Stochastic reconstruction of sandstones

Manwart, C.; Torquato, Salvatore; Hilfer, R.

doi:10.1103/physreve.62.893

Cited by 204 publications

(119 citation statements)

References 24 publications

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“…This reconstruction problem leads to anisotropic microstructures, which is in contrast to other such works in literature that use a single reference (2D) image and make assumptions of http://www.immijournal.com/content/3/1/19 microstructural isotropy, i.e., slices in every direction look similar to a single input image [1]. The most popular among these methods involves matching statistical features like two-point correlation functions of a single planar image to a random 3D image using optimization procedures like simulated annealing [2,3]. Extension of these methods to achieve anisotropic microstructures has been proposed in the past using directionally dependent statistical features [4].…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of three-dimensional anisotropic microstructures from two-dimensional micrographs imaged on orthogonal planes

Sundararaghavan

2014

Integr Mater Manuf Innov

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A pervasive method for reconstructing microstructures from two-dimensional microstructures imaged on orthogonal planes is presented. The algorithm reconstructs 3D images through matching of 3D slices at different voxels to the representative 2D micrographs and an optimization procedure that ensures patches from the 2D micrographs meshed together seamlessly in the 3D image. We show that the method effectively models the three-dimensional features in the microstructure using three cases (i) disperse spheres, (ii) anisotropic lamellar microstructure, and (iii) a polycrystalline microstructure. The method is validated by comparing the point probability functions of the reconstructed images to the original 2D image, as well as by comparing the elastic properties of reconstructed image to the experimental data.

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Section: Introductionmentioning

confidence: 99%

Reconstruction of three-dimensional anisotropic microstructures from two-dimensional micrographs imaged on orthogonal planes

Sundararaghavan

2014

Integr Mater Manuf Innov

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“…In the past decades, several approaches have been proposed to numerically reconstruct the microstructure of a natural porous medium [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Among these approaches is the commonly used stochastic rock reconstruction [1-3, 6, 8, 11, 15, 18-20], which relies on matching statistical properties of a three-dimensional model to those of a real rock microstructure.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of Sedimentary Rock Based on MechanicalProperties

Jin¹,

Patzek²,

Silin³

2004

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We describe a general, physics-based approach to numerical reconstruction of the geometrical structure and mechanical properties of natural sedimentary rock in 3D. Our procedure consists of three main steps: sedimentation, compaction, and diagenesis, followed by the verification of rock mechanical properties. The dynamic geologic processes of grain sedimentation and compaction are simulated by solving a dimensionless form of Newton's equations of motion for an ensemble of grains. The diagenetic rock transformation is modeled using a cementation algorithm, which accounts for the effect of rock grain size on the relative rate of cement overgrowth.Our emphasis is on unconsolidated sand and sandstone. The main input parameters are the grain size distribution, the final rock porosity, the type and amount of cement and clay minerals, and grain mechanical properties: the inter-grain friction coefficient, the cement strength, and the grain stiffness moduli. We use a simulated 2D Fontainebleau sandstone to obtain the grain mechanical properties. This Fontainebleau sandstone is also used to study the initiation, growth, and coalescence of microcracks under increasing vertical stress. The box fractal dimension of the micro-crack distribution, and its variation with the applied stress are estimated.

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“…However, reconstructions of experimental data sets based on these characterisations have been shown to give a poor representation of the connectivity of the systems [26]. Functions that may provide more complete information about connectivity [16] are unfortunately too complex to incorporate into reconstruction schemes [26].…”

Section: Spatial Structures: Experimental Data and Stochastic Modelsmentioning

confidence: 99%

“…Of course, one can derive more complex model systems which incorporate other two-point correlation information (e.g., chord distribution functions [47,53]. Recent work [26] has shown that these measures give a poor representation of connectivity. Preliminary results on Minkowski functionals of these more complex models indicate that this is reflected in a poor match to the v 2 measure.…”

Section: Characteristics Of a Sandstone Samplementioning

confidence: 99%

Characterising the Morphology of Disordered Materials

Arns

Knackstedt

Mecke

2002

Morphology of Condensed Matter

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Abstract. We introduce Minkowski functionals to characterise, reconstruct and discriminate different complex material microstructures, for instance, experimental data sets generated from X-ray computer tomography imaging; samples include a suite of Fontainebleau sandstone, and a heterogeneous cross-bedded sandstone. Three distinct classes of digitised complex microstructure are considered: particle based Boolean models, structures generated by level-cuts through Gaussian fields, and models based on a Voronoi tesselation of space. One can define a set of measures for random composite media from a single image at any phase fraction φ which allows one to accurately reconstruct the medium for all other phase fractions and to predict, for instance, the percolation threshold pc. The evolution of the Minkowski functions during erosion and dilation operations on non-convex morphologies leads to a very accurate discrimination of morphologybetter than commonly used techniques such as structure functions or chord length distributions. Spatial Structures: Experimental Data and Stochastic ModelsThe structure of a disordered material -an oil bearing rock, a piece of paper, or a polymer composite -is a remarkably incoherent concept. Despite this, scientists and engineers are asked to predict the properties of a disordered material based on the "structure" of its constituent components. A major shortcoming in the understanding of processes involving complex materials has been an inability to accurately characterize microstructure. The specification of "structure" requires topological as well as geometric descriptors to characterize the connectivity and the shape of the spatial configuration. In oil recovery from petroleum reservoir rocks, an area of particular interest to the authors, recovery depends crucially on the topology of the pore space and on the mean curvature of the surfaces where immiscible phases meet at a contact angle. To determine accurate flow models and to devise intelligent recovery strategies requires an accurate characterization of reservoir rocks in terms of topology and geometry.To date, the main toolkit used to quantify complex structures has been primarily that of the statistical physicist and not the advanced techniques developed in spatial statistics [11,59]

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Stochastic reconstruction of sandstones

Cited by 204 publications

References 24 publications

Reconstruction of three-dimensional anisotropic microstructures from two-dimensional micrographs imaged on orthogonal planes

Reconstruction of three-dimensional anisotropic microstructures from two-dimensional micrographs imaged on orthogonal planes

Reconstruction of Sedimentary Rock Based on MechanicalProperties

Characterising the Morphology of Disordered Materials

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