Geology Reference
In-Depth Information
Section 7 below). Ideally, surface signal processors would determine these
frequencies for the bottomhole assembly under consideration (using standard
mechanical engineering formulas) and automatically remove their effects before
application of our echo cancellation and other filters.
6.3. Attenuation Mechanisms (software reference, Alpha2,
Alpha3, MWDFreq, datarate) .
Numerous models are available for wave attenuation modeling in the
engineering literature, however, they are developed for ultrasonic applications
where wavelengths are very, very small and interactions with particles are
considered in detail. In MWD applications, wavelengths are typically hundreds
of feet and reliable measurements are not available due to mudpump transients.
These are typically made in wells with flowing non-Newtonian mud, or in very
long flow loops with multiple twists, turns and (undocumented) area changes.
Vortex flows, density segregation, secondary flows, and so on, may be present.
The action of positive displacement mud pumps and their unsteady pistons
renders fluid flows highly transient; moreover, the effects of constructive and
destructive interference, and those associated with nodes and antinodes for
standing wave patterns, are usually not separated out. Good data is difficult to
find. Also, given the complexity of the mathematical problem, and the fact that
field situations are rarely controlled, approximate methods are appropriate and
are therefore considered here.
6.3.1 Newtonian model.
Almost all oil service companies use a classic formula during job planning
for sound wave attenuation developed for steady laminar Newtonian flow in a
circular pipe, e.g., see Kinsler et al (2000). It appears to be reliable if used
properly and cautiously, and is derived from rigorously formulated fluid-
dynamic models. If Z is circular frequency, P is viscosity, U is mass density, c
is sound speed and R is pipe radius, then the pressure P corresponding to an
initial signal P 0 is determined from
P = P 0 e - D x
(6.3a)
where x is the distance traveled by the wave and D is the attenuation
D = (Rc) -1 — {(PZ)/(2U)} (6.3b)
In other words, the damping rate varies as the square root of frequency and
depends on density and viscosity only through the “kinematic viscosity” P/U.
The software model ALPHA2.EXE, emphasizing “Newtonian” in Figure 6.3a,
performs the required calculations. Once the input data are entered in the white
text boxes, clicking on “Find” will give the value of D and the pressure ratio
P/P 0 as shown in Figure 6.3b.
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