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Transport in Porous Media

, Volume 125, Issue 1, pp 5–22 | Cite as

Accurate Reconstruction of Porous Materials via Stochastic Fusion of Limited Bimodal Microstructural Data

  • Hechao Li
  • Pei-En Chen
  • Yang JiaoEmail author
Article

Abstract

Porous materials such as sandstones have important applications in petroleum engineering and geosciences. An accurate knowledge of the porous microstructure of such materials is crucial for the understanding of their physical properties and performance. Here, we present a procedure for accurate reconstruction of porous materials by stochastically fusing limited bimodal microstructural data including limited-angle X-ray tomographic radiographs and 2D optical micrographs. The key microstructural information contained in the micrographs is statistically extracted and represented using certain lower-order spatial correlation functions associated with the pore phase, and a probabilistic interpretation of the attenuated intensity in the tomographic radiographs is developed. A stochastic procedure based on simulated annealing that generalizes the widely used Yeong–Torquato framework is devised to efficiently incorporate and fuse the complementary bimodal imaging data for accurate microstructure reconstruction. The information content of the complementary microstructural data is systematically investigated using a 2D model system. Our procedure is subsequently applied to accurately reconstruct a variety of 3D sandstone microstructures with a wide range of porosities from limited X-ray tomographic radiographs and 2D optical micrographs. The accuracy of the reconstructions is quantitatively ascertained by directly comparing the original and reconstructed microstructures and their corresponding clustering statistics.

Keywords

Microstructure reconstruction Porous materials Limited bimodal microstructural data Stochastic data fusion 

Notes

Acknowledgements

The authors are very grateful to Prof. Muhammad Sahimi and Prof. Pejman Tahmasebi for their kind invitation for this special issue. This work is supported by ACS Petroleum Research Fund under Grant No. 56474-DNI10 (Program manager: Dr. Burtrand Lee).

