An analysis for unipole acoustic logging while drilling wavefields with varying eccentered collar positions

Abstract

Abstract The unipole logging while drilling (LWD) tool is a recently developed acoustic logging tool that uses an azimuthal emitting source to generate acoustic waves in the borehole to measure the longitudinal and transverse wave speeds of the surrounding stratum. In this study, the unipole transmitter transducer is modeled as a surface force source, and the analytical solution for unipole LWD wavefield is derived. The received waveforms are composed of infinite-order contributions owing to the directivity of the excitation of the unipole source. Using up to eight lowest-order modes, the acoustic waveforms excited by the unipole are calculated in both soft and hard formations, and then slowness-time coherence and velocity dispersion analysis are performed. The pure mode waves are obtained using the mode wave decomposition method. The influence of tool eccentricity (off-center positioning) on the wavefields excited by the unipole transmitter is also discussed. Based on the addition theorem of the Bessel function, the analytical solution of the received waveforms when the tool is eccentered can be obtained. In soft and hard formations, the received waveforms with tool eccentricities of 0 to 90% are compared. Tool eccentricity has a smaller effect for the soft formation than the hard formation. The received waveforms on the side closest to the borehole wall are also affected most when the tool is off center, with a sharp increase in amplitude in the fast formation and a late arrival wave group in the soft formation. These conclusions are important for the design and data interpretation of a unipole LWD tool.