Fracture Permeability and Specific Stiffness Relations Across Varying Fracture Roughness and Aperture Correlation Length

Abstract:

The coupling between hydraulic and mechanical properties of porous and fractured geologic media are critical for many geophysical processes and practical applications. Thus, the prediction of linkage between these properties are broadly important. Here we present a parameterized model that links fracture permeability and specific stiffness with scaling coefficients dependent on fracture roughness and correlation length. The model was developed empirically from results of modeling the deformation and flow through synthetic fractures with aperture fields that follow a normal distribution. The fractures were subjected to increasing normal stress and deformed follow an elastic model. Specific stiffness was directly quantified from these numerical experiments with resultant displacement. Moreover, intrinsic permeability was estimated through calculation of the local flow field while considering effects of local fracture roughness and tortuosity through the modified Local Cubic Law.

We found that fracture displacement increases non-linearly with applied normal stress, while specific stiffness is expectedly proportional to normal stress. Most importantly, permeability decreases exponentially with increasing specific stiffness following different deformation paths depending mainly on fracture roughness rather than correlation length. Based on the calculated permeability and specific stiffness, we propose an empirical model that predicts a clustered linkage between specific stiffness and permeability. The model can capture the transition from effective medium to percolation flow regimes with increasing specific stiffness.