Skip to main content
SpringerLink
Log in

3D Percolation Modeling for Connectivity and Permeability of Sandstone with Different Pore Distribution Characteristics

  • Original Paper
  • Published:
Natural Resources Research Aims and scope Submit manuscript

Abstract

In order to further expand the understanding of the pore-throat structure of sandstone, a new method is proposed in this paper to reconstruct three-dimensional (3D) virtual sandstone and replicate the natural sandstone pore-throat structure. While reconstructing 3D virtual sandstone, a particle distribution factor M and a dilation filter D were introduced into the site percolation model. The function of M was to control the initial size of the solid particle while ensuring the randomness of the shape of the solid particle, whereas D gave acceptable deformation of the pore-throat structure while changing the porosity (P) of the 3D virtual sandstone. It was found that the virtual sandstone with high similarity to the real sandstone could be reconstructed by changing the combination of M and D regardless of the P, tortuosity, and pore coordination number of the real sandstone. The percolation thresholds of 3D virtual sandstone generated under different M and D were obtained, and the pore connectivity and permeability changes with M, D, and P were also investigated. The proposed method for virtual sandstone generation in this paper provides a novel approach for assessing and predicting the connectivity and permeability of sandstone reservoirs in oil and gas exploration.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14

Similar content being viewed by others

References

  • Bultreys, T., De Boever, W., & Cnudde, V. (2016). Imaging and image-based fluid transport modeling at the pore scale in geological materials: A practical introduction to the current state-of-the-art. Earth-Science Reviews, 155, 93–128.

    Article  Google Scholar 

  • Caulk, R. A., Ghazanfari, E., Perdrial, J. N., & Perdrial, N. (2016). Experimental investigation of fracture aperture and permeability change within Enhanced Geothermal Systems. Geothermics, 62, 12–21.

    Article  Google Scholar 

  • Colombier, M., Wadsworth, F. B., Gurioli, L., Scheu, B., Kueppers, U., Di Muro, A., & Dingwell, D. B. (2017). The evolution of pore connectivity in volcanic rocks. Earth and Planetary Science Letters, 462, 99–109.

    Article  Google Scholar 

  • Colombier, M., Vasseur, J., Houghton, B. F., Cáceres, F., Scheu, B., Kueppers, U., et al. (2021). Degassing and gas percolation in basaltic magmas. Earth and Planetary Science Letters, 573, 117134.

    Article  Google Scholar 

  • Cornette, V., Ramirez-Pastor, A. J., & Nieto, F. (2003). Percolation of polyatomic species on a square lattice. European Physical Journal B, 36, 391–399.

    Article  Google Scholar 

  • Cornette, V., Ramirez-Pastor, A. J., & Nieto, F. (2006). Percolation of polyatomic species with the presence of impurities. Journal of Chemical Physics, 125, 204702.

    Article  Google Scholar 

  • Daïan, J. F., Fernandes, C. P., Philippi, P. C., & da Cunha Neto, J. A. B. (2004). 3D reconstitution of porous media from image processing data using a multiscale percolation system. Journal of Petroleum Science and Engineering, 42(1), 15–28.

    Article  Google Scholar 

  • Dehghanpoor Abyaneh, S., Wong, H. S., & Buenfeld, N. R. (2013). Modelling the diffusivity of mortar and concrete using a three-dimensional mesostructure with several aggregate shapes. Computational Materials Science, 78, 63–73.

    Article  Google Scholar 

  • Du Plessis, J. P. (1999). Introducing a percolation threshold in pore-scale modelling. Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy, 24(7), 617–620.

    Article  Google Scholar 

  • Durrett, R. T. (1984). Percolation theory for mathematicians (Harry Kesten). SIAM Review, 26, 446–448. https://doi.org/10.1137/1026095

    Article  Google Scholar 

  • Fu, J., Thomas, H. R., & Li, C. (2021). Tortuosity of porous media: Image analysis and physical simulation. Earth-Science Reviews, 212, 103439.

