Fractures with correlated and uncorrelated random aperture distributions were used to explore a fundamental scaling relationship between fracture stiffness and fluid flow in a fracture. Three computational methods were used:

  1. a stratified percolation approach to generate pore-scale fracture void geometry for fractures,

  2. a combined conjugate-gradient method and fast-multipole method for determining fracture deformation, and

  3. a flow network model for simulating fluid flow, fluid velocity and fluid pressures within a fracture.

Fracture specific stiffness captures the deformation of the fracture void geometry that includes both changes in contact area and aperture. The numerical flow-stiffness data, simulated at multiple length scales, collapsed to a single scaling function that displays different exponential regions above and below the transition into the critical regime. This hydro-mechanical scaling relationship provides the first step in determining fluid flow remotely through fractured rock because fracture specific stiffness affects seismic wave attenuation and velocity, which are routinely measured in the field.

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