References

  1. Blacklock, M., Bale, H., Begley, M., Cox, B.: Generating virtual textile composite specimens using statistical data from micro-computed tomography: 1D tow representations for the Binary Model. J. Mech. Phys. Solids 60(3), 451–470 (2012)CrossRefGoogle Scholar
  2. Bostanabad, R., Bui, A.T., Xie, W., Apley, D.W., Chen, W.: Stochastic microstructure characterization and reconstruction via supervised learning. Acta Mater. 103, 89–102 (2016)CrossRefGoogle Scholar
  3. Castañeda, P.P.: Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. J. Mech. Phys. Solids 44(6), 827–862 (1996)CrossRefGoogle Scholar
  4. Chen, D., Teng, Q., He, X., Xu, Z., Li, Z.: Stable-phase method for hierarchical annealing in the reconstruction of porous media images. Phys. Rev. E 89(1), 013305 (2014)CrossRefGoogle Scholar
  5. Chen, S., Li, H., Jiao, Y.: Dynamic reconstruction of heterogeneous materials and microstructure evolution. Phys. Rev. E 92(2), 023301 (2015)CrossRefGoogle Scholar
  6. Chen, S., Kirubanandham, A., Chawla, N., Jiao, Y.: Stochastic multi-scale reconstruction of 3D microstructure consisting of polycrystalline grains and second-phase particles from 2D micrographs. Metall. Mater. Trans. A 47, 1–11 (2016)Google Scholar
  7. Childs, E.C., Collis-George, N.: The permeability of porous materials. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 201(1066), 392–405 (1950)CrossRefGoogle Scholar
  8. Cnudde, V., Boone, M.N.: High-resolution X-ray computed tomography in geosciences: a review of the current technology and applications. Earth Sci. Rev. 123, 1–17 (2013)CrossRefGoogle Scholar
  9. Collins, R.E.: Flow of Fluids Through Porous Materials. Reinhold Pub. Corp, New York (1976)Google Scholar
  10. Davis, M.E.: Ordered porous materials for emerging applications. Nature 417(6891), 813–821 (2002)CrossRefGoogle Scholar
  11. Fullwood, D., Kalidindi, S., Niezgoda, S., Fast, A., Hampson, N.: Gradient-based microstructure reconstructions from distributions using fast Fourier transforms. Mater. Sci. Eng. A 494(1), 68–72 (2008)CrossRefGoogle Scholar
  12. Fullwood, D.T., Niezgoda, S.R., Kalidindi, S.R.: Microstructure reconstructions from 2-point statistics using phase-recovery algorithms. Acta Mater. 56(5), 942–948 (2008)CrossRefGoogle Scholar
  13. Gerke, K.M., Karsanina, M.V.: Improving stochastic reconstructions by weighting correlation functions in an objective function. EPL (Europhysics Letters) 111(5), 56002 (2015)CrossRefGoogle Scholar
  14. Gerke, K.M., Karsanina, M.V., Vasilyev, R.V., Mallants, D.: Improving pattern reconstruction using directional correlation functions. EPL (Europhysics Letters) 106(6), 66002 (2014)CrossRefGoogle Scholar
  15. Gerke, K.M., Karsanina, M.V., Mallants, D.: Universal stochastic multiscale image fusion: an example application for shale rock. Sci. Rep. 5, 15880 (2015)CrossRefGoogle Scholar
  16. Gommes, C.J., Friedrich, H., De Jongh, P.E., De Jong, K.P.: 2-Point correlation function of nanostructured materials via the grey-tone correlation function of electron tomograms: a three-dimensional structural analysis of ordered mesoporous silica. Acta Mater. 58(3), 770–780 (2010)CrossRefGoogle Scholar
  17. Gommes, C., Jiao, Y., Torquato, S.: Density of states for a specified correlation function and the energy landscape. Phys. Rev. Lett. 108(8), 080601 (2012a)CrossRefGoogle Scholar
  18. Gommes, C.J., Jiao, Y., Torquato, S.: Microstructural degeneracy associated with a two-point correlation function and its information content. Phys. Rev. E 85(5), 051140 (2012b)CrossRefGoogle Scholar
  19. Grechka, V., Vasconcelos, I., Kachanov, M.: The influence of crack shape on the effective elasticity of fractured rocks. Geophysics 71(5), D153–D160 (2006)CrossRefGoogle Scholar
  20. Groeber, M., Ghosh, S., Uchic, M.D., Dimiduk, D.M.: A framework for automated analysis and simulation of 3D polycrystalline microstructures. Part 1: statistical characterization. Acta Mater. 56(6), 1257–1273 (2008)CrossRefGoogle Scholar
  21. Guo, E.-Y., Chawla, N., Jing, T., Torquato, S., Jiao, Y.: Accurate modeling and reconstruction of three-dimensional percolating filamentary microstructures from two-dimensional micrographs via dilation–erosion method. Mater. Charact. 89, 33–42 (2014)CrossRefGoogle Scholar
