Geology Reference
In-Depth Information
3
Harmonic Analysis:
Elementary Pipe and Collar Models
In Chapter 2, we developed a comprehensive six-segment downhole
acoustic waveguide model in order to understand interactions between the
pulser, bottomhole assembly and the geometry of the borehole. The harmonic
analysis is useful for detailed analysis and in designing hardware and telemetry
schemes for signal optimization. In other applications, simpler models suffice,
e.g., when it is not possible to characterize the environment accurately. Also,
simple models descriptive of idealized geometries may be useful for interpreting
tests made in specially designed laboratory facilities. In this chapter, we
continue our study of wave motions under harmonic excitation, that is, those
underlying “frequency shift keying” (FSK) schemes. The “simple” geometric
models considered here consist of, at most, a finite length drill collar and a semi-
infinite drillpipe. For clarity, we present our results in two categories: (A) those
in which the waveguide is uniform in area (i.e., drillpipe only) and (B) solutions
for which an MWD signal originating in a drill collar travels up the drillpipe. In
the latter case, the source can be located anywhere within the collar, the
frequency (and, hence, wavelength) is general, and the collar cross-sectional
area (that is, the collar area minus that of the central hub) may be less than,
equal to, or greater than that of the drillpipe.
3.1 Constant area drillpipe wave models
Here we develop four mathematical models for which the MWD source
resides in a “drillpipe only” environment without a drill collar. The source is
situated away from the drillbit end of the pipe. The drillbit may be a solid or
open reflector. As in Chapter 2, we caution against visual judgement; whether
the bit is solid or open depends on acoustic frequency and geometric
characteristics like bit box lengths, and not, for instance, on “how small” the
nozzles appear visually.
86
Search WWH ::
Custom Search