Relation Between First Arrival Time and Permeability in Self-Affine Fractures with Areas in Contact

TL;DR

This paper establishes a direct relationship between the first arrival time in dispersive flow through self-affine fractures and the fractures' permeability, linking flow dynamics to fracture geometry.

Contribution

It introduces a novel connection between first arrival time and a specific length scale in fractures, generalizing the concept of bottlenecks to two dimensions.

Findings

Linear relationship between first arrival time and the length scale.

First arrival time can be expressed directly in terms of permeability.

The relationship holds even with strong surface overlap causing zero permeability areas.

Abstract

We demonstrate that the first arrival time in dispersive processes in self-affine fractures are governed by the same length scale characterizing the fractures as that which controls their permeability. In one-dimensional channel flow this length scale is the aperture of the bottle neck, i.e., the region having the smallest aperture. In two dimensions, the concept of a bottle neck is generalized to that of a minimal path normal to the flow. The length scale is then the average aperture along this path. There is a linear relationship between the first arrival time and this length scale, even when there is strong overlap between the fracture surfaces creating areas with zero permeability. We express the first arrival time directly in terms of the permeability.