Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 97

4
Transient Constant Area
Surface and Downhole Wave Models
Overview
In Chapters 2 and 3, we assumed harmonic or sinusoidal 'p(t) excitations,
for the purposes of analysis; these two chapters considered, respectively,
comprehensive six-segment waveguides and simpler pipe-alone and collar-pipe
models for downhole signal analysis and optimization. The results are directly
applicable to “frequency shift keying” (FSK) telemetry. They are also useful in
determining the extent to which constructive wave interference methods might
be employed in signal enhancement, since destructive signal cancellations
associated with random phase-shifting are not present. We focused on a
particular downhole “forward” problem in Chapters 2 and 3, that is, the
mathematical properties of the total created pressure field when a harmonic 'p
is prescribed at a specific source location at a given frequency. The strength of
'p, that is, its dependence on flow rate, valve geometry, rotation rate, mud
properties, and so on, is measured separately in flow loops or wind tunnels.
In this chapter, we introduce the study of uphole models. These methods
apply at the surface and are principally developed to model reflections of the net
upgoing MWD signal at the desurger and mudpump, and to evaluate single and
multi-transducer echo cancellation and pump noise removal signal processing
methods. Several uphole methods are presented and different models are
evaluated and compared computationally against each other. The recovery of
the upcoming 'p signal from noisy signals contaminated by surface reflections
and mudpump action defines the “surface inverse problem.” The transient
models here and in Chapter 5 are “true transient” models derived in the time
domain and do not rely on FFT and similar constructions.
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