantification for permeability of three-dimensional porous media through image analysis and pore-scale simulations

In this paper, we propose an efficient coupled approach for uncertainty quantification of permeability for randomly reconstructed three-dimensional (3D) pore images, where the porosity and two-point correlations of a realistic sandstone sample are honored. The Joshi-Quiblier-Adler approach and Karhunen-Loève expansion are utilized for quick reconstruction of 3D pore images with reduced random dimensionality. The eigenvalue problem for the covariance matrix of 3D intermediate Gaussian random fields is solved equivalently by a kernel method. Then, the lattice Boltzmann method is adopted to simulate fluid flow in reconstructed pore space and evaluate permeability. Lastly, the sparse polynomial chaos expansion (sparse PCE) integrated with a feature selection method is employed to predict permeability distributions incurred by the randomness in microscopic pore structures. The feature selection process, which is intended to discard redundant basis functions, is carried out by the least absolute shrinkage and selection operator-modified least angle regression along with cross validation. The competence of our proposed approach is validated by the results from Monte Carlo simulation. It reveals that a small number of samples is sufficient for sparse PCE with feature selection to produce convincing results. Then, we utilize our method to quantify the uncertainty of permeability under different porosities and correlation parameters. It is found that the predicted permeability distributions for reconstructed 3D pore images are close to experimental measurements of Berea sandstones in the literature. In addition, the results show that porosity and correlation length are the critical influence factors for the uncertainty of permeability.

Reconstruction of porous media from extremely limited information using conditional generative adversarial networks

Porous media are ubiquitous in both nature and engineering applications. Therefore, their modeling and understanding is of vital importance. In contrast to direct acquisition of three-dimensional (3D) images of this type of medium, obtaining its subregion (s) such as 2D images or several small areas can be feasible. Therefore, reconstructing whole images from limited information is a primary technique in these types of cases. Given data in practice cannot generally be determined by users and may be incomplete or only partially informed, thus making existing reconstruction methods inaccurate or even ineffective. To overcome this shortcoming, in this study we propose a deep-learning-based framework for reconstructing full images from their much smaller subareas. In particular, conditional generative adversarial network is utilized to learn the mapping between the input (a partial image) and output (a full image). To ensure the reconstruction accuracy, two simple but effective objective functions are proposed and then coupled with the other two functions to jointly constrain the training procedure. Because of the inherent essence of this ill-posed problem, a Gaussian noise is introduced for producing reconstruction diversity, thus enabling the network to provide multiple candidate outputs. Our method is extensively tested on a variety of porous materials and validated by both visual inspection and quantitative comparison. It is shown to be accurate, stable, and even fast (∼0.08 s for a 128×128 image reconstruction). The proposed approach can be readily extended by, for example, incorporating user-defined conditional data and an arbitrary number of object functions into reconstruction, while being coupled with other reconstruction methods.

Reconstruction of a digital core containing clay minerals based on a clustering algorithm

It is difficult to obtain a core sample and information for digital core reconstruction of mature sandstone reservoirs around the world, especially for an unconsolidated sandstone reservoir. Meanwhile, reconstruction and division of clay minerals play a vital role in the reconstruction of the digital cores, although the two-dimensional data-based reconstruction methods are specifically applicable as the microstructure reservoir simulation methods for the sandstone reservoir. However, reconstruction of clay minerals is still challenging from a research viewpoint for the better reconstruction of various clay minerals in the digital cores. In the present work, the content of clay minerals was considered on the basis of two-dimensional information about the reservoir. After application of the hybrid method, and compared with the model reconstructed by the process-based method, the digital core containing clay clusters without the labels of the clusters' number, size, and texture were the output. The statistics and geometry of the reconstruction model were similar to the reference model. In addition, the Hoshen-Kopelman algorithm was used to label various connected unclassified clay clusters in the initial model and then the number and size of clay clusters were recorded. At the same time, the K-means clustering algorithm was applied to divide the labeled, large connecting clusters into smaller clusters on the basis of difference in the clusters' characteristics. According to the clay minerals' characteristics, such as types, textures, and distributions, the digital core containing clay minerals was reconstructed by means of the clustering algorithm and the clay clusters' structure judgment. The distributions and textures of the clay minerals of the digital core were reasonable. The clustering algorithm improved the digital core reconstruction and provided an alternative method for the simulation of different clay minerals in the digital cores.

