Permeability of self-affine aperture fields.

Area of Science:

• Geophysics
• Fluid Dynamics
• Material Science

Background:

• Fracture permeability is crucial for fluid flow in porous media.
• Understanding permeability in rough fractures is complex due to geometric variations.
• Previous models often simplify fracture geometry, limiting applicability.

Purpose of the Study:

• To develop a predictive model for the permeability of self-affine rough channels and 2D fractures.
• To investigate the scaling behavior of permeability across a wide range of fracture apertures.
• To identify and characterize different scaling regimes based on fracture properties.

Main Methods:

• Utilized the lubrication approximation to model fluid flow.
• Analyzed permeability scaling in one-dimensional (channels) and two-dimensional fractures.
• Introduced an equivalent aperture, b(c), for two-dimensional fracture analysis.
• Investigated the influence of the Hurst exponent (H) on scaling regimes.

Main Results:

• Identified three distinct permeability scaling regimes.
• Permeability scales with the cube of the aperture in limiting cases (large or near-zero aperture).
• A third regime exhibits scaling influenced by self-affine roughness, with exponents 3-1/H for channels.
• For 2D fractures, scaling exponents depend on the equivalent aperture and Hurst exponent (e.g., 2.25 for H=0.8).

Conclusions:

• The developed model accurately predicts fracture permeability across various apertures.
• Self-affine roughness significantly impacts permeability scaling, especially in the intermediate aperture range.
• The concept of equivalent aperture is essential for understanding permeability in 2D rough fractures.