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A Planar-3D Mathematical Model for Studying the Effect of Heterogeneity of Rock Fracture Toughness on Hydraulic Fracture Propagation: Early-Time Solution including the Stage before Propagation

Author

Listed:
  • Kairui Li

    (School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China)

  • Nickolay N. Smirnov

    (Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow 119991, Russia
    Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Nakhimovskiy Str. 36-1, Moscow 117218, Russia)

  • Chengzhi Qi

    (School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China)

  • Mingyang Wang

    (State Key Laboratory for Explosion & Impact and Disaster Prevention & Mitigation, Faculty of Defense Engineering, Army Engineering University of PLA, Nanjing 210007, China)

  • Dmitry A. Pestov

    (Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Nakhimovskiy Str. 36-1, Moscow 117218, Russia)

  • Anastasia A. Shamina

    (Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow 119991, Russia
    Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Nakhimovskiy Str. 36-1, Moscow 117218, Russia)

Abstract

Among the studies of the effect of rock’s heterogeneity on hydraulic fracture propagation, very little information on the effects of the heterogeneity of rock’s fracture toughness is available. The objective of the present paper is to develop a planar-3D model for studying the effect of the heterogeneity of rock’s fracture toughness on hydraulic fracture propagation. Not only the stage of fracture propagation, but also the stage before the fracture propagation is considered in this model. Based on the proposed model, the evolution of hydraulic fracture propagation under a typical heterogeneous distribution of rock’s fracture toughness and the solution at the stage before fracture propagation are analyzed in detail. Furthermore, a series of numerical comparison experiments including five different distributions of rock’s fracture toughness are made in order to study the effect of the heterogeneity of rock’s toughness. The results indicate that the minimum fracture radius and the contrast of rock’s fracture toughness between adjacent layers are important parameters for determining the size and location of the maximum fracture opening. Most importantly, the fracture contour is greatly affected by the heterogeneity of rock’s fracture toughness.

Suggested Citation

  • Kairui Li & Nickolay N. Smirnov & Chengzhi Qi & Mingyang Wang & Dmitry A. Pestov & Anastasia A. Shamina, 2023. "A Planar-3D Mathematical Model for Studying the Effect of Heterogeneity of Rock Fracture Toughness on Hydraulic Fracture Propagation: Early-Time Solution including the Stage before Propagation," Mathematics, MDPI, vol. 11(9), pages 1-27, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2083-:d:1134582
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    References listed on IDEAS

    as
    1. Ke Li & Xinghong Jiang & Hao Ding & Xuebing Hu, 2019. "Three-Dimensional Propagation Simulation and Parameter Analysis of Rock Joint with Displacement Discontinuity Method," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-11, July.
    2. Nickolay Smirnov & Kairui Li & Evgeniya Skryleva & Dmitriy Pestov & Anastasia Shamina & Chengzhi Qi & Alexey Kiselev, 2022. "Mathematical Modeling of Hydraulic Fracture Formation and Cleaning Processes," Energies, MDPI, vol. 15(6), pages 1-35, March.
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