Imaging connected porosity of crystalline rock by contrast agent-aided X-ray microtomography and scanning electron microscopy

We set out to study connected porosity of crystalline rock using X-ray microtomography and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM-EDS) with caesium chloride as a contrast agent. Caesium is an important radionuclide regarding the final deposition of nuclear waste and also forms dense phases that can be readily distinguished by X-ray microtomography and SEM-EDS. Six samples from two sites, Olkiluoto (Finland) and Grimsel (Switzerland), where transport properties of crystalline rock are being studied in situ, were investigated using X-ray microtomography and SEM-EDS. The samples were imaged with X-ray microtomography, immersed in a saturated caesium chloride (CsCl) solution for 141, 249 and 365 days and imaged again with X-ray microtomography. CsCl inside the samples was successfully detected with X-ray microtomography and it had completely penetrated all six samples. SEM-EDS elemental mapping was used to study the location of caesium in the samples in detail with quantitative mineral information. Precipitated CsCl was found in the connected pore space in Olkiluoto veined gneiss and in lesser amounts in Grimsel granodiorite. Only a very small amount of precipitated CsCl was observed in the Grimsel granodiorite samples. In Olkiluoto veined gneiss caesium was found in pinitised areas of cordierite grains. In the pinitised areas caesium was found in notable excess compared to chloride, possibly due to the combination of small pore size and negatively charged surfaces. In addition, elevated concentrations of caesium were found in kaolinite and sphalerite phases. The findings concerning the location of CsCl were congruent with X-ray microtomography.

Reconstructing the microstructure of polyimide-silicalite mixed-matrix membranes and their particle connectivity using FIB-SEM tomography

Properties of a composite material made of a continuous matrix and particles often depend on microscopic details, such as contacts between particles. Focusing on processing raw focused-ion beam scanning electron microscope (FIB-SEM) tomography data, we reconstructed three mixed-matrix membrane samples made of 6FDA-ODA polyimide and silicalite-1 particles. In the first step of image processing, backscattered electron (BSE) and secondary electron (SE) signals were mixed in a ratio that was expected to obtain a segmented 3D image with a realistic volume fraction of silicalite-1. Second, after spatial alignment of the stacked FIB-SEM data, the 3D image was smoothed using adaptive median and anisotropic nonlinear diffusion filters. Third, the image was segmented using the power watershed method coupled with a seeding algorithm based on geodesic reconstruction from the markers. If the resulting volume fraction did not match the target value quantified by chemical analysis of the sample, the BSE and SE signals were mixed in another ratio and the procedure was repeated until the target volume fraction was achieved. Otherwise, the segmented 3D image (replica) was accepted and its microstructure was thoroughly characterized with special attention paid to connectivity of the silicalite phase. In terms of the phase connectivity, Monte Carlo simulations based on the pure-phase permeability values enabled us to calculate the effective permeability tensor, the main diagonal elements of which were compared with the experimental permeability. In line with the hypothesis proposed in our recent paper (Čapek, P. et al. (2014) Comput. Mater. Sci. 89, 142-156), the results confirmed that the existence of particle clusters was a key microstructural feature determining effective permeability.

