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Numerical simulation of hydraulic–natural fracture interaction based on the continuous–discontinuous element method
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  • Published: 05 January 2026

Numerical simulation of hydraulic–natural fracture interaction based on the continuous–discontinuous element method

  • Kai Yang1,2,
  • Guopeng Huang1,2,
  • Fujian Zhou1,2,
  • Tianbo Liang1,2,
  • Jie Zuo1,2 &
  • …
  • Minghui Li3,4 

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

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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
  • Engineering
  • Natural hazards
  • Solid Earth sciences

Abstract

Shale reservoirs commonly contain numerous geological discontinuities, such as natural fractures, faults, and lithological interfaces. These discontinuities significantly influence the formation of hydraulic fracture networks. Therefore, to investigate the impact of different natural fracture parameters on fracture network development, this study establishes a stress-seepage-fracture multi-field coupling model for fractured reservoirs based on the continuous-discontinuous algorithm. The effects of natural fracture angle, stress difference, natural fracture strength, and injection rate on fracture network morphology, injection pressure, and fracture complexity are systematically analyzed. The results indicate that the natural fracture angle and stress difference jointly control fracture propagation patterns. At high natural fracture angles and high stress differences, hydraulic fractures tend to directly cross natural fractures. Additionally, as natural fracture strength increases, the difficulty of natural fracture activation gradually rises, while the number of branch fractures increases. Under high injection rates, the fluid pressure builds up rapidly, facilitating better activation of natural fractures. Meanwhile, as the injection rate increases, the growth rate of fracture complexity accelerates significantly. However, under the same injected volume, the fracture complexity is highest at 0.001 m³/s and lowest at 0.01 m³/s. This study aims to provide guidance for understanding the interaction mechanisms between hydraulic and natural fractures and optimizing fracturing design parameters.

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Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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Funding

Supported by the National Natural Science Foundation of China (No. 52174045, No. U23B2084 and No.5241002).

Author information

Authors and Affiliations

  1. State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum (Beijing), Beijing, 102249, China

    Kai Yang, Guopeng Huang, Fujian Zhou, Tianbo Liang & Jie Zuo

  2. Unconventional Petroleum Research Institute, China University of Petroleum (Beijing), Beijing, 102249, China

    Kai Yang, Guopeng Huang, Fujian Zhou, Tianbo Liang & Jie Zuo

  3. Research Institute of Petroleum Exploration & Development, PetroChina Corporation, Beijing, 100083, China

    Minghui Li

  4. Oil & Gas and New Energy Branch, PetroChina Corporation, Beijing, 100010, China

    Minghui Li

Authors
  1. Kai Yang
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  2. Guopeng Huang
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Contributions

K.Y: Writing – review & editing, Writing – original draft,, Software, Formal analysis, Data curation. G.H. : Writing – review & editing, Software, Resources, Methodology, Data curation. F.Z. : Writing – review & editing, Supervision, Resources, Methodology, Funding acquisition. T.L. & J.Z.: review & editing, Software, Data curation. M.L.: Formal analysis, Data curation.

Corresponding author

Correspondence to Fujian Zhou.

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The authors declare no competing interests.

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Cite this article

Yang, K., Huang, G., Zhou, F. et al. Numerical simulation of hydraulic–natural fracture interaction based on the continuous–discontinuous element method. Sci Rep (2026). https://doi.org/10.1038/s41598-025-34508-z

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  • Received: 17 August 2025

  • Accepted: 29 December 2025

  • Published: 05 January 2026

  • DOI: https://doi.org/10.1038/s41598-025-34508-z

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Keywords

  • Continuous-discontinuous element method
  • Natural fracture
  • Fracture network
  • Hydraulic fracturing
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