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turbine may block the signal.” However, this concern is unfounded and
disproved in all field experiments. This is obvious in retrospect. The “see
through area” for turbines is about 50% of the cross-section. If signals can pass
through siren rotor-stator combinations with much lower percentages, as they
have time and again, they will have little difficulty with turbines.
1.2.5 New technology elements.
The above discussion introduces the physical ideas that guided our
research. An early prototype single-siren tool designed for downhole testing is
shown assembled and disassembled in Figures 1.1a and 1.1b. Multiple siren
tools have been evaluated. To further refine our approach and understanding of
the scientific issues, math models and test facilities were developed to fine-tune
engineering details and to obtain “numbers” for actual design hardware and
software. We now summarize the technology.
1.2.5.1 Downhole source and signal optimization.
As a focal point for discussion, consider the hypothetical MWD drill collar
shown in Figure 1.2a. Here, physical dimensions are fixed while siren
frequency and position are flexible. Up and downgoing signals (with
antisymmetric pressures about the source) will propagate away from the pulser,
reflect at the pipe-collar intersection, not to mention the interactions that involve
complicated wave transfer through the drillbit and in the borehole annulus.
A six-segment acoustic waveguide math model was formulated and solved,
with the following flow elements: drillpipe (satisfying radiation conditions),
MWD drill collar, mud motor or other logging sub, bit box, annulus about the
drill collar, and finally, annulus about the drillpipe (also satisfying radiation
conditions). The “mud motor” in Figure 1.2a could well represent a resistivity-
at-bit sub. At locations with internal impedance changes, continuity of pressure
and mass was invoked. The siren source was modeled as a point dipole using a
displacement formulation so that created pressures are antisymmetric.
Numerical methods introduce artificial viscosities with unrealistic attenuation
and also strong phase errors to traveling waves. Thus, the coupled complex
wave equations for all six sections were solved analytically, that is, exactly in
closed form, to provide uncompromised results.
Calculated results were interesting. Figure 1.2b displays the actual signal
that travels up the drillpipe (after all complicated waveguide interferences are
accounted for) as functions of transmission frequency and source position from
the bottom. Here, “'p” represents the true signal strength due to siren flow, i.e.,
the differential pressure we later measure in the short wind tunnel. For low
frequencies less than 2 Hz, the red zones indicate that optimal wave amplitudes
are always found whatever the source location. But at the 12 Hz used in present
siren designs, source positioning is crucial: the wrong location can mean poor
signal generation and, as can be seen, even “good locations” are bad.
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