Acoustic signatures of porous rocks permeated by partially saturated, aligned planar fractures

The presence of sets of vertical, parallel fractures is very common in the Earth's upper crust. Notably, open fractures exert critical control on the mechanical and hydraulic properties of the host formation. There is great interest in understanding how fractures interact with seismic waves, as this knowledge could be used to detect and characterize fractures from seismic data. When a seismic wave travels through a fractured formation, it induces oscillatory fluid pressure diffusion between the fractures and the embedding porous background, a physical process that produces attenuation and dispersion of the seismic wave. Although there are numerous studies on this topic, the case of parallel fractures saturated with different immiscible fluids, such as brine and CO2, remains rather unexplored. With these motivations, in this work, we propose an analytical approach to compute the phase velocity and attenuation of P-waves travelling perpendicularly to a set of planar, parallel fractures. While we consider that the background is saturated with brine, the fractures can be saturated with brine or gas. Our numerical analysis shows for the first time that two manifestations of fluid pressure diffusion arise in these cases. One of them, associated with relatively high levels of attenuation, is due to fluid pressure diffusion occurring between consecutive fractures saturated with different fluids. In this case, the fluid pressure diffusion process is initiated at a fracture saturated with brine and reaches a consecutive fracture saturated with gas. The other fluid pressure diffusion manifestation, on the other hand, arises at higher frequencies, is characterized by lower levels of attenuation and results from the interaction in the background of fluid pressure diffusion processes initiated at consecutive fractures, irrespective of the fluid content. Finally, by considering a stochastic distribution of the two fluids and a classical frequency of interest in seismic experiments, we obtain P-wave attenuation and phase velocity as functions of the fracture gas saturation. This approach could be of interest for the remote detection and quantification of pore fluids using seismic waves.