Effects of radial layering when logging in saturated porous formations

Abstract

In a fluid-filled borehole embedded in a radially semi-infinite saturated porous formation with a permeable borehole wall, numerical simulations have shown that the Stoneley wave dispersion and attenuation are sensitive to the in situ permeability. In this article, the configuration of a damaged (invaded or flushed) zone resulting from a general formulation, based on the Thomson–Haskell method, is used to propagate the wave field through several saturated porous layers. The two phase media are modeled following a modified Biot’s theory. Whatever the boundary conditions at the borehole wall, the Stoneley wave integrates the properties of the inner layer in the entire frequency range. With a permeable borehole wall, the Stoneley wave dispersion and attenuation are mainly representative of the rheological properties of the first layer. Such a coupling increases with increasing thickness and/or decreasing velocities, porosity, and saturant fluid mobility of the inner layer. Of course, it also increases with increasing frequency. As a result, the estimation of the in situ permeability of the virgin formation, based on the Stoneley wave characteristics, is ill-posed. Whatever the configuration, the phase velocity and attenuation of the first pseudo-Rayleigh mode start at those of the virgin formation. The low-frequency (high-velocity) part of the pseudo-Rayleigh wavetrain can then be used for the indirect estimation of the virgin formation shear wave characteristics. Higher in frequency, the inner shell becomes the controlling layer. Full wave synthetic microseismograms illustrate these behaviors in the time domain.