Analysing the nonlinear dynamics of drill strings using control-based continuation

Drilling provides access to the reservoirs in order to produce hydrocarbons. Some reservoirs
require complex technical solutions, for example, to allow us to drill over 15km with long
sections almost horizontal. A significant challenge is understanding and controlling the
complex nonlinear dynamics of the drill string including undesirable effects such as whirl,
which results in damaging shocks and vibrations. These shocks and vibrations in turn cause
major equipment failure, inefficiencies and lost operational time which can cost millions of
pounds per incident and billions of pounds annually to the industry.
To understand the phenomena, numerous numerical models have been developed,
however they do not predict the behaviour of individual cases. To refine and validate the
modelling, experimental testing on scaled setups are conducted. However due to the
complexity of the system, these tests are challenging to run as, for example, well-behaved
solutions and whirling solutions can exist under the same test conditions. We believe that
Control-based Continuation (CBC), an experiment-based approach which combines
feedback control with numerical bifurcation analysis, has potential to rigorously investigate
the nonlinear physical phenomena associated with drill string behaviour in a way that
numerical models and current experimental testing approaches cannot achieve.
The overarching aim of the project is to determine how CBC can be applied to the existing
experimental rigs at Schlumberger's research lab in Cambridge and subsequently
investigate the different mechanisms for instability and their nonlinear dynamics. This will
require extensive modelling work and development of suitable control methods which are
able to deal with noise and uncertainty. Furthermore, it is also likely to require further
algorithm development to allow CBC to deal with the noise and, possibly, time varying
effects. Work will begin by building up experience with CBC on existing experiments at
Bristol and getting to grips with the methodology required. This will require careful
experimentation, data processing and model building.