Skip to main content

Advertisement

Log in

Fractal Analysis of Pore Structure Differences Between Shale and Sandstone Based on the Nitrogen Adsorption Method

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

Abstract

Pore structure, a critical factor influencing the physical properties of oil and gas reservoirs, shows great variation with the reservoir rock type. Efficient exploration and development of oil and gas resources require comprehensive understanding of pore structure differences between various reservoirs. In this study, to clarify these differences, pore size distributions and pore structure parameters were obtained through low-pressure nitrogen (N2) adsorption–desorption experiments using shale, low-permeability sandstone, and tight sandstone as rock types. Pore space fractal dimension obtained from a proposed calculating method and pore surface fractal dimension obtained from the Frenkel–Halsey–Hill model were combined with N2 adsorption results to analyze quantitatively the pore structures of shale and sandstone. The results show that shale consisted mainly of inkbottle-shaped pores whereas sandstone was composed of slit-shaped pores. Compared with sandstone, shale had a larger specific surface area but smaller average pore diameter and pore volume. In addition, the pore structure heterogeneity and pore surface irregularity of shale were more significant, considering its larger fractal dimensions. Relationships among fractal dimensions and porosity, permeability, and pore structure parameters explained that pore size and pore distribution were the main influencing factors of porosity and permeability. These results highlight the practicability of fractal theory in characterizing pore structure and petrophysical properties of unconventional reservoirs.

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

Access this article

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

Instant access to the full article PDF.

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

Similar content being viewed by others

Notes

  1. 1 md = 1 millidarcy = 0.986923 × 10−15 m2.

References

  • Avnir, D., & Jaroniec, M. (1989). An isotherm equation for adsorption on fractal surfaces of heterogeneous porous materials. Langmuir, 5(6), 1431–1433.

    Article  Google Scholar 

  • Barrett, E. P., Joyner, L. G., & Halenda, P. P. (1951). The determination of pore volume and area distributions in porous substances. I. Computations from nitrogen isotherms. Journal of the American Chemical Society, 73(1), 373–380.

    Article  Google Scholar 

  • Bera, A., & Belhaj, H. (2016). Application of nanotechnology by means of nanoparticles and nanodispersions in oil recovery—A comprehensive review. Journal of Natural Gas Science and Engineering, 34, 1284–1309.

    Article  Google Scholar 

  • Brunauer, S., Emmett, P. H., & Teller, E. (1938). Adsorption of gases in multimolecular layers. Journal of the American Chemical Society, 60(2), 309–319.

    Article  Google Scholar 

  • Burgess, C. G. V., & Everett, D. H. (1970). The lower closure point in adsorption hysteresis of the capillary condensation type. Journal of Colloid and Interface Science, 33(4), 611–614.

    Article  Google Scholar 

  • Cai, J., Lin, D., Singh, H., Zhou, S., Meng, Q., & Zhang, Q. (2019). A simple permeability model for shale gas and key insights on relative importance of various transport mechanisms. Fuel, 252, 210–219.

    Article  Google Scholar 

  • Cai, J., Xia, Y., Lu, C., Bian, H., & Zou, S. (2020). Creeping microstructure and fractal permeability model of natural gas hydrate reservoir. Marine and Petroleum Geology, 115, 104282.

    Article  Google Scholar 

  • Chalmers, G. R., Bustin, R. M., & Power, I. M. (2012). Characterization of gas shale pore systems by porosimetry, pycnometry, surface area, and field emission scanning electron microscopy/transmission electron microscopy image analyses: Examples from the Barnett, Woodford, Haynesville, Marcellus, and Doig units. AAPG Bulletin, 96(6), 1099–1119.

    Article  Google Scholar 

  • Clarkson, C. R., Solano, N., Bustin, R. M., Bustin, A. M. M., Chalmers, G. R. L., He, L., Melnichenko, Y. B., Radliński, A. P., & Blach, T. P. (2013). Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion. Fuel, 103, 606–616.

    Article  Google Scholar 

  • Daigle, H., Johnson, A., & Thomas, B. (2014). Determining fractal dimension from nuclear magnetic resonance data in rocks with internal magnetic field gradients. Geophysics, 79(6), D425–D431.

    Article  Google Scholar 

  • El Shafei, G. M. S., Philip, C. A., & Moussa, N. A. (2004). Fractal analysis of hydroxyapatite from nitrogen isotherms. Journal of Colloid and Interface Science, 277(2), 410–416.

