TY - JOUR
T1 - The influence of fracture geometry variation on non-Darcy flow in fractures under confining stresses
AU - Chen, Yuedu
AU - Lian, Haojie
AU - Liang, Weiguo
AU - Yang, Jianfeng
AU - Vinh Phu Nguyen, null
AU - Bordas, Stephane P. A.
PY - 2019/1
Y1 - 2019/1
N2 - To investigate the influence of geometric characteristics of deformable rough fractures under confining stresses on the behaviors of non-Darcy flow, four fractured sandstone specimens were used for hydraulic tests in the experiments. According to the experimental results of the relationships between the hydraulic gradient and the flow rate, it is demonstrated that the Forchheimer's equation can offer a good description of the non-Darcy flow in rough fractures. In addition, the coefficients A and B in Forchheimer's equation are sensitive to the fracture geometric characteristics, and their values also increase as the confining stress rises, mainly owing to the reduction of the hydraulic aperture and the heterogeneous distribution of the interconnected void areas with the confining stress rising. Then, the surface and interior geometric properties of rough fractures were quantitatively characterized with the peak asperity height xi and the box-counting fractal dimension D of the heterogeneous distribution of the interconnected void areas, respectively. Furthermore, an empirical relationship between the fractal dimension D and the fracture apertures was constructed according to the experimental results. Lastly, a quantitative model was proposed to represent the relationship between the fracture geometric characteristics and the non-Darcy coefficient beta. This model was further used to link the non-linear coefficient B of Forchheimer's equation and the critical Reynold number Re-c, with the fracture geometric characteristics. The proposed models were validated by the experimental data and would be helpful to characterize the non-Darcy flow behavior in rough fractures under various confining stresses.
AB - To investigate the influence of geometric characteristics of deformable rough fractures under confining stresses on the behaviors of non-Darcy flow, four fractured sandstone specimens were used for hydraulic tests in the experiments. According to the experimental results of the relationships between the hydraulic gradient and the flow rate, it is demonstrated that the Forchheimer's equation can offer a good description of the non-Darcy flow in rough fractures. In addition, the coefficients A and B in Forchheimer's equation are sensitive to the fracture geometric characteristics, and their values also increase as the confining stress rises, mainly owing to the reduction of the hydraulic aperture and the heterogeneous distribution of the interconnected void areas with the confining stress rising. Then, the surface and interior geometric properties of rough fractures were quantitatively characterized with the peak asperity height xi and the box-counting fractal dimension D of the heterogeneous distribution of the interconnected void areas, respectively. Furthermore, an empirical relationship between the fractal dimension D and the fracture apertures was constructed according to the experimental results. Lastly, a quantitative model was proposed to represent the relationship between the fracture geometric characteristics and the non-Darcy coefficient beta. This model was further used to link the non-linear coefficient B of Forchheimer's equation and the critical Reynold number Re-c, with the fracture geometric characteristics. The proposed models were validated by the experimental data and would be helpful to characterize the non-Darcy flow behavior in rough fractures under various confining stresses.
KW - Rough fracture
KW - Non-Darcy flow
KW - Fracture geometric characteristics
KW - Forchheimer's equation
KW - Critical Reynolds number
KW - ROUGH-WALLED FRACTURES
KW - FLUID-FLOW
KW - NONLINEAR FLOW
KW - SURFACE-ROUGHNESS
KW - CUBIC LAW
KW - MATHEMATICAL-MODEL
KW - SINGLE FRACTURE
KW - ROCK FRACTURE
KW - NAVIER-STOKES
KW - PERMEABILITY
U2 - 10.1016/j.ijrmms.2018.11.017
DO - 10.1016/j.ijrmms.2018.11.017
M3 - Article
SN - 1365-1609
VL - 113
SP - 59
EP - 71
JO - International Journal of Rock Mechanics and Mining Sciences
JF - International Journal of Rock Mechanics and Mining Sciences
ER -