Incorporating mechanisms of fluid pressure relaxation into inclusion-based models of elastic wave velocities

Our new method incorporates fluid pressure communication into inclusion-based models of elastic wave velocities in porous rocks by defining effective elastic moduli for fluid-filled inclusions. We illustrate this approach with two models: (1) flow between nearest-neighbor pairs of inclusions and (2) flow through a network of inclusions that communicates fluid pressure throughout a rock sample. In both models, we assume that pore pressure gradients induce laminar flow through narrow ducts, and we give expressions for the effective bulk moduli of inclusions. We compute P-wave velocities and attenuation in a model sandstone and illustrate that the dependence on frequency and water-saturation agrees qualitatively with laboratory data. We consider levels of water saturation from 0 to 100% and all wavelengths much larger than the scale of material heterogeneity, obtaining near-exact agreement with Gassmann theory at low frequencies and exact agreement with inclusion-based models at high frequencies.