Nonlinear flow behavior at low Reynolds numbers through rough-walled fractures subjected to normal compressive loading

Zhou, Jing; Hu, Shaohua; Fang, Shu; Chen, Yifeng; Zhou, Chuangbing

doi:10.1016/j.ijrmms.2015.09.027

Cited by 207 publications

(121 citation statements)

References 46 publications

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“…However, for samples under shear with > 0 mm, with the increment of confining pressure, Re firstly increases and then decreases as shown in Figure 13, presenting the same trends with most of the samples in Figure 12. For = 1.0∼3.0 MPa, the range of Re (Re = 1.50∼13.03) in the work of Rong et al [104] is a little larger than that (Re = 0.16∼9.24) of Zhou et al [98]. …”

Section: Effects Of Normal Stress And/or Confining Pressurementioning

confidence: 68%

“…In the previous works, it is assumed that the critical Reynolds number (Re ) is the Re that corresponds to = 0.1 [93,[95][96][97]. Besides the dimensionless Re that is used for characterizing the transition from linear to nonlinear flow regimes, the dimensionless Forchheimer number ( 0 ) is another widely accepted parameter, which is defined as the ratio of nonlinear to linear pressure losses, written as [20,92,98] …”

Section: Cubicmentioning

confidence: 99%

“…The reasons may be that the boreholes at different depths contain fractures having different geometric properties such as aperture, persistence, orientation, and surface roughness. To simplify the model and clearly investigate the influence of normal stress and/or confining pressure on Re , Zhou et al [98] prepared four granite rock samples (G1∼G4) taken from the depth 450∼550 m in the Beishan area in Gansu Province, China, and two sandstone rock samples (S1∼S2) taken from the depth of about 20 m in the Three Gorges Reservoir area, Hubei Province, China. The confining pressure varies from 1.0 to 30.0 MPa and Re under each confining pressure is calculated.…”

Section: Effects Of Normal Stress And/or Confining Pressurementioning

confidence: 99%

See 2 more Smart Citations

A Review of Critical Conditions for the Onset of Nonlinear Fluid Flow in Rock Fractures

Jiang

2017

Geofluids

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Selecting appropriate governing equations for fluid flow in fractured rock masses is of special importance for estimating the permeability of rock fracture networks. When the flow velocity is small, the flow is in the linear regime and obeys the cubic law, whereas when the flow velocity is large, the flow is in the nonlinear regime and should be simulated by solving the complex NavierStokes equations. The critical conditions such as critical Reynolds number and critical hydraulic gradient are commonly defined in the previous works to quantify the onset of nonlinear fluid flow. This study reviews the simplifications of governing equations from the Navier-Stokes equations, Stokes equation, and Reynold equation to the cubic law and reviews the evolutions of critical Reynolds number and critical hydraulic gradient for fluid flow in rock fractures and fracture networks, considering the influences of shear displacement, normal stress and/or confining pressure, fracture surface roughness, aperture, and number of intersections. This review provides a reference for the engineers and hydrogeologists especially the beginners to thoroughly understand the nonlinear flow regimes/mechanisms within complex fractured rock masses.

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Section: Effects Of Normal Stress And/or Confining Pressurementioning

confidence: 68%

Section: Cubicmentioning

confidence: 99%

Section: Effects Of Normal Stress And/or Confining Pressurementioning

confidence: 99%

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A Review of Critical Conditions for the Onset of Nonlinear Fluid Flow in Rock Fractures

Jiang

2017

Geofluids

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“…Using (11), of the fracture networks was calculated. Figure 10 shows the relationships between and .…”

