Pore-pressure wave and diffusion induced by fluid-mass sources in partially saturated porous media

Abstract

The dynamic and quasi-static spatiotemporal responses of pore water induced by fluid-mass sources in unsaturated porous media are determined and compared. An explicit fundamental solution for pore water pressure is derived using the known Green's function of dynamic poroelasticity. Based on the order of the low-frequency approximations for the source impulsive time function, different physical regimes are identified, describing the transition from diffusion to wave propagation. The diffusive regime bears only two diffusions equivalent to diffusive slow P2 and P3 waves. Non-dispersion diffusion and dispersion diffusion regimes, where P1 waves and diffusions coexist, are present. The similarity and diversity of induced pore water pressures owing to diffusive slow waves and fast waves may depend on the fluid loading rate (e.g. fluid injection) in contrast to the critical frequencies of a partially saturated porous medium. The short-term fluctuation in the injection rate may create very similar slow diffusive P2 waves along with a fast-compressional P1 wave by low impulsive frequencies and various slow P2 modes with transmitted radiation to the P1 wave by the comparatively high impulsive frequencies in different regimes. The results indicate that the diffusion and wave processes may generate uniform dynamic and quasi-static responses in partially saturated media for hydraulic tests and induced microseismic analysis.