Fractal fronts in fractal fractures: large and small-scale structure

TL;DR

This study uses numerical simulations to analyze how displacement fronts evolve and develop fractal structures within self-affine fractures, revealing the influence of fracture geometry on front morphology.

Contribution

It demonstrates that displacement fronts in self-affine fractures become self-affine with the same Hurst exponent as the walls, influenced by aperture and lateral shift.

Findings

Fronts become self-affine with wall Hurst exponent

Lower cutoff depends on aperture and shift

Upper cutoff scales with front width

Abstract

The evolution and spatial structure of displacement fronts in fractures with self-affine rough walls are studied by numerical simulations. The fractures are open and the two faces are identical but shifted along their mean plane, either parallel or perpendicular to the flow. An initially flat front advected by the flow is progressively distorted into a self-affine front with Hurst exponent equal to that of the fracture walls. The lower cutoff of the self-affine regime depends on the aperture and lateral shift, while the upper cutoff grows linearly with the width of the front.