    Article  Google Scholar 

  • English, J. M., English, K. L., Corcoran, D. V., & Toussaint, F. (2016). Exhumation charge: The last gasp of a petroleum source rock and implications for unconventional shale resources. AAPG Bulletin, 100(1), 1–16.

    Article  Google Scholar 

  • Erturk, M. (2011). Economic analysis of unconventional liquid fuel sources. Renewable and Sustainable Energy Reviews, 15(6), 2766–2771.

    Article  Google Scholar 

  • Han, T., Liu, S., Fu, L., & Yan, H. (2021). Understanding how overpressure affects the physical properties of sandstones. Geophysics, 86(4), MR203–MR210.

    Article  Google Scholar 

  • Hazra, B., Wood, D. A., Vishal, V., Varma, A. K., Sakha, D., & Singh, A. K. (2018). Porosity controls and fractal disposition of organic-rich Permian shales using low-pressure adsorption techniques. Fuel, 220, 837–848.

    Article  Google Scholar 

  • Hu, J., Tang, S., & Zhang, S. (2016). Investigation of pore structure and fractal characteristics of the Lower Silurian Longmaxi shales in western Hunan and Hubei Provinces in China. Journal of Natural Gas Science and Engineering, 28, 522–535.

    Article  Google Scholar 

  • Jia, C., Zheng, M., & Zhang, Y. (2012). Unconventional hydrocarbon resources in China and the prospect of exploration and development. Petroleum Exploration and Development, 39(2), 139–146.

    Article  Google Scholar 

  • Jiang, F., Chen, D., Chen, J., Li, Q., Liu, Y., Shao, X., Hu, T., & Dai, J. (2016). Fractal analysis of shale pore structure of continental gas shale reservoir in the Ordos Basin, NW China. Energy & Fuels, 30(6), 4676–4689.

    Article  Google Scholar 

  • Kadlec, O., & Dubinin, M. M. (1969). Comments on the limits of applicability of the mechanism of capillary condensation. Journal of Colloid and Interface Science, 31(4), 479–489.

    Article  Google Scholar 

  • Katz, A. J., & Thompson, A. H. (1985). Fractal sandstone pores: Implications for conductivity and pore formation. Physical Review Letters, 54(12), 1325–1328.

    Article  Google Scholar 

  • Keshavaraja, A., Ramaswamy, V., Soni, H. S., Ramaswamy, A. V., & Ratnasamy, P. (1995). Synthesis, characterization, and catalytic properties of micro-mesoporous, amorphous titanosilicate catalysts. Journal of Catalysis, 157(2), 501–511.

    Article  Google Scholar 

  • Khalili, N. R., Pan, M., & Sandí, G. (2000). Determination of fractal dimensions of solid carbons from gas and liquid phase adsorption isotherms. Carbon, 38(4), 573–588.

    Article  Google Scholar 

  • Konno, Y., Fujii, T., Sato, A., Akamine, K., Naiki, M., Masuda, Y., Yamamoto, K., & Nagao, J. (2017). Key findings of the world’s first offshore methane hydrate production test off the coast of Japan: Toward future commercial production. Energy & Fuels, 31(3), 2607–2616.

    Article  Google Scholar 

  • Kuila, U., & Prasad, M. (2013). Specific surface area and pore-size distribution in clays and shales. Geophysical Prospecting, 61(2), 341–362.

    Article  Google Scholar 

  • Kumar, S., Mendhe, V. A., Kamble, A. D., Varma, A. K., Mishra, D. K., Bannerjee, M., Buragohain, J., & Prasad, A. K. (2019). Geochemical attributes, pore structures and fractal characteristics of Barakar shale deposits of Mand-Raigarh Basin, India. Marine and Petroleum Geology, 103, 377–396.

    Article  Google Scholar 

  • Lai, J., Wang, G., Fan, Z., Zhou, Z., & Chen, J. (2018a). Fractal analysis of tight shaly sandstones using nuclear magnetic resonance measurements. AAPG Bulletin, 102(2), 175–193.

    Article  Google Scholar 

  • Lai, J., Wang, G., Wang, Z., Chen, J., Pang, X., Wang, S., Zhou, Z., He, Z., Qin, Z., & Fan, X. (2018b). A review on pore structure characterization in tight sandstones. Earth-Science Reviews, 177, 436–457.

