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Reconstruction of porous media using ISOMAP-based MPS

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Abstract

Acquiring the structures of porous media is very important when predicting flow properties in porous media. However, direct measurements of 3D microstructures of porous media with the resolution of microns or even nanometers are difficult to achieve due to the expensive cost of high-precision equipment. Therefore, as a typical stochastic simulation method, multiple-point statistics (MPS) was used to perform reconstruction based on real 3D volume data of porous media scanned by micro-CT. Because the ensemble of patterns extracted from a training image (TI) cannot be embedded into a linear space, the traditional MPS methods using linear dimensionality reduction, including filter-based simulation and distance-based pattern simulation, are not suitable to deal with the nonlinear situation. A new MPS method using isometric mapping, which is a method of nonlinear dimensionality reduction, to achieve nonlinear dimensionality reduction is proposed to decrease redundant data of TIs so that the subsequent simulation can be faster and more accurate for the reconstruction of porous media. Entropy theory is introduced to select a proper size of data template to balance the CPU cost and reconstructed quality. The comparisons between the reconstructed images and the target image show that the structural characteristics of reconstructed porous media using our method are similar to those of real volume data. This method also has shown advantages in reconstruction quality over typical methods using linear dimensionality reduction.

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Acknowledgments

We really appreciate the reviewers for the valuable comments and suggestions on our manuscript. This work is supported by National Program on Key Basic Research Project of China (973 Program, No. 2011CB707305), the National Science and Technology Major Project (No. 2011ZX05009-006), CAS Strategic Priority Research Program (XDB10030402), Shanghai Municipal Natural Science Foundation (No. 12ZR1412000), Talented People Introduction Foundation of Shanghai University of Electric Power (No. K2012-004, K2013-019, K2014-020), and the Excellent University Young Teachers Training Program of Shanghai Municipal Education Commission (No. ZZsdl12002, ZZsdl13015).

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Authors and Affiliations

  1. College of Computer Science and Technology, Shanghai University of Electric Power, 2588 Changyang Road, Shanghai, 200090, People’s Republic of China

    Ting Zhang & Fangfang Lu

  2. School of Computer and Information, Shanghai Second Polytechnic University, 2360 Jinhai Road, Shanghai, 201209, People’s Republic of China

    Yi Du

  3. Department of Modern Mechanics, University of Science and Technology of China, 96 Jinzhai Road, Hefei, 230027, People’s Republic of China

    Yi Du, Tao Huang & Xue Li

  4. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 149 Yanchang Road, Shanghai, 200072, People’s Republic of China

    Jiaqing Yang

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  1. Ting Zhang
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  2. Yi Du
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  3. Tao Huang
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  4. Jiaqing Yang
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  5. Fangfang Lu
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Correspondence to Yi Du.

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Zhang, T., Du, Y., Huang, T. et al. Reconstruction of porous media using ISOMAP-based MPS. Stoch Environ Res Risk Assess 30, 395–412 (2016). https://doi.org/10.1007/s00477-015-1142-1

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