Transient Variable Area Downhole Inverse Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 140

5
Transient Variable Area
Downhole Inverse Models
In Chapters 2 and 3, we examined the forward problem associated with
harmonic 'p(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
'p(t) functions. It also introduced downhole inverse problems, that is, the
recovery of transient 'p(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 be the same, and there could be significant acoustic impedance mismatches.
Such effects lead to unwanted reverberations within the drill collar that result in
a distorted or “blurry” signals transmitted into the drillpipe.
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