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Fractal dimension and morphological heterogeneity of pore in carbonate rocks: implications for production differences between adjacent wells
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  • Published: 02 April 2026

Fractal dimension and morphological heterogeneity of pore in carbonate rocks: implications for production differences between adjacent wells

  • Ya Zhang1,2,3,
  • Hongyu Long2,
  • Yong Li2,
  • Yuan He2,
  • Di Chen2,
  • Chi Zhang2,
  • Chenglong Li2,
  • Huachuan Jiang2 &
  • …
  • Jing Wang2 

Scientific Reports , Article number:  (2026) Cite this article

We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Energy science and technology
  • Solid Earth sciences

Abstract

This work investigates the morphological heterogeneity of pore systems in the carbonate rocks of the Canglangpu Formation, Sichuan Basin, aiming to explain the significant gas production disparity between two adjacent wells. An integrated methodology combining scanning electron microscopy (SEM) with digital image analysis was employed to classify pore morphologies and calculate fractal dimensions for 132 and 153 SEM images from Wells P7 and P9, respectively. The results demonstrate that Well P7 exhibits a more heterogeneous and intricate pore network, characterized by a higher median D value and a broader distribution, dominated by sub-circle pores across a wide complexity spectrum. In contrast, Well P9 possesses a more homogeneous pore structure with a lower, more clustered D value distribution. This morphological difference provides a mechanistic explanation for the production data, where the complex pore architecture of P7 likely impedes fluid flow, resulting in minimal production, while the more uniform system of P9 suggests better matrix connectivity. This matrix characteristic, combined with a more developed natural fracture network (the primary driver for high flow rates in such tight rock), correlates with its high daily gas output. In contrast, the complex pore architecture of P7 likely impedes matrix flow, contributing to its minimal production. The findings underscore that quantitative pore-scale characterization is critical for accurately assessing reservoir quality and predicting productivity in heterogeneous carbonate reservoirs, with direct implications for optimizing exploration and development strategies.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

References

  1. Huo, Z. et al. Carbonate source rock with low total organic carbon content and high maturity as effective source rock in China: A review. J. Asian Earth Sci. 176, 8–26 (2019).

    Google Scholar 

  2. Xu, Z. X. et al. A review of development methods and EOR technologies for carbonate reservoirs. Pet. Sci. 17 (4), 990–1013 (2020).

    Google Scholar 

  3. Lin, Y. H. et al. New insights into uranium source and mineralization process of the world-class jingchuan sandstone-hosted uranium deposit, ordos basin, China: Evidence from geology, carbonate textures and geochemistry. Ore Geol. Rev. 185, 106795 (2025).

    Google Scholar 

  4. Peng, G. et al. Seasonal and regional differences of carbonate dissolution in China: Insights from carbonate rock tablet experiments. Geomorphology 486, 109856 (2025).

    Google Scholar 

  5. Li, L. et al. Coal measure gas resources matter in China: Review, challenges, and perspective. Phys. Fluids. 36 (7), 071301 (2024).

    Google Scholar 

  6. Zhang, Z. et al. Diagenetic evolution and cementation mechanism in deep Carbonate reservoirs: A case study of Dengying Fm. 2 in Penglai, Sichuan Basin, China. Mar. Pet. Geol. 170, 107084 (2024).

    Google Scholar 

  7. Xia, L. W., Cao, J., Wang, M., Mi, J. L. & Wang, T. T. A review of carbonates as hydrocarbon source rocks: basic geochemistry and oil–gas generation. Pet. Sci. 16 (4), 713–728 (2019).

    Google Scholar 

  8. Tang, H., Jia, C., Lu, H., Deng, Y. & Zhu, B. Numerical simulation of residual oil distribution characteristic of carbonate reservoir after water flooding. Volume 12–2024. (2024).

  9. Dou, Q., Sun, Y. & Sullivan, C. Rock-physics-based carbonate pore type characterization and reservoir permeability heterogeneity evaluation, Upper San Andres reservoir, Permian Basin, west Texas. J. Appl. Geophys. 74 (1), 8–18 (2011).

    Google Scholar 

  10. Leger, M. & Luquot, L. Importance of Microstructure in Carbonate Rocks: Laboratory and 3D-Imaging Petrophysical Characterization Applied Sciences [Online], (2021).