Electro-osmosis in inhomogeneously charged microporous media by pore-scale modeling

Surface charge at solid-electrolyte interface is generally coupled with the local electrolyte properties (ionic concentration, pH, etc.), and therefore not as assumed homogeneous on the solid surfaces in the previous studies. The inhomogeneous charge brings huge challenges in predictions of electro-osmotic transport and has never been well studied. In this work, we first propose a classification of electro-osmosis based on a dimensionless number which is the ratio of the Debye length to the characteristic pore size. In the limit of thin electrical double layer, we establish a pore-scale numerical model for inhomogeneously charged electro-osmosis including four ions: Na⁺,Cl^-,H⁺ and OH^-. Based on reconstructed porous media, we simulate the electro-osmosis with inhomogeneous charge using lattice Boltzmann method. The nonlinear response of electro-osmotic velocity to applied electrical field and the reverse flow have been observed and analyzed.

Statistics for Poisson Models of Overlapping Spheres

In this paper we consider the stationary Poisson Boolean model with spherical grains and propose a family of nonparametric estimators for the radius distribution. These estimators are based on observed distances and radii, weighted in an appropriate way. They are ratio unbiased and asymptotically consistent for a growing observation window. We show that the asymptotic variance exists and is given by a fairly explicit integral expression. Asymptotic normality is established under a suitable integrability assumption on the weight function. We also provide a short discussion of related estimators as well as a simulation study.

Statistics for Poisson Models of Overlapping Spheres

In this paper we consider the stationary Poisson Boolean model with spherical grains and propose a family of nonparametric estimators for the radius distribution. These estimators are based on observed distances and radii, weighted in an appropriate way. They are ratio unbiased and asymptotically consistent for a growing observation window. We show that the asymptotic variance exists and is given by a fairly explicit integral expression. Asymptotic normality is established under a suitable integrability assumption on the weight function. We also provide a short discussion of related estimators as well as a simulation study.

Differential porosimetry and permeametry for random porous media

Accurate determination of geometrical and physical properties of natural porous materials is notoriously difficult. Continuum multiscale modeling has provided carefully calibrated realistic microstructure models of reservoir rocks with floating point accuracy. Previous measurements using synthetic microcomputed tomography (μ-CT) were based on extrapolation of resolution-dependent properties for discrete digitized approximations of the continuum microstructure. This paper reports continuum measurements of volume and specific surface with full floating point precision. It also corrects an incomplete description of rotations in earlier publications. More importantly, the methods of differential permeametry and differential porosimetry are introduced as precision tools. The continuum microstructure chosen to exemplify the methods is a homogeneous, carefully calibrated and characterized model for Fontainebleau sandstone. The sample has been publicly available since 2010 on the worldwide web as a benchmark for methodical studies of correlated random media. High-precision porosimetry gives the volume and internal surface area of the sample with floating point accuracy. Continuum results with floating point precision are compared to discrete approximations. Differential porosities and differential surface area densities allow geometrical fluctuations to be discriminated from discretization effects and numerical noise. Differential porosimetry and Fourier analysis reveal subtle periodic correlations. The findings uncover small oscillatory correlations with a period of roughly 850μm, thus implying that the sample is not strictly stationary. The correlations are attributed to the deposition algorithm that was used to ensure the grain overlap constraint. Differential permeabilities are introduced and studied. Differential porosities and permeabilities provide scale-dependent information on geometry fluctuations, thereby allowing quantitative error estimates.

Transport properties of a Bentheim sandstone under deformation

The mechanical and transport properties of a Bentheim sandstone are studied both experimentally and numerically. Three classical classes of loads are applied to a sample whose permeability is measured. The elasticity and the Stokes equations are discretized on unstructured tetrahedral meshes which precisely follow the deformations of the sample. Numerical results are presented, discussed, and compared to the available experimental data.

