A hydrologic view on Biot's theory of poroelasticity

摘要

The main objective of this work is to obtain a simplified asymptotic representation of the reflection of seismic signal from a fluid-saturated porous medium in the low-frequency domain. In the first part, we derive the equations of low-frequency harmonic waves in a fluid-saturated elastic porous medium from the basic concepts of filtration theory. We demonstrate that the obtained equations can be related to the poroelasticity model of Frenkel-Gassmann-Biot, and to pressure diffusion model routinely used in well test analysis as well. We thus try to put the poroelastic and filtration theories on the same ground. We study the reflection of a low-frequency signal from a plane interface between elastic and elastic fluid-saturated porous media. We obtain an asymptotic scaling of the frequency-dependent component of the reflection coefficient with respect to a dimensionless parameter depending on the frequency of the signal and the reservoir fluid mobility. We also investigate the impact of the relaxation time and tortuosity on this scaling.