Percolation in three-dimensional fracture networks for arbitrary size and shape distributions

Area of Science:

• Geosciences
• Computational Mechanics
• Network Theory

Background:

• Percolation phenomena are critical in understanding fluid flow and transport in fractured media.
• Fracture network geometry, including shape and size distribution, significantly impacts bulk properties.
• Existing models often simplify fracture geometry, limiting their predictive power.

Purpose of the Study:

• To investigate the percolation threshold of 3D fracture networks with diverse fracture shapes and size distributions.
• To develop a predictive model for percolation threshold considering geometric complexities.
• To rationalize simulation results using a dimensionless density and propose a new shape factor.

Main Methods:

• Extensive direct numerical simulations of 3D fracture networks.
• Consideration of a wide range of regular, irregular, and random fracture shapes.
• Analysis of both monodisperse and polydisperse networks (varying shapes and/or sizes).

Main Results:

• A dimensionless density parameter effectively rationalizes percolation threshold results.
• A novel shape factor model accurately accounts for fracture shape influence.
• A polydispersity index was identified as a key factor for network corrections.

Conclusions:

• The proposed shape factor model offers high accuracy for monodisperse and moderately polydisperse networks.
• The findings provide a robust estimation for percolation thresholds in complex fracture networks.
• The study advances the understanding of connectivity in disordered systems relevant to subsurface applications.