The influence of fracture geometry variation on non-Darcy flow in fractures under confining stresses

Yuedu Chen, Haojie Lian, Weiguo Liang, Jianfeng Yang, Vinh Phu Nguyen, Stephane P. A. Bordas

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)59-71
Number of pages13
JournalInternational Journal of Rock Mechanics and Mining Sciences
Volume113
DOIs
Publication statusPublished - Jan 2019

Cite this

Chen, Yuedu ; Lian, Haojie ; Liang, Weiguo ; Yang, Jianfeng ; Vinh Phu Nguyen ; Bordas, Stephane P. A. / The influence of fracture geometry variation on non-Darcy flow in fractures under confining stresses. In: International Journal of Rock Mechanics and Mining Sciences. 2019 ; Vol. 113. pp. 59-71.
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abstract = "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.",
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The influence of fracture geometry variation on non-Darcy flow in fractures under confining stresses. / Chen, Yuedu; Lian, Haojie; Liang, Weiguo; Yang, Jianfeng; Vinh Phu Nguyen; Bordas, Stephane P. A.

In: International Journal of Rock Mechanics and Mining Sciences, Vol. 113, 01.2019, p. 59-71.

Research output: Contribution to journalArticle

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.

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KW - Non-Darcy flow

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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

VL - 113

SP - 59

EP - 71

JO - International Journal of Rock Mechanics and Mining Sciences

JF - International Journal of Rock Mechanics and Mining Sciences

SN - 0020-7624

ER -