I now have a fully funded PhD opportunity in Industrial Mathematics (specifically, nonlinear dynamics and control theory) to work with Schlumberger Research on an interesting problem of the nonlinear dynamics of drill strings. If you are interested and want to apply, see the advert on FindAPhD.com or get in touch with me by email. The studentship (iCASE award) is EPSRC funded at the standard rate for four years (£14,296 for 2016/17) with an additional top-up payment from Schlumberger (amount to be decided but is likely to take the stipend up to around £17,000 per year). Standard EPSRC eligibility rules apply.

Text from the advert is below.

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

This PhD project is an EPSRC industrial CASE (iCASE) award provided by Schlumberger. This project is suitable for a student with a strong mathematical background (applied mathematics, engineering, physics) who has a desire to apply mathematical ideas to physical problems.

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.

##### Further Particulars

This project will require a strong background in mathematics and an interest in implementing and conducting experiments using mathematical algorithms on physical systems. This will require good programming skills. It is anticipated that there will be opportunities to conducted experiments on an industrial test-bed in addition to a smaller-scale setup at the University.

##### Candidate Requirements

Strong mathematical background (including knowledge of ordinary differential equations) and good programming skills are required. Knowledge of nonlinear dynamics is beneficial but not essential.

##### Informal enquiries

For informal enquires please contact Dr David Barton (david.barton@bristol.ac.uk).

##### Funding Notes

Scholarship covers full UK/EU (EU applicants who have been resident in the UK for 3 years prior to application) PhD tuition fees, a tax-free stipend at the current RCUK rate (£14,057 in 2015/16) and a CASE award top-up (value to be determined). EU nationals resident in the EU may also apply and will qualify only for PhD tuition fees.