Transient Variable Area Downhole Inverse Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 141

Again, for Methods 4-1 to 4-4 in Chapter 4, our objective was to recover
all signals (good plus bad) originating from downhole. This was accomplished
successfully by removing surface reflections and pump generated noise.
However, we now re-emphasize that the upgoing MWD signal itself is not
“clean,” but contains additional “ghost reflections.” By ghost reflections, we
refer to the downhole signal generation process. When a signal is created at the
pulser that travels uphole, a pressure signal of opposite sign travels downhole,
reflects at the drillbit, and then propagates upward to interfere with new upgoing
signals. Thus, at the surface, the signal arriving first is the intended one, which
is followed by a ghost signal or shadow often with unknown phase and
amplitude. We emphasize that this ghost noise always exists in real MWD
tools, unless, of course, the signal source is actually a piston face coincident
with the drillbit - which it, of course, never is.
Tool design considerations. We stress the above point with the
illustration in Figure 5.0 below. In this topic, by “MWD collar area” we mean
the cross-sectional area inside the collar, minus the area of the hub upon which
the siren is installed. Depending on the tool, this net area may be greater than,
equal to or less than the area of the drillpipe. Unless the areas are identical, so
that no mismatches exist, reverberations will be created within the collar that
further distort the ghost-bearing signal that travels up the drillpipe. The
associated reverberations introduce “fuzziness” to the upgoing signal.
Area matching
A MWD collar - A hub = A drillpipe
Figure 5.0. MWD collar - drillpipe area mismatch.
Objectives. In this chapter, we develop methods to recover fully transient
'p(t) functions from pressure signals measured in the drillpipe (that is, obtained
as the result of surface signal processing using Methods 4-1, 4-2, 4-3 or 4-4).
Here, arbitrary differences in collar and pipe cross-sectional area are permitted
and no restrictions are made as to their relative magnitudes. Method 5-1
assumes that the drillbit is an open-end reflector, while Method 5-2 assumes that
it is a solid reflector. Difference delay equation approaches are used and exact
solutions provided in software demonstrate perfect consistency between the
complicated created signal field and the even more subtle process developed for
signal inversion.