Drillstring Vibrations: Classic Ideas and Modern Approaches - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 116

4.1.3.2 Example 4-2. Looking for resonance in all the wrong places.
In vibrations modeling, researchers assume simplified axial, torsional and
lateral mode boundary conditions, plus sinusoidal excitations where appropriate,
in order to study “normal modes” and system resonances. Workers tend to
force-fit drillstring models to classical solutions. Yet, many drillers have
attempted to drill at resonance to make hole faster, or simply to evaluate
theoretical predictions, without success (Dareing, 1972). Recent studies
question the applicability of classical normal mode analysis in real drilling.
4.1.3.3 Example 4-3. Drillstrings that don't drill.
The common use of sinusoidal bit displacement boundary conditions,
which bears superficial semblance to Fourier analysis, requires that the bit
remain stationary on the average. Thus, it does not make hole, it does not
bounce and it does not simulate reality. How can we use laboratory-defined
rock-bit interaction models, drillbit kinematics, rotary speed and BHA layout, to
predict rate-of-penetration, bit bounce and real vibration instabilities?
4.1.3.4 Example 4-4. Modeling coupled vibrations.
Axial, torsional and lateral vibration modes are highly coupled and
transient, yet no published model has addressed this interaction, let alone
develop a model for the full problem. We will formulate and test each of the
axial, torsional and lateral building blocks individually , and then integrate them
in numerical fashion, following physical arguments that make physical sense.
4.1.3.5 Example 4-5. Energy transfer mechanisms.
Recent workers in drillstring vibrations have recognized the need to have
continual dynamic energy transfer among axial, torsional and bending modes of
vibration, with the complete system viewed as the entity of physical interest.
This objective is only partially complete: energy transfer between mean and
dynamic stresses must be modeled. Consider torsional stresses: at the start of
drilling, torque-up merely winds the pipe, increasing its mean strain energy.
Once rotation begins, freed torque oscillations propagate up and down the
drillstring, and if bit friction cannot maintain this status quo , torque reversals are
likely, which significantly affect the mean strain field. This is also the case,
although less obvious, with axial vibrations. The mean DC field is usually
ignored, but it turns out that dynamic AC results can effect changes to DC
displacement levels and vice-versa, for certain types of rock-bit interaction.
“Making hole” requires, therefore, a strong coupling between mean and dynamic
stress fields, plus consideration of background DC penetration modes, both
traditionally ignored.