The use of discrete fracture network simulations in the design of horizontal hillslope drainage networks in fractured rock

Reeves, Donald M.; Parashar, Rishi; Pohll, Greg; Carroll, Rosemary; Badger, Tom; Willoughby, Kim

doi:10.1016/j.enggeo.2013.05.013

Cited by 41 publications

(13 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Jiang

2017

Geofluids

View full text Add to dashboard Cite

show abstract

“…The previous works of calculating the equivalent permeability of fracture networks commonly presumed that the fluid flow follows the cubic law by applying constant hydraulic gradients (J) on the opposite boundaries such as J = 1 (Long et al 1982;Zhang et al , 1999Klimczak et al 2010;Zhao et al 2010aZhao et al , 2011b, J = 0.1 , J = 0.001 (Cvetkovic et al 2004;Zhao 2013), and J = unknown constants (Min et al 2004;Jing 2007, 2008;Parashar and Reeves 2012;Reeves et al 2013;Latham et al 2013), which, however, deviates from the in-situ hydraulic test results where increasing the hydraulic gradient would decrease the permeability of rock masses when the hydraulic gradient is sufficiently large (Gale 1984;Kohl et al 1997;Chen et al 2015a, c). Liu et al (2016a) established a series of DFN models as described in section 'Permeability and number of intersections', and studied the effects of hydraulic gradient on the equivalent permeability of rock fracture networks.…”

Section: Permeability and Hydraulic Gradientmentioning

confidence: 99%

“…Actually, in natural fractured rock masses, the fracture length has very broad distributions and is observed to follow the power-law, exponential, and lognormal types of functions (Chelidze and Gueguen 1990;Chang and Yortsos 1990;Sahimi 1993;Watanabe and Takahashi 1995a, b;Andrade et al 2009;Torabi and Berg 2011;Torabi 2012, 2013). Among them, the power law distribution has been most widely utilized (Segall and Pollard 1983;Gudmundsson 1987;Childs et al 1990;Sornette et al 1993;Davy 1993;Bour and Davy 1997;Bogdanov et al 2007;Reeves et al 2013), with a typical form of…”

Section: Permeability and Fracture-length Distributionmentioning

confidence: 99%

“…It is still not clear whether a single fractal dimension or a mathematical parameter could characterize the surface roughness of fractures at different scales, although the fractal theory basically indicates so. Previous studies on the fracture surface roughness have focused on establishing mathematical expressions for the relation between hydraulic aperture and roughness parameters, based on a great amount of flow tests and numerical simulations on single rock fractures (Lomize 1951;Louis 1969;Patir and Cheng 1978;Walsh 1981;Hakami 1995;Renshaw 1995;Waite et al 1999;Rasouli and Hosseinian 2011;Li B et al 2016). Zimmerman and Bodvarsson (1996a) established a function that relates the hydraulic aperture (e) to the mechanical aperture (E), contact ratio (C r ), and the standard deviation of mean mechanical aperture (σ apert ) (Eq.…”

Section: Permeability and Fracture Surface Roughnessmentioning

confidence: 99%

See 1 more Smart Citation

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

et al. 2016

View full text Add to dashboard Cite

Fracture networks play a more significant role in conducting fluid flow and solute transport in fractured rock masses, comparing with that of the rock matrix. Accurate estimation of the permeability of fracture networks would help researchers and engineers better assess the performance of projects associated with fluid flow in fractured rock masses. This study provides a review of previous works that have focused on the estimation of equivalent permeability of twodimensional (2-D) discrete fracture networks (DFNs) considering the influences of geometric properties of fractured rock masses. Mathematical expressions for the effects of nine important parameters that significantly impact on the equivalent permeability of DFNs are summarized, including (1) fracturelength distribution, (2) aperture distribution, (3) fracture surface roughness, (4) fracture dead-end, (5) number of intersections, (6) hydraulic gradient, (7) boundary stress, (8) anisotropy, and (9) scale. Recent developments of 3-D fracture networks are briefly reviewed to underline the importance of utilizing 3-D models in future research.

show abstract

“…It is well-known that the interconnected fracture network forms the preferred flow paths in the formation [22,58,59]. These pathways are "paths of least resistance", where most of the flow and solute is concentrated [7,26,36,60], resulting in early arrivals. Matrix block size, which is typically characterized using fracture spacing, affects trapping time and influences late-time tailing in BTCs.…”

Section: Impact Of Fracture Density On Non-fickian Transportmentioning

confidence: 99%

Application of Tempered-Stable Time Fractional-Derivative Model to Upscale Subdiffusion for Pollutant Transport in Field-Scale Discrete Fracture Networks

Zhang

Reeves

et al. 2018

Mathematics

View full text Add to dashboard Cite

Abstract:Fractional calculus provides efficient physical models to quantify non-Fickian dynamics broadly observed within the Earth system. The potential advantages of using fractional partial differential equations (fPDEs) for real-world problems are often limited by the current lack of understanding of how earth system properties influence observed non-Fickian dynamics. This study explores non-Fickian dynamics for pollutant transport in field-scale discrete fracture networks (DFNs), by investigating how fracture and rock matrix properties influence the leading and tailing edges of pollutant breakthrough curves (BTCs). Fractured reservoirs exhibit erratic internal structures and multi-scale heterogeneity, resulting in complex non-Fickian dynamics. A Monte Carlo approach is used to simulate pollutant transport through DFNs with a systematic variation of system properties, and the resultant non-Fickian transport is upscaled using a tempered-stable fractional in time advection-dispersion equation. Numerical results serve as a basis for determining both qualitative and quantitative relationships between BTC characteristics and model parameters, in addition to the impacts of fracture density, orientation, and rock matrix permeability on non-Fickian dynamics. The observed impacts of medium heterogeneity on tracer transport at late times tend to enhance the applicability of fPDEs that may be parameterized using measurable fracture-matrix characteristics.

show abstract

The use of discrete fracture network simulations in the design of horizontal hillslope drainage networks in fractured rock

Cited by 41 publications

References 42 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

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

Application of Tempered-Stable Time Fractional-Derivative Model to Upscale Subdiffusion for Pollutant Transport in Field-Scale Discrete Fracture Networks

Contact Info

Product

Resources

About