Residual saturated porous media – from oscillating water blobs to waves in ground earth

Abstract

A model for wave propagation in residual saturated porous media is presented distinguishing enclosed fluid clusters with respect to their eigenfrequency and damping properties. The additional micro-structure information of cluster specific damping is preserved during the formal upscaling process and allows a stronger coupling between micro-and macro-scale than characterisation via eigenfrequencies alone. A numerical example of sandstone filled with air and liquid clusters of different eigenfrequency and damping distributions is given. If energy dissipation due to viscous damping dominates energy storage due to cluster oscillations, the damping distribution is more influential than the eigenfrequency distribution and vice versa. Spreading the damping distribution around a constant mean value supported the effect of capillary forces and spreading the eigenfrequency distribution around a constant mean value supported the effect of viscous damping in the investigated samples. For a wide distribution of the liquid clusters' damping properties, two damping mechanisms of propagating waves occur at the same time: damping due to viscous effects (for highly damped clusters) and energy storage by cluster oscillations (for underdamped clusters).