Elastic Wave Velocity Changes Due to the Fracture Aperture and Density, and Direct Correlation With Permeability: An Energetic Approach to Mated Rock Fractures.

In an effort to reveal the subsurface hydraulic changes in fractures by seismic monitoring, aperture‐related velocity changes need to be investigated. We developed a numerical approach for calculating changes in elastic wave velocity with fracture aperture opening by determining the internal energy of a digitized fracture model based on natural rough surfaces. The simulated local elastic energy revealed that the interaction energy converged within 1.5 mm of the mean fracture position, and was insignificant unless the fractures intersected. This energetic approach clarified the aperture‐velocity relationship and reproduced the experimental results. Further calculations using digital fractures with various sizes and densities demonstrated that the velocity can be accounted for by the superposition of a linear function of fracture density and quadratic function of aperture, and is insensitive to the fracture size. Although the relationship between fracture permeability and elastic wave velocity (i.e., the k‐V relationship) depends on the fracture density, the offset‐normalized k‐V relationship shows clear linearity with the fracture density. The proposed k‐V relationship as a function of the aperture and fracture density indicates that laboratory‐scale fracture properties of a single fracture can be applied to multiple fractures on a larger scale. Our findings can be used to interpret temporal changes in seismic observations and to monitor fluid flow in fractures. Plain Language Summary: A monitoring of seismic velocity will be useful to find changes in the permeability of fractures, if the relationship between elastic wave velocity and fracture aperture is known. This study presents a numerical approach to calculating changes in elastic wave velocity, based on the elastic energy calculated using a digital rock model having simulated natural fractures. The proposed approach revealed the relationship between fracture aperture and elastic wave velocities propagating through the fracture. Further calculations showed linear decreases of wave velocities with the number of fractured layers per unit thickness (i.e., the fracture density), whereas the velocities do not significantly change with fracture size. Our results will allow us to formulate the relationship between fracture permeability and elastic wave velocity as a function of fracture density. The proposed equation suggests that the properties of a single fracture on the laboratory scale can be used for a large‐scale multiple fracture system. The results will provide a prospective application of seismic data to be used in the sustainable development of fractured reservoirs such as geothermal resources. Key Points: A numerical approach based on internal energy calculations was developed to calculate precise velocity changes with fracture openingVelocity can be accounted for by superposition of a linear function of the fracture density and quadratic function of the aperture sizeNormalized velocity has a linear relationship with normalized permeability, and the trend depends on fracture density [ABSTRACT FROM AUTHOR]