Mud Acoustics in Modern Drilling - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 257

5
Mud Acoustics in Modern Drilling
From a propagation perspective, borehole mud acoustics is synonymous
with conventional (small amplitude) sound in air and underwater media: it is
nondispersive and linear. Thermodynamic loss mechanisms, while different, are
usually modeled after-the-fact using lumped exponential damping since they are
high-order effects, e.g., as in Chapter 2. Conventional applications utilizing
classical models involve area-modulated horns, transducer design, three-
dimensional concert halls, and other short wavelength phenomena, which will
not be discussed here. In this chapter, we specialize traditional modeling
concepts to modern drilling applications such as mud pulse telemetry and swab-
surge, problems where wavelengths are long compared to cross-sectional
dimensions. For instance, in a continuous MWD mud pulse telemetry system,
order-of-magnitude sound speeds and frequencies are 5,000 ft/s and 10 Hz. The
wave length = 5,000/10 = 500 ft greatly exceeds an average diameter taken as
1 ft. Ratios exceeding 500 are not uncommon, and these may, for example,
decrease to a still-large value of 50 in a hypothetical high-data-rate system.
While long wave acoustics represents a subset of classical theory, it would
be misleading to believe that it is simpler - in fact, it is quite the opposite. Very
often, the source of the disturbance field resides within the channel far from
system boundaries. Overall pressure fields, which are strongly affected by
reflections, must be characterized in terms of the monopole or dipole nature of
the source - that is, if created sound disturbances are antisymmetric or
symmetric with respect to source position. Then there are abrupt area or
impedance discontinuities, for example, at pipe-collar interfaces within the
drillstring and in the annulus, through bit boxes, past logging sensors or drill
motors, not unlike the telescoping waveguides used by telephone companies for
signal enhancement before modern advances in digital processing. Proper
treatment of the mathematics is critical to improving drilling efficiency. How
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