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Acoustic logging while drilling (LWD), characterised by simultaneous drilling and logging, is widely used to obtain the elastic parameters of the formation around the borehole. Most published monopole acoustic LWD simulation waveforms are routinely presented as pressure. However, these pressure waveforms disagree with the voltage waveforms recorded in the experiments. Here, to find out the reason of the inconsistent of these two waveforms, both the piezoelectric effect of the transducer and the propagation of the acoustic wave are integrally calculated with the finite-element method, obtaining the voltage waveform as well as the mechanical waveforms. The quantitative comparisons between the mechanical waveforms and the voltage waveform show that the output voltage cannot represent the pressure signal, but a combination of multiple mechanical signals. Based on the piezoelectric equation and the structure of the piezoelectric transducer used in this paper, we formulate the output voltage in terms of the four mechanical quantities, i.e. the radial strain and axial stress of the transducer as well as the acoustic pressure and the radial displacement of the borehole fluid. Furthermore, the contributions of these four mechanical quantities to different wave groups are explored. Finally, the waveforms comparisons after drill collar grooving reveal that the displacement waveform before and after grooving should also be displayed when evaluating the grooving effect instead of only the pressure waveform as in previous studies.

The mechanical responses in monopole acoustic LWD and their relation with the output voltage waveform