We have used numerical modeling to capture the physics related to coupled fluid-solid interaction (FSI) and the frequency dependence of pore scale fluid flow in response to pore pressure heterogeneities at the pore scale. First, we perform numerical simulations on a simple 2D geometry consisting of a pair of connected cracks to benchmark the numerical method. We then compute and contrast the stresses and pore pressures obtained from our numerical method with the commonly used method that considers only structural mechanics, ignoring FSI. Our results demonstrate that the stresses and pore pressures of these two cases are similar for low frequencies (1 Hz). However, at higher frequencies (1 kHz), we observe pore-pressure heterogeneities from the FSI numerical method that cannot be representatively modeled using the structural mechanics approach. At even higher frequencies (100 MHz), scattering effects in the fluid give rise to higher pressure heterogeneities in the pore space. The dynamic effective P-wave modulus M, attenuation Q1, and P-wave velocity VP were calculated using the results obtained from the numerical simulations. These results indicate a shift in the dispersion curves toward lower frequencies when the fluid viscosity is increased or when the aspect ratio of the microcrack is decreased. We then applied the numerical method on a 3D digital rock sample of Berea sandstone for a sweep of frequencies ranging from 10 Hz to 100 MHz. The calculated pore pressure at the low frequency (1 kHz) is homogeneous and the fluid is in a relaxed state, whereas at the high frequency (100 kHz), the pore pressure is heterogeneous, and the fluid is in an unrelaxed state. This type of numerical method helps in modeling and understanding the dynamic effects of fluid at different frequencies that result in velocity dispersion and attenuation.

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