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engineering applications. For example, highly refined theoretical and numerical
models are available for industrial ultrasonics, telephonic voice filtering,
medical imaging, underwater sonar for submarine detection, sonic boom
analysis for aircraft signature minimization, and so on, several dealing with
complicated three-dimensional, short-wave interactions in anisotropic media.
By contrast, MWD mud pulse telemetry can be completely described by a
single partial differential equation, in particular, the classical wave equation for
long wave acoustics. This is the same equation used, in elementary calculus and
physics, to model simple organ pipe resonances and is subject of numerous
researches reaching back to the 1700s. Why few MWD designers use wave
equation models analytically, or experimentally, by means of wind tunnel
analogies implied by the identical forms of the underlying equations, is easily
answered: there are no physical analogies that have motivated scientists to even
consider models that bear any resemblance to high-data-rate MWD operation.
For instance, while it has been possible to model Darcy flows in reservoirs using
temperature analogies on flat plates or electrical properties in resistor networks,
such approaches have not been possible for the problem at hand.
1.2.3 MWD telemetry basics.
Why is mud pulse telemetry so difficult to model? In all industry
publications, signal propagation is studied as a piston-driven “high blockage”
system where the efficiency is large for positive pulsers and smaller for sirens.
The source is located at the very end of the telemetry channel (near the drillbit)
because the source-to-bit distance (tens of feet) is considered to be negligible
when compared to a typical wavelength (hundreds of feet).
For low frequencies, this assumption is justified. However, the
mathematical models developed cannot be used for high-data-rate evaluation,
even for the crudest estimates. In practice, a rapidly oscillating positive pulser
or rotating siren will create pressure disturbances as drilling mud passes through
it that are antisymmetric with respect to source position. For instance, as the
valve closes, high pressures are created at the upstream side, while low pressures
having identical magnitudes are found on the downstream side. The opposite
occurs when the pulser valve opens.
The literature describes only the upgoing signal. However, the equally
strong downgoing signal present at the now shorter wavelengths will “reflect at
the drillbit” (we will expand on this later) with or without a sign change - and
travel through the pulser to add to upgoing waves that are created later in time.
Thus, the effect is a “ghost signal” or “shadow” that haunts the intended upgoing
signal. But unlike a shadow that simply follows its owner, the use of “phase-
shift-keying” (PSK) introduces a certain random element that complicates signal
processing: depending on phase, the upgoing and downgoing signals can
constructively or destructively interfere. Modeling of such interactions is not
difficult in principle since the linearity of the governing equation permits simple
superposition methods. However, it is now important to model the source itself:
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