Mud Acoustics in Modern Drilling - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 286

Mud

X = X

s

Figure 5.6. Mud siren.

5.5.3.4 Signal generation at the source.
So far, we have described the symmetries and antisymmetries associated
with pressure and velocity fields for positive pressure valves, negative pulsers
and mud sirens. We indicated that poppet valves and sirens satisfy Equation
5.6.1, while negative pulsers satisfy Equation 5.6.5. The “delta-p” strength P s (t)
appears in the former, while the “delta-velocity” strength V s (t) appears in the
latter. These wave differential equations can be solved using the analytical and
numerical methods devised thus far for axial and torsional vibrations, and swab-
surge modeling in the annulus, directly without change. Typical boundary
conditions may be solid reflectors, acoustic free ends, radiation conditions, and
so on (see Chapters 1 and 4 for details). We have not discussed the exact values
for P s (t) and V s (t) yet. The signal time history will, of course, depend on the
telemetry scheme used to represent downhole information for transmission to the
surface. For example, analogies to AM and FM transmission in radio and
television broadcasts are easily made, which we will expand upon later. The
magnitude of the respective jumps in pressure and velocity are crucial to a good
MWD signal with audible signal strengths. Here, the mechanical design, to
include size and shape, can be crucial, since the signal generation process
depends sensitively on the details of the unsteady hydraulic flow acting at the
valve.