Abstract

Modelling seismic wave propagation in poroelastic media is based on macroscopic equations, such as proposed by Biot. It is clear, however, that some microstructural information must enter into the computation of the macroscopic parameters. One example is the flow permeability in Biot's theory. Though it is a macroscopic quantity, it is commonplace to find permeability estimates using microstructural descriptors. From a wave-propagation point of view, there is also a temporal upscaling involved. If the wave frequency is high enough, then the flow permeability will lose its meaning. This phenomenon is often captured by postulating a generalized Darcy law with a frequency-dependent (so-called dynamic) permeability. Within the viscosity-extended Biot framework, the dynamic permeability can be modelled as conversion scattering process from the Biot slow compressional wave into the slow shear wave. The latter accounts for viscous dissipation through vorticity diffusion in the fluid phase. This stochastic dynamic permeability model accounts for pore-scale heterogeneity through the two-point correlation function. Using digitized images of a limestone sample, we extract the correlation function and predict the dynamic permeability.

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