Propagating Waves in Rocks and other Porous Media with Embedded Fluid Clusters

Mechanical waves in residual saturated porous media are of great importance for scientific investigations and applications in Geophysics and Engineering. Exploration techniques, ganglia mobilization and characterization are strongly related to the understanding and control of propagating waves. However, wave propagation in residual saturated porous media is not fully understood yet. Especially the damping mechanisms are not described with sufficient accuracy. Such systems of very low saturated media contain one continuous solid and fluid phase and, in addition, a distribution of disconnected single clusters of a second immiscible fluid. Each of those fluid clusters is different in geometry and its dynamical behavior. The standard continuous approach is not able to account for the effects of such a variety of possible enclosures and to distinguish between them. Hence, we present a model that uses an oscillator-like rheology for the discontinuous fluid. Therein, the fluid clusters are characterized by their eigenfrequency and damping distribution. As a result, two important enhancements are made. First, the presented model allows distinguishing between different types of fluid clusters by their eigenfrequency and relates them to characteristic properties. Second, an additional damping mechanism is introduced compared to damping via viscous effects of the fluid phases: the presented model also accounts for the energy that is stored by the oscillating fluid clusters. If these clusters are stimulated by a passing wave, energy is stored due to their oscillations, which corresonds to a loss of energy for the passing wave. Finally, an inverse analysis relates the predicted, frequency dependent damping to typical cluster sizes. Basic physical phenomena are presented and described on the macroscopic scale of the wave as well as on the microscopic scale of the fluid clusters. A detailed numerical investigation of the oscillating fluid clusters depicts their behavior and enables for a classification. On this basis, the model is developed from balance equations over assumptions up to the dispersion relations. Important influences on wave propagation are discussed in general and with the help of a specific example. This shows that wave propagation in a porous medium can be affected by the presence of a discontinuous residual wetting fluid, whether the residual fluid oscillates or not.; Oscillating water bridge