Geology Reference
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inexpensive centrifugal (as opposed to positive displacement) pumps. This
illustration offers the strongest, most compelling evidence supporting the wave
nature underlying MWD signals. Pistons on positive displacement mud pumps
function as solid reflectors, which double the upgoing signal at the piston face;
centrifugal pumps with open ends, to the contrary, enforce “zero acoustic
pressure” constraints which destroy signals. An understanding of basic
acoustics would have reduced frustration levels greatly and saved significantly
on time and money.
Despite the problems raised, there are reasons for optimism in terms of
understanding the physics and modeling it precisely. At high data rates, acoustic
wavelengths O are short but not too short. For example, from O = c/f where c is
mud sound speed and f is excitation frequency in Hertz, a siren in a 3,000-5,000
ft/sec - 12 Hz environment would have a O of about 300-500 ft. At 100 Hz, the
wavelength reduces to 30-50 ft, which still greatly exceeds a typical drillpipe
diameter. It is “long” acoustically. Thus, one-dimensionality applies to
downhole signal generation and three-dimensional complications do not arise.
More importantly, the waves are still long even in wind tunnels. Hence, signal
creation and acoustic-hydraulic interactions at the pulser can be studied
experimentally in convenient laboratory environments.
For those who have forgotten, one-dimensional acoustics is taught in high
school and amply illustrated with organ pipe examples. Classical mathematics
topics give the general solution “f(x + ct) + g(x - ct)” showing that any solution
is the sum of left and right-going waves; topics on sound discuss impedance
mismatches and conservation laws applicable at such junctions. Basic
frequency-dependent attenuation laws have been available for over a hundred
years. In this sense, the field is well developed. But in other respects the field
offers fertile ground for nurturing new and practically useful ideas.
These new ideas include, for example, (1) formal derivations for receiver
array reflection and noise cancellation based on the wave equation, (2) model
development for elastic distortions of MWD signal at desurgers, (3) constructive
and destructive wave interference in waveguides with multiple telescoping
sections, (4) downhole signal optimization by constructive wave interference,
(5) reflection deconvolution of multiple echoes created within the downhole
MWD drill collar, and so on. All of these topics are addressed in this topic. In
fact, forward models are developed which create transient pressure signals when
complicated waveguide geometries and telemetering schemes are specified, and
complementary inverse models are constructed that extract position-encoded
signals from massively reverberant fields under high-data-rate conditions, with
mathematical consistency between the two demonstrated in numerous examples.
While innovative use of physical principles is emphasized for downhole
telemetry design and signal processing, testing and evaluation of hardware and
tool concepts are equally important, but often viewed as extremely time-
consuming, labor-intensive and, simply, expensive. This need not be - and is
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