Sonic logging in deviated wellbores in the presence of a drill collar

Abstract

Acquiring sonic logs while drilling is far more challenging than acquiring sonic logs from a wireline tool, notably because of the higher noise level in the drilling environment. The presence of a drill collar in the form of a thick steel pipe motivates a different tool design strategy. In addition, interference of drilling noise with the formation signal requires new processing and inversion algorithms for estimating the formation compressional and shear slownesses. Generally, all wireline sonic tools estimate the formation shear slowness by processing the borehole flexural arrival that is not severely affected by the tool structure. However, to mitigate interference between the drill collar and formation arrivals in the LWD (Logging-While-Drilling) environment, there has been a growing interest in inverting the borehole quadrupole dispersive arrival for the formation shear slowness. Inversion of quadrupole dispersion yields the same formation shear as that from a dipole shear logging tool in an isotropic and transversely-isotropic (TI) formation when the borehole axis is parallel to the TI-symmetry axis. Nevertheless, it is known that in anisotropic formations, we can have three different shear moduli in the three orthogonal planes. It is then necessary to understand which of the three shear moduli or some combination thereof, would be estimated from the inversion of quadrupole sonic data from a LWD tool in deviated boreholes in TI formations. A finite-difference time domain (FDTD) formulation with a perfectly-matched layer (PML) enables analysis of elastic wave propagation in a fluid-filled borehole in an arbitrarily anisotropic formation in the presence of a drill collar. Introduction of a perfectly-matched boundary layer minimizes reflections from the boundary with a limited grid volume. The FDTD formulation yields synthetic waveforms at an array of receivers produced by a monopole, dipole or quadrupole source placed on the borehole axis. Synthetic waveforms are then processed by a modified matrix pencil algorithm to isolate both non-dispersive and dispersive arrivals in the wavetrain. Computational results have been obtained for various modal arrivals generated by either a monopole, dipole, or quadrupole source placed in a fluid-filled borehole. While dipole flexural dispersions provide estimates of shear rigidity in the two orthogonal borehole axial planes, the monopole Stoneley dispersion can be inverted to estimate the shear rigidity in the borehole cross-sectional plane. In contrast, quadrupole waves simultaneously vibrate the formation in the two orthogonal axial planes. Therefore, inversion of low-frequency quadrupole dispersion based on an isotropic model yields a shear modulus that is some combination of the fast and slow shear moduli in the two orthogonal axial planes. © 2020 Elsevier B.V., All rights reserved.