Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 135

where the created MWD pulser is antisymmetric with respect to the source
position. This p 2 (L,t) is identical to the “p pipe ” in Chapter 2. The two terms on
the right side of Equation 4.6g are the incident and ghost waves. We need to
extract 'p in order to obtain the 0's and 1's information stream encoded in
'p(t). Once Methods 4-1, 4-2, 4-3 or 4-4 are applied at the surface for standpipe
signal processing, Methods 4-5 or 4-6 are carried out as needed.
4.6.4 Run 1. Low data rate run.
Here a single near-rectangular pulse is considered. The time delay
between pulser and bit is 0.01 sec. In Figure 4.6b, the black curve is the
upgoing pressure wave created ahead of the pulser. The red curve is the
negative of this (shown reversed so that comparison of the time delay is
enhanced), which propagates down to the drillbit open end and reflects with a
sign change - it now has same sign as the wave ahead of the valve. Thus, the
green signal shows enhanced superposition and the green waveform is a little
wider than the black one. Using the green data, the blue curve is recovered, and
duplicates the black one successfully. In this run, the pulse width is
approximately 0.25 sec, representing a high data rate by conventional standards.
From our calculations, it is very obvious that nozzle size is very important, and
determines whether the bit is a solid reflector or an acoustic free-end. This in
turn dictates the shape of the wave - that is, the all-important green curve - that
travels to the surface with all the downhole information.
C CASE 1
A = 0.8
R = 100.0
SIGNAL = A*(TANH(R*(T-0.1))-TANH(R*(T-0.35)))/2.
Figure 4.6b . Rectangular pulse run.