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Single-well acoustic imaging in logging-while-drilling (LWD) has important application potential in evaluating cluster-well drilling safety as it can be applied to the real-time detection of an existing cased borehole from a new well during drilling. Forward modelling can help us understand the mechanism of elastic-wave radiation, scattering and reception. In this work, we investigate the characteristics of acoustic wavefields associated with LWD in an unconsolidated formation. We use the time-domain finite difference (FDTD) method to simulate the wavefields corresponding to a ring dipole source. The modeling results reveal the existence of a new Mach wave apart from the conventional P- and S-waves. The Mach waves are secondary waves resulting from the constructive interference of the collar waves. Such wave is often overlooked in the previous studies of single-well acoustic imaging in LWD. We found that not only P- and S-waves but also the Mach waves could be scattered by the nearby cased borehole and propagate back to the original borehole. The simulations indicate that both the scattered P-waves and the scattered Mach S-waves exhibit strong amplitudes. This study provides a theoretical foundation for the borehole detection by LWD single-well acoustic imaging technique in unconsolidated formations.

Elastic-Wave Radiation, Scattering, and Reception of a Dipole Acoustic Logging-While-Drilling Source in Unconsolidated Formations