Percolation conditions in fractured hard rocks: A numerical approach using the three‐dimensional binary fractal fracture network (3D‐BFFN) model

Nakaya, Shinji; Nakamura, Kiminori

doi:10.1029/2006jb004670

Cited by 21 publications

(8 citation statements)

References 59 publications

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“…For example, many models have been developed with modified marked processes, especially for modelling different fracture shapes: the enhanced Baecher model [58] shown in Figure 1g (fractures can clip each other); the Baecher algorithm revised terminations (BART) model [33,41] shown in Figure 1h (fractures may have random sizes and shapes); the Poisson rectangle model [33] shown in Figure 1i (fractures are set as rectangles); and the random polygon model [21,46] shown in Figure 1j (fractures are set as random polygons). Models have also been developed with different point processes: the nearest neighbour model [33,34] shown in Figure 1k (this uses non-stationary Poisson point processes, see [21]); the war zone model [34] shown in Figure 1l; the Levy-Lee fractal model [33,41] shown in Figure 1m; the parent-daughter model [21,59] shown in Figure 1n; the binary fractal fracture network (BFFN) model [60,61] shown in Figure 1o; the non-planar zone model shown in Figure 1p; and the density-controlled DFN model shown in Figure 1q (which uses both a densitycontrolled Poisson point process and the random polygon models). In addition, some models have replaced the MPP by other methods: the GEOFRAC model shown in Figure 1r, which is based on Poisson line (2D) or Poisson plane (3D) processes (an improvement on the Veneziano model).…”

Section: Modelling Of Fracture Network In Rock Massesmentioning

confidence: 99%

Modelling of Coupled Hydro-Thermo-Chemical Fluid Flow through Rock Fracture Networks and Its Applications

Dong

Wang

et al. 2021

Geosciences

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Most rock masses contain natural fractures. In many engineering applications, a detailed understanding of the characteristics of fluid flow through a fractured rock mass is critically important for design, performance analysis, and uncertainty/risk assessment. In this context, rock fractures and fracture networks play a decisive role in conducting fluid through the rock mass as the permeability of fractures is in general orders of magnitudes greater than that of intact rock matrices, particularly in hard rock settings. This paper reviews the modelling methods developed over the past four decades for the generation of representative fracture networks in rock masses. It then reviews some of the authors’ recent developments in numerical modelling and experimental studies of linear and non-linear fluid flow through fractures and fracture networks, including challenging issues such as fracture wall roughness, aperture variations, flow tortuosity, fracture intersection geometry, fracture connectivity, and inertia effects at high Reynolds numbers. Finally, it provides a brief review of two applications of methods developed by the authors: the Habanero coupled hydro-thermal heat extraction model for fractured reservoirs and the Kapunda in-situ recovery of copper minerals from fractures, which is based on a coupled hydro-chemical model.

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Section: Modelling Of Fracture Network In Rock Massesmentioning

confidence: 99%

Modelling of Coupled Hydro-Thermo-Chemical Fluid Flow through Rock Fracture Networks and Its Applications

Dong

Wang

et al. 2021

Geosciences

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“…Two DFN metrics are worth being mentioned (Maillot et al, ): the total fracture surface per unit volume (often named p 32 Dershowitz & Herda, ), which controls permeability of dense networks (Kirkpatrick, ; Oda, ), and the percolation parameter p , which controls the network connectivity (Bour & Davy, , ; de Dreuzy et al, ; Nakaya & Nakamura, ):

p_{32} = \frac{π}{4 V} \int_{θ} \int_{l} l^{2} n ((),, l, θ) normald l normald θ p = \frac{π^{2}}{8 normalV} \int_{θ} \int_{l} l^{3} n ((),, l, θ) normald l normald θ

…”

Section: Relationship Between Fracture Network Densities and Elastic mentioning

confidence: 99%

Elastic Properties of Fractured Rock Masses With Frictional Properties and Power Law Fracture Size Distributions

et al. 2018

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We derive the relationships that link the general elastic properties of rock masses to the geometrical properties of fracture networks, with a special emphasis to the case of frictional crack surfaces. We extend the well‐known elastic solutions for free‐slipping cracks to fractures whose plane resistance is defined by an elastic fracture (shear) stiffness ks and a stick‐slip Coulomb threshold. A complete set of analytical solutions have been derived for (i) the shear displacement in the fracture plane for stresses below the slip threshold and above, (ii) the partitioning between the resistances of the fracture plane on the one hand and of the elastic matrix on the other hand, and (iii) the stress conditions to trigger slip. All the expressions have been checked with numerical simulations. The Young's modulus and Poisson's ratio were also derived for a population of fractures. They are controlled both by the total fracture surface for fractures larger than the stiffness length lS (defined by ks and the intact matrix elastic properties) and by the percolation parameter of smaller fractures. These results were applied to power law fracture size distributions, which are likely relevant to geological cases. We show that if the fracture size exponent is in the range −3 to −4, which corresponds to a wide range of geological fracture networks, the elastic properties of the bulk rock are almost exclusively controlled by ks and the stiffness length, meaning that the fractures of size lS play a major role in the definition of the elastic properties.

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“…Two DFN metrics are worth being mentioned [Maillot et al, 2016]: the total fracture surface per unit volume (often named 32 [Dershowitz and Herda, 1992]), which controls permeability of dense networks [Kirkpatrick, 1973;Oda, 1985] and the percolation parameter , which controls the network connectivity [Bour and Davy, 1997;de Dreuzy et al, 2000;Nakaya and Nakamura, 2007]:…”

Section: Relationship Between Fracture Network Densities and Elastic mentioning

confidence: 99%

Elastic properties of fractured rock masses

Davy¹,

Darcel²,

Goc³

et al. 2018

Preprint

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We derive the relationships that link the general elastic properties of rock masses to the geometrical properties of fracture networks, with a special emphasis to the case of frictional crack surfaces. We extend the wellknown elastic solutions for free-slipping cracks to fractures whose plane resistance is defined by an elastic fracture (shear) stiffness and a stick-slip Coulomb threshold. A complete set of analytical solutions have been derived for i) the shear displacement in the fracture plane for stresses below the slip threshold and above, ii) the partitioning between the resistances of the fracture plane in the one hand, and of the elastic matrix in the other hand, and iii) the stress conditions to trigger slip. All the expressions have been checked with numerical simulations. The Young's modulus and Poisson's ratio were also derived for a population of fractures. They are controlled both by the total fracture surface for fractures larger than the mechanical length (defined by and the intact matrix elastic properties), and by the percolation parameter of smaller fractures. These results were applied to power-law fracture size distributions, which are likely relevant to geological cases. We show that, if the fracture size exponent is in the range-3 to-4, which corresponds to a wide range of geological fracture networks, the elastic properties of the bulk rock are almost exclusively controlled by and the mechanical length, meaning that the fractures of size play a major role in the definition of the elastic properties.

show abstract

Percolation conditions in fractured hard rocks: A numerical approach using the three‐dimensional binary fractal fracture network (3D‐BFFN) model

Cited by 21 publications

References 59 publications

Modelling of Coupled Hydro-Thermo-Chemical Fluid Flow through Rock Fracture Networks and Its Applications

Modelling of Coupled Hydro-Thermo-Chemical Fluid Flow through Rock Fracture Networks and Its Applications

Elastic Properties of Fractured Rock Masses With Frictional Properties and Power Law Fracture Size Distributions

Elastic properties of fractured rock masses

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