Large-scale physics of hydrodynamic transport in random fracture networks

We study flow and hydrodynamic transport in spatially random fracture networks.
The flow and transport behavior is characterized by first passage
times and displacement statistics, which show heavy tails
and anomalous dispersion with a strong dependence on the injection
condition. The origin of these behaviors is investigated
in terms of Lagrangian velocities sampled equidistantly along particle
trajectories, unlike classical sampling strategies at a constant rate. The
fluctuating velocity series is analyzed by its copula density, the
joint distribution of the velocity unit scores, which reveals a simple correlation
structure that can be described by a Gaussian copula. This insight
leads to the formulation of stochastic particle motion in terms of a
Klein-Kramers equation for the joint density of particle position and
velocity. The upscaled model captures the heavy-tailed first passage
time distribution and anomalous dispersion, and their dependence on the
injection conditions in terms of the velocity point statistics and
average fracture length. The first passage times and displacement
moments are dominated by extremes occurring at the first step.
The developed approach integrates the complex interaction of flow and structure
into a predictive model for large scale transport in random fracture networks.