    Article  Google Scholar 

  • Lei, G., Liao, Q., Lin, Q., Zhang, L., & Chen, W. (2020). Stress dependent gas-water relative permeability in gas hydrates: A theoretical model. Advances in Geo-Energy Research, 4(3), 326–338.

    Article  Google Scholar 

  • Li, H., Guo, H., Yang, Z., & Wang, X. (2015). Tight oil occurrence space of Triassic Chang 7 Member in Northern Shaanxi Area, Ordos Basin, NW China. Petroleum Exploration and Development, 42(3), 434–438.

    Article  Google Scholar 

  • Li, X., Cao, Z., & Xu, Y. (2020). Characteristics and trends of coal mine safety development. Energy Sources, Part a: Recovery, Utilization, and Environmental Effects. https://doi.org/10.1080/15567036.2020.1852339

    Article  Google Scholar 

  • Liu, K., Ostadhassan, M., Jang, H. W., Zakharova, N. V., & Shokouhimehr, M. (2021a). Comparison of fractal dimensions from nitrogen adsorption data in shale via different models. RSC Advances, 11(4), 2298–2306.

    Article  Google Scholar 

  • Liu, S., Li, X., Wang, D., & Zhang, D. (2021b). Experimental study on temperature response of different ranks of coal to liquid nitrogen soaking. Natural Resources Research, 30(2), 1467–1480.

    Article  Google Scholar 

  • Liu, Z., Yan, D., & Niu, X. (2020). Insights into pore structure and fractal characteristics of the Lower Cambrian Niutitang Formation shale on the Yangtze Platform, South China. Journal of Earth Science, 31(1), 169–180.

    Article  Google Scholar 

  • Mandelbrot, B. B. (1982). The fractal geometry of nature. WH Freeman.

    Google Scholar 

  • McGlade, C., Speirs, J., & Sorrell, S. (2013). Unconventional gas—A review of regional and global resource estimates. Energy, 55, 571–584.

    Article  Google Scholar 

  • Memon, A., Li, A., Memon, B. S., Muther, T., Han, W., Kashif, M., Tahir, M. U., & Akbar, I. (2021). Gas adsorption and controlling factors of shale: Review, application, comparison and challenges. Natural Resources Research, 30(1), 827–848.

    Article  Google Scholar 

  • Meng, Q., Xu, S., & Cai, J. (2019). Microscopic studies of immiscible displacement behavior in interconnected fractures and cavities. Journal of Energy Resources Technology, 141(9), 092901.

    Article  Google Scholar 

  • Neimark, A. (1992). A new approach to the determination of the surface fractal dimension of porous solids. Physica a: Statistical Mechanics and Its Applications, 191(1), 258–262.

    Article  Google Scholar 

  • Nelson, P. H. (2009). Pore-throat sizes in sandstones, tight sandstones, and shales. AAPG Bulletin, 93(3), 329–340.

    Article  Google Scholar 

  • Pape, H., Clauser, C., & Iffland, J. (1999). Permeability prediction based on fractal pore-space geometry. Geophysics, 64(5), 1447–1460.

    Article  Google Scholar 

  • Peyton, R. L., Gantzer, C. J., Anderson, S. H., Haeffner, B. A., & Pfeifer, P. (1994). Fractal dimension to describe soil macropore structure using X ray computed tomography. Water Resources Research, 30(3), 691–700.

    Article  Google Scholar 

  • Pfeifer, P., Obert, M., Cole, M. W., Fleischmann, M., Tildesley, D. J., & Ball, R. C. (1989a). Fractal BET and FHH theories of adsorption: A comparative study. Proceedings of the Royal Society of London. a. Mathematical and Physical Sciences, 423(1864), 169–188.

    Article  Google Scholar 

  • Pfeifer, P., Wu, Y. J., Cole, M. W., & Krim, J. (1989b). Multilayer adsorption on a fractally rough surface. Physical Review Letters, 62(17), 1997–2000.

    Article  Google Scholar 

  • Rafiei, Y., & Motie, M. (2019). Improved reservoir characterization by employing hydraulic flow unit classification in one of Iranian carbonate reservoirs. Advances in Geo-Energy Research, 3(3), 277–286.

