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Emergence of Stable Laws for First Passage Times in Three-Dimensional Random Fracture Networks.

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Particle movement in random fracture networks shows heavy-tailed distributions. This study quantifies motion using a random walk model, predicting first passage times based on network properties.

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Area of Science:

  • Geosciences
  • Physics
  • Applied Mathematics

Background:

  • Fluid flow in fractured rock is complex due to network heterogeneity.
  • Understanding particle transport is crucial for subsurface resource management and contaminant transport.

Purpose of the Study:

  • To investigate first passage behaviors in 3D random fracture networks.
  • To develop a predictive theory for first passage times in heterogeneous flow systems.

Main Methods:

  • Analysis of first passage time distributions and their evolution with distance.
  • Stochastic quantification of particle motion using a time domain random walk model.
  • Identification of key parameters influencing transport: advective tortuosity, velocity distribution, and fracture link length.

Main Results:

  • Heavy-tailed first passage time distributions emerge and evolve towards stable laws with increasing distance.
  • Particle motion can be modeled as a random walk conditioned on initial velocity.
  • Advective tortuosity, velocity distribution, and average fracture link length are identified as critical predictors.

Conclusions:

  • A theoretical framework is established for predicting first passage times in random fracture networks.
  • The study provides insights into the scaling behavior of transport phenomena in complex geological media.