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<p>Under in-situ stress, rock fractures may slip and dilate, creating complex void-space geometries. When fluid flows through these fractures, the connectivity of void spaces governs tortuosity and can induce nonlinear behaviour. The Forchheimer equation is widely used to model such nonlinearity. However, parametric expressions for its application to&#xa0;shear fractures are rarely addressed in the literature. This study develops a Forchheimer-based hydromechanical model that captures the evolving void-space connectivity, providing a more accurate representation of fluid tortuosity. The model incorporates a novel path searching algorithm to efficiently identify preferential flow pathways, thereby accounting for the connectivity of void spaces that contribute to the overall flow rate. A systematic analysis of fracture permeability was conducted by integrating 8 conceptual hydraulic aperture models into the proposed framework. The models were validated using a dataset of 384 coupled shear-flow tests covering a range of fracture irregularities, stress conditions, and flow regimes. Benchmarking against a recently introduced Forchheimer equation-based model for sheared fractures, the proposed model demonstrated strong agreement with experimental data, achieving a mean absolute percentage error of 16.7%, a Normalised Objective Function of 0.18, and a regression slope between the measured and simulation results of 0.93. These results highlight the improvement in fracture permeability predictions, driven by the incorporation of detailed void spaces and their connectivity, making this approach valuable for seepage-related applications.</p>

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A Connectivity-Based Forchheimer Model for Nonlinear Flow in Sheared Rough-Wall Fractures

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月9日

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  • Min Gao,
  • Xige Liu,
  • Zizhuo Xiang,
  • Won-Hee Kang,
  • Joung Oh,
  • Ismet Canbulat

摘要

Under in-situ stress, rock fractures may slip and dilate, creating complex void-space geometries. When fluid flows through these fractures, the connectivity of void spaces governs tortuosity and can induce nonlinear behaviour. The Forchheimer equation is widely used to model such nonlinearity. However, parametric expressions for its application to shear fractures are rarely addressed in the literature. This study develops a Forchheimer-based hydromechanical model that captures the evolving void-space connectivity, providing a more accurate representation of fluid tortuosity. The model incorporates a novel path searching algorithm to efficiently identify preferential flow pathways, thereby accounting for the connectivity of void spaces that contribute to the overall flow rate. A systematic analysis of fracture permeability was conducted by integrating 8 conceptual hydraulic aperture models into the proposed framework. The models were validated using a dataset of 384 coupled shear-flow tests covering a range of fracture irregularities, stress conditions, and flow regimes. Benchmarking against a recently introduced Forchheimer equation-based model for sheared fractures, the proposed model demonstrated strong agreement with experimental data, achieving a mean absolute percentage error of 16.7%, a Normalised Objective Function of 0.18, and a regression slope between the measured and simulation results of 0.93. These results highlight the improvement in fracture permeability predictions, driven by the incorporation of detailed void spaces and their connectivity, making this approach valuable for seepage-related applications.