Characterizing the Influence of Fracture Density on Network Scale Transport

Abstract

The topology of natural fracture networks is inherently linked to the structure of the fluid velocity field and transport therein. Here we study the impact of network density on flow and transport behaviors. We stochastically generate fracture networks of varying density and simulate flow and transport with a discrete fracture network model, which fully resolves network topology at the fracture scale. We study conservative solute trajectories with Lagrangian particle tracking and find that as fracture density decreases, solute channelization to large local fractures increases, thereby reducing plume spreading. Furthermore, in sparse networks mean particle travel distance increases and local network features, such as velocity zones where flow is counter to the primary pressure gradient, become increasingly important for transport. As the network density increases, network statistics homogenize and such local features have a reduced impact. We quantify local topological influence on transport behavior with an effective tortuosity parameter, which measures the ratio of total advective distance to linear distance at the fracture scale; large tortuosity values are correlated to slow-velocity regions. These large tortuosity, slow-velocity regions delay downstream transport and enhance tailing on particle breakthrough curves. Finally, we predict transport with an upscaled, Bernoulli spatial Markov random walk model and parameterize local topological influences with a novel tortuosity parameter. Bernoulli model predictions improve when sampling from a tortuosity distribution, as opposed to a fixed value as has previously been done, suggesting that local network topological features must be carefully considered in upscaled modeling efforts of fracture network systems. and topology, and the corresponding flow field. The flow field within an individual fracture is typically highly correlated, commonly causing solute velocity to display persistent, low variability behavior over the in-fracture scale; consequently, the greatest Lagrangian accelerations occur at fracture intersections . As the fracture density increases, solute encounters more intersections on average, and the velocity correlation scale decreases. Furthermore, strong preferential flow paths form within interconnected networks of large fractures and channel a significant portion of mass, enabling solute to persist at high velocities for distances greater than the single fracture scale Sherman et al., 2019). This channelization becomes enhanced in sparse networks, where particles encounter fewer intersections, enabling them to persist on single fractures for longer distances. Resolving all these intranetwork features in 3-D DFN models is still computationally costly, and so upscaled modeling approaches, which account for network variability through effective parameter schemes, while maintaining a parsimonious framework, present an attractive alternative. However, how to properly parameterize network properties, such as velocity correlation and geometry, and inco...

Anomalous Transport in Three‐Dimensional Discrete Fracture Networks: Interplay Between Aperture Heterogeneity and Injection Modes

“…Sherman et al. (2020) discussed the tortuosity effect in detail and concludes that honoring the tortuosity distribution can improve model performance. Our results show that using an average tortuosity value is sufficient to capture overall transport behavior.…”

“…Many studies in the literature (Benke & Painter, 2003; Hyman et al., 2019b; Kang, Brown, et al., 2016; Le Borgne et al., 2008; Sund et al., 2016) have shown that the Lagrangian velocity series { v n }, if sampled in space, can be modeled as Markov processes. These observations have led to the development of CTRW formulations based on velocity Markov models (Dentz et al., 2016; Hakoun et al., 2019a; Kang et al., 2017; Le Borgne et al., 2008) that are able to predict anomalous transport in porous and fractured media (Comolli et al., 2019; Hyman et al., 2019b; Kang, Brown, et al., 2016; Kang et al., 2014; Le Borgne et al., 2008; Sherman et al., 2020; Sund et al., 2016). The empirical estimation of the transition matrix, equation (), from numerical or experimental data can be a challenging issue in practice (Sherman et al., 2017).…”

“…We assigned average tortuosity into the CTRW model, but the tortuosity of each particle should be different, and tortuosity will be in general smaller for particles that arrive faster. Sherman et al (2020) discussed the tortuosity effect in detail and concludes that honoring the tortuosity distribution can improve model performance. Our results show that using an average tortuosity value is sufficient to capture overall transport behavior.…”

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

“…This multiscale structural heterogeneity leads to multiscale flow channelization at length scales ranging from the entire system down to the subfracture size. At the largest scale, network density and connectivity alter the distribution of flow within the network, but this connection has only been qualitatively identified at this time (Huseby et al., 2001; Hyman & Jiménez‐Martínez, 2018; Hyman et al., 2019a; Sherman et al., 2020; Sweeney & Hyman, 2020). While it is generally accepted that a lower degree of flow channeling ought to occur in higher‐density networks, how to quantify the degree of flow channeling and link those measurements to geological features remains unclear.…”

“…For example, Sherman et al. (2020) observed that network density affected flow channeling and then studied the ability of upscaled transport models to reproduce high‐fidelity transport simulations using DFN models at these various densities. However, they did not systematically study the link between network structure attributes and flow channel formation nor develop new methods to compare flow channelization between networks.…”