Harmonic Analysis: Six-Segment Downhole Acoustic Waveguide - Measurement While Drilling Signal Analysis, Optimization and Design - page 51

uniform pipe is exactly 0.5. We also emphasize that 'p is an “acoustic delta-p”
and not the pressure drop associated with viscous pressure losses in the wake of
a blunt body. For example, a nearly-closed stationary poppet valve is associated
with high pressure losses, but these do not propagate and therefore cannot be
used to create traveling sound waves. While viscous pressure drops may be
important insofar as mudpump power requirements or tool losses are concerned,
they are irrelevant to high data rate MWD signal generation.
When a mud siren closes, the upstream flow slows significantly and the
associated over-pressure travels uphole; at the same time, fluid pulls away at its
downstream side and an under-pressure travels downhole. The reverse occurs
when the siren opens. This, of course, applies whether the siren rotor rotates
about its axis or simply oscillates back-and-forth. This physical description
from the acoustical perspective is identical to that provided above for rapidly
reciprocating positive pulsers, that is, both pulser classes are associated with
pressure disturbances that are antisymmetric with respect to source position.
Both sirens and positive pulsers represent realizations of dipole tools. In this
wave propagation sense, positive pulsers and mud sirens function identically
although there are obvious mechanical and practical design differences. As
before, the siren signal can also be characterized by a “source strength” we shall
term “'p.” In general, the 'p for a positive pulser or a siren valve will depend
on geometry, the size of the drill collar, flow rate, mud sound speed and
reciprocation or rotation; it can be determined independently in a flow loop, or
in a wind tunnel, if measured results are properly rescaled. We importantly
emphasize that 'p may be frequency dependent - with all parameters fixed, it
may increase or decrease with frequency depending on mechanical design.
Negative pulsers function differently. When the drill collar orifice opens,
an under-pressure is locally created, but this under-pressure propagates both
uphole and downhole; likewise, when the valve closes, a local over-pressure is
created that propagates both uphole and downhole. The pressure difference, if
measured at identical distances upstream and downstream of the orifice,
identically vanishes because the disturbance pressure field is symmetric with
respect to source position. Negative pulsers therefore represent “monopole”
tools. For historical reasons, we will continue to refer to such pulsers as
negative pulsers. It is clear that a non-zero 'p is not necessary for negative
pulser operation and, in fact, is never achieved because 'p is always zero (for
such pulsers, it is “delta velocity” that is important). As with positive pulsers
and sirens, the source strength associated with a negative pulser depends on the
acoustic “water hammer” component of the valve motion and not the pressure
drop due to viscous losses across the drill collar wall. The pressure symmetries
and antisymmetries noted for different pulser types are not speculative and have
been observed and recorded in detailed wind tunnel and mud flow loop studies.