Fast and slow flexural waves in a deviated borehole in homogeneous and layered anisotropic formations

Abstract

S U M M A R YDipole acoustic fields in an arbitrarily deviated well penetrating a homogeneous as well as a stratified transversely isotropic formation are simulated using a 3-D finite-difference timedomain algorithm in cylindrical coordinates. The modelling results show that a dipole source can excite a fast-and a slow-flexural mode due to the shear wave anisotropy when the borehole is inclined with respect to the symmetry axis of transverse isotropy. Both flexural slownesses change with the wellbore deviation angle. The splitting of flexural modes is prominent in full wave arrays when the shear anisotropy is strong enough. It is revealed that the dipole orientation influences the relative amplitudes of the fast-and slow-flexural waves but it has no effect on their slownesses or phases. In a vertical well parallel to the symmetry axis, the two flexural waves degenerate and propagate at the same speed. The degenerated flexural wave travels approximately at the shear speed along the borehole wall except in a few formations. Our study shows, for example, that it is about 10 per cent slower than the shear wave in Mesaverde clayshale 5501. Even in that kind of formations, however, extraction of the fastand slow-shear velocities from the flexural modes is still possible if the borehole deviation is large enough. To examine the effect of layering, we modelled the full waves in a formation with a sandwich. When the well is perpendicular to the layer interfaces, reflection is obvious and can be recognized. It becomes weaker or even invisible as the deviation angle increases, so it is difficult to detect a thin layer embedded in a formation directly from reflected waves. The sandwich can, instead, be recognized from the irregularity in the spectra of the full waveforms displayed versus depth.

3d Finite Difference Simulations of Acoustic Logs in Tilted Layered Porous Formations

“…4(a) as the cylindrical wave obliquely propagates through the layer interface. Similar phenomenon can also be observed when the source transmitter is a dipole, as in the work by He et al 6 To further reveal the influence of the layer inclination on borehole wave fields, we compare the synthetic full waves at the upper layers with β = 30 • , 45 • , and 60 • . During the inclination β varying from 30 • to 60 • , it is evident that the S wave group arrivals earlier and …”

“…Lin et al 5 presented the comparison of the apparent slowness of head waves with various layer inclinations with respect to the borehole axis based on the FDTD modeling results. He et al 6 numerically simulated dipole acoustic logs in an anisotropic formation with an interlayer, and discussed the influence of layer thickness on the borehole acoustic response.…”

Azimuthal cement evaluation with an acoustic phased-arc array transmitter: numerical simulations and field tests

“…The partial differential equations are substituted by differential schemes after discretization. The elastic equations, stiffness coeffi cients, densities and the splitting perfectly matched layer (PML) are referred to former studies (Che and Qiao, 2009;He and Hu, 2009;He et al, 2010).…”

A numerical investigation of the acoustic mode waves in a deviated borehole penetrating a transversely isotropic formation

“…A finite difference time domain (FDTD) method is widely used to study this problem by computing the waveforms [11][12][13][14][15][16][17]. Dispersion curves can be obtained from the results in time domain [18][19].…”