Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 126

4.5 Method 4-5. Downhole reflection and deconvolution at
the bit, waves created by MWD dipole source, bit assumed as
perfect solid reflector (software reference, DELTAP*.FOR) .
In Methods 4-1 to 4-4, our objective was to recover all signals (good and
bad) originating from downhole. This was accomplished successfully by
removing surface reflections and pump generated noise. However, we now re-
emphasize that the upgoing MWD signal itself is not “clean,” but contains
“ghost reflections.” By ghost reflections, we refer to the downhole signal
generation process. When a signal is created at the pulser that travels uphole, a
pressure signal of opposite sign travels downhole, reflects at the drillbit, and
then propagates upward to interfere with new upgoing signals. Thus, at the
surface, the signal arriving first is the intended one, which is followed by a ghost
signal or shadow.
For the purposes of evaluating Methods 4-1 to 4-4, it was acceptable to
focus on recovering everything originating from downhole. But once surface
reflections at the pump and desurger, and mudpump generated noise, are
removed, we must not forget that the recovered signal itself contains ghost
echoes from downhole which must be eliminated through further processing. At
high data rates, the signals arriving from downhole are never ideal and will
always contain the intended signal plus ghost reflections. At low frequencies of
0-1 bit/sec, the effects of ghost reflections can be very constructive or very
destructive depending on the way the drillbit reflects and on the degree of collar-
pipe area mismatch. Methods 4-1 to 4-4 will always yield the combined
“intended plus ghost” signal. Once this is extracted from standpipe processing,
the “intended” and “ghost” components must be separated. In Methods 4-5 and
4-6, we accomplish this objective, assuming a straight telemetry channel without
area changes; the former assumes that the drillbit is a solid reflector while the
latter assumes an acoustic open-end. Area discontinuity restrictions are
completely removed in Chapter 5 to provide very powerful deconvolution tools.
4.5.1 Software note.
The net upgoing pressure signal (designated below by “p 2 L,t”)
originating from downhole is assumed to be known from Methods 4-1 to 4-4.
But this signal is generally not the 'p(t) across the MWD pulser that is directly
related to position-encoding by the pulser. Method 4-5 solves for 'p(t) if p 2 (L,t)
is known from Methods 4-1 to 4-4 using the DELTAP*.FOR software series.
In this series, the drillbit is treated as a solid reflector. We caution the
reader against visual judgments. The “solid reflector” assumption does not
always mean “small drillbit nozzles.” Reflection characteristics can only be
inferred from the results of a comprehensive model such as that in Chapter 2
where the axial and cross dimensions of the bit box and other geometric
elements are considered. Of course, if in a field experiment, a test signal reflects
with the same sign, that would confirm solid reflector characteristics.