Stable-phase method for hierarchical annealing in the reconstruction of porous media images

In this paper, we introduce a stable-phase approach for hierarchical annealing which addresses the very large computational costs associated with simulated annealing for the reconstruction of large-scale binary porous media images. Our presented method, which uses the two-point correlation function as the morphological descriptor, involves the reconstruction of three-phase and two-phase structures. We consider reconstructing the three-phase structures based on standard annealing and the two-phase structures based on standard and hierarchical annealings. From the result of the two-dimensional (2D) reconstruction, we find that the 2D generation does not fully capture the morphological information of the original image, even though the two-point correlation function of the reconstruction is in excellent agreement with that of the reference image. For the reconstructed three-dimensional (3D) microstructure, we calculate its permeability and compare it to that of the reference 3D microstructure. The result indicates that the reconstructed structure has a lower degree of connectedness than that of the actual sandstone. We also compare the computation time of our presented method to that of the standard annealing, which shows that our presented method of orders of magnitude improves the convergence rate. That is because only a small part of the pixels in the overall hierarchy need to be considered for sampling by the annealer.

Fast two-dimensional bubble analysis of biopolymer filamentous networks pore size from confocal microscopy thin data stacks

The average pore size ξ0 of filamentous networks assembled from biological macromolecules is one of the most important physical parameters affecting their biological functions. Modern optical methods, such as confocal microscopy, can noninvasively image such networks, but extracting a quantitative estimate of ξ0 is a nontrivial task. We present here a fast and simple method based on a two-dimensional bubble approach, which works by analyzing one by one the (thresholded) images of a series of three-dimensional thin data stacks. No skeletonization or reconstruction of the full geometry of the entire network is required. The method was validated by using many isotropic in silico generated networks of different structures, morphologies, and concentrations. For each type of network, the method provides accurate estimates (a few percent) of the average and the standard deviation of the three-dimensional distribution of the pore sizes, defined as the diameters of the largest spheres that can be fit into the pore zones of the entire gel volume. When applied to the analysis of real confocal microscopy images taken on fibrin gels, the method provides an estimate of ξ0 consistent with results from elastic light scattering data.

A bicontinuous mesophase geometry with hexagonal symmetry

We report that a specific realization of Schwarz's triply periodic hexagonal minimal surface is isotropic with respect to the Doi-Ohta interface tensor and simultaneously has minimal packing and stretching frustration similar to those of the commonly found cubic bicontinuous mesophases. This hexagonal surface, of symmetry P6(3)/mmc with a lattice ratio of c/a = 0.832, is therefore a likely candidate geometry for self-assembled lipid/surfactant or copolymer mesophases. Furthermore, both the peak position ratios in its powder diffraction pattern and the elastic moduli closely resemble those of the cubic bicontinuous phases. We therefore argue that a genuine possibility of experimental misidentification exists.

Minkowski tensor shape analysis of cellular, granular and porous structures

Predicting physical properties of materials with spatially complex structures is one of the most challenging problems in material science. One key to a better understanding of such materials is the geometric characterization of their spatial structure. Minkowski tensors are tensorial shape indices that allow quantitative characterization of the anisotropy of complex materials and are particularly well suited for developing structure-property relationships for tensor-valued or orientation-dependent physical properties. They are fundamental shape indices, in some sense being the simplest generalization of the concepts of volume, surface and integral curvatures to tensor-valued quantities. Minkowski tensors are based on a solid mathematical foundation provided by integral and stochastic geometry, and are endowed with strong robustness and completeness theorems. The versatile definition of Minkowski tensors applies widely to different types of morphologies, including ordered and disordered structures. Fast linear-time algorithms are available for their computation. This article provides a practical overview of the different uses of Minkowski tensors to extract quantitative physically-relevant spatial structure information from experimental and simulated data, both in 2D and 3D. Applications are presented that quantify (a) alignment of co-polymer films by an electric field imaged by surface force microscopy; (b) local cell anisotropy of spherical bead pack models for granular matter and of closed-cell liquid foam models; (c) surface orientation in open-cell solid foams studied by X-ray tomography; and (d) defect densities and locations in molecular dynamics simulations of crystalline copper.

Grain reconstruction of porous media: application to a Bentheim sandstone

The two-point correlation measured on a thin section can be used to derive the probability density of the radii of a population of penetrable spheres. The geometrical, transport, and deformation properties of samples derived by this method compare well with the properties of the digitized real sample and of the samples generated by the standard grain reconstruction method.

