Unified model for microscopic and mesoscopic wave-induced fluid flow in a fluid-saturated porous periodically layered medium

The interlayer mesoscopic wave-induced fluid flow and the squirt flow are two important mechanisms for seismic attenuation and dispersion in the fluid-saturated porous layered rock. Although numerous studies have been conducted on these two mechanisms, their combined effects (especially the resulting frequency-dependent anisotropy features) have not been sufficiently investigated. Hence, we propose a concise and rigorous theoretical model to quantify the combined effects of these two mechanisms. We first quantify the squirt flow effects through a wet rock frame for each layer that has frequency-dependent and complex-valued elastic properties. Then, we apply Biot's quasi-static poroelasticity theory to derive the analytical solutions for the effective stiffness coefficients of the periodically layered rock. Using the derived rock stiffness coefficients, we calculate the seismic attenuation and dispersion, as well as the frequency-dependent anisotropy. Two cases are studied, one with alternating water- and gas-saturated layers (constant rock frame properties) and the other with periodically distributed fracture layers (constant saturating fluid properties). The P-waves in these two cases are both influenced by the mesoscopic interlayer wave-induced fluid flow and the squirt flow. However, the SV-wave is solely affected by the squirt flow in the first case and primarily influenced by the mesoscopic interlayer wave-induced fluid flow in the second case, respectively. The wave velocity and attenuation in the first case are isotropic, whereas those in the second case exhibit frequency-dependent anisotropy (induced by the mesoscopic interlayer wave-induced fluid flow). To validate our model, we compare our model to the measured extensional attenuation in a partially saturated sandstone sample under different effective pressures. The joint effects of the mesoscopic interlayer wave-induced fluid flow and the squirt flow observed in the experiments are well predicted by our model. Our model has potential applications in the seismic characterization of reservoirs composed of layered rocks, such as shale reservoirs.