Drillstring Vibrations: Classic Ideas and Modern Approaches - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 189

Close, Owens and MacPherson (1988), using downhole MWD data,
reiterate the fact that lateral vibrations can be extremely damaging. They
concluded that bending accelerations were an order of magnitude greater than
axial accelerations. In one case study where destructive vibrations were
uncovered, sudden lateral accelerations exceeded axial values by up to twenty-
three times. These authors also observed extreme bending problems while
running with a diamond bit, apparently induced by torsional oscillations. Their
conclusions cast doubt on long accepted industry standards. For example,
critical rotary speed formulas provided in API RP 7 G since 1970, to prevent bit-
excited lateral vibrations in the drill stem, appear to be limited in usefulness.
With respect to the applicability of classical harmonic analysis, field results
indicated the presence of severe downhole shock levels even when modeled
critical rotary speeds and real-time surface vibrations had been avoided. Thus,
there appears to be a different physical mechanism at work, and which, in part,
motivated our new approach to the problem. Close et al importantly suggest
that shock behavior is perhaps more stable than a purely resonant response. The
recurrent themes cited in our observations (i) and (ii) pervade the literature.
From an operational standpoint, it is unacceptable and dangerous that the most
damaging downhole vibrations cannot be anticipated from direct surface
measurements and corrected. Drillers have long recognized this unfortunate
problem; its impact on drilling efficiency, cost and safety, is obviously
important, and a good explanation is needed together with avoidance strategies.
Unfortunately, the neutral point instability has been observed but not quite
explained even as recently as 2012, e.g., see Costo et al (2012), a matter we will
satisfactorily address.
4.3.3.3 Wave trapping, a simple analogy.
Catastrophic drillstring failures are often attributed to various linear and
nonlinear instabilities, while failure to detect their occurrence from the surface is
blamed on attenuation due to borehole wall contact. However, conventional
approaches have yet to produce any results, even qualitative ones, that
completely explain the observations indicated above by means of a single self-
consistent model, let alone highlight the mysterious role of the neutral point.
One might even suppose that catastrophic events such as twist-offs cannot be
described within any linear framework, and that special studies would be needed
on a case-by-case basis. Fortunately, this is not true.
A new wave instability theory, proposed at the Massachusetts Institute of
Technology by Professor Marten T. Landahl and the present author, draws upon
the ”kinematic wave theory” developed at the California Institute of Technology
(Whitham, 1974). The basic elements of KWT were introduced in Chapter 2.
The wave trapping model was successfully applied to several catastrophic
failures in nature, such as vortex breakdown over aircraft delta wings, laminar