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telescoping acoustic waveguides with internal area changes. For many
bottomhole assemblies, efficiencies approaching 3.0 have been calculated for
higher frequencies, although the attenuation effects will limit their usefulness.
These observations point to the importance of retaining drillbit nozzles (or
more correctly, the “bit box” or “bit sub”) as important conduits for wave
transmission modeling insofar as optimizing MWD signals in the drillpipe is
concerned. However, they also play an important role in signal production for
the annulus. There are two important applications. First, the ability to correlate
MWD signals in the annulus with those in the drillpipe (or lack of) is often taken
as an indicator of gas influx detection; this is an important safety measurement.
Second, the annular signal, which is inherently less noisy than the drillpipe
signal, can be used to improve drillpipe signal decoding, since it is not
contaminated as much by mudpump or desurger noise. Thus, in some
applications, one might aim at optimizing signals in both drillpipe and annulus
for the purpose of minimizing bit error, an objective that is not impossible. Not
only is the bit sub important - all impedance changes within the drillpipe and
drill collar system, as well as different annuli dimensions surrounding drillpipe
and drill collar, form important elements of the acoustic channel model. The
ratio of nozzle to total area, while dimensionless, is relevant only to hydraulic
studies related to viscous pressure loss and not to acoustic transmission directly.
2.2.5 Source modeling subtleties and errors
.
Proper source modeling is another area which is incorrectly addressed in
all published analyses. It is generally argued that the distance between the
MWD source and the drillbit reflector (located at the origin “x = 0”) is small
compared to a wavelength, so that the source can be modeled as a moving piston
located at x = 0. This seems reasonable, and if so, the analysis would apply to
all pulsers, whether their disturbance pressure fields are antisymmetric or
symmetric with respect to the source. However, the method completely ignores
the presence and sign of the downgoing wave discussed above. Thus, the effects
of destructive interference (disastrous from a well logging perspective) and
constructive interference (significant to signal enhancement without additional
power and erosion penalties) cannot be modeled. Whether method-of-
characteristics or finite difference approaches are used (to solve the plane wave
formulations usually given) is irrelevant. The “x = 0” piston model implicitly
assumes very, very low frequencies where downgoing wave effects are
extremely simple (this statement, in fact, will be seen from detailed calculations
using the more rigorous model valid for all frequencies to be derived later).
The correct theoretical approach requires us to more generally place the
source
within
the MWD drill collar away from the bit and not to introduce any
piston or solid reflector assumptions that would unrealistically preclude
important classes of reflected wave motions.
A priori
assumptions related to
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