  22. Hajizadeh, A., Safekordi, A., Farhadpour, F.A.: A multiple-point statistics algorithm for 3D pore space reconstruction from 2D images. Adv. Water Resour. 34(10), 1256–1267 (2011)CrossRefGoogle Scholar
  23. Hardin, T., Ruggles, T., Koch, D., Niezgoda, S., Fullwood, D., Homer, E.: Analysis of traction-free assumption in high-resolution EBSD measurements. J. Microsc. 260(1), 73–85 (2015)CrossRefGoogle Scholar
  24. Hlushkou, D., Liasneuski, H., Tallarek, U., Torquato, S.: Effective diffusion coefficients in random packings of polydisperse hard spheres from two-point and three-point correlation functions. J. Appl. Phys. 118(12), 124901 (2015)CrossRefGoogle Scholar
  25. Iglauer, S., Favretto, S., Spinelli, G., Schena, G., Blunt, M.J.: X-ray tomography measurements of power-law cluster size distributions for the nonwetting phase in sandstones. Phys. Rev. E 82(5), 056315 (2010)CrossRefGoogle Scholar
  26. Imdakm, A., Sahimi, M.: Computer simulation of particle transport processes in flow through porous media. Chem. Eng. Sci. 46(8), 1977–1993 (1991)CrossRefGoogle Scholar
  27. Jiao, Y., Chawla, N.: Modeling and characterizing anisotropic inclusion orientation in heterogeneous material via directional cluster functions and stochastic microstructure reconstruction. J. Appl. Phys. 115(9), 093511 (2014)CrossRefGoogle Scholar
  28. Jiao, Y., Stillinger, F., Torquato, S.: Modeling heterogeneous materials via two-point correlation functions: basic principles. Phys. Rev. E 76(3), 031110 (2007)CrossRefGoogle Scholar
  29. Jiao, Y., Stillinger, F., Torquato, S.: Modeling heterogeneous materials via two-point correlation functions. II. Algorithmic details and applications. Phys. Rev. E 77(3), 031135 (2008)CrossRefGoogle Scholar
  30. Jiao, Y., Stillinger, F., Torquato, S.: A superior descriptor of random textures and its predictive capacity. Proc. Nat. Acad. Sci. 106(42), 17634–17639 (2009)CrossRefGoogle Scholar
  31. Jiao, Y., Stillinger, F.H., Torquato, S.: Geometrical ambiguity of pair statistics. II. Heterogeneous media. Phys. Rev. E 82(1), 011106 (2010)CrossRefGoogle Scholar
  32. Jiao, Y., Padilla, E., Chawla, N.: Modeling and predicting microstructure evolution in lead/tin alloy via correlation functions and stochastic material reconstruction. Acta Mater. 61(9), 3370–3377 (2013)CrossRefGoogle Scholar
  33. Kak, A.C., Slaney, M.: Principles of Computerized Tomographic Imaging. IEEE Press, New York (1988)Google Scholar
  34. Kansal, A.R., Torquato, S.: Prediction of trapping rates in mixtures of partially absorbing spheres. J. Chem. Phys. 116(24), 10589–10597 (2002)CrossRefGoogle Scholar
  35. Karsanina, M.V., Gerke, K.M., Skvortsova, E.B., Mallants, D.: Universal spatial correlation functions for describing and reconstructing soil microstructure. PLoS ONE 10(5), e0126515 (2015)CrossRefGoogle Scholar
  36. Katz, A.J., Thompson, A.: Fractal sandstone pores: implications for conductivity and pore formation. Phys. Rev. Lett. 54(12), 1325 (1985)CrossRefGoogle Scholar
  37. Ketcham, R.A., Carlson, W.D.: Acquisition, optimization and interpretation of X-ray computed tomographic imagery: applications to the geosciences. Comput. Geosci. 27(4), 381–400 (2001)CrossRefGoogle Scholar
  38. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. science 220(4598), 671–680 (1983)CrossRefGoogle Scholar
  39. Korost, D., Mallants, D., Balushkina, N., Vasilyev, R., Khamidullin, R., Karsanina, M., Gerke, K., Kalmikov, G.: Determining physical properties of unconventional reservoir rocks: from laboratory methods to pore-scale modeling. In: SPE Unconventional Resources Conference and Exhibition-Asia Pacific. Society of Petroleum Engineers (2013)Google Scholar
  40. Li, H., Chawla, N., Jiao, Y.: Reconstruction of heterogeneous materials via stochastic optimization of limited-angle X-ray tomographic projections. Scripta Mater. 86, 48–51 (2014)CrossRefGoogle Scholar
  41. Li, H., Kaira, S., Mertens, J., Chawla, N., Jiao, Y.: Accurate stochastic reconstruction of heterogeneous microstructures by limited X-ray tomographic projections. J. Microsc. 264, 339 (2016a)CrossRefGoogle Scholar
