Geology Reference
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Close, Owens and MacPherson (1988) found, upon detailed analysis of
MWD data, that PDC diamond bits may be responsible for high levels of lateral
vibration as well. Correlation between surface measured WOB and RPM, and
downhole lateral vibrations, was obtained. Torque and bending coupling may
also arise when borehole sticking due to large lateral displacements cause the
drillstring to twist in place. Later we will show exactly how this and the above
dynamic coupling arises, and present the governing partial differential
equations, numerical formulation and typical solutions. Again, it is significant
to note that the quasi-periodic transfer between mean torsional strain energy and
dynamic rotational energy, responsible for stick-slip oscillations, is
mathematically analogous to the energy transfer that causes changes in axial
mean load and fluctuating weight-on-bit in longitudinal vibrations.
Rewcastle and Burgess (1992) also noted stick-slip motion in cases where
the bit or stabilizers stall in contact with the formation. String torque builds up
until sufficient torque is available to overcome the resisting force and the energy
is suddenly released. Stick-slip behavior is usually seen as cyclical signatures in
surface measured torque; real-time surface torque measurements, therefore, are
valuable in detecting rough drilling conditions. Stick-slip oscillations can cause
the bit to spin backwards and destroy a PDC bit, unscrew the bottomhole
assembly, induce lateral vibrations which are detrimental to the BHA and to
downhole MWD instruments. Thus, there is substantial interest in active control
over torsional vibrations. For example, Sananikone, Kamoshima and White
(1992) have investigated the use of “active feedback and control systems” which
appear to be operationally simple and effective. Lin and Wang (1990) gave a
preliminary explanation that attempts to define the relationship between stick-
slip and observed beating phenomena using a simplified one-degree-of-freedom
mathematical model.
4.4.2.1 Energy considerations.
The above observations on stick-slip oscillations indicate that significant
energy transfer occurs between static and dynamic torsional states. Thus, as in
the case for axial vibrations, although for different reasons, there is little
incentive or rationale to consider separate formulations for the static and
dynamic problems. It is of operational interest to determine the critical
rotational speed beyond which stick-slip stops, but this critical speed may be
unique to each operation, and may be overly optimistic. It may well be that such
a parameter cannot be determined from purely torsional considerations alone;
from our discussions, the role of important axial vibrations certainly cannot be
ignored - both modes co-exist and interact with each other during drilling.
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