Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 102

x Roundtrip delay time = 0.02 sec
x Sampling time = 0.01 sec = 10 ms
x Pulse width is 0.600 - 0.100 or 0.500 sec.
Figure 4.1b . Wide signal - low data rate.
Fortran source code XDUCER*.FOR is used to produce the results in
Method 4-1, Run 1. Figure 4.1b shows pressure measurements at a single
standpipe transducer. The incident upgoing assumed signal (black) is a broad
pulse with a width of about 0.5 sec. The reflection (red) is the reflection
obtained at a solid reflector with no attenuation assumed; there is very little
shifting of the red curve relative to the black curve, since the total travel distance
to the piston is very short. The transducer will measure the superposition of
incident and reflected signals which broadly overlap. This superposition
appears in the green curve - about twice the incident signal due to constructive
wave interference, it does not cause any problems and actually enhances signal
detection. The blue curve is the signal extracted from data using only the green
curve and the algorithm described above. This blue curve clearly recovers the
black incident wave very successfully. This is a low data rate run, typical of
existing MWD systems. (For readers of the black and white version of this
topic, colors above are, respectively, black, red, green and blue, starting from the
bottom curve.) The previous run is next repeated with finer sampling time, in
particular,
x Roundtrip delay time = 0.02 sec
x Sampling time = 0.005 sec = 5 ms
Again, the superposition of incident and reflected waves enhances signal
detection, noting that the time pulse width (0.5 sec, for 1 or 2 bits/sec) is large
compared to the roundtrip delay time (0.02 sec). Reflections do not cause
confusion, and both coarse and fine sampling times are acceptable. The
computed results are shown in Figure 4.1c.