Boolean reconstructions of complex materials: Integral geometric approach

We show that for the Boolean model of random composite media one can, from a single image of a system at any particle fraction, define a set of parameters which allows one to accurately reconstruct the medium for all other phase fractions. The morphological characterization is based on a family of measures known in integral geometry which provides powerful formulas for the Boolean model. The percolation thresholds of either phase are obtained with good accuracy. From the reconstructions one can subsequently predict property curves for the material across all phase fractions from the single three-dimensional image. We illustrate this for transport and mechanical properties of complex Boolean systems and for experimental sandstone samples.

Towards precise prediction of transport properties from synthetic computer tomography of reconstructed porous media

Transport properties of a multiscale carbonate rock are predicted from pore scale models, reconstructed using a continuum geometrical modeling technique. The method combines crystallite information from two-dimensional high-resolution images with sedimentary correlations from a three-dimensional low-resolution microcomputed tomography ( micro-CT) image to produce a rock sample with calibrated porosity, structural correlation, and transport properties at arbitrary resolutions. Synthetic micro-CT images of the reconstructed model match well with experimental micro-CT images at different resolutions, making it possible to predict physical transport parameters at higher resolutions.

Robust pore size analysis of filamentous networks from three-dimensional confocal microscopy

We describe a robust method for determining morphological properties of filamentous biopolymer networks, such as collagen or other connective tissue matrices, from confocal microscopy image stacks. Morphological properties including pore size distributions and percolation thresholds are important for transport processes, e.g., particle diffusion or cell migration through the extracellular matrix. The method is applied to fluorescently labeled fiber networks prepared from rat-tail tendon and calf-skin collagen, at concentrations of 1.2, 1.6, and 2.4 mg/ml. The collagen fibers form an entangled and branched network. The medial axes, or skeletons, representing the collagen fibers are extracted from the image stack by threshold intensity segmentation and distance-ordered homotopic thinning. The size of the fluid pores as defined by the radii of largest spheres that fit into the cavities between the collagen fibers is derived from Euclidean distance maps and maximal covering radius transforms of the fluid phase. The size of the largest sphere that can traverse the fluid phase between the collagen fibers across the entire probe, called the percolation threshold, was computed for both horizontal and vertical directions. We demonstrate that by representing the fibers as the medial axis the derived morphological network properties are both robust against changes of the value of the segmentation threshold intensity and robust to problems associated with the point-spread function of the imaging system. We also provide empirical support for a recent claim that the percolation threshold of a fiber network is close to the fiber diameter for which the Euler index of the networks becomes zero.

Development of optimal models of porous media by combining static and dynamic data: the permeability and porosity distributions

We describe a method for the development of the optimal spatial distributions of the porosity phi and permeability k of a large-scale porous medium. The optimal distributions are constrained by static and dynamic data. The static data that we utilize are limited data for phi and k, which the method honors in the optimal model and utilizes their correlation functions in the optimization process. The dynamic data include the first-arrival (FA) times, at a number of receivers, of seismic waves that have propagated in the porous medium, and the time-dependent production rates of a fluid that flows in the medium. The method combines the simulated-annealing method with a simulator that solves numerically the three-dimensional (3D) acoustic wave equation and computes the FA times, and a second simulator that solves the 3D governing equation for the fluid's pressure as a function of time. To our knowledge, this is the first time that an optimization method has been developed to determine simultaneously the global minima of two distinct total energy functions. As a stringent test of the method's accuracy, we solve for flow of two immiscible fluids in the same porous medium, without using any data for the two-phase flow problem in the optimization process. We show that the optimal model, in addition to honoring the data, also yields accurate spatial distributions of phi and k, as well as providing accurate quantitative predictions for the single- and two-phase flow problems. The efficiency of the computations is discussed in detail.