    Article  Google Scholar 

  • Garboczi, E. J., & Bentz, D. P. (1995). Percolation phenomena by computer simulation. United States. https://www.osti.gov/biblio/214888

  • Garboczi, E. J., & Bentz, D. P. (2000). Percolation aspects of cement paste and concrete-properties and durability. In American Concrete Institute, ACI Special Publication (Vol. SP-189). https://doi.org/10.14359/5851

  • González, M. I., Centres, P., Lebrecht, W., Ramirez-Pastor, A. J., & Nieto, F. (2013). Site-bond percolation on triangular lattices: Monte Carlo simulation and analytical approach. Physica A: Statistical Mechanics and its Applications, 392(24), 6330–6340.

    Article  Google Scholar 

  • Guo, P., Gu, J., Su, Y., Wang, J., & Ding, Z. (2021). Effect of cyclic wetting–drying on tensile mechanical behavior and microstructure of clay-bearing sandstone. International Journal of Coal Science and Technology, 8(5), 956–968.

    Article  Google Scholar 

  • Hellemans, J., Forrez, P., & De Wilde, R. (1980). Experiment illustrating Bernoulli’s equation and Hagen–Poiseuille’s law. American Journal of Physics, 48(3), 12154.

    Article  Google Scholar 

  • Kallikragas, D. T., & Svishchev, I. M. (2019). Percolation transitions of physically and hydrogen bonded clusters in supercritical water. Journal of Molecular Liquids, 290, 111213.

    Article  Google Scholar 

  • Kang, Z., Wang, W., Zhao, Y., Liang, W., Yang, D., Zhao, J., & Zhao, D. (2014). Three-dimensional percolation mechanism in oil shale under different temperatures based on micro-CT. Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering, 33(9), 1837–1842.

    Google Scholar 

  • King, P. R., & Masihi, M. (2018). Percolation theory in reservoir engineering. https://doi.org/10.1142/q0154

  • Kurzawski, Ł, & Malarz, K. (2012). Simple Cubic Random-Site Percolation Thresholds for Complex Neighbourhoods. Reports on Mathematical Physics, 70(2), 163–169.

    Article  Google Scholar 

  • Latief, F. D. E., Biswal, B., Fauzi, U., & Hilfer, R. (2010). Continuum reconstruction of the pore scale microstructure for Fontainebleau sandstone. Physica A: Statistical Mechanics and its Applications, 389(8), 1607–1618.

    Article  Google Scholar 

  • Lin, J., & Chen, H. (2018). Effect of particle morphologies on the percolation of particulate porous media: A study of superballs. Powder Technology, 335, 388–400.

    Article  Google Scholar 

  • Lin, J., Chen, H., & Liu, L. (2020). Impact of polydispersity of particle shape and size on percolation threshold of 3D particulate media composed of penetrable superellipsoids. Powder Technology, 360, 944–955.

    Article  Google Scholar 

  • Liu, J., & Regenauer-Lieb, K. (2011). Application of percolation theory to microtomography of structured media: Percolation threshold, critical exponents, and upscaling. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 83(1), 016106.

    Article  Google Scholar 

  • Liu, J., & Regenauer-Lieb, K. (2021). Application of percolation theory to microtomography of rocks. Earth-Science Reviews, 214, 103519.

    Article  Google Scholar 

  • Liu, B., Zhao, Y., Zhang, C., Zhou, J., Li, Y., & Sun, Z. (2021). Characteristic strength and acoustic emission properties of weakly cemented sandstone at different depths under uniaxial compression. International Journal of Coal Science and Technology, 8(6), 1288–1301.

    Article  Google Scholar 

  • Liu, G., Xie, S., Tian, W., Wang, J., Li, S., Wang, Y., & Yang, D. (2022a). Effect of pore-throat structure on gas-water seepage behaviour in a tight sandstone gas reservoir. Fuel, 310, 121901.

    Article  Google Scholar 

  • Liu, J., Li, L., Zhang, C., Jiang, Y., Swennen, R., Zhao, C., & Hou, S. (2022b). Identification and quantitative evaluation of pores and throats of a tight sandstone reservoir (Upper Triassic Xujiahe Formation, Sichuan Basin, China). Marine and Petroleum Geology, 140, 105663.

