Drillstring Vibrations: Classic Ideas and Modern Approaches - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 185

And third, any analytical and numerical formalism for drillstring
vibrations, such as that offered in this topic, cannot claim to be applicable
generally and capable of extension (e.g., to highly deviated drillstrings) unless
this first hurdle is overcome through clearly stated engineering principles. In
this section, a deterministic and predictive explanation is given. The paradox is
simply and straightforwardly explained using new ideas based on the “kinematic
wave theory” and “group velocity” interpretations of the conventional beam
equation. These modern ideas were introduced in Chapter 2, representing
extensions to the author' s doctoral thesis at the Massachusetts Institute of
Technology.
The analytical model shows how bending disturbances generated both at
the drillbit downhole, and uphole by drillstring and borehole interaction, “focus”
and “trap” at the “neutral point,” thus leading to large local accumulations of
vibration energy which are undetectable uphole. Leaky waves that do escape to
the surface will stretch beyond recognition, even when dissipation is
unimportant, due to refractive effects. Of course, the presence of any borehole
attenuation will hasten the disappearance of these lateral waves. Having
identified the dominant physical mechanisms, we then derive a general partial
differential equation model for further study. More finite difference essentials
are introduced, above and beyond those discussed earlier, and numerical
formulations and solution approaches are developed in a step-by-step manner.
One might, incidentally, render the present subject more exciting with a proper
choice of words - were this a physics topic, it would not be inappropriate to
refer to our catastrophic event as a “singularity in space” or a “black hole.”
4.3.2 Lateral vibrations in deepwater operations.
While the emphasis of lateral vibrations in this topic is in drilling, such
vibrations also figure prominently in deepwater operations. Here, we discuss
the basic problems.
4.3.2.1 Marine risers.
A “marine riser” is a conductor that links a floating vessel to the manifold
on the sea bottom, with the sea depth ranging from hundreds to thousands of
feet. The riser can be a single rigid pipeline for the drilling system, or a bundle
of flowlines assembled as an integral unit for a production system (the
production riser system can be installed on a tension leg platform or on a
floating production and storage unit). To avoid the collapse and buckling of a
riser by its own weight, and to reduce excess load on the manifold in the deep
sea, a constant tension is generally required. This is applied at the top end of the
riser. The conductor acts like a stiffened cable as far as the end tension is
concerned. Also, syntactic foam or foamed aluminum is strapped around
production risers at intervals to provide additional buoyancy and to reduce top