Nonlinear single‐phase flow in real rock joints

Ranjith, P.G.; Darlington, William James

doi:10.1029/2006wr005457

Cited by 117 publications

(62 citation statements)

References 21 publications

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“…Another macroscopic nonlinear flow equation to characterize the nonlinear flow in rock fractures is Izbash's law (Izbash 1931), but it cannot well quantify the linear flow properties at a sufficiently low Re. Therefore, the two equations can both be utilized to describe the nonlinear relationships between flow rate and pressure drop, especially for strong inertial regime; however, only the Forchheimer equation is used to depict the critical Reynolds number by directly plotting the normalized transmissivity-Reynolds number curves [92][93][94].…”

Section: Cubicmentioning

confidence: 99%

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: Cubicmentioning

confidence: 99%

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

Jiang

2017

Geofluids

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“…The ratio between the discharge along the selected direction and the imposed hydraulic head is proportional to the hydraulic conductivity value, if an equivalent porous medium is considered in accordance with the Darcy Law [49]. The simulated hydraulic conductivity range is very wide, from 10 − 12 to 10 − 3 [m/s] (Figure 6).…”

Section: Hydraulic Conductivity Dataset From the Hydrostructuralmentioning

confidence: 89%

“…Though several studies outlining the limit of the cubic law [48,49], it is a point of reference for the rock mechanics and it is usually used for flow in fractured systems [50][51][52]. During the construction of the numerical model, fractures were represented as planes subdivided via a freetriangular mesh.…”

Section: Hydraulic Conductivity Evaluationmentioning

confidence: 99%

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A Double Scale Methodology to Investigate Flow in Karst Fractured Media via Numerical Analysis: The Cassino Plain Case Study (Central Apennine, Italy)

2018

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A methodology to evaluate the hydraulic conductivity of the karst media at a regional scale has been proposed, combining pumping tests and the hydrostructural approach, evaluating the hydraulic conductivity of fractured rocks at the block scale. Obtaining hydraulic conductivity values, calibrated at a regional scale, a numerical flow model of the Cassino area has been developed, to validate the methodology and investigate the ambiguity, related to a nonunique hydrogeological conceptual model. The Cassino plain is an intermontane basin with outstanding groundwater resources. The plain is surrounded by karst hydrostructures that feed the Gari Springs and Peccia Springs. Since the 1970s, the study area was the object of detailed investigations with an exceptional density of water-wells and piezometers, representing one of the most important karst study-sites in central-southern Italy. Application of the proposed methodology investigates the hydraulic conductivity tensor at local and regional scales, reawakening geological and hydrogeological issues of a crucial area and tackling the limits of the continuum modelling in karst media.

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“…When assessing the fluid flow through a single rock fracture, the Reynolds number (Re), which is defined as the ratio of inertial forces to viscous forces, is typically used to quantify the onset of nonlinear flow. As noted above, the variations of normalized transmissivity ( / 0 ) versus Re can be determined by extending the linear Darcy law with = /(−∇ ) [23,25,34,43],…”

Section: Test Results and Discussionmentioning

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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Nonlinear single‐phase flow in real rock joints

Cited by 117 publications

References 21 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

A Double Scale Methodology to Investigate Flow in Karst Fractured Media via Numerical Analysis: The Cassino Plain Case Study (Central Apennine, Italy)

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

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