Macroscopic permeability of three-dimensional fracture networks with power-law size distribution

Abstract

Fracture network permeability is investigated numerically by using a three-dimensional model of plane polygons uniformly distributed in space with sizes following a power-law distribution. Each network is triangulated via an advancing front technique, and the flow equations are solved in order to obtain detailed pressure and velocity fields. The macroscopic permeability is determined on a scale which significantly exceeds the size of the largest fractures. The influence of the parameters of the fracture size distribution--the power-law exponent and the minimal fracture radius--on the macroscopic permeability is analyzed. Eventually, a general expression is proposed, which is the product of a dimensional measure of the network density, weighted by the individual fracture conductivities, and of a fairly universal function of a dimensionless network density, which accounts for the influences of the fracture shapes and of the parameters of their size distribution. Two analytical formulas are proposed which successfully fit the numerical data over a wide range of network densities.

A 3D Computational Study of Effective Medium Methods Applied to Fractured Media

“…There have been several attempts to estimate the value of f a priori from statistical fracture parameters (Gueguen and Dienes, 1989;Hestir and Long, 1990;Mourzenko et al, 2004). Recently, Mourzenko et al (2011) presented a very successful model for f as a function of ρ , the mean number of intersections per fracture.…”

Fluid flow and effective permeability of an infinite matrix containing disc-shaped cracks

“…The equivalent infiltration vector in the crack section is deduced from the relation (3) where the thickness e is given, for the ellipsoidal inclusion, by 2 2 e d r = ε − and v is constant and given by (49). The limit of the equivalent infiltration q = 2ev for ε→ 0 is found to be: where, c = 2d 3 k * .…”

“…Koudina et al [ [1] presented a method to generate a triangular mesh on three-dimensional network of polygonal fracture surfaces, and used the finite volume method to compute the permeability of fractured media. The numerical tool developed in this way was employed to study the effective permeability of fractures network with statistical distribution [ [2]. However, the rock matrix was supposed to be impervious in these works which does not correspond to some real cases.…”

Integrated Prospecting Prediction of Multi-scale Structure Information at Gaosong Field in Gejiu, Yunnan Province

“…At present multi-scale research focused on trace elements fractal statistics with the application of the mining method, study the singularity features of local enrichment of mineralization elements [1][2][3]。Using the generalized self-similarity principle method of nonlinear theory to carry out the old regional exploration geochemistry data processing and delineat ore anomalies.Zeng-hua Li study the size of the magnetic pyrite particles, irregularity and space distribution characteristics based on GIS fractal model (circumference -area)。Gao yin concludes element distribution has the characteristics of scale invariance by analysising Gejiu tin stream sediment elements(Sn, Cu and Pb) multifractal in large scale and small scale range respectively [4][5][6][7]. Gaosong field is one of the major producing mines of Yunnan Tin company, which is located in north east of gejiu mining district.…”