Numerical calculations of critical densities for lines and planes

Robinson, Peter

doi:10.1088/0305-4470/17/14/025

Cited by 108 publications

(91 citation statements)

References 3 publications

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“…As these differences will impact permeability independent from variations in the aperture distribution, we quantify connectivity using two percolation parameters (Table 1). The first parameter is the commonly used percolation probability defined by fracture density and the number of intersections, normalized by the outcrop area [Robinson, 1983[Robinson, , 1984. However, as this method does not fully consider fracture length, we also perform a cluster analysis, where the percolation probability is a function of the area of rock covered by a connected network versus total outcrop area [Berkowitz and Balberg, 1993;Berkowitz, 1995].…”

Section: Journal Of Geophysical Research: Solid Earthmentioning

confidence: 99%

“…Critical stress analysis assumes a N-S maximum horizontal stress: (a) Critically stressed aperture for power law aperture scaling with an exponent of 0.8; (b) aperture as a function of length, using total fracture length; and (c) Barton-Bandis aperture distribution. The percolation probability as defined by [Robinson, 1983[Robinson, , 1984 This constant trend results from the large contrast between matrix and fracture, as the intrinsic fracture permeability is 2.1 × 10 6 darcy. The relative impact of fractures on permeability in the different pavements is a function of fracture intensity.…”

Section: Coulomb Criterionmentioning

confidence: 99%

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The impact of different aperture distribution models and critical stress criteria on equivalent permeability in fractured rocks

2016

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Predicting equivalent permeability in fractured reservoirs requires an understanding of the fracture network geometry and apertures. There are different methods for defining aperture, based on outcrop observations (power law scaling), fundamental mechanics (sublinear length‐aperture scaling), and experiments (Barton‐Bandis conductive shearing). Each method predicts heterogeneous apertures, even along single fractures (i.e., intrafracture variations), but most fractured reservoir models imply constant apertures for single fractures. We compare the relative differences in aperture and permeability predicted by three aperture methods, where permeability is modeled in explicit fracture networks with coupled fracture‐matrix flow. Aperture varies along single fractures, and geomechanical relations are used to identify which fractures are critically stressed. The aperture models are applied to real‐world large‐scale fracture networks. (Sub)linear length scaling predicts the largest average aperture and equivalent permeability. Barton‐Bandis aperture is smaller, predicting on average a sixfold increase compared to matrix permeability. Application of critical stress criteria results in a decrease in the fraction of open fractures. For the applied stress conditions, Coulomb predicts that 50% of the network is critically stressed, compared to 80% for Barton‐Bandis peak shear. The impact of the fracture network on equivalent permeability depends on the matrix hydraulic properties, as in a low‐permeable matrix, intrafracture connectivity, i.e., the opening along a single fracture, controls equivalent permeability, whereas for a more permeable matrix, absolute apertures have a larger impact. Quantification of fracture flow regimes using only the ratio of fracture versus matrix permeability is insufficient, as these regimes also depend on aperture variations within fractures.

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Section: Journal Of Geophysical Research: Solid Earthmentioning

confidence: 99%

Section: Coulomb Criterionmentioning

confidence: 99%

The impact of different aperture distribution models and critical stress criteria on equivalent permeability in fractured rocks

2016

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“…Another approach to modeling flow and transport in fracture networks, which is able to capture distinct preferential flow paths and channeling, is based on percolation theory [e.g., Engtman et at., 1983; Robinson, 1983Robinson, , 1984Hestir and Long, 1990; Batberg et at., 1991; Berkowitz and Batberg, 1993; Berkowitz, 1995]. In this framework, network structures that are near the percolation threshold display channeling patterns and transport properties that are quantifiable by power law relationships.…”

Section: Paper Number 98wr01648mentioning

confidence: 99%

Structure, flow, and generalized conductivity scaling in fracture networks

Margolin¹,

Berkowitz²,

Scher³

1998

Water Resources Research

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Abstract. We present a three-dimensional (3-D) model of fractures that within the same framework, allows a systematic study of the interplay and relative importance of the two key factors determining the character of flow in the system. The two factors of complexity are (1) the geometry of fracture plane structure and interconnections and (2) the aperture variability within these planes. Previous models have concentrated on each separately. We introduce anisotropic percolation to model a wide range of fracture structures and networks. The conclusion is that either of these elements, fracture geometry and aperture variability, can give rise to channeled flow and that the interplay between them is especially important for this type of flow. Significant outcomes of our study are (1) a functional relationship that quantifies the dependence of the effective hydraulic conductivity, on aperture variability. and on the network structure and fracture element density, (2) a relation between aperture variability and the Peclet number, and (3) a basis for a new explanation for the field-length dependence of permeability observed in fractured and heterogeneous porous formations. IntroductionThe investigation of flow and contaminant movement through fractured aquifers is currently one of the most important fields of groundwater research. It is also of critical impor- In this report, we examine the interplay and relative impor-2103

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“…In the limit p= 1 the model reduces to the extensively studied case of a uniformly random network [4,[14][15][16][17][18]24,32]. However, for p B1 there are effective interactions between the particles that tend to enhance cluster formation.…”

Section: Flocculation Modelmentioning

confidence: 99%

“…In addition to their practical applications, 2D deposition models have been the topic of intense study in their own right. In particular, they have been extensively studied in the context of continuum percolation theory [14][15][16][17][18][19][20][21][22][23][24][25][26][27]. These models have included both uniformly random networks of various objects as well as some that include hard and soft-core interactions between the constituent particles.…”

Section: Introductionmentioning

confidence: 99%

Fiber deposition models in two and three spatial dimensions

Provatas

Haataja

Asikainen

et al. 2000

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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We review growth, percolation, and spatial correlations in deposition models of disordered fiber networks. We first consider 2D models with effective interactions between the deposited particles represented by simple parametrization. In particular, we discuss the case of single cluster growth, growth of uniformly random networks, and flocculated networks with nontrivial spatial correlations. We also consider a 3D deposition model of flexible fibers that describes the growth of multilayer structures of disordered networks. We discuss the statistical properties of such structures, transport of fluid through the network, and the asymptotics of growth in the limit of infinite thickness.

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Numerical calculations of critical densities for lines and planes

Cited by 108 publications

References 3 publications

The impact of different aperture distribution models and critical stress criteria on equivalent permeability in fractured rocks

The impact of different aperture distribution models and critical stress criteria on equivalent permeability in fractured rocks

Structure, flow, and generalized conductivity scaling in fracture networks

Fiber deposition models in two and three spatial dimensions

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