Nested multiresolution hierarchical simulated annealing algorithm for porous media reconstruction

Lemmens, Laurent; Rogiers, Bart; Jacques, Diederik; Huysmans, Marijke; Swennen, Rudy; Urai, János; Desbois, Guillaume; Laloy, Eric

doi:10.1103/physreve.100.053316

Cited by 31 publications

(15 citation statements)

References 37 publications

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“…Secondly, multiscale images could be obtained by stochastically combining several scales and in contrast to image superposition, these models aim to jointly improve pore surfaces and fine-scale connectivity. Such multiscale images typically use expanding image grids to improve resolution through simulated annealing (SA) [61,[76][77][78] or multiple-point geostatistics (MPS) [72,76]. Thirdly, super-resolution methods aim to introduce high resolution patterns into low resolution images by mapping a translation of low resolution features to high resolution equivalents.…”

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confidence: 99%

Computed Tomography 3D Super-Resolution with Generative Adversarial Neural Networks: Implications on Unsaturated and Two-Phase Fluid Flow

2020

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Fluid flow characteristics are important to assess reservoir performance. Unfortunately, laboratory techniques are inadequate to know these characteristics, which is why numerical methods were developed. Such methods often use computed tomography (CT) scans as input but this technique is plagued by a resolution versus sample size trade-off. Therefore, a super-resolution method using generative adversarial neural networks (GANs) was used to artificially improve the resolution. Firstly, the influence of resolution on pore network properties and single-phase, unsaturated, and two-phase flow was analysed to verify that pores and pore throats become larger on average and surface area decreases with worsening resolution. These observations are reflected in increasingly overestimated single-phase permeability, less moisture uptake at lower capillary pressures, and high residual oil fraction after waterflooding. Therefore, the super-resolution GANs were developed which take low (12 µm) resolution input and increase the resolution to 4 µm, which is compared to the expected high-resolution output. These results better predicted pore network properties and fluid flow properties despite the overestimation of porosity. Relevant small pores and pore surfaces are better resolved thus providing better estimates of unsaturated and two-phase flow which can be heavily influenced by flow along pore boundaries and through smaller pores. This study presents the second case in which GANs were applied to a super-resolution problem on geological materials, but it is the first one to apply it directly on raw CT images and to determine the actual impact of a super-resolution method on fluid predictions.Materials 2020, 13, 1397 2 of 33 examples requires detailed knowledge on fluid storage and flow properties which could be estimated through experiments, either carried out in specialized laboratories or deduced from digital rocks. Laboratory measurements, however, require expensive and complex set-ups, take a long time to complete, are often destructive, do not always entirely capture the studied properties and on top of that, experiments often fail to produce reproducible results between laboratories [9,[12][13][14][15][16][17][18][19]. Therefore, numerical solutions have been developed allowing to compute fluid storage and flow properties on digital rocks [7,[20][21][22][23]. Such digital rocks are acquired through direct imaging or numerical simulations of rocks.Computed tomography (CT) is a technique to rapidly capture the three-dimensional structure of materials [22,24,25]. However, like any imaging technique, CT is plagued by a sample size versus resolution trade-off, which is adversely affecting fluid flow simulations. Both a high resolution and sufficiently large volume are required for accurate fluid flow estimations at the pore-scale [9,[26][27][28]. Resolution impacts how well pore network topology and pore surfaces are resolved. At lower resolution, i.e., lower resolving power, pore sizes are often overestimated and specific surf...

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confidence: 99%

Computed Tomography 3D Super-Resolution with Generative Adversarial Neural Networks: Implications on Unsaturated and Two-Phase Fluid Flow

2020

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“…Due to this shortcoming in adapting a cluster function for stochastic reconstructions, its application is limited to small images (Jiao et al, 2009; Jiao & Chawla, 2014) and has found no widespread use in practical applications. Hierarchical reconstruction and different CF computation schemes are expected to alleviate such computational constraints (Gao, Li, Xu, Wu, & Wang, 2019; Karsanina & Gerke, 2018; Lemmens et al, 2019; Wu, Tahmasebi, Lin, Ren, & Dong, 2019).…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…The spatial distribution of these phases can easily affect some crucial soil properties, for example, unsaturated flow and wettability (Bachmann, Deurer, & Arye, 2007; Gerke, Sidle, & Mallants, 2015). Correlation (including cross‐correlations between phases) functions can be computed for multiple phases and used for stochastic reconstructions (Jiao & Chawla, 2014; Lemmens et al, 2019; Losic, Thovert, & Adler, 1997; Schlüter & Vogel, 2011). Notably, this will improve the information content of the CFs set due to the inclusion of cross‐correlations.…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…Although there are plenty of relevant stochastic reconstruction methods, including multiple‐point statistics (Ding, Teng, Wang, He, & Feng, 2018; Gravey & Mariethoz, 2020; Tahmasebi & Sahimi, 2012) or machine learning‐based techniques (Feng et al, 2019; Mosser, Dubrule, & Blunt, 2017), the methods based on correlation functions (CFs) possess a number of distinct advantages: (a) they can describe the structure of soil by way of a rigorous mathematical function (Torquato, 2002), (b) they allow rescaling of the structural data by manipulating correlation functions (Gerke, Karsanina, & Mallants, 2015; Karsanina & Gerke, 2018), (c) they provide a hierarchical annealing scheme to create a multiscale structure of desired resolution (Karsanina & Gerke, 2018; Lemmens et al, 2019), (d) they allow expression of an estimation of physical properties using rigorous bounds (Torquato, 2002), (e) they provide a tool to access structure stationarity as related to representativity (Gerke et al, 2020), (f) they are capable of incorporating experimentally measured correlation functions obtained using small‐angle scattering (Debye, Anderson Jr, & Brumberger, 1957; Karsanina et al, 2019), (g) they can facilitate correct tensorial physical property simulations based on geometrically‐periodic replicas of real soil samples (Gerke, Karsanina, & Katsman, 2019), and (h) they can describe the dynamics of soil structure (Chen, Xu, Chawla, Ren, & Jiao, 2019; Karsanina, Gerke, Skvortsova, & Mallants, 2015). Note that not all of the aforementioned separate advantages are exclusive to correlation functions; some of them can be achieved using more conventional descriptors, such as, for example, Minkowski functionals and other metrics (Schlüter & Vogel, 2011).…”

