Evaluation of the 2-D permeability tensor for fractured rock masses

Zhang, X.; Sanderson, David J.; Harkness, R. M.

doi:10.1016/0148-9062(95)00042-9

Cited by 121 publications

(41 citation statements)

References 13 publications

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“…This result is comparable to the permeability variation with depth reported in [29] with the depth corresponding to stress changes. Similar numerical results in [19,20] with constant normal stiffness of fracture also showed the decrease of permeability corresponding to the increase of stresses. However, the application of the non-linear normal stiffness of fractures in the fracture model in this study led to more sensitive responses of permeability change at lower normal stress magnitudes, and the permeability change becomes small when the stress reaches the laboratory level of residual stress (30 MPa) of fractures.…”

Section: Permeability Change As a Function Of Stress Change With A Fisupporting

confidence: 71%

“…Despite the insightful illumination regarding abrupt increase of permeability in [21], the mechanical REV issue was not considered, which could make the mechanical behavior less representative and shear displacement overestimated. The other previous studies in [19,20] did not show such sudden increase of permeability because the dilation mechanisms are not modeled. Permeability continued to decrease with the increase of stress ratio up to 8 when zero dilation angle was used and stress ratio up to 9 when a high cohesion (1.8 MPa) was used as an input for fracture parameter compared to the minimum principal stress (1 MPa), which could not capture the dilation behavior [20,19].…”

Section: Permeability Change As a Function Of Increasing Stress Ratiomentioning

confidence: 98%

“…As far as we know, the above three aspects were not considered, at least not systematically, in the previous studies of numerical experiments for stress-dependent permeability of fractured rock masses, including those reported in [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…The influence of stresses on permeability of fractured rock masses was extensively investigated considering various geometries of fracture systems [19][20][21]. Such numerical experiments will be increasingly important with the advance of computing capacity due to the strength of distinct element modeling that can incorporate both hydraulic and mechanical analysis with explicit representation of fractures.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stress-dependent permeability of fractured rock masses: a numerical study

Min

Rutqvist

Tsang

et al. 2004

International Journal of Rock Mechanics and Mining Sciences

443

233

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We investigate the stress-dependent permeability issue in fractured rock masses considering the effects of nonlinear normal deformation and shear dilation of fractures using a two-dimensional distinct element method program, UDEC, based on a realistic discrete fracture network realization.A series of "numerical" experiments were conducted to calculate changes in the permeability of simulated fractured rock masses under various loading conditions. Numerical experiments were conducted in two ways: (1) increasing the overall stresses with a fixed ratio of horizontal to vertical stresses components; and (2) increasing the differential stresses (i.e., the difference between the horizontal and vertical stresses) while keeping the magnitude of vertical stress constant.These numerical experiments show that the permeability of fractured rocks decreases with increased stress magnitudes when the stress ratio is not large enough to cause shear dilation of fractures, whereas permeability increases with increased stress when the stress ratio is large enough.Permeability changes at low stress levels are more sensitive than at high stress levels due to the nonlinear fracture normal stress-displacement relation. Significant stress-induced channeling is observed as the shear dilation causes the concentration of fluid flow along connected shear fractures.Anisotropy of permeability emerges with the increase of differential stresses, and this anisotropy can become more prominent with the influence of shear dilation and localized flow paths. A set of empirical equations in closed-form, accounting for both normal closure and shear dilation of the fractures, is proposed to model the stress-dependent permeability. These equations prove to be in good agreement with the results obtained from our numerical experiments.2

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Section: Permeability Change As a Function Of Stress Change With A Fisupporting

confidence: 71%

Section: Permeability Change As a Function Of Increasing Stress Ratiomentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stress-dependent permeability of fractured rock masses: a numerical study

Min

Rutqvist

Tsang

et al. 2004

International Journal of Rock Mechanics and Mining Sciences

443

233

View full text Add to dashboard Cite

show abstract

“…The discrete fracture network (DFN) model, which can consider most of the above parameters, has been increasingly utilized to simulate fluid flow in the complex 2 Geofluids fractured rock masses [57][58][59][60], although it cannot model the aperture heterogeneity of each fracture [61][62][63]. In the numerical simulations and/or analytical analysis, the linear governing equation such as the cubic law is solved to simulate fluid flow in fractures by applying constant hydraulic gradients ( ) on the two opposing boundaries, such as = 1 [57,[64][65][66][67][68]], = 0.1 [41], = 0.001 [69,70], and = unknown constants [11,34,46,[71][72][73]. This assumption that fluid flow obeys the cubic law is suitable for characterizing hydraulic behaviors of deep underground engineering, in which the flow rate is sufficiently small.…”

Section: Introductionmentioning

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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Permeability tensor of three‐dimensional fractured porous rock and a comparison to trace map predictions

2014

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The reduction from three‐ to two‐dimensional analysis of the permeability of a fractured rock mass introduces errors in both the magnitude and direction of principal permeabilities. This error is numerically quantified for porous rock by comparing the equivalent permeability of three‐dimensional fracture networks with the values computed on arbitrarily extracted planar trace maps. A method to compute the full permeability tensor of three‐dimensional discrete fracture and matrix models is described. The method is based on the element‐wise averaging of pressure and flux, obtained from a finite element solution to the Laplace problem, and is validated against analytical expressions for periodic anisotropic porous media. For isotropic networks of power law size‐distributed fractures with length‐correlated aperture, two‐dimensional cut planes are shown to underestimate the magnitude of permeability by up to 3 orders of magnitude near the percolation threshold, approaching an average factor of deviation of 3 with increasing fracture density. At low‐fracture densities, percolation may occur in three dimensions but not in any of the two‐dimensional cut planes. Anisotropy of the equivalent permeability tensor varies accordingly and is more pronounced in two‐dimensional extractions. These results confirm that two‐dimensional analysis cannot be directly used as an approximation of three‐dimensional equivalent permeability. However, an alternative expression of the excluded area relates trace map fracture density to an equivalent three‐dimensional fracture density, yielding comparable minimum and maximum permeability. This formulation can be used to approximate three‐dimensional flow properties in cases where only two‐dimensional analysis is available.

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Evaluation of the 2-D permeability tensor for fractured rock masses

Cited by 121 publications

References 13 publications

Stress-dependent permeability of fractured rock masses: a numerical study

Stress-dependent permeability of fractured rock masses: a numerical study

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

Permeability tensor of three‐dimensional fractured porous rock and a comparison to trace map predictions

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