Dipole dispersion crossover and sonic logs in a limestone reservoir

Abstract

Analyses of sonic logs in a horizontal well provide new information about mechanical properties of rocks, made possible by recent developments in our understanding of acoustic wave propagation in prestressed formations. Most sections of this horizontal well exhibit azimuthal shear isotropy, indicating isotropic stresses in the plane perpendicular to the well trajectory, leading to stable wellbore conditions. However, two sections show dipole dispersion crossovers that confirm the presence of stress‐induced shear anisotropy caused by a difference between the maximum and minimum stresses in the plane perpendicular to the well trajectory. The two dipole dispersions are obtained by processing the recorded waveforms by a modified matrix pencil algorithm. The fast‐shear direction is estimated from Alford rotation of the cross‐dipole waveforms. One section of the well exhibits the fast‐shear direction parallel to the overburden stress as the maximum stress direction, whereas the other section has the fast‐shear direction parallel to the horizontal stress that is larger than the overburden stress. The cause of this change in the fast‐shear direction is believed to be the well’s penetration into a 3-ft-thick bed with lower porosity and permeability and significantly higher elastic stiffnesses than those in the other part of the homogeneous, high‐permeability reservoir. A stiff bed is likely to have greater stresses in its plane than perpendicular to it, which would make the horizontal stresses greater than the vertical.

Investigation of borehole cross-dipole flexural dispersion crossover through numerical modeling

“…Boreholes drilled in the earth are often noncircular. Sinha et al (2000) find that the commonly encountered borehole ellipticity is around 1.25 in a limestone reservoir. Our modeling results indicate that a borehole ellipticity of 1.1 is large enough to separate the flexural dispersion curves at high frequencies, so the effect of borehole ellipticity is as important as stress-induced and intrinsic anisotropies.…”

“…Sinha and Kostek (1996) find that formation anisotropic stresses cause radially varying heterogeneities in acoustic-wave velocities that vary with azimuth relative to the two principal stresses perpendicular to the wellbore and can result in a crossover in cross-dipole flexural dispersion curves, in which the azimuthal orientations of fast and slow waves differ between low and high frequencies. This flexural dispersion crossover has long been taken to be an indicator of borehole stress-induced anisotropy because the crossover cannot occur for a circular borehole located in a homogeneous anisotropic formation (Sinha and Kostek, 1996;Sinha et al, 2000). Sinha (2001), Sinha and Liu (2002; and Liu and Sinha (2003) study the influence of small uniaxial and triaxial stresses on the flexural dispersion and confirm the existence of flexural dispersion crossover caused by borehole stress alteration.…”

“…Figure 3. Decomposition of actual stresses (S H , S h , and S V ) into a confining stress S V and biaxial deviatoric stresses S H − S V and S h − S V in the borehole cross-sectional plane (modified from Sinha et al, 2000). microcracks and making the deviatoric stresses less efficient in producing stress-induced anisotropy around a borehole.…”

“…We assume that the wellbore is permeable and the borehole fluid pressure is equal to pore pressure, so we only consider effective stress in our study. Following Sinha et al (2000), we decompose the stress field into a reference confining stress S V and deviatoric stresses S H − S V and S h − S V , as shown in Figure 3, to analyze the effect of in situ stresses on borehole sonic wave propagation. When S H ¼ S h ¼ S V , the terms containing cos 2θ or sin 2θ in equation 1 vanish and the stress tensor in equation 1 represents the stress state under hydrostatic compression.…”

Acoustoelastic effects of Stoneley waves in a borehole surrounded by a transversely isotropic elastic solid

“…1,2 An alternative approach that has been successfully applied to the estimation of stress is based on the acoustoelastic theory. 6,[9][10][11][12][13][14] The acoustoelastic effect, i.e., the velocity change of the acoustic waves in the presence of stresses, has been investigated for more than about sixty years. 15 The acoustoelastic effect is not new to rock physicists, having already been applied in various contexts such as underground mines, 16 laboratory experiments, [17][18][19][20] and boreholes.…”