    Article  Google Scholar 

  • Liu, J., Zhang, C., Jiang, Y., & Hou, S. (2022c). Investigation on pore structure characteristics of ultra-tight sandstone reservoirs in the upper Triassic Xujiahe Formation of the northern Sichuan Basin, China. Marine and Petroleum Geology, 138, 105552.

    Article  Google Scholar 

  • Liu, P., Nie, B., Zhao, Z., Zhao, Y., & Li, Q. (2023). Characterization of ultrasonic induced damage on multi-scale pore/fracture in coal using gas sorption and μ-CT 3D reconstruction. Fuel, 332, 126178.

    Article  Google Scholar 

  • Mostaghimi, P., Blunt, M. J., & Bijeljic, B. (2013). Computations of absolute permeability on micro-CT images. Mathematical Geosciences, 45, 103–125.

    Article  Google Scholar 

  • Pasinetti, P. M., Centres, P. M., & Ramirez-Pastor, A. J. (2019). Jamming and percolation of k 2-mers on simple cubic lattices. Journal of Statistical Mechanics: Theory and Experiment, 2019(10), 103204.

    Article  Google Scholar 

  • Payton, R. L., Chiarella, D., & Kingdon, A. (2022). The upper percolation threshold and porosity-permeability relationship in sandstone reservoirs using digital image analysis. Scientific Reports, 12(1), 1–15.

    Article  Google Scholar 

  • Pervago, E., Mousatov, A., Kazatchenko, E., & Markov, M. (2018). Computation of continuum percolation threshold for pore systems composed of vugs and fractures. Computers and Geosciences, 116(October 2017), 53–63.

    Article  Google Scholar 

  • Reviews, A., Leonard, J., & Poiseuille, M. (1953). The history of Poiseuille’s law. Annual Review of Fluid Mechanics, 25, 1–19.

    Google Scholar 

  • Revil, A., Kessouri, P., & Torres-Verdín, C. (2014). Electrical conductivity, induced polarization, and permeability of the Fontainebleau sandstone. Geophysics, 79(5), D301–D318.

    Article  Google Scholar 

  • Rostron, B. J. (2018). Multiphase flow in permeable media. A pore-scale perspective. Groundwater. https://doi.org/10.1111/gwat.12812

    Article  Google Scholar 

  • Sakhaee-Pour, A., & Agrawal, A. (2018). Integrating acoustic emission into percolation theory to predict permeability enhancement. Journal of Petroleum Science and Engineering, 160(July 2017), 152–159.

    Article  Google Scholar 

  • Sanderson, D. J., & Nixon, C. W. (2018). Topology, connectivity and percolation in fracture networks. Journal of Structural Geology, 115, 167–177.

    Article  Google Scholar 

  • Siavashi, J., Najafi, A., Ebadi, M., & Sharifi, M. (2022). A CNN-based approach for upscaling multiphase flow in digital sandstones. Fuel, 308, 122047.

    Article  Google Scholar 

  • Stauffer, D., & Aharony, A. (2018). Introduction to percolation theory. Introduction To Percolation Theory. https://doi.org/10.1201/9781315274386

    Article  Google Scholar 

  • Swanson, S. K., Bahr, J. M., Bradbury, K. R., & Anderson, K. M. (2006). Evidence for preferential flow through sandstone aquifers in Southern Wisconsin. Sedimentary Geology, 184(3–4), 331–342.

    Article  Google Scholar 

  • Tavagh-Mohammadi, B., Masihi, M., & Ganjeh-Ghazvini, M. (2016). Point-to-point connectivity prediction in porous media using percolation theory. Physica A: Statistical Mechanics and its Applications, 460, 304–313.

    Article  Google Scholar 

  • Wang, F., Liu, Y., Hu, C., Wang, Y., Shen, A., & Liang, S. (2018). Experimental study on feasibility of enhanced gas recovery through CO2 flooding in tight sandstone gas reservoirs. Processes, 6(11), 214.

