An inclusion-based model of elastic wave velocities incorporating patch-scale fluid pressure relaxation

We consider elastic wave velocities in fluid-saturated porous media with pore fluids distributed in patches (i.e., heterogeneity much larger than the typical pore size). We model elastic properties of such materials using inclusion-based effective medium theory (IBEMT). The standard IBEMT formulation assumes insufficient time during the wave cycle for pore fluids to flow in response to wave-induced pressure gradients. Our approach accounts for this flow, incorporating wave-frequency dependent flow effects in the definition of effective elastic moduli for patches. Effective moduli are used in conjunction with IBEMT to estimate elastic moduli of the composite material. In the low- and high-frequency limits, the model reproduces previous theoretical results. At intermediate frequencies, it yields results qualitatively similar to other patch-scale models. We demonstrate this approach, estimating elastic P-wave velocities and attenuation in a porous rock that simultaneously contains fluid-saturated patches of different sizes.