    Article  Google Scholar 

  • Rembert, F., Jougnot, D., & Guarracino, L. (2020). A fractal model for the electrical conductivity of water-saturated porous media during mineral precipitation-dissolution processes. Advances in Water Resources, 145, 103742.

    Article  Google Scholar 

  • Ren, D., Zhou, D., Liu, D., Dong, F., Ma, S., & Huang, H. (2019). Formation mechanism of the Upper Triassic Yanchang Formation tight sandstone reservoir in Ordos Basin—Take Chang 6 reservoir in Jiyuan oil field as an example. Journal of Petroleum Science and Engineering, 178, 497–505.

    Article  Google Scholar 

  • Shen, W., Li, X., Ma, T., Cai, J., Lu, X. B., & Zhou, S.W. (2021). High-pressure methane adsorption behavior on deep shales: Experiments and modeling. Physics of Fluids, 33(6), 063103.

    Article  Google Scholar 

  • Sing, K. S. W., Everett, D. H., Haul, R. A. W., Moscou, L., Pierotti, R. A., Rouquerol, J., & Siemienewska, T. (1985). Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity. Pure and Applied Chemistry, 57(4), 603–619.

    Article  Google Scholar 

  • Song, Y., Li, Z., Jiang, L., & Hong, F. (2015). The concept and the accumulation characteristics of unconventional hydrocarbon resources. Petroleum Science, 12(4), 563–572.

    Article  Google Scholar 

  • Sun, M., Zhao, J., Pan, Z., Hu, Q., Yu, B., Tan, Y., Sun, L., Bai, L., Wu, C., Blach, T. P., Zhang, Y., Zhang, C., & Cheng, G. (2020). Pore characterization of shales: A review of small angle scattering technique. Journal of Natural Gas Science and Engineering, 78, 103294.

    Article  Google Scholar 

  • Thommes, M., Kaneko, K., Neimark, A. V., Olivier, J. P., Rodriguez-Reinoso, F., Rouquerol, J., & Sing, K. S. W. (2015). Physisorption of gases, with special reference to the evaluation of surface area and pore size distribution. Pure and Applied Chemistry, 87(9–10), 1051–1069.

    Article  Google Scholar 

  • Tian, Z., Wei, W., Zhou, S., Wood, D. A., & Cai, J. (2021). Experimental and fractal characterization of the microstructure of shales from Sichuan Basin, China. Energy & Fuels, 35(5), 3899–3914.

    Article  Google Scholar 

  • Wang, F., & Li, S. (1997). Determination of the surface fractal dimension for porous media by capillary condensation. Industrial & Engineering Chemistry Research, 36(5), 1598–1602.

    Article  Google Scholar 

  • Wang, X., Yin, H., Zhao, X., Li, B., & Yang, Y. (2019). Microscopic remaining oil distribution and quantitative analysis of polymer flooding based on CT scanning. Advances in Geo-Energy Research, 3(4), 448–456.

    Article  Google Scholar 

  • Wardlaw, N. C., & McKellar, M. (1981). Mercury porosimetry and the interpretation of pore geometry in sedimentary rocks and artificial models. Powder Technology, 29(1), 127–143.

    Article  Google Scholar 

  • Wei, W., Cai, J., Hu, X., Fan, P., Han, Q., Lu, J., Cheng, C.-L., & Zhou, F. (2015a). A numerical study on fractal dimensions of current streamlines in two-dimensional and three-dimensional pore fractal models of porous media. Fractals, 23(01), 1540012.

    Article  Google Scholar 

  • Wei, W., Cai, J., Hu, X., & Han, Q. (2015b). An electrical conductivity model for fractal porous media. Geophysical Research Letters, 42(12), 4833–4840.

    Article  Google Scholar 

  • Wood, D. A. (2021a). Deriving coal fractal dimensions from low-pressure nitrogen adsorption isotherms applying an integrated method. Applied Geochemistry, 131, 105042.

    Article  Google Scholar 

  • Wood, D. A. (2021b). Estimating organic-rich shale fractal dimensions from gas adsorption isotherms: Combining different methods leads to more reliable values and insight. Natural Resources Research, 30(5), 3551–3574.

    Article  Google Scholar 

  • Wu, S., Zhu, R., Li, X., Jin, X., Yang, Z., & Mao, Z. (2018). Evaluation and application of porous structure characterization technologies in unconventional tight reservoirs. Earth Science Frontiers, 25(2), 191–203. in Chinese.

