Logging in Multilayered Saturated Porous Formations

Abstract

We present a general formulation based on the Thomson-Haskell method which allows the study of complex models. The surrounding formation may be composed of several coaxial porous shells or of a combination of both porous and elastic layers. At any kind of interface, welded contact is assumed. The two phase media are modeled following Biot's theory which is modified through a unified definition of frequency dependent coupling coefficients in accordance with homogenization theory. Calculations of dispersion and attenuation of both the Stoneley wave and first pseudo-Rayleigh mode are performed. Also displayed are synthetic microseismograms computed using the discrete wavenumber method.

The configuration of a damaged (invaded or flushed) zone resulting from radial variation of permeability and/or porosity, with or without modification of the saturant fluid is investigated. When the borehole wall is impermeable, the effects of a porous radial layering are analogous to those observed in the presence of only elastic media, with body wave attenuations added, whatever the formation (fast or slow). When the borehole is permeable, as soon as the inner layer thickness reaches a few centimeters, Stoneley wave dispersion and attenuation are representative of the rheological properties of that inner layer. As a result, the determination of the in situ permeability of the virgin formation, based on Stoneley wave characteristics, is ill posed.

Also studied is the presence of a mudcake at the borehole wall. Whatever its rheological properties, this additional layer leads to a decrease of Stoneley wave phase velocity compared to the sealed pores situation. Compared to the simple open hole model with a permeable borehole wall, the same effect can be noted but only for frequencies greater than≃ 2 kHz, and a significantly thick mudcake. With any elastic or low permeability mudcake, with the absence or inefficient pressure continuity between the bore and saturant fluids, one cannot generate the variations of attenuations displayed by real data. Further investigations will need experimental measurements of the mudcake properties.

Whatever the configuration, the phase velocity and attenuation of the first pseudo-Rayleigh mode starts at those of the virgin formation. The low frequency part of the pseudo-Rayleigh wavetrain can then be used for the indirect estimation of the formation shear wave characteristics.