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Stochastic model for mixing interface evolution through three-dimensional fracture networks.

Daniel M C Hallack1, Diogo Bolster1, Jeffrey D Hyman2

  • 1University of Notre Dame, Civil and Environmental Engineering and Earth Sciences, Notre Dame, Indiana 46556, USA.

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Summary
This summary is machine-generated.

Mixing in fractured networks differs from porous media due to network heterogeneity. A new model links fracture topology to mixing dynamics, revealing unique growth patterns distinct from chaotic exponential growth.

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Area of Science:

  • Geosciences
  • Fluid Dynamics
  • Chemical Engineering

Background:

  • Mixing is crucial for solute transport in subsurface systems.
  • Understanding mixing in fractured media is complex due to heterogeneous flow paths.
  • Existing models often assume continuous media, failing to capture fracture network specifics.

Purpose of the Study:

  • To investigate the effective mixing behavior of solutes in steady flows through 3D random fracture networks.
  • To characterize the unique phenomena of mixing in fractured systems compared to porous media.
  • To develop an analytical model for mixing interface growth in fracture networks.

Main Methods:

  • High-fidelity simulations of fluid flow and solute transport in 3D fracture networks.
  • Derivation of an analytical model for mixing interface growth.
  • Comparison of simulation results with the analytical model predictions.

Main Results:

  • Mixing in fracture networks exhibits distinct phenomena, including splitting events in mixing interface growth at intersections.
  • Network topology significantly influences mixing dynamics.
  • The derived analytical model accurately predicts mixing interface growth based on network properties.
  • Chaotic exponential growth, common in porous media, was not observed.

Conclusions:

  • Fracture network heterogeneity creates complex flow fields that dictate solute mixing.
  • A fundamental difference exists in mixing behavior between fractured and porous media.
  • The developed model provides insights into mixing dynamics unique to fractured media and offers asymptotic predictions beyond current simulation capabilities.