Multi-scale Wave-induced Fluid Flow in Partially Saturated Dual-Porosity Media: Theory and Numerical Validation of the Biot-patchy-spherical-squirt Model

Summary We develop a novel comprehensive theoretical framework, the Biot-patchy-spherical-squirt (BIPSSQ) model, for wave propagation in partially saturated dual-porosity media. This model simultaneously incorporates three key fluid flow mechanisms: macroscopic flow (Biot flow or global flow), mesoscopic flow, and microscopic flow (three-dimensional spherical squirt flow). The constitutive relations and fluid pressure expressions for the BIPSSQ model are first derived and then the governing wave equations are established using a Lagrangian approach based on the system’s kinetic energy, potential energy, and dissipation functions. Through plane wave analysis, we obtain the phase velocity and attenuation of the fast P-wave. Numerical examples demonstrate that the BIPSSQ model predicts multiple dispersion transition bands and corresponding attenuation peaks, attributed to two squirt flows and two Biot global flows from two immiscible fluids. Furthermore, the presence of squirt flow significantly suppresses the mesoscopic patchy saturation effect, leading to the disappear of mesoscopic dispersion transition band and attenuation peak. The influences of permeability, saturation, porosity, squirt-flow length and inclusion radius on velocity dispersion and attenuation are also analyzed. Finally, excellent agreement between theoretical predictions and experimental measurements from an Aksu outcrop rock sample (800 kHz), a gas-water-saturated Estaillades limestone (1 kHz), and an oil-brine-saturated Vosgian sandstone (350 kHz), validates the applicability and effectiveness of the BIPSSQ model. Moreover, the BIPSSQ model can degenerate to other theories (i.e. Biot, BISSQ, BR) under certain conditions. Our proposed model provides a unified and robust tool for interpreting wave propagation phenomena in complex, partially saturated reservoir rocks.