Flow in Rough Self-Affine Fractures Joints

TL;DR

This study uses numerical simulations to analyze flow in self-affine fracture joints, revealing how permeability depends on the Hurst exponent and how velocity fluctuations behave across scales.

Contribution

It introduces a novel analysis of flow regimes in self-affine fractures, highlighting the dependence of permeability on the Hurst exponent and scale-dependent velocity fluctuations.

Findings

Permeability varies weakly for Hurst exponent > 1/2

Permeability varies strongly for Hurst exponent < 1/2

Velocity fluctuations are correlated at small scales and decorrelate at larger scales

Abstract

We investigate viscous and non-viscous flow in two-dimensional self-affine fracture joints through direct numerical simulations of the Navier-Stokes equations. As a novel hydrodynamic feature of this flow system, we find that the effective permeability at higher Reynolds number to cubic order, falls into two regimes as a function of the Hurst exponent $h$ characterizing the fracture joints. For $h>1/2$, we find a weak dependency whereas for $h<1/2$, the dependency is strong. A similar behavior is found for the higher order coefficients. We also study the velocity fluctuations in space of a passive scalar. These are strongly correlated on smaller length scales, but decorrelates on larger scales. Moreover, the fluctuations on larger scale are insensitive to the value of the Reynolds number.