Local Cubic Law Simulation of Stress-dependent Aperture-based Permeability

Research on calculating fracture permeability has been undergoing for decades (Witherspoon, 1980). Local Cubic Law (LCL) has been proposed to be one feasible way to simulate the fracture permeability with variable aperture changes (Brown, 1987). The purpose of this research is to present an evaluation of LCL based on a set of experimental results of permeability, aperture distribution and effective stress. We concurrently measure fracture permeability and fracture aperture distribution changes (using X-Ray CT) with cycling stress. Fractured Berea sandstone and Zenifim sandstone are measured, representing rough and smooth rock fracture surfaces. Using thin section data, we evaluate the grain size and apply Stokes fluid flow simulation in a synthetic field to estimate the stagnant fluid level between rock grains. By accounting for the stagnant fluid level, LCL simulation provides a reliable prediction for fracture permeability. Comparing with previous research (Konzuk and Kueper, 2004), we propose that LCL simulation requires detailed information about local grain arrangement.

The experiment shows that permeability change is greater than expected from mean aperture change at different stress levels. LCL simulation demonstrates that this is mainly due to the change of fluid flow pattern with stress, which is caused by aperture distribution change. LCL simulation also exhibits that channeling behavior plays an important role in fluid flow in fractures, and sometimes a small number of channels dominate the flow. In the experiment, we apply different flow rates to assess the LCL simulation at different Reynolds number. The simulation results show that fluid flow rate (1.24 < Re < 15.28) does not have a large impact on LCL predictability in the highly tortuous and rough rock fractures, which agrees with the results of Konzuk and Kueper (2004).

References:

Brown, S. R., 1987, Fluid flow through rock joints: The effect of surface roughness, J. Geophys. Res., 92(B2), 1337-1347

Konzuk, J. and Kueper, B.H., 2004. Evaluation of cubic law based models describing single-phase flow through a rough-walled fractured. Water Resources Research, Vol. 40, No. 2

Witherspoon, P.A., JSY. Wang, K. Iwai, and J.E. Gale (1980), “Validity of cubic law for fluid-flow in a deformable rock fracture”, Water Resour. Res., 16:1016-1024