  42. Li, H., Singh, S., Kaira, S., Mertens, J., Williams, J.J., Chawla, N., Jiao, Y.: Microstructural quantification and property prediction using limited X-ray tomography data. JOM 68, 2288 (2016b)CrossRefGoogle Scholar
  43. Li, H., Singh, S., Chawla, N., Jiao, Y.: Direct extraction of spatial correlation functions from limited X-ray tomography data for microstructure quantification (2016c, in preparation)Google Scholar
  44. Lindquist, W.B., Venkatarangan, A., Dunsmuir, J., Wong, Tf: Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainebleau sandstones. J. Geophys. Res. Solid Earth 105(B9), 21509–21527 (2000)CrossRefGoogle Scholar
  45. Liu, X., Shapiro, V.: Random heterogeneous materials via texture synthesis. Comput. Mater. Sci. 99, 177–189 (2015)CrossRefGoogle Scholar
  46. Lu, A.H., Schüth, F.: Nanocasting: a versatile strategy for creating nanostructured porous materials. Adv. Mater. 18(14), 1793–1805 (2006)CrossRefGoogle Scholar
  47. Lu, B., Torquato, S.: Lineal-path function for random heterogeneous materials. Phys. Rev. A 45(2), 922 (1992a)Google Scholar
  48. Lu, B., Torquato, S.: Lineal-path function for random heterogeneous materials. II. Effect of polydispersivity. Phys. Rev. A 45(10), 7292 (1992b)Google Scholar
  49. Nugent, P., Belmabkhout, Y., Burd, S.D., Cairns, A.J., Luebke, R., Forrest, K., Pham, T., Ma, S., Space, B., Wojtas, L.: Porous materials with optimal adsorption thermodynamics and kinetics for CO\(_2\) separation. Nature 495(7439), 80–84 (2013)CrossRefGoogle Scholar
  50. Pettijohn, F.J., Potter, P.E., Siever, R.: Sand and Sandstone. Springer, New York (2012)Google Scholar
  51. Pham, D., Torquato, S.: Exactly realizable bounds on the trapping constant and permeability of porous media. J. Appl. Phys. 97(1), 013535 (2005)CrossRefGoogle Scholar
  52. Pilotti, M.: Reconstruction of clastic porous media. Transp. Porous Media 41(3), 359–364 (2000)CrossRefGoogle Scholar
  53. Prager, S.: Interphase transfer in stationary two-phase media. Chem. Eng. Sci. 18(4), 227–231 (1963)CrossRefGoogle Scholar
  54. Rinaldi, R.G., Blacklock, M., Bale, H., Begley, M.R., Cox, B.N.: Generating virtual textile composite specimens using statistical data from micro-computed tomography: 3D tow representations. J. Mech. Phys. Solids 60(8), 1561–1581 (2012)CrossRefGoogle Scholar
  55. Roberts, A.P.: Statistical reconstruction of three-dimensional porous media from two-dimensional images. Phys. Rev. E 56(3), 3203 (1997)CrossRefGoogle Scholar
  56. Rowsell, J.L., Yaghi, O.M.: Metal-organic frameworks: a new class of porous materials. Microporous Mesoporous Mater. 73(1), 3–14 (2004)CrossRefGoogle Scholar
  57. Sahimi, M.: Flow phenomena in rocks: from continuum models to fractals, percolation, cellular automata, and simulated annealing. Rev. Mod. Phys. 65(4), 1393 (1993)CrossRefGoogle Scholar
  58. Sahimi, M.: Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches. Wiley, New York (2011)CrossRefGoogle Scholar
  59. Sahimi, M., Gavalas, G.R., Tsotsis, T.T.: Statistical and continuum models of fluid–solid reactions in porous media. Chem. Eng. Sci. 45(6), 1443–1502 (1990)CrossRefGoogle Scholar
  60. Saylor, D.M., Fridy, J., El-Dasher, B.S., Jung, K.-Y., Rollett, A.D.: Statistically representative three-dimensional microstructures based on orthogonal observation sections. Metall. Mater. Trans. A 35(7), 1969–1979 (2004)CrossRefGoogle Scholar
  61. Schwartz, L., Auzerais, F., Dunsmuir, J., Martys, N., Bentz, D., Torquato, S.: Transport and diffusion in three-dimensional composite media. Phys. A 207(1–3), 28–36 (1994)CrossRefGoogle Scholar
  62. Tahmasebi, P., Hezarkhani, A.: A fast and independent architecture of artificial neural network for permeability prediction. J. Petrol. Sci. Eng. 86, 118–126 (2012)CrossRefGoogle Scholar
  63. Tahmasebi, P., Sahimi, M.: Reconstruction of three-dimensional porous media using a single thin section. Phys. Rev. E 85(6), 066709 (2012)CrossRefGoogle Scholar
