American Journal of Science, Engineering and Technology

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A Study of Sandstone Permeability Anisotropy Through Fractal Concept

Received: 08 August 2018    Accepted: 28 August 2018    Published: 12 October 2018
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Abstract

Most correlation equations of rock permeability are usually based on the Euclidean geometry concept. Pore geometry and structure of most porous rocks are very complex, therefore non-Euclidean geometry concept, e.g. fractal theory, is needed to handle such a complexity. This paper presents a new equation for sandstone permeability involving other properties and fractal dimensions of pore space and surface. The equation is derived by combining Newton’s Law of viscosity, Darcy equation, and fractal geometry concept. It is shown that parameters such as tortuosity, internal surface area, and shape factor can be replaced by fractal dimensions. As natural porous media are mostly anisotropic, this study enables us to identify factors that affect the anisotropy. Eighteen sandstone samples with porosity and permeability range from 21 to 37% and 2.76 to 3,644 millidarcies, were employed in this study. The pore space and surface fractal dimensions for each orthogonal direction for each sample was determined by box counting method. The results of this study demonstrate that calculated directional permeability of the high permeability samples is very close to the measured one after corrections were made for pore sizes of less than one micron. This finding suggests that micropores of the samples may be a major factor not contributing to fluid flow. For the low and medium permeability samples, however, an additional pore geometrical correction is needed. The additional correction factor is considerably different for different directions of fluid flow, indicating that the anisotropy is due to the difference in directional pore structural characteristics.

DOI 10.11648/j.ajset.20180302.12
Published in American Journal of Science, Engineering and Technology (Volume 3, Issue 2, June 2018)
Page(s) 34-45
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Permeability, Tortuosity, Hydraulic Diameter, Fractal Dimension, Anisotropy

References
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Author Information
  • Department of Petroleum Engineering, Universitas Pembangunan Nasional “Veteran” Yogyakarta, Yogyakarta, Indonesia; Department of Petroleum Engineering, Institut Teknologi Bandung, Bandung, Indonesia

  • Department of Petroleum Engineering, Institut Teknologi Bandung, Bandung, Indonesia

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    Yosaphat Sumantri, Pudji Permadi. (2018). A Study of Sandstone Permeability Anisotropy Through Fractal Concept. American Journal of Science, Engineering and Technology, 3(2), 34-45. https://doi.org/10.11648/j.ajset.20180302.12

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    ACS Style

    Yosaphat Sumantri; Pudji Permadi. A Study of Sandstone Permeability Anisotropy Through Fractal Concept. Am. J. Sci. Eng. Technol. 2018, 3(2), 34-45. doi: 10.11648/j.ajset.20180302.12

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    AMA Style

    Yosaphat Sumantri, Pudji Permadi. A Study of Sandstone Permeability Anisotropy Through Fractal Concept. Am J Sci Eng Technol. 2018;3(2):34-45. doi: 10.11648/j.ajset.20180302.12

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  • @article{10.11648/j.ajset.20180302.12,
      author = {Yosaphat Sumantri and Pudji Permadi},
      title = {A Study of Sandstone Permeability Anisotropy Through Fractal Concept},
      journal = {American Journal of Science, Engineering and Technology},
      volume = {3},
      number = {2},
      pages = {34-45},
      doi = {10.11648/j.ajset.20180302.12},
      url = {https://doi.org/10.11648/j.ajset.20180302.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajset.20180302.12},
      abstract = {Most correlation equations of rock permeability are usually based on the Euclidean geometry concept. Pore geometry and structure of most porous rocks are very complex, therefore non-Euclidean geometry concept, e.g. fractal theory, is needed to handle such a complexity. This paper presents a new equation for sandstone permeability involving other properties and fractal dimensions of pore space and surface. The equation is derived by combining Newton’s Law of viscosity, Darcy equation, and fractal geometry concept. It is shown that parameters such as tortuosity, internal surface area, and shape factor can be replaced by fractal dimensions. As natural porous media are mostly anisotropic, this study enables us to identify factors that affect the anisotropy. Eighteen sandstone samples with porosity and permeability range from 21 to 37% and 2.76 to 3,644 millidarcies, were employed in this study. The pore space and surface fractal dimensions for each orthogonal direction for each sample was determined by box counting method. The results of this study demonstrate that calculated directional permeability of the high permeability samples is very close to the measured one after corrections were made for pore sizes of less than one micron. This finding suggests that micropores of the samples may be a major factor not contributing to fluid flow. For the low and medium permeability samples, however, an additional pore geometrical correction is needed. The additional correction factor is considerably different for different directions of fluid flow, indicating that the anisotropy is due to the difference in directional pore structural characteristics.},
     year = {2018}
    }
    

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    AU  - Yosaphat Sumantri
    AU  - Pudji Permadi
    Y1  - 2018/10/12
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    AB  - Most correlation equations of rock permeability are usually based on the Euclidean geometry concept. Pore geometry and structure of most porous rocks are very complex, therefore non-Euclidean geometry concept, e.g. fractal theory, is needed to handle such a complexity. This paper presents a new equation for sandstone permeability involving other properties and fractal dimensions of pore space and surface. The equation is derived by combining Newton’s Law of viscosity, Darcy equation, and fractal geometry concept. It is shown that parameters such as tortuosity, internal surface area, and shape factor can be replaced by fractal dimensions. As natural porous media are mostly anisotropic, this study enables us to identify factors that affect the anisotropy. Eighteen sandstone samples with porosity and permeability range from 21 to 37% and 2.76 to 3,644 millidarcies, were employed in this study. The pore space and surface fractal dimensions for each orthogonal direction for each sample was determined by box counting method. The results of this study demonstrate that calculated directional permeability of the high permeability samples is very close to the measured one after corrections were made for pore sizes of less than one micron. This finding suggests that micropores of the samples may be a major factor not contributing to fluid flow. For the low and medium permeability samples, however, an additional pore geometrical correction is needed. The additional correction factor is considerably different for different directions of fluid flow, indicating that the anisotropy is due to the difference in directional pore structural characteristics.
    VL  - 3
    IS  - 2
    ER  - 

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