Non-linear regimes of fluid flow in rock fractures

Zimmerman, Robert W.; Al-Yaarubi, Azzan; Pain, Christopher C.; Grattoni, Carlos A.

doi:10.1016/j.ijrmms.2003.12.045

Cited by 193 publications

(188 citation statements)

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“…This has been shown to produce results in agreement with experimental flow in natural fractures [20,21]. The scope of the present work is on smaller Reynolds numbers where the treatment of the full Navier-Stokes equation is not required.…”

Section: Introductionmentioning

confidence: 57%

“…In this study, we are interested in the influence of a realistic geometry of the fracture on its hydraulic permeability [13][14][15][16][17][18][19][20][21]. The morphology of fresh fractures is sampled and compared to a geometrical model that can be used in numerical codes for the fluid flow.…”

Section: Introductionmentioning

confidence: 99%

“…The scope of the present work is on smaller Reynolds numbers where the treatment of the full Navier-Stokes equation is not required. Relatively to these studies [20,21], the present work focuses on a finer statistical description of the fracture morphology, and on the influence of the various modes of wavelength of the fracture morphology on the transport properties. We will show indeed that the largest wavelengths of the fracture opening control its hydraulic conductivity.…”

Section: Introductionmentioning

confidence: 99%

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Fracture morphology and viscous transport

Schmittbuhl

Steyer

Jouniaux

et al. 2008

International Journal of Rock Mechanics and Mining Sciences

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The morphology of a fracture in a granite block is sampled using a high resolution profiler providing a 3999 Â 4000 pixel image of the roughness. We checked that a self-affine model is an accurate geometrical model of the fracture morphology on the basis of a spectral analysis. We also estimated the topothesy of the experimental surface to be l r % 2 Â 10 À7 mm and the roughness exponent to be z % 0:78. A finite difference scheme of the Stokes equation with a lubrication approximation was used to model the viscous flow through a fracture aperture defined as the gap between the experimental fracture surface and a flat plane. We finally compare our numerical results to experimental measurements of the flux through the fracture of a glycerol/water mixture (to be at sufficiently low Reynolds number where Stokes equations holds) changing the average aperture of the fracture. The comparison is successful despite a limited resolution of the experimental measurements. Interestingly we show that only long wavelengths of the fracture morphology control the fracture hydraulic conductivity. r

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Section: Introductionmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fracture morphology and viscous transport

Schmittbuhl

Steyer

Jouniaux

et al. 2008

International Journal of Rock Mechanics and Mining Sciences

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“…In addition, natural rock fractures are often characteristic of rough walls, intersections, and asperity contacts, which make the fluid flow process even more complex and difficult to accurately describe [18][19][20][21][22]. Therefore, a thorough understanding of Relationships between / 0 and Re (after [23]). (b) Relationships between and (after [24]).…”

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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“…This equation is based on flow equations for rock fractures and has been employed in that context previously (Zimmerman et al, 2004;Rajaram et al, 2009;Chaudhuri et al, 2013). Most existing subglacial hydrology models prescribe a hydraulic conductivity parameter and assume the flow to be turbulent everywhere.…”

mentioning

confidence: 99%

SHaKTI: Subglacial Hydrology and Kinetic Transient Interactions v1.0

Sommers¹,

Rajaram²,

Morlighem³

2018

Preprint

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Abstract. Subglacial hydrology has a significant influence on ice sheet dynamics, yet remains poorly understood. Complex feedbacks play out between the liquid water and the ice, with constantly changing drainage geometry and flow mechanics.A clear tradition has been established in the subglacial hydrology modeling literature of distinguishing between channelized (efficient) and distributed (inefficient) drainage systems or components. Imposing a distinction that changes the governing physics under different flow regimes, however, may not allow for the full array of drainage characteristics to arise. Here, we capabilities of the model, and we are able to reproduce seasonal behavior of the subglacial water pressure that is consistent with observed seasonal velocity behavior in many Greenland outlet glaciers, supporting the notion that subglacial hydrology may be a key influencer in shaping these patterns.

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Non-linear regimes of fluid flow in rock fractures

Cited by 193 publications

References 0 publications

Fracture morphology and viscous transport

Fracture morphology and viscous transport

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

SHaKTI: Subglacial Hydrology and Kinetic Transient Interactions v1.0

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