    Article  Google Scholar 

  • Wierman, J. C. (2003). Pairs of graphs with site and bond percolation critical probabilities in opposite orders. Discrete Applied Mathematics, 129(2–3), 545–548.

    Article  Google Scholar 

  • Wu, H., Ju, Y., Han, X., Ren, Z., Sun, Y., Zhang, Y., & Han, T. (2022). Size effects in the uniaxial compressive properties of 3D printed models of rocks: an experimental investigation. International Journal of Coal Science and Technology, 9(1), 83.

    Article  Google Scholar 

  • Xiao, D., Jiang, S., Thul, D., Lu, S., Zhang, L., & Li, B. (2018). Impacts of clay on pore structure, storage and percolation of tight sandstones from the Songliao Basin, China: Implications for genetic classification of tight sandstone reservoirs. Fuel, 211, 390–404.

    Article  Google Scholar 

  • Xu, W., & Jiao, Y. (2019). Theoretical framework for percolation threshold, tortuosity and transport properties of porous materials containing 3D non-spherical pores. International Journal of Engineering Science, 134, 31–46.

    Article  Google Scholar 

  • Xu, F., Xu, Z., & Yakobson, B. I. (2014). Site-percolation threshold of carbon nanotube fibers: Fast inspection of percolation with Markov stochastic theory. Physica A: Statistical Mechanics and its Applications, 407, 341–349.

    Article  Google Scholar 

  • Yang, C. H., Hsu, C. L., Chen, N. Y., & Shih, C. T. (2011). Temporal dynamics of site percolation in nanoparticle assemblies. Computer Physics Communications, 182(1), 71–73.

    Article  Google Scholar 

  • Yonezawa, F., Sakamoto, S., & Hori, M. (1989). Percolation in two-dimensional lattices. I. A technique for the estimation of thresholds. Physical Review B, 40(1), 636.

    Article  Google Scholar 

  • Zendehboudi, S., Rezaei, N., & Lohi, A. (2018). Applications of hybrid models in chemical, petroleum, and energy systems: A systematic review. Applied Energy, 228, 2539–2566.

    Article  Google Scholar 

  • Zhu, P., Lin, C., Ren, H., Zhao, Z., & Zhang, H. (2015). Micro-fracture characteristics of tight sandstone reservoirs and its evaluation by capillary pressure curves: A case study of Permian sandstones in Ordos Basin, China. Journal of Natural Gas Science and Engineering, 27, 90–97.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Key Research and Development Program of China (Grant Nos. 2019YFA0705501 and 2019YFA0705502), National Natural Science Foundation of China (Grant No. 52104128), Basic Research Program of Shanxi Province (Grant No. 20210302123177), Key R&D and Promotion Projects in Henan Province (Grant No. 212102310010)

Author information

Authors and Affiliations

  1. Key Lab of In-situ Property-improving Mining of Ministry of Education, Taiyuan University of Technology, Taiyuan, 030024, China

    Xudong Huang, Jing Zhao, Dong Yang & Zhiqin Kang

  2. The In-situ Steam Injection Branch of State Center for Research and Development of Oil Shale Exploitation, Taiyuan University of Technology, Taiyuan, 030024, China

    Xudong Huang, Jing Zhao, Dong Yang & Zhiqin Kang

  3. School of Energy Science and Engineering, Henan Polytechnic University, Jiaozuo, 454002, China

    Guoying Wang

  4. Petrochina Changqing Oilfield Company, Xi’an, 710200, China

    Zhiping Zhou

Authors
  1. Xudong Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jing Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhiping Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dong Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Guoying Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zhiqin Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhiqin Kang.

Ethics declarations

Conflict of Interest

The authors have no competing interests to declare, and no financial or non-financial interests to disclose.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, X., Zhao, J., Zhou, Z. et al. 3D Percolation Modeling for Connectivity and Permeability of Sandstone with Different Pore Distribution Characteristics. Nat Resour Res 33, 191–212 (2024). https://doi.org/10.1007/s11053-023-10277-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11053-023-10277-2

Keywords

Search

Navigation