A pore-scale investigation of the dynamic response of saturated porous media to transient stresses

The dynamical response of saturated porous media to transient stresses is complex because of the coupling between the solid and fluid phases. Over the last three decades, theoretical models have emerged and they predict that the transient response of porous media to pore-pressure fluctuations depends only on a single dimensionless number. This single parameter represents the ratio of the forcing frequency to a characteristic frequency of the medium. Although theoretical models for the frequency dependence of the effective permeability of the medium have successfully predicted the response of porous media at high frequency observed in laboratory and numerical experiments, they rely on assumptions that limit their applicability to homogeneous media and narrow pore-size distributions. We use pore-scale flow simulations with four different porous media topologies to study the effect of pore geometry and pore-size distribution on the dynamic response to transient pore-pressure forcing. We find a good agreement with published theoretical work for all but one medium that exhibits the broadest pore-size distribution and therefore the largest degree of pore-scale heterogeneity. Our results suggest the presence of a resonance peak at high frequency where the discharge, and therefore the effective permeability, is significantly amplified compared to their value around the resonant frequency. We suggest two interpretations to explain resonance. At the continuum scale, a finite speed of pore-pressure propagation during transients requires the addition of a correction term to Darcy's law. We derive a hyperbolic mass conservation equation that admits resonance under certain conditions. This model can explain the peak observed for one medium but fails to explain the absence of resonance displayed by the three other media. The second interpretation, motivated by the different pore-size distribution for the texture where resonance is observed, calls for pore-scale processes and heterogeneous pore-pressure distribution among primary and secondary flow pathways.