Drillstring Vibrations: Classic Ideas and Modern Approaches - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 186

end tension. The drilling or production fluid that flows internally from one end
to the other, of course, experiences centrifugal forces along the inside curved
path, where the curved path may be time dependent. The external flowing fluid,
on the other hand, may induce vibration; this depends on flow velocity and
unsteady loads arising from vortex shedding. Chen and Gair (1992) consider a
marine riser carrying fluid flow internally, and study instances where internal
fluid density and composition, and wave and current loads may vary.
4.3.2.2 Bending vibrations in directional control.
Dynamic lateral bottomhole forces can aid drilling by providing improved
directional control and increasing penetration rate. Kane (1984) notes that
drillers have little control over lithology, so that bits must be designed to behave
well all-around. He notes that many formations react to peak and not just
average force. It may be possible to use dynamic side forces (which arise only
when the bit is rotated, as opposed to the static side force of a pendulum
assembly) successfully when the bit begins to break more formation at one side
of the hole than another - therefore applying imbalances and eccentrically
weighted collars in the drillstring to guide the bit.
4.3.2.3 Plan for remainder of chapter.
Subsequent to this section, we temporarily return to a simpler problem, i.e.,
a classical wave equation model dealing with torsional oscillations. These are
coupled to the axial vibrations treated earlier by way of boundary conditions at
the drill bit. Finally, in the concluding section, all three vibrations modes, that
is, axial, torsional and (two) lateral, will be dynamically coupled for the first
time, and numerically solved for a realistic test problem. The individual
numerical algorithms introduced separately in all four sections will be
integrated. Example calculations show how smooth and rough drilling can both
be simulated, and in the process, we demonstrate modern notions such as “bit
bounce” and “torque reversal.”
4.3.3 A downhole paradox -- “Case of the vanishing waves.”
The shock and vibration loads generated during drilling are very intense.
Typical mile-long, million-pound drillstrings will often break, the result of large
static forces and moments, and high cyclic fatigue loadings. Different modes of
vibration are excited by rock-bit interaction and drillstring-borehole contact.
Unfortunately, exact dynamical analysis appears to be difficult because it is not
always possible to characterize these excitation sources accurately. So much
depends on the particular tricone and polycrystalline drillbit configurations used
and on their “wobble signatures” as they enter unknown rock formations.
Transient drillstring and borehole contacts are equally difficult to describe
accurately. The combined pipe motion due to whirling, whipping, axial,