Energy partitioning and attenuation of guided waves in a radially layered borehole

Abstract

Recently published results (Tubman et al., 1984; Baker,. 1984) indicate that synthetic full waveform acoustic logs generated in cased or damaged boreholes differ significantly from those generated in an open hole with the same formation parameters. In particular, the guided waves appear to be the most affected by such radial layering. In order to gain some understanding of these effects, the amplitude response and energy distribution of the pseudo-Rayleigh and Stoneley waves are studied for the cased and invaded borehole models. The expressions derived by Cheng et al. (1 982) are used to calculate partition coefficients (partial derivatives of phase velocity with respect to body wave velocities) for the guided wave modes. The attenuation of the guided wave can then be represented by the sum of the layer attenuation values weighted by their respective partition coefficients. The results indicate that the attenuation of the Stoneley wave is dominated by the fluid attenuation at all frequencies in fast formations, both in the open hole geometry and in the presence of casing or invaded zones. In a slow formation, the Stoneley wave attenuation becomes more sensitive to the shear wave attenuation of the formation at higher frequencies in both the open and cased hole situations. For the pseudoRayleigh wave, the introduction of casing reduces the effect of the fluid attenuation, while the presence of an invaded zone reduces the effect of the formation shear attenuation. Plots of the partition coefficients indicate that the casing and invasion layers are most important over a limited frequency range which is related to the thickness of the layer. Radial displacement curves illustrate the depth of penetration of the various frequency components of the pseudo-Rayleigh wave. INTROpUCTION Recent interest in the field acquisition of Full Waveform Acoustic Logs (FWALs) has resulted in many studies of wave propagation in a cylindrical borehole (Cheng and Toksaz, 1981; Tsang and Rader, 1979; Paillet and White, 1982). The majority of these addressed the simple case of a homogeneous, Isotropic, infinite solid surrounding a fluid filled cylindrical borehole. Several recent papers (Tubman et aI., 1984; Baker, 1984; Chan and Tsang, 1983; Shoenberg et al., 1981) have addressed the more complex problem of solid radial layers surrounding a fluid filled borehole. The common occurrence of drilling induced formation damage or the presence of steel casing and associated cement justify the need to treat this more complicated geometry. The results of Tubman et al. (1984) indicate that synthetic FWALs generated in cased or damaged boreholes can differ significantly from those 57