Chapter 5Transient Variable Area Downhole Inverse Models

In Chapters 2 and 3, we examined the forward problem associated with harmonic Δp(t) excitations in general drilling telemetry channels with multiple area changes. These area changes, or acoustic impedance mismatches, are physically important because propagating waves do not transmit unimpeded without reflection. Depending on geometry, sound speed and frequency, constructive and destructive wave interference are possible. Constant frequency excitations are interesting in these respects, but also, they are useful in enhancing frequency-shift-keying telemetry methods. For example, the use of constructive interference can provide signal optimization without the penalties associated with metal erosion and high mechanical power in pulser design.

Chapter 4 dealt with surface reflection signal processing and pump noise removal assuming constant area telemetry channels, an assumption that is acceptable for conventional standpipe applications, focusing on general transient Δp(t) functions. It also introduced downhole inverse problems, that is, the recovery of transient Δp(t)’s from pressures measured at the drillpipe inlet which are contaminated by MWD drill collar reverberations. For these problems, never before discussed in the literature, the mathematics was simplified by assuming constant area. However, in many unavoidable practical field situations, the cross-sectional area in the MWD drill collar and the drillpipe will not ...

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