Full Wave Synthetic Acoustic Logs In Saturated Porous Media Part II: Simple Configuration

Abstract

The discrete wavenumber method is used to compute synthetic full waveform acoustic logs in an axisymmetric fluid-filled borehole surrounded by a porous medium. The two phase formation is modeled following Biot's theory. It is modified by the introduction of an unified definition of the coupling coefficients related to the pore shape in accordance with homogenization theory. Both permeable and impermeable borehole walls are considered. The study focuses on the permeabilty, source center frequency and radius effects on guided modes and especially the Stoneley wave for various types of formations and saturant fluids. Comparison is made with homogeneous elastic formations. Plots of the spectral energy density in the frequency axial wavenumber domain allow the recognition and identification of the different wave types. When the pores are occluded at the borehole wall, the wavefield behavior is nearly equivalent to that of an elastic formation (with body wave attenuation added). The Stoneley wave is only very slightly affected. When the fluid flow is free, the distortions are more important because of the relative motion between the two phases at the borehole wall. With increasing permeability, Stoneley wave absolute and relative energy decreases and is relegated to a narrower low frequency band. It is then associated with a phase velocity lower than the" tube" wave velocity in an elastic formation. Its dispersion increases, especially in the low frequency range. Its attenuation correspondingly increases, reinforced by an increase of the shear wave attenuation. Due to an apparent increase of the borehole radius, the low cut-off frequencies of the pseudo-Rayleigh modes are shifted toward lower frequencies. The P to guided wave amplitude ratio is enhanced. For a given permeability, porosity and pore geometry, these characteristics are enhanced when the saturant fluid mobility increases and/or when the borehole radius decreases.