Propaga on of seismic waves in par ally saturated porous media depends on various materialproper es, including satura on, porosity, elas c proper es of the skeleton, viscousproper es of the pore fl uids, and, addi onally, capillary pressure and eff ec ve permeability.If the we ng fl uid is in a discon nuous state (i.e., residual saturated confi gura on),phase veloci es and frequency-dependent a enua on addi onally depend on microscopical(pore-scale) proper es such as droplet and/or ganglia size. To model wave propaga onin residual saturated porous media, we developed a three-phase model based on anenriched con nuum mixture theory capturing the strong coupling between the micro- andthe macroscale. The three-phase model considers a con nuous and a discon nuous part.The con nuous part exhibits similar behavior as the poroelas c model introduced by Biot.The discon nuous part describes the movement of blobs/clusters of the we ng fl uid andis based on an oscillator rheology. In comparison with other three-phase models, the presentedone accounts for the heterogeneity of the discon nuous fl uid clusters by use oftheir dynamic proper es, i.e., their sta s cally distributed iner a, eigenfrequency, anddamping eff ects. This heterogeneous and discon nuous distribu on of the we ng fl uid inthe form of single blobs or fl uid clusters is represented by a model-embedded distribu onfunc on of the cluster sizes. We defi ne a dimensionless parameter that determines if theoverall mo on of the residual fl uid is dominated by oscilla ons (underdamped, resonance)or not (overdamped). Our results show that the residual fl uid has a signifi cant impact on thevelocity dispersion and a enua on no ma er if it oscillates or not. For long wavelengthsour model coincides with the Biot–Gassmann equa ons. We show under which condi onsand how the classical biphasic models can be used to approximate the dynamic behavior ofresidual saturated porous media.
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