  11. Mirshadi, A., Javaherian, A., Saberi, M. R., Kadkhodaie, A. & Khoshdel, H. Estimation of pore-type distribution utilizing petrophysical data and rock physics modeling on an Iranian carbonate reservoir. J. Pet. Explor. Prod. Technol. 14 (8), 2379–2397 (2024).

    Google Scholar 

  12. Dong, H. et al. Quantitative characterization of the carbonate rock microstructure considering topological features: a case study from the Gaoshiti–Moxi block of the Sichuan Basin. Volume 12–2024. (2024).

  13. Li, H. B., Zhang, J. J., Cai, S. J. & Pan, H. J. A two-step method to apply Xu–Payne multi-porosity model to estimate pore type from seismic data for carbonate reservoirs. Pet. Sci. 17 (3), 615–627 (2020).

    Google Scholar 

  14. Hu, Y., Zhao, J., Sun, L., Long, T. & Wang, Z. Digital rock physics on carbonate pore type characterization and its effect on acoustic properties. In Rock Physics and Digital Rock Applications Workshop, Beijing, China, ; pp 5–8. (2018).

  15. Liu, X. et al. Pore Structure Petrophysical Characterization of the Upper Cretaceous Oil Shale from the Songliao Basin (NE China) Using Low-Field NMR. Journal of Spectroscopy 2020, 1–11. (2020).

  16. Lu, Z. H., Li, K., Liu, X. B., Zhao, P. & Liu, J. Low-field NMR application in the characterization of CO2 Geological storage and utilization related to shale gas reservoirs: a brief review. Front. Earth Sci. 17 (3), 739–751 (2023).

    Google Scholar 

  17. Gang, S. et al. Pore Structure Characteristics of Carbonate Rocks and Their Influence on Permeability. ACS Omega. 10 (22), 22613–22626 (2025).

    Google Scholar 

  18. Cheng, Y., Luo, X., Zhuo, Q., Gong, Y. & Liang, L. Description of Pore Structure of Carbonate Reservoirs Based on (Fractal Dimension Processes [Online], 2024).

  19. Hu, C. et al. Characterization of pore systems in fine-grained carbonate rocks using digital core technology. Adv. Geo-Energy Res. 12 (1), 77–80 (2024).

    Google Scholar 

  20. Yao, Y., Liu, J., Wu, H. & Sun, X. Robust Low-Field NMR for CO2 Geo-Sequestration: Advances, Challenges, and Perspectives. Energ. Fuel. 39 (40), 19111–19129 (2025).

    Google Scholar 

  21. Li, L. et al. CO2-Enhanced Multiphase Flow in Heterogenous Coal Measures: Thermal-Hydraulic-Mechanic (THM) Model for Enhancing Gas Co-Production with CO2 Geo-Sequestration. Fuel 407, 137479 (2026).

    Google Scholar 

  22. Yan, W. et al. Natural gas geology and exploration direction of the Cambrian Lower Canglangpu Member in central Sichuan paleo-uplift, Sichuan Basin, SW China. Pet. Explor. Dev. 48 (2), 337–353 (2021).

    Google Scholar 

  23. Huang, H. et al. Multistage dolomitization of deeply buried dolomite in the Lower Cambrian Canglangpu Formation, central and northern Sichuan Basin. Mar. Pet. Geol. 152, 106261 (2023).

    Google Scholar 

  24. Li, K. et al. A comparison of hydrothermal events and petroleum migration between Ediacaran and lower Cambrian carbonates, Central Sichuan Basin. Mar. Pet. Geol. 150, 106130 (2023).

    Google Scholar 

  25. Yading, L. et al. Research on sedimentary evolution characteristics of Cambrian Canglangpu Formation, Sichuan Basin. Nat. Gas Geoscience. 32 (9), 1334–1346 (2021).

    Google Scholar 

  26. Arganda-Carreras, I. et al. Trainable Weka Segmentation: a machine learning tool for microscopy pixel classification. Bioimage Inf. 33, 2424–2426 (2017).

    Google Scholar 

  27. Lormand, C. et al. Weka Trainable Segmentation Plugin in ImageJ: A Semi-Automatic Tool Applied to Crystal Size Distributions of Microlites in Volcanic Rocks. Microsc Microanal. 24 (6), 667–675 (2018).

