Abstract
Fracture intersections are the main components of fracture networks with significant effects on the distribution of flow velocity and fluid pressure near the intersection. A nonlinear flow model for fracture intersections correlating to geometric parameters of two-dimensional fracture intersections was proposed, which was applicable to different flow patterns in fracture intersections. A total of 68 fracture intersection models were established and simulated. By fitting these calculated results, regression functions in terms of each kind of geometric parameter were obtained to determine nonlinear coefficients. Through independent and comprehensive analysis of the influence of geometric parameters on flow characteristics, the quantitative relationships between the nonlinear coefficients of the fracture intersection flow model and multiple geometric parameters, such as the intersecting angle (θ), aperture (e), and roughness, were obtained. The parametric expressions of nonlinear flow models were verified by flow experiments of typical fracture intersections and simulated cases with complicated combinations of geometric parameters. It was proven that the parametric expressions of nonlinear flow models were capable of describing the nonlinear flow through fracture intersections. The results of this study show that fracture intersections have an obvious influence on the flow characteristics of different flow paths, which indicates that the influence of fracture intersections can enhance the hydraulic heterogeneity of fractured rock and need to be considered in the flow analysis of fracture networks.
Highlights
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A nonlinear flow model for fracture intersections of two-dimensional fracture intersections was proposed.
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Quantitative relationships between the nonlinear coefficients and geometric parameters of the fracture intersections were obtained.
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Flow experiments of typical fracture intersections were carried out.
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The parametric expressions of nonlinear flow models were verified by flow experiments and simulations of complicated cases.
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Abbreviations
- A :
-
Linear coefficient
- B :
-
Nonlinear coefficient
- e :
-
Fracture aperture
- g :
-
Gravity acceleration
- i, j :
-
Number of fracture branch
- J :
-
Hydraulic gradient
- JRC:
-
Joint roughness coefficient
- l :
-
Length of the fracture
- P :
-
Water pressure
- ΔP :
-
Pressure drop
- Q :
-
Flow rate
- Re:
-
Reynolds number
- R r :
-
Influence scale of intersections
- w :
-
Width of fracture
- β :
-
Non-Darcy parameter
- δ e :
-
Aperture ratio
- θ :
-
Intersecting angle
- μ :
-
Dynamic viscosity
- ρ :
-
Fluid density
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Funding
This study was financially supported by the National Natural Science Foundation of China under contract Nos. 51779045, 51579141 and 42177157, the Fundamental Research Funds for the Central Universities under contract Nos. N180104022, N2001026 and N2101020, Liao Ning Revitalization Talents Program under contract No. XLYC1807029 and Liaoning Natural Science Foundation under contract No. 2019-YQ-02.
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Liu, J., Wang, Z., Qiao, L. et al. Nonlinear Flow Model for Rock Fracture Intersections: The Roles of the Intersecting Angle, Aperture and Fracture Roughness. Rock Mech Rock Eng 55, 2385–2405 (2022). https://doi.org/10.1007/s00603-022-02784-0
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DOI: https://doi.org/10.1007/s00603-022-02784-0