Section: Introductionmentioning

confidence: 99%

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Compressing soil structural information into parameterized correlation functions

Karsanina

Lavrukhin

Fomin

et al. 2020

European J Soil Science

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Soil structure is highly interconnected to all of its properties and functions. The structure for most soils is very complex and hierarchical in nature. Considering the fact that a truly multiscale digital 3D soil structure model for a single genetic horizon, even with the resolution not finer than 1 μm, will contain an enormous amount (approx. up to 1015 voxels or even more) of data, it is an appealing idea to compress this structural information. Effective management and pore‐scale simulations based on such datasets do not seem feasible at the moment. Another approach would be to reduce the complexity to a limited but meaningful set of characteristics/parameters, for example using universal correlation functions (CFs). In this study, we successfully compressed the soil structural information in the form of 3D binary images into a set of correlation functions, each of which is described using only six parameters. We used four different correlation functions (two‐point probability, lineal, cluster and surface‐surface functions) computed in three orthogonal directions for the pores. The methodology was applied to 16 different soil 3D images obtained using X‐ray microtomography (XCT) and segmented into pores and solids. All computed CFs were fitted using a superposition of three basis functions. In other words, we reduced 900–13003 voxel images into sets of 72 parameters. Fitting of computed correlation functions and reducing them to a number of parameters is a powerful way of compressing soil structural information. However, the analysis based on parameters alone is different from the one where correlation functions are used. This problem can be negated by uncompressing the correlation functions back from these parameters before any application. This way, correlation functions are not only a way to compress the soil structural information with minimal loss, but also may be used to solve a number of additional problems, including the comparison and differentiation of soil samples, location of elementary volumes, effective physical property prediction using machine learning, and fusion of hierarchical soil structures. Highlights The 900–13003 voxels soil XCT scans were compressed into sets of 72 parameters The use of fitted parameters alone may result in the inconsistent analysis of the soil structures Each soil structure was uniquely described by a set of directional correlation functions Correlation functions were found to be sensitive to the structural difference of all the studied soils

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“…However, it is computationally expensive and may produce repetitive textures based on the number of points used for statistics. Quite surprisingly, some MPS methods are even slower and less accurate than SA based on twopoint statistics [21]. Deep learning approaches [22][23][24] are getting popular and show great promise, but even more computationally expensive than MPS and SA, with lower accuracies not balanced by massive training times.…”

Section: Introductionmentioning

confidence: 99%

Adaptive phase-retrieval stochastic reconstruction with correlation functions: 3D images from 2D cuts

Cherkasov,

Ananev,

Karsanina

et al. 2021

Preprint

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Precise characterization of three-dimensional heterogeneous media is indispensable in finding the relationships between structure and macroscopic physical properties (permeability, conductivity, and others). The most widely used experimental methods (electronic and optical microscopy) provide high-resolution bi-dimensional images of the samples of interest. However, 3D material inner microstructure registration is needed to apply numerous modeling tools. Numerous research areas search for cheap and robust methods to obtain "full" 3D information about the structure of the studied sample from its 2D cuts. In this work, we develop a dynamic phase-retrieval stochastic reconstruction algorithm that can create 3D replicas from 2D original images -DDTF. The DDTF is free of artifacts characteristic of previously proposed phase-retrieval techniques. While based on a two-point S2 correlation function, any correlation function or other morphological metrics can be accounted for during the reconstruction, thus, paving the way to the hybridization of different reconstruction techniques. In this work, we use two-point probability and surface-surface functions for optimization. To test DDTF, we performed reconstructions for three binary porous media samples of different genesis: sandstone, carbonate, and ceramic. Based on computed permeability and connectivity (C2 and L2 correlation functions), we have shown that the proposed technique in terms of accuracy is comparable to the classic simulated annealing-based reconstruction method but is computationally very effective. Our findings open the possibility of utilizing DDTF to produce fast or crude replicas further polished by other reconstruction techniques such as simulated annealing or process-based methods. Improving the quality of reconstructions based on phase-retrieval by adding additional metrics into the reconstruction procedure is possible for future work.

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Nested multiresolution hierarchical simulated annealing algorithm for porous media reconstruction

Cited by 31 publications

References 37 publications

Computed Tomography 3D Super-Resolution with Generative Adversarial Neural Networks: Implications on Unsaturated and Two-Phase Fluid Flow

Computed Tomography 3D Super-Resolution with Generative Adversarial Neural Networks: Implications on Unsaturated and Two-Phase Fluid Flow

Compressing soil structural information into parameterized correlation functions

Adaptive phase-retrieval stochastic reconstruction with correlation functions: 3D images from 2D cuts

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