Self-affine fronts in self-affine fractures: large and small-scale structure

Area of Science:

• Geophysics
• Fluid Dynamics
• Materials Science

Background:

• Understanding fluid flow in fractured porous media is crucial for subsurface resource management and contaminant transport.
• Fracture wall roughness significantly influences flow dynamics and front propagation.
• Self-affine surfaces are common in natural fractures, impacting their hydraulic properties.

Purpose of the Study:

• To investigate the evolution and spatial structure of displacement fronts in fractures with self-affine rough walls.
• To determine how fracture geometry, specifically wall roughness and lateral shift, affects front dynamics.
• To establish the relationship between front characteristics and fracture properties.

Main Methods:

• Numerical simulations were employed to model fluid displacement in fractures.
• Fractures with identical, self-affine rough walls were simulated, with varying parallel or perpendicular shifts.
• The evolution of an initially flat displacement front under flow was tracked.

Main Results:

• The initially flat displacement front progressively distorted into a self-affine front.
• The Hurst exponent of the evolved front matched that of the fracture walls.
• The lower cutoff of the self-affine regime was solely dependent on fracture aperture.
• The upper cutoff increased with the lateral shift and linearly with the front width.

Conclusions:

• Displacement front evolution in rough fractures leads to self-affine structures mirroring wall roughness.
• Fracture aperture and lateral shift are key parameters controlling the spatial development of displacement fronts.
• The findings provide insights into fluid transport mechanisms in heterogeneous fractured systems.