The accuracy of velocity measurements made using a monopole acoustic logging-while-drilling (ALWD) measurement tool is influenced by the eccentering of the tool due to complex drill string movements. We have used the velocity of collar flexural mode (at the source frequency range) as a reference and classified the fast formations into (1) fast-fast (FF) formations with compressional velocity far larger than the collar flexural velocity and (2) slow-fast (SF) formations with compressional velocity approaching that of the collar flexural velocity. We use a 3D finite-difference method to simulate the response of an eccentered monopole ALWD tool with different eccentering magnitudes (offsets) for the two types of formations to facilitate better interpretation of velocity measurements made in an actual drilling environment. We find that the collar extensional mode, existing in the centralized and eccentered tool cases, only affects the formation P-wave measurement and can be eliminated by using an isolator. The collar flexural mode, which is a shear motion in the collar and can only be excited in a centralized tool by a dipole source, is also excited when a monopole tool is eccentered, and it significantly affects the measurement of the compressional velocity in the SF formation and that of the shear velocity in the FF formation, even for small eccentering offsets. Thus, the uncorrected monopole ALWD tool provides unreliable formation velocities (either the compressional or shear velocities) in fast formations because of the significant influence of the tool offsets on the measurement. To minimize the influence of tool offset on the measurements, we compared the differences between the waveforms collected for different azimuths and tool offsets and the centralized monopole waveforms.

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