Advective Transport in Discrete Fracture Networks With Connected and Disconnected Textures Representing Internal Aperture Variability

Abstract

Flow and transport in three‐dimensional discrete fracture networks with internal variability in aperture and permeability are investigated using a numerical model. The analysis is conducted for three different texture types representing internal variability considering various correlation lengths and for an increase in domain size corresponding to an increase in network complexity. Internal variability in discrete fracture networks generally increases median travel times and delays arrival of bulk mass transport when compared against reference cases without texture, corresponding to smooth fractures. In particular, internal variability textures with weak connectivity increase travel times nonlinearly with domain size increase, further delaying bulk mass arrival. Textures with strong connectivity can however decrease median travel times, accelerating bulk mass arrival, but only for limited ranges of correlation length and domain size. As domain size increases, travel times of textures with strong connectivity converge toward travel times obtained for classical multivariant Gaussian textures. Thus, accounting for internal fracture variability is potentially significant for improving conservative estimates of bulk mass arrival, flow channeling, and advective and reactive transport in large‐scale discrete fracture networks. Further, early mass arrival can arrive significantly earlier for textures with strong connectivity and classical Gaussian textures corresponding to intermediate connectivity but are only slightly affected by textures with weak connectivity. Thus, accounting for internal variability in fractures is also important for accurate estimates of early solute mass arrival. The overall impact on predictive transport modeling will depend on the extent of, or lack of, internal fracture connectivity structure in real‐world fractured rocks.

Inference of Transmissivity in Crystalline Rock Using Flow Logs Under Steady‐State Pumping: Impact of Multiscale Heterogeneity

“…The fracture internal aperture variability is a source of uncertainty due to difficulties in field measurement of fracture roughness or the aperture fields. For theoretical and numerical studies, correlated multivariant Gaussian, lognormal, and fractal fields are often used to describe the fracture aperture variability (Frampton et al, 2019; Huang et al, 2019). In this study, we use the spatially correlated lognormal fields to represent the fracture internal aperture variability, which is in analogy to previous studies (e.g., Frampton et al, 2019) and is partially supported by laboratory measurement data for rock fracture apertures (e.g., Pyrak‐Nolte et al, 1997).…”

“…For theoretical and numerical studies, correlated multivariant Gaussian, lognormal, and fractal fields are often used to describe the fracture aperture variability (Frampton et al, 2019; Huang et al, 2019). In this study, we use the spatially correlated lognormal fields to represent the fracture internal aperture variability, which is in analogy to previous studies (e.g., Frampton et al, 2019) and is partially supported by laboratory measurement data for rock fracture apertures (e.g., Pyrak‐Nolte et al, 1997). Therefore, the mean transmissivity of each discrete fracture is semicorrelated to its size and follows the power law, while the internal aperture field for each fracture is a correlated lognormal field with assigned mean transmissivity ( semicorrelated to its size), variance, and correlation length.…”

“…Various correlation lengths (i.e., λ x = λ y = 0.75,1,1.25,and 1.5 m) of the lognormal fields were considered in preliminary testing but the impact was minor and the results are not presented here. The chosen ranges of these parameters are in analogy to those presented in the literature (e.g., Baghbanan & Jing, 2007; Frampton et al, 2019). σ 2 = 0 represents the homogeneous case without fracture roughness, which is one of the two reference cases.…”

Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves

“…Fracture apertures are uniform within each fracture and equal to b = 10 −4 m, which is a physically reasonable aperture value for a 1 m fracture in crystalline rock under assumptions of a positively correlated power law relationship between fracture size and radius (Svensk Kärnbränslehantering, 2010). While it is well documented that aperture variability leads to local dispersion within an individual fracture (Boutt et al, 2006;Cardenas et al, 2007;Detwiler et al, 2000;Kang et al, 2016), recent high-fidelity DFN simulations in fracture networks have shown that aperture variability does not significantly influence behavior at the network scale, BTC (Frampton et al, 2019;Makedonska et al, 2016), or effective permeability (de Dreuzy et al, 2012), except at high aperture variance or long correlation lengths relative to the domain size. Rather, it is the fracture network structure that controls flow and transport behavior.…”

Flow Channeling in Fracture Networks: Characterizing the Effect of Density on Preferential Flow Path Formation

“…At the scale of individual fractures, their orientations (Rubin & Buddemeier, 1996) and apertures (Bogdanov et al., 2007; de Dreuzy et al., 2002; Frampton & Cvetkovic, 2010; Hyman et al., 2016; Joyce et al., 2014; Wellman et al., 2009) can also cause variations of the flow field. At the even smaller scale within a single fracture, aperture variability/roughness is well known to lead to flow channelization (Boutt et al., 2006; Cardenas et al., 2007; Detwiler et al., 2000; de Dreuzy et al., 2012; Frampton et al., 2019; Kang et al., 2016; Makedonska et al., 2016; Méheust & Schmittbuhl, 2000, 2001). In summation, the integration of these multiple scales renders linking structural attributes to the formation of flow channels a particularly challenging task.…”