Direct relations between morphology and transport in Boolean models

Scholz, Christian; Wirner, Frank; Klatt, Michael A.; Hirneise, Daniel; Schröder‐Turk, Gerd E.; Mecke, Klaus; Bechinger, Clemens

doi:10.1103/physreve.92.043023

Cited by 41 publications

(36 citation statements)

References 51 publications

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“…It has been shown that flow properties at the porescale can be related to morphological characteristics of the void-solid interface of a porous medium [39]. Hadwiger's theorem states that the size of a body in a ddimensional space can be described by a linear combination of d + 1 independent parameters characterizing the body.…”

Section: Morphological Measuresmentioning

confidence: 99%

Reconstruction of three-dimensional porous media using generative adversarial neural networks

2017

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To evaluate the variability of multiphase flow properties of porous media at the pore scale, it is necessary to acquire a number of representative samples of the void-solid structure. While modern x-ray computer tomography has made it possible to extract three-dimensional images of the pore space, assessment of the variability in the inherent material properties is often experimentally not feasible. We present a method to reconstruct the solid-void structure of porous media by applying a generative neural network that allows an implicit description of the probability distribution represented by three-dimensional image data sets. We show, by using an adversarial learning approach for neural networks, that this method of unsupervised learning is able to generate representative samples of porous media that honor their statistics. We successfully compare measures of pore morphology, such as the Euler characteristic, two-point statistics, and directional single-phase permeability of synthetic realizations with the calculated properties of a bead pack, Berea sandstone, and Ketton limestone. Results show that generative adversarial networks can be used to reconstruct high-resolution three-dimensional images of porous media at different scales that are representative of the morphology of the images used to train the neural network. The fully convolutional nature of the trained neural network allows the generation of large samples while maintaining computational efficiency. Compared to classical stochastic methods of image reconstruction, the implicit representation of the learned data distribution can be stored and reused to generate multiple realizations of the pore structure very rapidly.

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Section: Morphological Measuresmentioning

confidence: 99%

Reconstruction of three-dimensional porous media using generative adversarial neural networks

2017

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“…The influence of model parameters on transport properties has been recently investigated for Boolean models with more general grains. 18 For our case study, we consider two SMM that generate different types of microstructures: the stochastic spatial graph model 10 (SSGM) and a simplified version of the multiscale sphere model (MSM). 14,19 By means of the SSGM microstructures within a wide range of different values for volume fraction, mean geodesic tortuosity, and constrictivity can be generated.…”

Section: Stochastic Microstructure Modelingmentioning

confidence: 99%

Big data for microstructure‐property relationships: A case study of predicting effective conductivities

et al. 2017

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The analysis of big data is changing industries, businesses and research as large amounts of data are available nowadays. In the area of microstructures, acquisition of (3-D tomographic image) data is difficult and time-consuming. It is shown that large amounts of data representing the geometry of virtual, but realistic 3-D microstructures can be generated using stochastic microstructure modeling. Combining the model output with physical simulations and data mining techniques, microstructure-property relationships can be quantitatively characterized. Exemplarily, we aim to predict effective conductivities given the microstructure characteristics volume fraction, mean geodesic tortuosity, and constrictivity. Therefore, we analyze 8119 microstructures generated by two different stochastic 3-D microstructure models. This is-to the best of our knowledge-by far the largest set of microstructures that has ever been analyzed. Fitting artificial neural networks, random forests and classical equations, the prediction of effective conductivities based on geometric microstructure characteristics is possible.

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“…the Euler characteristic triggered predictions of flow in porous media that are based on the Minkowski functionals [65,66]. More precisely, we here refer to the density of the Euler characteristic χ, that is, before taking the limit of an infinitely large observation window the functional value is rescaled by the size of the window [33].…”

Section: Euler Characteristic Approximationmentioning

confidence: 99%

Anisotropy in finite continuum percolation: threshold estimation by Minkowski functionals

Klatt¹,

Schröder‐Turk²,

Mecke³

2017

J. Stat. Mech.

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Abstract. We examine the interplay between anisotropy and percolation, i. e., the spontaneous formation of a system spanning cluster in an anisotropic model. We simulate an extension of a benchmark model of continuum percolation, the Boolean model, which is formed by overlapping grains. Here we introduce an orientation bias of the grains that controls the degree of anisotropy of the generated patterns. We analyze in the Euclidean plane the percolation thresholds above which percolating clusters in x-and in y-direction emerge. Only in finite systems, distinct differences between effective percolation thresholds for different directions appear. If extrapolated to infinite system sizes, these differences vanish independent of the details of the model. In the infinite system, the uniqueness of the percolating cluster guarantees a unique percolation threshold. While percolation is isotropic even for anisotropic processes, the value of the percolation threshold depends on the model parameters, which we explore by simulating a score of models with varying degree of anisotropy. To which precision can we predict the percolation threshold without simulations? We discuss analytic formulas for approximations (based on the excluded area or the Euler characteristic) and compare them to our simulation results. Empirical parameters from similar systems allow for accurate predictions of the percolation thresholds (with deviations of < 5% in our examples), but even without any empirical parameters, the explicit approximations from integral geometry provide, at least for the systems studied here, lower bounds that capture well the qualitative dependence of the percolation threshold on the system parameters (with deviations of 5%-30%). As an outlook, we suggest further candidates for explicit and geometric approximations based on second moments of the so-called Minkowski functionals.

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Direct relations between morphology and transport in Boolean models

Cited by 41 publications

References 51 publications

Reconstruction of three-dimensional porous media using generative adversarial neural networks

Reconstruction of three-dimensional porous media using generative adversarial neural networks

Big data for microstructure‐property relationships: A case study of predicting effective conductivities

Anisotropy in finite continuum percolation: threshold estimation by Minkowski functionals

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