Analysis of the frequency dependence characteristics of wave attenuation and velocity dispersion using a poroelastic model with mesoscopic and microscopic heterogeneities

Seismic waves passing through partially saturated porous rocks produce pressure gradients in the fluid phase, and, hence, the resulting fluid flow is accompanied by various length scales. The major mechanism responsible for seismic attenuation and dispersion is arguably known as wave‐induced fluid flow between inhomogeneities of microscopic, mesoscopic and macroscopic scales. Previous studies have revealed that differentiating the influence of heterogeneities at various scales on wave attenuation within seismic exploration and sonic frequencies, nevertheless, is very difficult. This is because wave attenuation mechanisms due to different heterogeneities are practically impossible to be unrelated. Therefore, it is important for a more quantitative interpretation of the relative contribution of inter‐dependent energy loss mechanisms through improved understanding of the combined influences associated to the microscopic squirt flow and mesoscopic fluid flow. We introduce a scaled poroelastic model to evaluate frequency‐dependent attenuation and velocity dispersion characteristics by considering the combined presence of microscopic and mesoscopic heterogeneities. To do so, the capillarity effects are incorporated into the poroelastic model with random distributions of the sizes of mesoscopic‐scale heterogeneities. A range of pertinent scenarios are calculated, and the acoustic properties indicate wave attenuation decreases whereas the phase velocity increases corresponding to additional capillary forces. Meanwhile, numerical results of the proposed model were compared with experimental measurements of a tight sandstone to examine its validity. Results of numerical simulations suggest that seismic reflections produce more complicated signatures in the presence of an interbedded structure of a reservoir exhibiting velocity dispersion. Therefore, the proposed procedure can help in assessing the sensitivities of frequency‐dependent seismic signatures to reservoir fluid mobility and patch heterogeneities.