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solved by most graduate engineers. But as we will demonstrate, this
simplification amounts to “throwing out the baby with the bath water.”
And why is this? Piston models are unable to deal with source properties:
they cannot distinguish between created pressures that are antisymmetric with
respect to source position and those that are symmetric. Thus they predict like
physics for both dipoles and monopoles. What's worse, the possibility that
upgoing waves can interact constructively with those that travel downward and
then reflect up cannot be addressed - this potential application is extremely
important to signal enhancement by constructive wave interference, which is
achievable by tailoring the telemetry scheme to take advantage of phase
properties associated with the mud sound speed and bottomhole assembly.
Moreover, the simple piston model precludes signal propagation up the
borehole annulus, which as discussed, has proven to be useful in gas influx
detection while drilling. When the complete waveguide - to include the annulus
and bit-box as essential elements - is treated as an integrated system, as will be
done in Chapter 2, it becomes clear that our simple description of the drillbit as a
solid or an open reflector - offered only for illustrative purposes - is too
simplified. By extending our formulation to allow pulsers to reside within the
drill collar and not simply at the drillbit, we will demonstrate a wealth of
physical phenomena and engineering advantages previously unknown.
The subject of surface signal processing and reflection cancellation is
similarly shrouded in mystery. An early patent for “dual transducer, differential
detection” draws analogies with electric circuit theories, however, using
methods with sinusoidal e i Zt dependencies. But why time periodicity is relevant
at all in systems employing randomly occurring phase shifts is never explained.
Rules-of-thumb related to quarter-wavelength interactions, appropriate only to
steady-state waves (which do not convey information) used in the patent, prevail
to this day for transient situations. They can't possibly work and they don't.
Just as troubling are more recent company patents on multiple transducer
surface signal processing which sound more like accounting recipes than
scientific algorithms, e.g., “subtract this, delay that, add to the shifted value,”
when, in fact, formal methods based on the wave equation (derived later in this
topic) yield more direct, rigorous and generalizable results. We take our cues
directly from wave-equation-based seismic processing where all propagation
details, including those related to source properties, are treated in their full
generality. With this approach, new multiple transducer position and multiple
time level reflection cancellation schemes can be inferred straightforwardly
from finite difference discretizations of a basic solution to the wave equation.
As if all of this were not bad enough, we take as our final example, the
infamous “case of the missing signal,” the mystery which had stymied many of
the best minds one too many times - a situation in which MWD tools of all
kinds refused to yield discernible standpipe pressures despite their near-perfect
mechanical condition. It turned out that, of all things, operators were using
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