Vibrations of Drill Rigs
|The dynamical behaviour of an active drilling assembly
as used in the oil or gas industry is complex. There is a need to understand
the complex vibrational states experienced by such a system in order to better
control their constructive and destructive potential. A drilling assembly
consist essentially of a series of hollow cylindrical steel pipes connected to
form a long flexible drill-string to which is attached a short heavier
segment containing a cutting device at the free end (the drill-bit).
This segment may contain stabilising fins designed to minimise lateral motion
during drilling and together with the drill-bit constitutes the bottom-hole
assembly (BHA). The drill-string is driven in a rotary fashion from the
top end, often by means of an electric motor and gearbox, the
top-drive, and constrained to pass at a controlled rate through a
rotating mass (the rotary) near the surface. Such a drilling system is designed to construct a bore-hole
linking the earth's surface to a reservoir of oil or gas.
The bore-hole is lined (usually with steel) and the excess in the diameter of this cavity over the diameter of the drill-pipe is referred to below as the overgauge. This annular gap (which in general varies along the bore-hole) is necessary for the conduction of fluids. These are a source of external interaction along the drill-string in addition to gravity and the bore-liner. During the process of drilling pressurised fluid (mud) is continuously circulated down the centre of the drill-string, out of holes in the drill-bit and back to the surface via the space between the rotating drill-string and the surface of the bore-hole. Its primary purpose is to cool and lubricate the drill-bit as well as to remove cuttings produced by the bit. Such a system is prone to dynamic instabilities that are not fully understood. Field experience provides ample testament to the destructive consequences of such instabilities.
Although there exists an extensive literature devoted to the analysis of distinct aspects of the dynamics of the drill-string and BHA it is only recently that the virtues of treating the drilling assembly as an integrated system have been considered. Since the physics involved is inherently non-linear and recourse to modelling is inevitable to compensate for a lack of detailed dynamical information in the vicinity of the bit, many conclusions have been based on numerical simulations that ignore one or more aspects of the problem.
The steel strings under consideration have a ratio of average diameter to length of order 10-5 (which is less than that of the average human hair). Due to the earth's gravity their horizontal length differs from their vertical length by between 1 and 2 metres. This suggests that they can be effectively modelled by elastic space-curves with structure. The most important vibrational phenomena include torsional relaxation oscillations induced by non-linear frictional torques between the drill-bit at the rock surface (torsional "slip-stick"), axial vibrations that induce the drill-bit to intermittently lose contact with the rock surface ("bit-bounce"), whirling motion of the drill-string and the motion of the bit in the bore-hole (bit and BHA-whirl).
Torsional "slip-stick" is often regarded as one of the most damaging modes of vibration when drilling with low rotary speeds. For a typical drill-string of length around 5000 metres such a torsional disturbance consists of a travelling torsional pulse that bounces back and forth between the top rotary and the drill-bit every few seconds periodically forcing the drill-bit to "slip" and "stick" for extended periods at the rock surface. The amplitude of this torsional excitation can be two to four times the target or average angular speed (typically between 30 and 150 RPM) set by the top-drive and this can give rise to enormously destructive fluctuating torques in the drill-string that, once out of control, invariably cause damage to the bit or drill-string.
Even small amplitude "slip-stick" vibrations are thought to be a major cause of bit wear. Various control techniques have been devised to combat this instability but field evidence suggests that they often exhibit undesirable volatility thereby detracting from their overall efficiency.
In addition to these violent excitations that can lead to rapid failure in the drilling operation there are more subtle vibrations that are thought to contribute to fatigue crack growth leading to ultimate failure of components. These include the transfer of energy between axial, lateral and torsional motion induced by the interactions of the drill-string and BHA with their environment. The nature of such inter-mode coupling can be dramatically influenced by drilling strategies and initial conditions.