Similarities and differences in inherent mechanism and characteristic frequency between the one-dimensional poroelastic model and the layered White model

Abstract

The similarities and differences in inherent mechanism and characteristic frequency between the one-dimensional (1D) poroelastic model and the layered White model were investigated. This investigation was conducted under the assumption that the rock was homogenous and isotropic at the mesoscopic scale. For the inherent mechanism, both models resulted from quasi-static flow in a slow P-wave diffusion mode, and the differences between them originated from saturated fluids and boundary conditions. On the other hand, for the characteristic frequencies of the models, the characteristic frequency of the 1D poroelastic model was first modified because the elastic constant and formula for calculating it were misused and then compared to that of the layered White model. Both of them moved towards higher frequencies with increasing permeability and decreasing viscosity and diffusion length. The differences between them were due to the diffusion length. The diffusion length for the 1D poroelastic model was determined by the sample length, whereas that for the layered White model was determined by the length of the representative elementary volume (REV). Subsequently, a numerical example was presented to demonstrate the similarities and differences between the models. Finally, published experimental data were interpreted using the 1D poroelastic model combined with the Cole-Cole model. The prediction of the combined model was in good agreement with the experimental data, thereby validating the effectiveness of the 1D poroelastic model. Furthermore, the modified characteristic frequency in our study was much closer to the experimental data than the previous prediction, validating the effectiveness of our modification of the characteristic frequency of the 1D poroelastic model. The investigation provided insight into the internal relationship between wave-induced fluid flow (WIFF) models at macroscopic and mesoscopic scales and can aid in a better understanding of the elastic modulus dispersion and attenuation caused by the WIFF at different scales.