Hydraulic properties of two‐dimensional random fracture networks following power law distributions of length and aperture

Abstract

[1] Field observations have revealed that the diffusion properties of fractured materials are strongly influenced by the presence of fractures. Using power law fracture length and fracture permeability distributions currently observed on natural fractured networks, we model the equivalent permeability of two-dimensional (2D) discrete fracture networks by using numerical simulations and theoretical arguments. We first give the dependence of the network equivalent permeability, obtained at the scale of the network, on the characteristic power law exponents of the fracture length and fracture permeability distributions. We especially show that the equivalent permeability depends simply on the geometrical mean of the local fracture permeability distribution. Such networks are characterized by an increase of permeability with scale without limitations, provided that the fracture length and fracture permeability distributions are broad enough. Although a correlation length cannot be systematically defined, the flow structure is still characterized by simple properties. The flow is either extremely channeled in one dominant path or distributed in several separated structures. We show finally that the observed scale effects and flow structure are very different from the one obtained in the lognormal fracture permeability distribution case.

Crack Features and Shear-Wave Splitting Associated with Fracture Extension during Hydraulic Stimulation of the Geothermal Reservoir in Soultz-sous-Forêts

“…Figure 6 shows that crack aperture is not an influential parameter during stimulation test: it remains more or less the same as the initial value of 10 À4 as shown by large green areas for all sets. This result is in agreement with theoretical studies (Simpson et al, 2001;de Dreuzy et al, 2002). On the contrary, crack length exhibits significant variations during hydraulic stimulation.…”

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

“…Fracture aperture is less commonly analyzed, resulting in large uncertainties in fluid flow modeling, as small variations in aperture have large implications on rock flow [de Dreuzy et al, 2001[de Dreuzy et al, , 2002[de Dreuzy et al, , 2012Matthäi and Belayneh, 2004;Klimczak et al, 2010;Schultz et al, 2013] and transport properties [Nick et al, 2011]. Borehole imaging tools provide an estimate of aperture [Luthi and Souhaite, 1990], although with some uncertainty, especially in the absence of accurate calibration [Makel, 2007;Ponziani et al, 2015].…”

“…The impact of each method on fluid flow in fractures has been studied extensively [e.g., Baghbanan and Jing, 2008;Lei et al, 2014;Moos and Barton, 2008;Tao et al, 2009]. In particular, the impact of power law aperture scaling and similar statistical distributions on permeability has been studied in 2-D and 3-D [de Dreuzy et al, 2001[de Dreuzy et al, , 2002[de Dreuzy et al, , 2012. However, there is no direct comparison between the fundamentally different LEFM, Barton-Bandis and power law scaling methods, and their impact on equivalent (i.e., combined matrix and fracture) permeability in large-scale natural fracture networks.…”

Hydrogeological properties of fault zones in a karstified carbonate aquifer (Northern Calcareous Alps, Austria)

“…Fracture aperture and fracture connectivity is controlling the permeability in fractured media, resulting in either extremely channelized or more distributed flow paths (e.g. de Dreuzy et al 2002). Breccias, resulting from various deformation processes like rock pulverization (Dor et al 2006;Mitchell et al 2011), or hydro fracturing (Tarasewicz et al 2005) may cause permeability enhancements of up to 4 or 5 orders of magnitude (Walker et al 2013), while, on the other hand, cementation due to the interaction with fluids (e.g.…”