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Fractal and Multifractal Analysis of Pore Size Distribution in Low Permeability Reservoirs Based on Mercury Intrusion Porosimetry

Author

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  • Penghui Su

    (PetroChina Research Institute of Petroleum Exploration and Development, Beijing 100083, China)

  • Zhaohui Xia

    (PetroChina Research Institute of Petroleum Exploration and Development, Beijing 100083, China)

  • Ping Wang

    (PetroChina Research Institute of Petroleum Exploration and Development, Beijing 100083, China)

  • Wei Ding

    (PetroChina Research Institute of Petroleum Exploration and Development, Beijing 100083, China)

  • Yunpeng Hu

    (PetroChina Research Institute of Petroleum Exploration and Development, Beijing 100083, China)

  • Wenqi Zhang

    (PetroChina Research Institute of Petroleum Exploration and Development, Beijing 100083, China)

  • Yujie Peng

    (Guizhou Polytechnic of Construction, Guizhou 551400, China)

Abstract

To quantitatively evaluate the complexities and heterogeneities of pore structures in sandstone reservoirs, we apply single fractal theory and multifractal theory to explore the fractal characteristics of pore size distributions based on mercury intrusion porosimetry. The fractal parameters were calculated and the relationships between the petrophysical parameters (permeability and entry pressure) and the fractal parameters were investigated. The results show that the single fractal curves exhibit two-stage characteristics and the corresponding fractal dimensions D 1 and D 2 can characterize the complexity of pore structure in different sizes. Favorable linear relationships between log( ε ) and log( μ ,( ε )) indicate that the samples satisfy multifractal characteristics and ε is the sub-intervals with size ε = J × 2 − k . The multifractal singularity curves used in this study exhibit a right shape, indicating that the heterogeneity of the reservoir is mainly affected by pore size distributions in sparse regions. Multifractal parameters, D (0), D (1), and Δ f , are positively correlated with permeability and entry pressure, while D (0), D (1), and Δ f are negatively correlated with permeability and entry pressure. The ratio of larger pores volumes to total pore volumes acts as a control on the fractal dimension over a specific pore size range, while the range of the pore size distribution has a definite impact on the multifractal parameters. Results indicate that fractal analysis and multifractal analysis are feasible methods for characterizing the heterogeneity of pore structures in a reservoir. However, the single fractal models ignore the influence of microfractures, which could result in abnormal values for calculated fractal dimension. Compared to single fractal analysis, multifractal theory can better quantitatively characterize the heterogeneity of pore structure and establish favorable relationships with reservoir physical property parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jeners:v:12:y:2019:i:7:p:1337-:d:220810
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    References listed on IDEAS

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    1. Gang Lei & Nai Cao & Di Liu & Huijie Wang, 2018. "A Non-Linear Flow Model for Porous Media Based on Conformable Derivative Approach," Energies, MDPI, vol. 11(11), pages 1-11, November.
    2. Subhakar, D. & Chandrasekhar, E., 2016. "Reservoir characterization using multifractal detrended fluctuation analysis of geophysical well-log data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 57-65.
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    Cited by:

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    2. Mehrdad Massoudi, 2020. "Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications," Energies, MDPI, vol. 13(6), pages 1-4, March.
    3. Haifei Lin & Yang Bai & Jingting Bu & Shugang Li & Min Yan & Pengxiang Zhao & Lei Qin, 2019. "Comprehensive Fractal Model and Pore Structural Features of Medium- and Low-Rank Coal from the Zhunnan Coalfield of Xinjiang, China," Energies, MDPI, vol. 13(1), pages 1-15, December.
    4. 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.
    5. Qingshun Gong & Zhanguo Liu & Chao Zhu & Bo Wang & Yijie Jin & Zhenghao Shi & Lin Xie & Jin Wu, 2023. "Heterogeneity of a Sandy Conglomerate Reservoir in Qie12 Block, Qaidam Basin, Northwest China and Its Influence on Remaining Oil Distribution," Energies, MDPI, vol. 16(7), pages 1-19, March.

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