Chapter 2Harmonic Analysis: Six-Segment Downhole Acoustic Waveguide

High-data-rate pulsers in continuous wave MWD telemetry not only create acoustic signals that propagate uphole, but in addition, down-going signals that “reflect at the drillbit,” reverse direction and combine with the former to create waves that may constructively or destructively interfere. The ultimate signal that travels up the drillpipe depends on mud sound speed, the position of the pulser in the drill collar and its operating frequency, and importantly, the details of the bottomhole assembly forming the host waveguide. The implications are both good and bad. Destructive interference in signal generation can severely limit data rate and transmission distance, but constructive wave interference, properly applied, can enhance MWD signal strength without the usual power and erosion penalties incurred by purely mechanical methods.

“Reflection at the bit,” a phenomenon noted above, actually is more complicated than simple acoustic “open” or “closed” models would have us believe. In reality, signals do propagate through nozzles that may be small, and signals are detectable in the annulus. Thus, a telemetry model used to study fundamental physics and potential technical capabilities must not disallow transmissions into the annulus; moreover, as explained in Chapter 1, it is additionally important to model the antisymmetric disturbance pressure field about the source, so that downhole constructive and destructive ...

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