Effect of Reactive Flow on Multi-size Scaling of Fluid Flow and Seismic Fracture Stiffness

A goal of geophysical monitoring is to detect and characterize alterations in the subsurface induced by natural and anthropogenic processes that affect local fracture geometry and local fluid flow. Recently, we demonstrated that a key seismic signature of a fracture (specific stiffness) is related to its hydraulic properties if the aperture distributions have only weak spatial correlations. An open challenge remains to determine if this relationship holds for correlated aperture distributions and whether this relationship differs for fractures altered only by stress or also for those altered by reactive flow and stress.

A finite-size scaling analysis was performed on fractures to determine the effect of correlated aperture distributions with and without chemical alteration on the fundamental scaling relationship between fracture stiffness and fracture flow behavior. Computational models were used to analyze fluid flow through a fracture undergoing deformation and chemical alteration. The numerical methods included a stratified percolation approach to generate pore-scale fracture void geometry, a combined conjugate-gradient method and fast-multipole method for determining fracture deformation, and a network model for simulating fluid flow through a fracture. Fracture apertures were chemically eroded based on the local flux field through the fracture.

For correlated aperture distributions without chemical alteration, fracture stiffness captures the deformation of the fracture void geometry that includes both changes in contact area and aperture. This enabled a collapse of the numerical flow-stiffness data, from multiple length scales, to a single scaling function. When fracture apertures were slightly eroded, the flow-stiffness relationship exhibited the same functional form as the unaltered case, but the scaling of flow depended on the aperture of the critical neck.

These results suggest that geophysical methods that characterize fracture stiffness have the potential to estimate relative flow among stressed and eroded fractures.

Acknowledgments: This work was supported by the U.S. Dept. of Energy, Office of Science, Office of Basic Energy Sciences, Geosciences Research Program under Award Number (DE-FG02-09ER16022) and by the Geo-mathematical Imaging Group at Purdue University.