In acoustic logging-while-drilling measurement (ALWD) operations, complex drill string movements and the weight of drill pipe often lead to a measurements being made by an eccentered tool, which inevitably affects the accuracy of velocity measurements. We use a finite difference method (FDM) to simulate the response of an eccentered monopole ALWD tool with different eccentering magnitudes (offsets) in fast formations to facilitate better interpretation of velocity measurements made in an actual drilling environment. We find that the collar extensional and flexural modes are excited when the monopole tool is eccentered. The extensional mode, existing in both centralized and eccentered tool cases, only affects the P wave measurement and can be eliminated by using an isolator. We use the velocity of collar flexural mode as a reference and propose a method to classify fast formations into (1) fast-fast (FF) formations with P velocity far larger than the collar flexural velocity and (2) slow-fast (SF) formations with P velocity approaching the collar flexural velocity. The collar flexural mode significantly affects the measurement of P velocity in the SF formation and S velocity in the FF formation even for a small eccentering offsets. The monopole ALWD tool cannot get accurate formation velocities (either the P velocity or S velocity) in fast formations because the significant influence of the tool offsets on the measurement.
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