Linking Structural and Transport Properties in Three‐Dimensional Fracture Networks

Abstract

We investigate large‐scale particle motion and solute breakthrough in sparse three‐dimensional discrete fracture networks characterized by power law distributed fracture lengths. The three networks we consider have the same fracture intensity values but exhibit different percolation densities, geometric properties, and topological structures. We considered two different average transport models to predict solute breakthrough, a streamtube model and a Bernoulli continuous time random walk model, both of which provide insights into the flow fields within the networks. The streamtube model provides acceptable predictions at short distances in two of the networks but fails in all cases to predict breakthrough times at the outlet plane, which indicates that particle motion in such fracture networks cannot be characterized by a constant velocity between the inlet and control plane at which the breakthrough curve is detected. Rather, the structure of the network requires that frequent velocity transitions be made as particles move through the system. Despite the relatively broad distribution of fracture radii and relatively small number of independent velocity transitions, the continuous time random walk approach conditioned on the initial velocity distribution provides reasonable predictions for the breakthrough curves at different distances from the inlet. The application of these averaged transport models provides a richer understanding of the link from the fracture network structure to flow and transport properties.

Characterizing the Influence of Fracture Density on Network Scale Transport

“…However, even in the densest networks at the kilometer scale, we still observe significant difference in tailing between the correlated and fixed tortuosity CTRW models at intermediate CCDF values [0.01,1]. Interestingly, the fixed CTRW underestimated tailing for this same CCDF regime in the fracture networks studied by Hyman et al (2019), although their networks had higher density. This again shows that the velocity-tortuosity correlation structure is important for breakthrough tailing, as slow velocity-large regions delay solute transport.…”

“…The inherent heterogeneous structure of natural fracture networks is characterized by a broad range of lengths, spanning from the aperture roughness to the full network scale Bonnet et al (). At the network scale, the topological properties set the flow field structure (de Dreuzy et al, ; Frampton et al, ; Makedonska et al, ), meaning velocity at the in‐fracture scale is highly correlated (Hyman et al, ; Kang, Le Borgne, et al, ) and subfracture scale features are less important. Complex network topologies naturally result in a very broadly distributed velocity field, which influences associated transport processes.…”

Stress‐Induced Anomalous Transport in Natural Fracture Networks

“…While several studies have investigated fluid flow in stressed 3‐D fracture networks (Garipov et al, ; Lei et al, ; McClure et al, ), the effects of geological stress on tracer transport through 3‐D fracture networks remain to be investigated. A recent study has shown that the Bernoulli CTRW model can capture particle transport through 3‐D fracture networks (Hyman et al, ), and the natural extension of this study will be the effects of geological stress on particle transport through stressed 3‐D fracture networks. Finally, since fracture network properties and in situ stress conditions can vary widely from location to location, additional studies are required to obtain more general conclusions.…”

“…DFN models represent fractures as discrete entities and enable the study of the effects of fracture geometrical properties on fluid flow and transport explicitly. Fluid flow and transport in DFNs have been the subjects of many investigations over the past decades, and recent advances in computational power have enabled more detailed flow and transport studies in complex three-dimensional (3-D) DFNs with multiscale heterogeneity (Benedetto et al, 2016;Hyman & Jiménez-Martínez, 2018;Hyman et al, 2019;Makedonska et al, 2015;Maillot et al, 2016;Viswanathan et al, 2018).…”

Transport under advective trapping

“…The methodology is based on a Lagrangian approach that allows to identify and quantify the stochastic rules of advective particle motion in disordered media. Similar approaches have been used in previous works for the analysis and upscaling of pore-scale transport (Morales et al 2017;Puyguiraud et al 2019) and for transport in multi-Gaussian hydraulic conductivity fields (Hakoun et al 2019) and fractured media (Hyman et al 2019). Here, we use a Lagrangian approach to gain understanding of the stochastic principles of transport in random composite media through the analysis of advective trapping events in low conductivity inclusions, and the distribution of flow speeds sampled between them.…”