Vibrations in drill rigs

Index

Prof. Robin Tucker

First published in "Engineering Technology", April 2000 and reproduced with kind permission of The Institution of Incorporated Engineers.

The dynamical behaviour of an active drilling assembly used in the oil or gas industry is complex. This article provides an overview of the vibrational states experienced by such a system and explains an approach taken to control them.

Digging a hole in the ground is an infamously mundane task. If, however, you are using a drill with a bit at the end of a 5km long shaft, then the task is anything but dull. The scale of the operation aside, one of the most complex aspects of this type of task is dealing with unwanted vibration. These problems can become even more demanding when the hole is under the sea. Work carried out in the Department of Physics at the University of Lancaster has been exploring some of these problems and suggesting new solutions to eliminate them.

Drilling assembly

A major component of a drilling assembly consists 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 it constitutes the bottom hole assembly (BHA). Drill-strings are driven in a rotary fashion from the tcp end, often by means of an electric motor and gearbox - the top-drive - and these are 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

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 called the over-gauge. 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 occasional contact with 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 bore-liner. Fig 1. Dangerous vibrational modes of the BHA

Fig 1. Dangerous vibrational modes of the BHA

Its primary purpose is to cool and lubricate the drill-bit, as well as to remove the cuttings produced by the drill-bit. When operating the drill-string and BHA are prone to dynamic instabilities that are not fully understood. Field experiences, however, have provided ample testament to the destructive consequences of such instabilities. Although extensive literature has been 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. 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.

Mathematical modelling of the drill-string

The steel strings under consideration have a ratio of average diameter to length of the order of I 0~ (which is less than that of the average human hair). Due to the earth's gravity a drill-string's horizontal length differs from its vertical length by between one and two metres. This suggests that it can be effectively modelled by elastic space-curves with structure. (That is to say the model treats the drill-string as an 'elastic band' that can stretch, twist, bend and shear). Supplemented with appropriate material constitutive relations and boundary conditions the model can fully accommodate the modes of vibration that are traditionally associated with the motion of drill strings in the engineering literature:

Axial motion or vibration along its length
Torsional or rotational motion about its long axis
Transverse or lateral motion
Whirling vibrations (motion in a plane about a vertical axis).

Although the model accommodates arbitrary displacements and deformations its use in describing small amplitude vibrations about various stationary configurations offers valuable guidance for the attainment of stable drilling processes. The fully nonlinear aspects of the motion are, however, needed to appreciate the significance of some of the most important non-perturbative vibrational phenomena observed in the field. These 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)
Collision of the rotating drill-string with the bore-liner.

Fig 2. Lancaster drill-string simulation test rig

Models of course need to be tested, and part of the work carried out at the University of Lancaster has included the dynamical testing of a scale model of a drill-string. The segmented drill-string is represented by a fine chain, hung vertically (with its extremity in mollasses!) and driven by a motor. Figure 2 shows one of our test rigs.

Torsional slip-stick

Torsional 'slip-stick' is often regarded as one of the most damaging modes of vibration when drilling with low rotary speeds. Fig 3. Torsional slip-stick control

For a typical drill-string, with length of around 5000m, 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 150RPM) set by the top-drive. The torsional excitation 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. Fig 4. Marine riser dynamics

Various control techniques have been devised to combat this instability, but field evidence suggests that they often exhibit undesirable volatility, thereby detracting from the 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, ultimately leading to component failure. These include the transfer of energy between axial, lateral and torsional motion induced by the interactions of the drill-string and a BHA with their environment. Drilling strategies and initial conditions can dramatically influence the nature of such inter-mode couplings.

Feedback control

Unless controlled, the vibrations of a drill string can lead to dramatic and damaging motions. One attempt to prevent the build up of such effects involves placing mechanical sensors on the side of the string. These respond by generating small electric currents in proportion to strains in the material. The resultant electrical signals can be analysed, and then after suitable filtering and amplification, sent to the power source driving the rotary motion. (See Figure 3).

Mud telemetry

Some sensors detect the motion of the end of the drill-string using gyroscopes cradled within the BHA. Information near the cutting action is sent to the surface as sound pulses through the 'mud' that is used to lubricate and effect the removal of rock cuttings. (Such 'mud telemetry' is more reliable than other techniques in this mechanically hostile environment - radio communication simply does not work well enough.) By varying the rate of torque production a compensating torsional wave can be sent down the drill-string to prevent the build-up of slip-stick vibrations at the drill-bit.

Negative feedback

This is an example of active feedback control and it is widely used to control unwanted torsional vibrations. The mechanism is analogous to the way an experienced driver can control his brakes to escape from a skid. Instead of continuously applying a pressure to the brake pedal, the driver alternately applies pressure on and off the pedal rapidly. The result is that the effective frictional adhesion between the road and the car tyres is dynamically modified and traction restored. In this case the feedback sensor is the driver's sensory apparatus. Active feedback is achieved via the driver's brain and the steering and brakes. (In modern cars the ABS servo-control replaces this feedback loop.)