    Google Scholar 

  28. He, B., Xie, L., Liu, X., Liu, J. & Elsworth, D. Mechanistic controls on permeability evolution in thermally-upgraded low-maturity oil shales: Application of machine learning outputs. Unconv. Resour. 6, 100133 (2025).

    Google Scholar 

  29. Liu, J., Yao, Y., Liu, D., Cai, Y. & Cai, J. Comparison of Pore Fractal Characteristics between Marine and Continental Shales. Fractals 26 (02), 1840016 (2018).

    Google Scholar 

  30. Su, P. H. et al. Fractal characteristics of low-permeability gas sandstones based on a new model for mercury intrusion porosimetry. J. Nat. Gas Sci. Eng. 60, 246–255 (2018).

    Google Scholar 

  31. Zheng, S. J., Yao, Y. B., Liu, D. M., Cai, Y. D. & Liu, Y. Characterizations of full-scale pore size distribution, porosity and permeability of coals: A novel methodology by nuclear magnetic resonance and fractal analysis theory. Int. J. Coal Geol. 196, 148–158 (2018).

    Google Scholar 

  32. Wang, H. J. et al. Study on fracture characteristics in coal and shale for coal-measure gas reservoir based on 3D CT reconstruction and fractal features. Front. Earth Sci. 17 (2), 514–526 (2023).

    Google Scholar 

  33. Liu, C., Shi, B., Zhou, J. & Tang, C. S. Quantification and characterization of microporosity by image processing, geometric measurement and statistical methods: Application on SEM images of clay materials. Appl. Clay Sci. 54 (1), 97–106 (2011).

    Google Scholar 

  34. Qi, J. F., Sui, W. H., Zhang, C. L. & Xu, J. S. Calculation and Analysis of the Porosity and Fractal Dimension of Red Stratum Sandstone based on SEM Images Processing. J. Eng. Geol. 22, 339–345 (2014). (In Chinese with English abstract).

    Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge Dr. Xi Wu from the Analytical & Testing Center of Sichuan University for his help with the SEM characterization.

Funding

This study was financially supported by the National Natural Science Foundation of China (No. U2344209), PetroChina Scientific Research Project (No. 2023ZZ16YJ01) and Oil & Gas Major Project (No. 2025ZD1400400).

Author information

Authors and Affiliations

  1. Institute of Sedimentary Geology, Chengdu University of Technology, Chengdu, 610059, Sichuan, China

    Ya Zhang

  2. Exploration and Development Research institute, Southwest Oil & Gas Field Company, PetroChina, Chengdu, 610041, Sichuan, China

    Ya Zhang, Hongyu Long, Yong Li, Yuan He, Di Chen, Chi Zhang, Chenglong Li, Huachuan Jiang & Jing Wang

  3. State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation, Chengdu University of Technology, Chengdu, 610059, Sichuan, China

    Ya Zhang

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Contributions

Ya Zhang and Hongyu Long contributed to the study design and methodology development, with Ya Zhang leading the manuscript drafting and Hongyu Long overseeing data acquisition and SEM experiments. Yong Li, provided overall supervision, project administration, and funding acquisition. Yuan He and Di Chen performed the digital image analysis using ImageJ software, including pore parameter extraction and fractal dimension calculations. Chi Zhang and Chenglong Li were responsible for data validation, geological interpretation, and statistical analysis. Huachuan Jiang and Jing Wang prepared all figures, including the geological settings, methodology workflows, SEM examples, and fractal dimension plots, and contributed to visualization and manuscript review. All authors participated in writing, reviewing, and approving the final manuscript.

Corresponding author

Correspondence to Yong Li.

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The authors declare no competing interests.

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Cite this article

Zhang, Y., Long, H., Li, Y. et al. Fractal dimension and morphological heterogeneity of pore in carbonate rocks: implications for production differences between adjacent wells. Sci Rep (2026). https://doi.org/10.1038/s41598-026-47223-0

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  • Received: 15 December 2025

  • Accepted: 30 March 2026

  • Published: 02 April 2026

  • DOI: https://doi.org/10.1038/s41598-026-47223-0

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Keywords

  • Carbonate reservoir
  • Pore morphology
  • Fractal dimension
  • Microscopic heterogeneity
  • Sichuan Basin
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