Harmonic Analysis: Six-Segment Downhole Acoustic Waveguide - Measurement While Drilling Signal Analysis, Optimization and Design - page 59

Figure 2.4 . Positive and mud siren pulsers in various telemetry channels.
2.3.1 Three distinct physical problems .
So far we have refrained from discussing wave propagation through the
entire drillpipe length itself and also the complicated problems associated with
reflections at the surface. We now address these issues and explain why these
problems can, at least from a modeling perspective, be considered separately.
For the downhole problem in Figure 2.4a, the typical length scale in the axial
direction is about 200 feet, that is, the distance from the drillbit to the top of the
highest collar. Over this distance, the effects of attenuation (meaning
irreversible thermodynamic loss) are unimportant and can be neglected. This is
not to say that zeros in pressure are not found; they are, but they are related to
reversible wave cancellations. With this simplification, the problem for Figure
2.4a can be solved analytically, using algebraic manipulation software or
numerical matrix solvers, as we will demonstrate later in this chapter.
What the drillpipe “sees” from afar is not the complicated interactions
implicit in Figure 2.4a, but only the net pressure wave p pipe /'p that ultimately
leaves the MWD collar - in this sense, the drillpipe problem, primarily one for
simple attenuation, is a separate one from that in the foregoing paragraph. In
Figure 2.4a, drilling mud is shown moving downward; it interacts with an
oscillating positive pulser or rotating mud siren to create signals of strength 'p
which depend on flow rate, valve geometry, sound speed “c,” rotation and so on.