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Fractal Dimension of Digital 3D Rock Models with Different Pore Structures

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  • Xiaobin Li

    (Key Laboratory of Tectonics and Petroleum Resources, China University of Geosciences, Ministry of Education, Wuhan 430074, China)

  • Wei Wei

    (Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China)

  • Lei Wang

    (Key Laboratory of Tectonics and Petroleum Resources, China University of Geosciences, Ministry of Education, Wuhan 430074, China)

  • Jianchao Cai

    (Key Laboratory of Tectonics and Petroleum Resources, China University of Geosciences, Ministry of Education, Wuhan 430074, China
    State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China)

Abstract

The macroscopic physical properties of rocks are profoundly determined by their microstructure, and the research of accurately characterizing rock pore structure has been extensively carried out in the fields of petroleum engineering and geoscience. Fractal geometry is an effective means of quantitatively estimating the pore structure properties of porous media. In this study, the evolution law of the fractal dimension and the quantitative relationship between the fractal dimension and porosity were investigated based on the digital 3D rock models. First, three kinds of models with gradually changing pore structures, namely sedimentation, compaction, and cementation, were systematically reconstructed by the process-based approach. Then, the fractal dimensions of the skeleton, pore, and surface of the models were computed and analyzed. Finally, the relationships among the fractal dimension, porosity, and complexity were explored qualitatively. These works reveal the changing laws of three types of fractal dimensions for different pore structure models. The pore structure differences in sedimentation model can only be distinguished by the surface fractal dimension, while both pore and surface fractal dimensions are available parameters for characterizing different pore structures in compaction and cementation models. The quantitative relations between box-counting fractal dimension and porosity were established, which can be expressed by combining linear and logarithmic formulas. The comparison of fractal dimensions of compaction and cementation models proves that fractal dimensions can distinguish the subtle pore structure differences in digital 3D rock models. Understanding the evolution law between the fractal dimension and pore structure parameters provides more references for classifying and evaluating rock pore structure features using fractal dimensions.

Suggested Citation

  • Xiaobin Li & Wei Wei & Lei Wang & Jianchao Cai, 2022. "Fractal Dimension of Digital 3D Rock Models with Different Pore Structures," Energies, MDPI, vol. 15(20), pages 1-16, October.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:20:p:7461-:d:938686
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    References listed on IDEAS

    as
    1. Penghui Su & Zhaohui Xia & Ping Wang & Wei Ding & Yunpeng Hu & Wenqi Zhang & Yujie Peng, 2019. "Fractal and Multifractal Analysis of Pore Size Distribution in Low Permeability Reservoirs Based on Mercury Intrusion Porosimetry," Energies, MDPI, vol. 12(7), pages 1-15, April.
    2. Biswal, B. & Manwart, C. & Hilfer, R. & Bakke, S. & Øren, P.E., 1999. "Quantitative analysis of experimental and synthetic microstructures for sedimentary rock," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 273(3), pages 452-475.
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