Transient Variable Area Downhole Inverse Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 146

intended signal, plus reflections at the drillbit) and would, in fact, be of the form
e - DL p surface (t). Instead of solving Equation 5.1.1 to recover 'p(t), which
contains all the well logging information, one would solve
'p(t) + 'p(t - 2L m /c) =
= e - DL {(A p /A c +1) p 3 (t - L m /c) - (A p /A c - 1) p 3 (t - L m /c - 2L c /c)} (5.1.7)
However, this is really not necessary, since the exponential is simply a constant
factor applicable to all parts of the signal that obviously results in a
proportionately reduced 'p. In other words, the shape of the 'p versus time
curve is the same, and this is all that is important to retrieving our downhole
well logging information - this is very fortunate, since we typically will not
measure D. Similar remarks apply to Method 5-2 and will not be repeated there.
Below, we run collar-pipe-open-16 for four different scenarios. The
“delta-p” functions are listed immediately before the graphical results.
Additional parameters are required and are presently entered directly in the
source code. We have not recorded these values as they are unimportant to
demonstrating the fundamental concepts and software capabilities. The basic
runs considered are obtained from the simulation menu as -
MWD dipole source models available ...
(1) 12 Hz PSK, sampling time DT = 0.0010 sec
(2) 24 Hz PSK, sampling time DT = 0.0001 sec
(3) 96 Hz PSK, sampling time DT = 0.0010 sec
(4) Short rectangular pulse, DT = 0.0010 sec
In the source code, the additional inputs are entered directly by editing the
values below. Descriptions are supplied within the parentheses.
C Hardcode above parameters for testing.
LM = 40. (distance, feet, pulser from drillbit)
LC = 50. (length, feet, of MWD drill collar)
C = 3600. (sound speed, ft/sec)
AP = 1. (pipe cross-sectional area, sq feet)
AC = 1.5 (collar cross-sectional area, sq feet)
C We wish to calculate the drillpipe pressure at a distance
C x = L > LC from the drillbit. At this distance, original
C drillpipe signal leaving the drill collar will have decayed
C exponentially due to attenuation (this satisfies a separate
C model). Assume that DECAY is the fraction of the original
C signal that remains. If no attenuation, DECAY = 1. Be sure
C to try L = 100.*LC for NCASE=2 for difficult test!
L = 5.*LC (location > LC, feet, where we want computed
values of P3 pressure)
DECAY = 0.75 (assumed decay fraction, 1.0 if no decay)
C
In Runs 1, 2, 3 and 4 below, green, red and black curves are shown,
respectively, from bottom to top. The green curve is the assumed input 'p(t)
function; red is the pressure traveling up the drillpipe that consists of the