Section: Test Results and Discussionmentioning

confidence: 99%

“…Rock fracture networks constitute the main pathways of fluid flow and solute migration in deep underground projects, and during the past several decades, substantial efforts have been devoted to the estimation of fluid flow behavior and transmissivity of fractures in many geoengineering and geosciences such as underground tunneling [1][2][3], CO 2 sequestration [4,5], geothermal energy extraction [6][7][8], and hazardous wastes isolation [9][10][11]. The fluid flow in rock fractures is commonly assumed to follow the cubic law, in which the flow rate is linearly proportional to the pressure gradient [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Experimental Study on Stress-Dependent Nonlinear Flow Behavior and Normalized Transmissivity of Real Rock Fracture Networks

et al. 2018

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The mechanism and quantitative descriptions of nonlinear fluid flow through rock fractures are difficult issues of high concern in underground engineering fields. In order to study the effects of fracture geometry and loading conditions on nonlinear flow properties and normalized transmissivity through fracture networks, stress-dependent fluid flow tests were conducted on real rock fracture networks with different number of intersections (1, 4, 7, and 12) and subjected to various applied boundary loads (7, 14, 21, 28, and 35 kN). For all cases, the inlet hydraulic pressures ranged from 0 to 0.6 MPa. The test results show that Forchheimer's law provides an excellent description of the nonlinear fluid flow in fracture networks. The linear coefficient and nonlinear coefficient in Forchheimer's law = + 2 generally decrease with the number of intersections but increase with the boundary load. The relationships between and can be well fitted with a power function. A nonlinear effect factor = 2 /( + 2 ) was used to quantitatively characterize the nonlinear behaviors of fluid flow through fracture networks. By defining a critical value of = 10%, the critical hydraulic gradient was calculated. The critical hydraulic gradient decreases with the number of intersections due to richer flowing paths but increases with the boundary load due to fracture closure. The transmissivity of fracture networks decreases with the hydraulic gradient, and the variation process can be estimated using an exponential function. A mathematical expression / 0 = 1 − exp(− −0.45 ) for decreased normalized transmissivity / 0 against the hydraulic gradient was established. When the hydraulic gradient is small, / 0 holds a constant value of 1.0. With increasing hydraulic gradient, the reduction rate of / 0 first increases and then decreases. The equivalent permeability of fracture networks decreases with the applied boundary load, and permeability changes at low load levels are more sensitive.

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Visualizing and quantifying the crossover from capillary fingering to viscous fingering in a rough fracture

Chen

Fang

et al. 2017

Water Resources Research

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121

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Immiscible fluid‐fluid displacement in permeable media is important in many subsurface processes, including enhanced oil recovery and geological CO2 sequestration. Controlled by capillary and viscous forces, displacement patterns of one fluid displacing another more viscous one exhibit capillary and viscous fingering, and crossover between the two. Although extensive studies investigated viscous and capillary fingering in porous media, a few studies focused on the crossover in rough fractures, and how viscous and capillary forces affect the crossover remains unclear. Using a transparent fracture‐visualization system, we studied how the two forces impact the crossover in a horizontal rough fracture. Drainage experiments of water displacing oil were conducted at seven flow rates (capillary number log10Ca ranging from −7.07 to −3.07) and four viscosity ratios (M=1/1000,1/500,1/100 and 1/50). We consistently observed lower invading fluid saturations in the crossover zone. We also proposed a phase diagram for the displacement patterns in a rough fracture that is consistent with similar studies in porous media. Based on real‐time imaging and statistical analysis of the invasion morphology, we showed that the competition between capillary and viscous forces is responsible for the saturation reduction in the crossover zone. In this zone, finger propagation toward the outlet (characteristic of viscous fingering) as well as void‐filling in the transverse/backward directions (characteristic of capillary fingering), are both suppressed. Therefore, the invading fluid tends to occupy larger apertures with higher characteristic front velocity, promoting void‐filling toward the outlet with thinner finger growth and resulting in a larger volume of defending fluid left behind.

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Nonlinear flow behavior at low Reynolds numbers through rough-walled fractures subjected to normal compressive loading

Cited by 207 publications

References 46 publications

A Review of Critical Conditions for the Onset of Nonlinear Fluid Flow in Rock Fractures

A Review of Critical Conditions for the Onset of Nonlinear Fluid Flow in Rock Fractures

Experimental Study on Stress-Dependent Nonlinear Flow Behavior and Normalized Transmissivity of Real Rock Fracture Networks

Visualizing and quantifying the crossover from capillary fingering to viscous fingering in a rough fracture

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