Drillstring Vibrations: Classic Ideas and Modern Approaches - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 171

the hardness of the rock being drilled. As noted in Lutz et al , workers at the
S etroles d'Aquitaine observed that static weight-on-bit

only partially accounted for penetration rate. The complete WOB signature,
therefore, had to contain lithology information; hence, the SNAP Lo g . This log
recorded raw axial vibration data at the top of the string. It is expected to be
important in detecting the approach to, and the entrance into, abnormally
pressured formations since it reflects the greater hardness of the caprock above
them and the lesser hardness and density of the abnormally pressured shales
themselves. One log taken in an upper soft shale formation of the Aquitanian
Basin showed that vibration measurements are able to detect shale compaction
in a manner very similar to sonic logs. The unprocessed data correlated well
with neutron, sonic and gamma ray results in holes made through compacted
shales and limestones. Lutz et al provides a large number of field examples of
instantaneous logging for comparative study.
Booer and Meehan (1992, 1993), for example, regard the drillstring as a
system with layered impedances arising from differences in collar and pipe
sizes. Their objective was to separate drillstring resonances from measured
surface vibrations to obtain the signal created at the bit. While their block
diagrams showed elements such as “drillstring transfer function,” “bit signature
analysis” and “lithology bit boundary condition,” the papers offered few of the
details needed in deconvolution modeling and processing. But the authors
importantly observed that in the frequency band typically generated by a rock
bit, that is, up to 100 Hz, approximately, changes in lithology are detectable, and
that drillstring axial or torsional imaging can detect major structural changes.

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4.2.11.3 Notes on rock-bit interaction.
We can see ahead of the bit while drilling, using the same ideas introduced
earlier in forward simulation. Again, this requires us to integrate existing
technologies in laboratory rock/bit interaction modeling, drillstring vibration
analysis, real-time data acquisition and downhole signal processing. A large
amount of necessarily empirical work on rock/bit interaction is available in the
literature, as we indicated in our discussion on its role in rate-of-penetration.
The cited works were driven by the need to understand cuttings formation, jet
hydraulics and bottomhole cleaning.
Outmans (1959) developed one of the earliest theoretical models for
rock/bit interaction. His work showed that the relationship between drillbit
WOB and instantaneous penetration rate is linear over a range of WOBs. This
applied to multiple rock types at different rotation rates and depths. Results for
a typical bit in different formations are shown in Figure 4.2.9. Strong rocks like
gray granite and pink quartzite, for example, are seen to drill more slowly.
Similar results due to Maurer (1962), Warren (1981), Podio and Gray (1965)
and Yang and Gray (1967) show definitive correlation between rate-of-