Vortices

The effects of moving air on solid bodies can be both subtle and dramatic. If one draws a solid rod through a tray of milk one can observe a swirling in the fluid in the wake of the motion. If the motion is rapid enough these swirls form vortices in which eddies of fluid appear to generate isolated tornadoes of fluid with their own overall translational motion. As the vortices escape from the rod they cause it to react slightly. The impulse reactions occur as each vortex is shed from the fluid in contact with the rod. If the solid rod were free to react to these forces as it moves through the fluid it would execute an oscillatory response. This is why, for example, a falling leaf in still air 'dances' as it falls to earth and why a flag flaps in the way it does in a stiff breeze. The origin of the famous Tacoma Narrows suspension bridge collapse was a wind-vortex induced torsional vibration of the bridge deck, in turn excited a lateral mode of the entire bridge. The ensuing resonance caused the bridge to collapse catastrophically. The effects of such vortex-induced vibrations are very important to take into account in the design of large span suspension bridges - and undersea drilling operations.

Offshore systems

In undersea oil and gas exploration the drill-string is connected to a floating rig and passes down a hollow 'marine riser' that is fixed both to the floating rig and the sea bed. The marine riser protects the rotating drill-string from the sea, keeps the drill cutting debris from escaping into the environment and offers a conduit for the collection of oil and gas. Unlike onshore drilling systems, one now has to reckon with the vibrational effects of both the drill string and the surrounding 'marine riser'. The integrity of the marine riser under a variety of conditions is crucial to the entire operation. However, our current ability to predict stress levels and fatigue rates in marine risers is inadequate, resulting in design criteria that rely on anecdotal evidence and simplified models. This is especially true for sheared flows, where the local fluid velocity of the ocean current varies with depth. Pressure on development costs and increasingly hostile field environments, including water depths over l000m, are demanding increasingly refined design strategies. Although the marine riser is kept in a state of mechanical tension to minimise its lateral motion, the effects of vortex shedding along its length can be important. The reaction forces on the marine riser as the vortices are shed cause a perceptible vibration to occur, that in time produce fatigue in the steel riser and a requirement that it be replaced before it breaks. (Any attempt to make the riser out of a more flexible material is likely to risk the excitation of enhanced lateral vibrations induced by internal hydrodynamic forces, as well as the fluid forces due to sea currents.)

Lock-in

More striking is the phenomenon of lock-in'. The frequency of vortex shedding depends on the overall speed of the sea current and the diameter of the marine riser. As this frequency approaches the natural frequency of one of the natural modes of the riser the structure and the fluid suddenly behave in unison and lock each other into a grand vibration with a common frequency that persists. This behaviour is hazardous, since the energy of the sea currents exploit the enhanced route into the motion of the riser, which now sustains motion with damaging fatigue stresses.

Stable and unstable motion induced by forced vibrations

If one tries to stand a thin rod (for example a pencil) vertically on its end on a horizontal table without constraints it proves impossible - the slightest perturbation tips it over. However, it is not too difficult to keep it from toppling over if one is allowed to move its lower end about in space. In fact, with a small amplitude oscillatory motion the lower end can be kept vertically stable if the frequency of oscillation is right. The longer the rod, the lower the frequency must be for this trick to work. The ability of an external intermittent or oscillatory motion to either amplify or stabilise the motion of a system is apparent in a wide variety of phenomena.

Cylinders in fluids - the power cable problem

Around 1930 it was noticed that overhead electrical power lines began to execute large swaying motion in light winds (less than 5mph) with sleet. In some cases cables between pylons were displaced more than 20 feet. A controversy arose as to whether this was due to some strange electrical effect (such as coronal discharge into the air) or mechanical forcing by the air. This motion came to be called 'galloping'. One (correct) suggestion was that the presence of sleet in the environment was the problem and that ice on the cable was forming to change its shape from a stranded cylinder. With a modified profile the aerodynamic forces of lift and drag on the iced cable due to even a light wind were sufficient to amplify its swaying motion and set the cable into a 'galloping mode'. This insight led to the introduction of damping devices that are now common on all overhead power lines world-wide, which serve to eliminate this kind of motion. (Interestingly, from time to time wind and rain induced vibrations reappear and their effects continue to puzzle. Modern long span cable-stay bridges are particularly prone to such subtle effects.)

Parametric oscillation

There is a more subtle effect that affects marine risers analogous to the amplification of sleet and rain wind-induced vibrations in cables. In those cases we saw the amplification of persistent small forcing excitations into a large-scale motion of the structure. Since the surface of the sea is not smooth as the platform rises and falls it will cause an under-sea riser to stretch in harmony as it is fixed to the sea bed. This in turn sets up axial stresses that travel down the riser and reflect off the junction where the riser terminates on the sea bed, returning to the surface. Although these axial vibrations may be small in amplitude and irregular in time their repetition can trigger an amplification mechanism that offers a new channel in which external energy can be directed into the motion of the structure. If the nature of the surface fluctuations enter a critical domain this energy slips effortlessly into the riser and deforms its shape. This triggers a lateral motion that along with the vortex shedding effects contributes to accelerated fatigue rates in the riser. This is known as parametric excitation. This article has provided just a glimpse of some of the fascinating, but difficult problems associated with drilling in the oil and gas industry. While we have suggested solutions to some problems, new ones are always appearing as we drill deeper into the earth and under ever deeper oceans.