Stories from the Field,Fundamental Questions and Solutions - Measurement While Drilling Signal Analysis, Optimization and Design - page 4

The key revelation would come years later as I watched children play
“jump rope” in the park. A first child would hold one end of the rope, while a
second would shake the opposing end at a given frequency. Transverse waves
on a rope are easy to visualize, but the ideas apply equally to longitudinal waves.
The main idea is this. At any given frequency, a standing wave system with
nodes and antinodes is created that depends on material properties. If the
frequency changes, the nodal pattern changes and moves. If one fixes his
attention at one specific location, the peak-to-peak displacement appears to
come and go. Node and anti-node positions move: what may be interpreted as
attenuation may in fact be amplitude reduction due to destructive wave
interference - a temporary effect that is not thermodynamically irreversible loss.
This was exactly the situation in the 10,000 feet LSU flow loop. At one
end is a mudpump whose pistons act like solid reflectors, assuming tight pump
seals, while at the opposite end, a reservoir serves as an open-end acoustic
reflector. Pressure transducers were located at fixed positions along the length
of the acoustic path. Unlike the jump-rope analogy, the MWD pulser was
situated a distance from one of the ends, adding some complexity to the wave
field since waves with antisymmetric pressures traveled in both directions from
the source. The exact details are unimportant for now. However, the main idea
drawn from the jump rope analogy applies: increasing frequency simply changes
the standing wave pattern and we (and others) were measuring nothing more
than expected movements nodes and antinodes. Attenuation results were buried
in the mass of resulting data. This is easy to understand in hindsight. Recent
calculations, in fact, show that large attenuation is impossible over the length of
the flow loop for the mud systems used.
One crucial difference was suggested above. Whereas, in our jump rope
example, excitations originated at the very end of the waveguide (i.e., “at the
bit”), the excitations in the LSU flow loop occurred within the acoustic path,
introducing subtleties. For example, when a positive pulser or a mud siren
closes, a high-pressure signal is created upstream while a low-pressure signal is
formed downstream, with both signals propagating away from the valve; the
opposite occurs on closure. These long waves travel to the ends of the acoustic
channel, reflect accordingly as the end is a solid or open, and travel back and
forth through the valve (which never completely closes) to set up a standing
wave patterns whose properties depend on mud, length and source.
Had our pulser created disturbance pressure fields that were symmetric
with respect to source position, as opposed to being antisymmetric - that is, had
we tested a “negative pulser,” our results and conclusions would have been
completely different. Any theory of wave propagation applicable to MWD
telemetry had to accommodate end boundary conditions, acoustic impedance
matching conditions at area (pipe and collar junctions) or material
discontinuities (rubber interfaces in mud motors), and importantly, signal source
“dipole” or “monopole” properties. Fortunately, such a general theory is now