  64. Tahmasebi, P., Sahimi, M.: Cross-correlation function for accurate reconstruction of heterogeneous media. Phys. Rev. Lett. 110(7), 078002 (2013)CrossRefGoogle Scholar
  65. Tahmasebi, P., Sahimi, M.: Reconstruction of nonstationary disordered materials and media: watershed transform and cross-correlation function. Phys. Rev. E 91(3), 032401 (2015)CrossRefGoogle Scholar
  66. Tang, T., Teng, Q.-Z., He, X.-H., Luo, D.: A pixel selection rule based on the number of different-phase neighbours for the simulated annealing reconstruction of sandstone microstructure. J. Microsc. 234(3), 262–268 (2009)CrossRefGoogle Scholar
  67. Torquato, S.: Interfacial surface statistics arising in diffusion and flow problems in porous media. J. Chem. Phys. 85(8), 4622–4628 (1986)CrossRefGoogle Scholar
  68. Torquato, S.: Random Heterogeneous Materials: Microstructure and Macroscopic Properties, vol. 16. Springer, New York (2013)Google Scholar
  69. Torquato, S., Avellaneda, M.: Diffusion and reaction in heterogeneous media: Pore size distribution, relaxation times, and mean survival time. J. Chem. Phys. 95(9), 6477–6489 (1991)CrossRefGoogle Scholar
  70. Torquato, S., Lado, F.: Effective properties of two-phase disordered composite media: II. Evaluation of bounds on the conductivity and bulk modulus of dispersions of impenetrable spheres. Phys. Rev. B 33(9), 6428 (1986)CrossRefGoogle Scholar
  71. Torquato, S., Pham, D.: Optimal bounds on the trapping constant and permeability of porous media. Phys. Rev. Lett. 92(25), 255505 (2004)CrossRefGoogle Scholar
  72. Torquato, S., Yeong, C.: Universal scaling for diffusion-controlled reactions among traps. J. Chem. Phys. 106(21), 8814–8820 (1997)CrossRefGoogle Scholar
  73. Torquato, S., Beasley, J., Chiew, Y.: Two-point cluster function for continuum percolation. J. Chem. Phys. 88(10), 6540–6547 (1988)CrossRefGoogle Scholar
  74. Trinchi, A., Yang, Y.S., Huang, J.Z., Falcaro, P., Buso, D., Cao, L.Q.: Study of 3D composition in a nanoscale sample using data-constrained modelling and multi-energy X-ray CT. Model. Simul. Mater. Sci. Eng. 20(20), 015013 (2012)CrossRefGoogle Scholar
  75. Turner, D.M., Kalidindi, S.R.: Statistical construction of 3-D microstructures from 2-D exemplars collected on oblique sections. Acta Mater. 102, 136–148 (2016)CrossRefGoogle Scholar
  76. Wang, H.P., Yang, Y.S., Wang, Y.D., Yang, J.L., Jia, J., Nie, Y.H.: Data-constrained modelling of an anthracite coal physical structure with multi-spectrum synchrotron X-ray CT. Fuel 106(2), 219–225 (2013a)CrossRefGoogle Scholar
  77. Wang, Y., Yang, Y., Xiao, T., Liu, K., Clennell, B., Zhang, G., Wang, H.: Synchrotron-based data-constrained modeling analysis of microscopic mineral distributions in limestone. Int. J. Geosci. 4(2), 344–351 (2013b)CrossRefGoogle Scholar
  78. Wellington, S.L., Vinegar, H.J.: X-ray computerized tomography. J. Petrol. Technol. 39(08), 885–898 (1987)CrossRefGoogle Scholar
  79. Xu, H., Greene, M.S., Deng, H., Dikin, D., Brinson, C., Liu, W.K., Burkhart, C., Papakonstantopoulos, G., Poldneff, M., Chen, W.: Stochastic reassembly strategy for managing information complexity in heterogeneous materials analysis and design. J. Mech. Des. 135(10), 101010 (2013)CrossRefGoogle Scholar
  80. Xu, W., Chen, H., Chen, W., Jiang, L.: Prediction of transport behaviors of particulate composites considering microstructures of soft interfacial layers around ellipsoidal aggregate particles. Soft Matter 10(4), 627–638 (2014)CrossRefGoogle Scholar
  81. Yang, Y.S., Liu, K.Y., Mayo, S., Tulloh, A., Clennell, M.B., Xiao, T.Q.: A data-constrained modelling approach to sandstone microstructure characterisation. J. Petrol. Sci. Eng. 105(3), 76–83 (2013)CrossRefGoogle Scholar
  82. Yeong, C., Torquato, S.: Reconstructing random media. II. Three-dimensional media from two-dimensional cuts. Phys. Rev. E 58(1), 224 (1998)CrossRefGoogle Scholar
  83. Yeong, C., Torquato, S.: Reconstructing random media. Phys. Rev. E 57(1), 495 (1998)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Mechanical EngineeringArizona State UniversityTempeUSA
  2. 2.Materials Science and EngineeringArizona State UniversityTempeUSA

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