The effects of fracture permeability on acoustic wave propagation in the porous media: A microscopic perspective

An illustrative theory is developed to analyze the acoustic wave propagation characteristics in the porous media with anisotropic permeability. We focus here on the role of fracture permeability in the unconsolidated porous media, looking in particular at the compressional P-wave phase velocity and attenuation. Two fluid pressure equilibration characteristic time factors are defined, which are corresponding to crack-pore system and crack-crack system, respectively. The theoretical results show that the dispersion and attenuation characteristics of acoustic wave are affected by porous matrix and fracture permeability simultaneously. Due to the fluid exchange that takes place between fractures and pores dominantly, the influence of the fracture connectivity on the wave propagation is very weak when the permeability of background medium is relatively high. However, correlation between wave propagation and fracture permeability is significant when the matrix permeability at a low level. A second attenuation peak occurs for the fluid flow within fractures in high-frequency region for more and more higher fracture permeability. The exact analytical solutions that are compared to numerical forward modeling of wave propagation in fractured media allow us to verify the correctness of the new model. If there exists another approach for obtaining the connectivity information of background media, we can use this model to analyze qualitatively the permeability of fractures or afford an indicator of in-situ permeability changes in a oil reservoir, for example, fracturing operations.