    Google Scholar 

  • Xia, Y., Cai, J., Perfect, E., Wei, W., Zhang, Q., & Meng, Q. (2019). Fractal dimension, lacunarity and succolarity analyses on CT images of reservoir rocks for permeability prediction. Journal of Hydrology, 579, 124198.

    Article  Google Scholar 

  • Yang, C., Zhang, J., Tang, X., Ding, J., Zhao, Q., Dang, W., Chen, H., Su, Y., Li, B., & Lu, D. (2017). Comparative study on micro-pore structure of marine, terrestrial, and transitional shales in key areas, China. International Journal of Coal Geology, 171, 76–92.

    Article  Google Scholar 

  • Yang, F., Ning, Z., & Liu, H. (2014). Fractal characteristics of shales from a shale gas reservoir in the Sichuan Basin, China. Fuel, 115, 378–384.

    Article  Google Scholar 

  • Yang, R., He, S., Yi, J., & Hu, Q. (2016). Nano-scale pore structure and fractal dimension of organic-rich Wufeng-Longmaxi shale from Jiaoshiba area, Sichuan Basin: Investigations using FE-SEM, gas adsorption and helium pycnometry. Marine and Petroleum Geology, 70, 27–45.

    Article  Google Scholar 

  • Yao, Y., Liu, D., Tang, D., Tang, S., & Huang, W. (2008). Fractal characterization of adsorption-pores of coals from North China: An investigation on CH4 adsorption capacity of coals. International Journal of Coal Geology, 73(1), 27–42.

    Article  Google Scholar 

  • Yu, B., & Cheng, P. (2002). A fractal permeability model for bi-dispersed porous media. International Journal of Heat and Mass Transfer, 45(14), 2983–2993.

    Article  Google Scholar 

  • Yuan, Z. Y., Wang, J. Z., Zhang, Z. L., Chen, T. H., & Li, H. X. (2001). Vanadium- and chromium-containing mesoporous MCM-41 molecular sieves with hierarchical structure. Microporous and Mesoporous Materials, 43(2), 227–236.

    Article  Google Scholar 

  • Zhang, B., & Li, S. (1995). Determination of the surface fractal dimension for porous media by mercury porosimetry. Industrial & Engineering Chemistry Research, 34(4), 1383–1386.

    Article  Google Scholar 

  • Zhang, S., Tang, S., Tang, D., Huang, W., & Pan, Z. (2014). Determining fractal dimensions of coal pores by FHH model: Problems and effects. Journal of Natural Gas Science and Engineering, 21, 929–939.

    Article  Google Scholar 

  • Zhang, Y., He, Z., Jiang, S., Lu, S., Xiao, D., Chen, G., & Zhao, J. (2018). Factors affecting shale gas accumulation in overmature shales case study from lower Cambrian shale in western Sichuan Basin, south China. Energy & Fuels, 32(3), 3003–3012.

    Article  Google Scholar 

  • Zou, C., Yang, Z., Tao, S., Yuan, X. J., Zhu, R. K., Hou, L. H., Wu, S. T., Sun, L., Zhang, G. S., Bai, B., Wang, L., Gao, X. H., & Pang, Z. L. (2013). Continuous hydrocarbon accumulation over a large area as a distinguishing characteristic of unconventional petroleum: The Ordos Basin, North-Central China. Earth-Science Reviews, 126, 358–369.

    Article  Google Scholar 

  • Zou, C., Zhu, R., Liu, K., Su, L., Bai, B., Zhang, X., Yuan, X., & Wang, J. (2012). Tight gas sandstone reservoirs in China: Characteristics and recognition criteria. Journal of Petroleum Science and Engineering, 88–89, 82–91.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 42172159, 42004086) and the Fundamental Research Funds for the Central Universities (No. CUGGC04). We would like to thank Dr. Yuxuan Xia for his helpful suggestions on our work.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jianchao Cai.

Ethics declarations

Conflict of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, S., Yang, Z., Wu, S. et al. Fractal Analysis of Pore Structure Differences Between Shale and Sandstone Based on the Nitrogen Adsorption Method. Nat Resour Res 31, 1759–1773 (2022). https://doi.org/10.1007/s11053-022-10056-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11053-022-10056-5

Keywords

Navigation