Speaker
Description
Advective mixing in fracture networks plays a central role in many environmental and geological processes by influencing contaminant dispersion, dilution, and mixing-driven biogeochemical reactions [1]. While longitudinal dispersion in fracture networks has received considerable attention, the dynamics of mixing, which governs the creation of fine concentration scales and reactive outcomes, are less understood. In particular, previous research has often focused on intersection-scale processes and flow partitioning [2,3], and it remains unclear how complex network topology and extreme fracture aspect ratios impact mixing at the network scale.
Here we develop a theoretical framework for advective mixing and uncover two distinct mixing mechanisms at vastly different length scales, termed fracture mixing and intersection mixing, that respectively arise due to streamline routing within fractures and at their intersections. We show that the large fracture aspect ratio effectively enforces discontinuous mixing, involving cutting and shuffling (CS) of fluid elements due to streamline routing [4]. This mixing is controlled by a combination of CS and fluctuating fluid deformation, forming a piecewise-smooth transform that leads to weak ergodic mixing.
We will present an efficient graph-based representation via a mixing graph $G_M$ that extends standard graph representations of fracture networks [5] and encodes the fracture-network topology and mixing mechanisms as a sequential dynamical system on concentrations. The local maps defining $G_M$ are parameterized from high-fidelity streamline-routing ensembles obtained from fully resolved DFN simulations. Numerical predictions of mixing from $G_M$ agree to high precision with direct simulation of discrete fracture networks. We also find that a simplified piecewise-isometric description remains in fair agreement at substantially reduced computational cost, enabling rapid screening of mixing efficiency from network architecture and intersection statistics.
| References | [1] B. Berkowitz (2002). ``Characterizing flow and transport in fractured geological media: A review.'' Advances in Water Resources, 25(8-12), 861--884. [2] B. Berkowitz, S. P. Naumann, \& L. Smith (1994). ``Mass transfer at fracture intersections: An evaluation of mixing models.'' Water Resources Research, 30(6), 1765--1773. [3] P. Davy, R. Le Goc, C. Darcel, B. Pinier, J. Selroos, \& T. Le Borgne (2024). ``Structural and hydrodynamic controls on fluid travel time distributions across fracture networks.'' Proc. Natl. Acad. Sci. U.S.A., 121(47), e2414901121. ,[4] R. Sturman (2012). ``The Role of Discontinuities in Mixing.'' Advances in Applied Mechanics, 45, 51--90. [5] S. Karra, D. O'Malley, J. D. Hyman, H. S. Viswanathan, \& G. Srinivasan (2018). ``Modeling flow and transport in fracture networks using graphs.'' Physical Review E, 97, 033304. |
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| Country | France |
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