Transient Variable Area Downhole Inverse Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 142

5.1 Method 5-1. Problems with acoustic impedance mismatch
due to collar-drillpipe area discontinuity, with drillbit
assumed as open-end reflector (software reference, collar-pipe-
open-16.for) .
5.1.1 Physical problem.
The engineering problem considered is shown in Figure 5.1a, where the
source represents both positive pulsers and mud sirens. The telemetry channel
consists of an MWD drill collar of finite length and a semi-infinite drillpipe.
The pulser is located generally within the collar away from the bit, in order to
allow for both left and right-going waves - it may execute generally transient
'p(t) signals so long as wavelengths are large compared to typical cross-
sectional dimensions. We consider two problems. The first determines the
transient pressure that enters the drillpipe as a result of reverberations within a
drill collar excited by a general 'p(t), while the second deals with 'p(t) signal
recovery when a fully transient drillpipe signal (that is, the result of using
Methods 4-1, 4-2, 4-3 or 4-4) is available. Note that Methods 4-1, 4-2, 4-3 and
4-4, Methods 5-1 and 5-2, and an attenuation model for signal propagation along
long drillpipes, can be combined to develop a first-generation high-data-rate
signal processor capable of handling all reflections.
Schematic
Figure 5.1a . MWD dipole pulser in drill collar and drillpipe system, with
drillbit modeled as open-end reflector.