Attenuation and Dispersion in Partially Saturated Porous Rock - Random vs Periodic Models

Mesoscopic heterogeneities often occur on a mesoscopic scale, that is scale which is greater than pore-scale but less than wavelength scale. Presence of mesoscopic fluid patches in a porous rock may cause a substantial phase velocity dispersion and attenuation. This is a result of wave induced fluid flow, which arises when a passing wave induces spatial gradients in fluid pressure. Attenuation and dispersion arising from mesoscopic heterogeneities is affected by the spatial distribution of saturating fluids. Here we compare theoretical models for attenuation and dispersion which utilize a 3D random and periodic distribution of fluid heterogeneities. In particular, the periodic model proposed by Johnson (2001) is reinterpreted within the context of the random model. Good agreement between estimates of attenuation and phase velocity is obtained showing that with the right choice of parameters Johnson’s model can describe random as well as periodic distribution of fluid patches.