Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 98

We will also continue our investigation of downhole signal generation,
studying the interaction between the wave traveling directly uphole from the
source and that propagating down toward the drillbit and then reflecting upward.
The transmitted signal, i.e., the sequence of 0's and 1's that is a consequence of
the 'p(t) pressure differential created by the position-encoded MWD pulser that
travels up the drillpipe, however, is not 'p(t). Instead, it is the cumulative
“confused” signal consisting of up and downgoing waves noted. For downhole
problems, our objective is the recovery of the 'p(t) signal from the “confused”
signal waveform entering the drillpipe - this signal is really complicated
because a completely transient signal not restricted to sinusoidal motions is now
permitted in our analysis. We term this the “downhole inverse problem.”
For the downhole inverse problem in this chapter, the telemetry channel is
assumed to be constant in area and is terminated at the “left” drillbit end -
differences in MWD collar and drillpipe area are ignored. This assumption is
not unrealistic: the MWD drill collar in practice contains a central hub (say,
three inches in diameter) to which mechanical siren, turbine and alternator
components are attached, and the resulting mismatch in collar and drillpipe
cross-sectional area is often small (refer to Figure 5.0 in Chapter 5 and its
discussion). If it isn't, it should be - area mismatches result in inefficient
acoustic reverberations that additionally “scramble” the 'p(t) wave into
unrecognizable upgoing pressure waveforms that are difficult to deconvolve.
This constant area model is introduced for simplicity only: the downhole inverse
problem allowing large general changes in cross-sectional area is studied in
detail in Chapter 5. The methods in this chapter are listed below. The
particular source code used appears within the individual write-ups.
.
Contents
x Method 4-1 . Upgoing wave reflection at solid boundary, single transducer
deconvolution using delay equation, no mud pump noise.
x Method 4-2 . Upgoing wave reflection at solid boundary, single transducer
deconvolution using delay equation, with mud pump noise.
x Method 4-3 . Directional filtering - difference equation method (two
transducers required).
x Method 4-4 . Directional filtering - differential equation method (two or
more transducers required).
x Method 4-5 . Downhole reflection and deconvolution at the bit, waves
created by MWD dipole source, bit assumed as perfect solid reflector (very,
very small drillbit nozzles).
x Method 4-6 . Downhole reflection and deconvolution at the bit, waves
created by MWD dipole source, bit assumed as perfect open-end, that is,
zero acoustic pressure reflector (typical nozzle sizes).