Measurement While Drilling, 2nd Edition

Chapter 3Harmonic 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 ...