Acoustic response of patchy-saturated porous media: Coupling Biot's poroelasticity equations for mono- and biphasic pore fluids

Patchy saturation is a term used in the seismic prospecting literature to describe the state of a geological formation in which two immiscible pore fluids prevail in mesoscopic-scale clusters. If the pore fluids have contrasting compressibilities, wave-induced fluid pressure diffusion (FPD) processes may induce significant attenuation and velocity dispersion on seismic waves. Biot's monophasic poroelasticity theory is widely used to model the seismic response of rocks containing binary patches of two immiscible pore fluids. Even though effective fluid approximations may help to represent more realistic partially saturated patches using Biot's monophasic equations, the so inferred dissipation may not be representative of actual biphasic FPD phenomena. In this work, Biot's equations for mono- and biphasic fluids are combined to model FPD processes in porous media, comprising fully and partially saturated patches. An analytical solution for one-dimensional layered patchy-saturated media is presented which permits to explain some, as of yet enigmatic, experimentally observed characteristics such as increased seismic attenuation and stiffening effects occurring at low saturations. The results show that the existence of an additional diffusive wave mode within partially saturated patches may render conventional binary and effective fluid approaches incorrect and error prone.