Critical Reynolds number for nonlinear flow through rough‐walled fractures: The role of shear processes
TLDR
In this article, a quantitative criterion was developed to quantify the onset of nonlinear flow by comprehensive combination of Forchheimer's law and Reynolds number, and several high-precision water flow tests were carried out with different hydraulic gradients then the critical Reynolds number was determined based on the developed criterion.Abstract:
This paper experimentally investigates the role of shear processes on the variation of critical Reynolds number and nonlinear flow through rough-walled rock fractures. A quantitative criterion was developed to quantify the onset of nonlinear flow by comprehensive combination of Forchheimer's law and Reynolds number. At each shear displacement, several high-precision water flow tests were carried out with different hydraulic gradients then the critical Reynolds number was determined based on the developed criterion. The results show that (i) the Forchheimer's law was fitted very well to experimental results of nonlinear fluid flow through rough-walled fractures, (ii) the coefficients of viscous and inertial pressure drops experience 4 and 7 orders of magnitude reduction during shear displacement, respectively, and (iii) the critical Reynolds number varies from 0.001 to 25 and experiences 4 orders of magnitude enlargement by increasing shear displacement from 0 to 20 mm. These findings may prove useful in proper understanding of fluid flow through rock fractures, or inclusions in computational studies of large-scale nonlinear flow in fractured rocks.read more
Citations
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VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship
Abstract: The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.
Experimental studies of scale effects on the shear behaviour of rock joints
TL;DR: In this paper, the effect of scale on the shear behavior of joints is studied by performing direct shear tests on different sized replicas cast from various natural joint surfaces, and it is shown that scale effects are more pronounced in the case of rough, undulating joints, whereas they are virtually absent for planar joints.
Journal ArticleDOI
Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures
TL;DR: In this article, the Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures were evaluated using a triaxial cell under confining stresses varying from 1.0 MPa to 30 MPa.
Journal ArticleDOI
Influence of surface roughness on nonlinear flow behaviors in 3D self-affine rough fractures: Lattice Boltzmann simulations
TL;DR: In this article, the impact of surface roughness on the nonlinear fluid flow through 3D self-affine rock fractures is investigated, and the authors show that the primary roughness mostly controls the pressure distribution and fracture flow paths at a large scale, whereas the secondary roughness determines the non-linear properties of the fluid flow at a local scale.
Journal ArticleDOI
Nonlinear flow behavior at low Reynolds numbers through rough-walled fractures subjected to normal compressive loading
TL;DR: In this article, the authors investigated the nonlinear flow characteristics at low Reynolds number through rough-walled fractures subjected to a wide range of confining pressures (1.0-30.0 MPa).
References
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Book
Dynamics of fluids in porous media
TL;DR: In this paper, the Milieux poreux Reference Record was created on 2004-09-07, modified on 2016-08-08 and the reference record was updated in 2016.
Journal ArticleDOI
Slip instability and state variable friction laws
TL;DR: In this paper, the dependence of the friction force on slip history is described by an experimentally motivated constitutive law where the friction forces are dependent on slip rate and state variables.
Journal ArticleDOI
Validity of Cubic Law for fluid flow in a deformable rock fracture
TL;DR: The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm.
VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship
Abstract: The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.
Journal ArticleDOI
Fundamentals of rock joint deformation
TL;DR: In this article, the deformation characteristics of rock joints under normal and shear loading were investigated by conducting loading/unloading and repeated load cycling tests on a wide variety of fresh and weathered joints in five different rock types.