Critical Reynolds number for nonlinear flow through rough-walled fractures: The role of shear processes

Javadi, M.; Sharifzadeh, Mostafa; Shahriar, K.; Mitani, Yasuhiro

doi:10.1002/2013wr014610

Cited by 241 publications

(128 citation statements)

References 110 publications

(154 reference statements)

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“…For the case of incompressible and steady-state Newtonian flow, the terms involving time drop out and the NS equations can be expressed as [1,17] …”

Section: Governing Equations Of Fluid Flow In Fracturesmentioning

confidence: 99%

“…Equation (2) is composed of a set of coupled nonlinear partial derivatives of varying orders. In order to solve these equations, an additional equation, called the mass conservation equation which can be achieved through mass continuity, is employed and the equation takes the form [1,15] …”

Section: Governing Equations Of Fluid Flow In Fracturesmentioning

confidence: 99%

“…To quantitatively estimate the nonlinearity of fluids flowing through the fracture networks, a nonlinear effect factor was introduced to determine the fluid flow regime [1,35,36]. It can be presented by…”

Section: Geofluidsmentioning

confidence: 99%

“…The Forchheimer number 0 is another widely accepted parameter to characterize the onset of flow transition to nonlinearity, which is defined as the ratio of nonlinear to linear pressure drops [1,13,17],…”

Section: Geofluidsmentioning

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%

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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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“…For the case of incompressible and steady-state Newtonian flow, the terms involving time drop out and the NS equations can be expressed as [1,17] …”

Section: Governing Equations Of Fluid Flow In Fracturesmentioning

confidence: 99%

Section: Governing Equations Of Fluid Flow In Fracturesmentioning

confidence: 99%

Section: Geofluidsmentioning

confidence: 99%

Section: Geofluidsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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Estimating hydraulic conductivity of fractured rocks from high‐pressure packer tests with an Izbash's law‐based empirical model

Chen

et al. 2015

Water Resources Research

117

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High-pressure packer test (HPPT) is an enhanced constant head packer test for characterizing the permeability of fractured rocks under high-pressure groundwater flow conditions. The interpretation of the HPPT data, however, remains difficult due to the transition of flow conditions in the conducting structures and the hydraulic fracturing-induced permeability enhancement in the tested rocks. In this study, a number of HPPTs were performed in the sedimentary and intrusive rocks located at 450 m depth in central Hainan Island. The obtained Q-P curves were divided into a laminar flow phase (I), a non-Darcy flow phase (II), and a hydraulic fracturing phase (III). The critical Reynolds number for the deviation of flow from linearity into phase II was 25266. The flow of phase III occurred in sparsely to moderately fractured rocks, and was absent at the test intervals of perfect or poor intactness. The threshold fluid pressure between phases II and III was correlated with RQD and the confining stress. An Izbash's law-based analytical model was employed to calculate the hydraulic conductivity of the tested rocks in different flow conditions. It was demonstrated that the estimated hydraulic conductivity values in phases I and II are basically the same, and are weakly dependent on the injection fluid pressure, but it becomes strongly pressure dependent as a result of hydraulic fracturing in phase III. The hydraulic conductivity at different test intervals of a borehole is remarkably enhanced at highly fractured zone or contact zone, but within a rock unit of weak heterogeneity, it decreases with the increase of depth. Key Points:The Q-P curves by HPPTs were divided into Darcy, non-Darcy, and fracking phases The characteristics of Q-P curves were correlated with the intactness of rocks The permeability in different phases was evaluated with an analytical modelCorrespondence to: (2015), Estimating hydraulic conductivity of fractured rocks from high-pressure packer tests with an Izbash's law-based empirical model,

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Linking microearthquakes to fracture permeability change: The role of surface roughness

Ishibashi

Watanabe

Asanuma

et al. 2016

Geophysical Research Letters

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Despite its importance, the relation between microearthquakes (MEQs) and changes in hydraulic properties during hydraulic stimulation of a fractured reservoir has rarely been explored, and it is still not well understood. To investigate this relation, we first formulate a plausible scale dependence, where fracture length and shear displacement are variables, for channeling flow through heterogeneous aperture distributions for joints and faults. By combining this formulation with the concept of the seismic moment, we derive quantitative relations between the moment magnitude (Mw) of MEQs and the fracture permeability change in the directions orthogonal to (kfault,⊥/kjoint) and parallel to (kfault,∥/kjoint) the shear displacement, in the form kfault,⊥true/knormaljnormalonormalinormalnnormalt=116.4×100.46Mw and kfault,true/true/true/knormaljnormaloint=13.1×100.46Mw. Despite the simplicity of the derivation, these relations have the potential to explain the results of field experiments on hydraulic stimulation, such as the enhanced geothermal systems at Soultz‐sous‐Fôret and Basel.

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Critical Reynolds number for nonlinear flow through rough-walled fractures: The role of shear processes

Cited by 241 publications

References 110 publications

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

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

Estimating hydraulic conductivity of fractured rocks from high‐pressure packer tests with an Izbash's law‐based empirical model

Linking microearthquakes to fracture permeability change: The role of surface roughness

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