Scaling of fluid flow versus fracture stiffness

Seismic characterization of fluid flow through fractures requires a fundamental understanding of the relationship between the hydraulic and mechanical properties of fractures. A finite-size scaling analysis was performed on fractures with weakly correlated random aperture distributions to determine the fundamental scaling relationship between fracture stiffness and fracture fluid flow. From computer simulations, the dynamic transport exponent, which provides the power law dependence, was extracted and used to collapse the flow-stiffness relationships from multiple scales into a single scaling function. Fracture specific stiffness was determined to be a surrogate for void area that is traditionally used in percolation studies. The flow-stiffness scaling function displays two exponentially dependent regions above and below the transition into the critical regime. The transition is governed by the stressed flow paths when the flow path geometry deforms from a sheet-like topology to a string-like topology. The resulting hydromechanical scaling function provides a link between fluid flow and the seismic response of a fracture.