Connectivity properties of two‐dimensional fracture networks with stochastic fractal correlation

Abstract

[1] We present a theoretical and numerical study of the connectivity of fracture networks with fractal correlations. In addition to length distribution, this spatial property observed on most fracture networks conveys long-range correlation that may be crucial on network connectivity. We especially focus on the model that comes out relevant to natural fracture network: a fractal density distribution for the fracture centers (dimension D) and a power law distribution for the fracture lengths (exponent a, n(l) $ l Àa ). Three different regimes of connectivity are identified depending on D and on a. For a < D + 1 the length distribution prevails against fractal correlation on network connectivity. In this case, global connectivity is mostly ruled by the largest fractures whose length is of the order of the system size, and thus the connectivity increases with scale. For a > D + 1 the connectivity is ruled by fractures much smaller than the system size with a strong control of spatial correlation; the connectivity now decreases with system scale. Finally, for the self-similar case (a = D + 1), which corresponds to the transition between the two previous regimes, connectivity properties are scale invariant: percolation threshold corresponds to a critical fractal density and the average number of intersections per fracture at threshold is a scale invariant as well.

Influence of Landscape Coverage on Measuring Spatial and Length Properties of Rock Fracture Networks: Insights from Numerical Simulation

“…Extensive measurements based on 2D trace maps reveal that generally D varies between [1.5, 2] and a falls between [1.3, 3.5] (Bonnet et al 2001). The D and a values as well as their relationship may control the connectivity, permeability and strength of fractured rocks (Darcel et al 2003;de Dreuzy et al 2004;Davy et al 2006). Thus, it is very important to accurately measure the D and a values of natural fracture networks, the observation of which, however, may be affected by landscape variation.…”

“…The spatial distribution of discrete fracture networks governed by a prescribed D f value could be constructed through a multiplicative cascade process (Darcel et al 2003). This cascade process is a recursive operation of fragmentation of the model domain into subdomains of identical sizes.…”

“…grain size) or the resolution of measurement (Bonnet et al 2001). For numerical simulations, the model size L usually meets l min ( L ( l max (Darcel et al 2003).…”

Joint Inversion of Fracture Model Properties for CO2Storage Monitoring or Oil Recovery History Matching

“…The multiplicative cascade algorithm generates multifractal images [18][19][20]. Its principle is to generate a scaling structure by recursively replicating a given pattern at different scales.…”

“…The cell size of this map is set equal to r 0 . In a second step, the multifractal behavior is extended below r 0 using the multiplicative cascade algorithm [18].…”