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Artificial Intelligence, Mathematical Modelling, and Improved Oil Production

Project Description

Artificial Intelligence is set to revolutionise every aspect of our lives and this PhD will enable you to start to make your contribution to this exciting field. You will combine mathematical modelling with experimental data to study a nonlinear dynamical system involving colliding particles suspended in a fluid flow. The project is co-funded by our industry partners and so this PhD will act as the perfect platform for you to have a career as a mathematician in industry.

Background and Motivation

Approximately 70% of the world’s oil and gas reserves are in reservoirs where the fluids that travel along the pipelines contain sand. This is a real problem for the engineers; for example, 14% of leaks in the UK Continental Shelf oil and gas production are caused by pipe erosion by the sand. Acoustic emission sensors are used to monitor this sand in a bid to prevent such disasters. Ultrasound sensors record the impact of the sand on the pipe walls but are currently limited to simply detecting the presence of the sand and, with regular calibration, the sand rate.

The Project

The technical objective of this PhD is to use mathematical techniques and machine learning to extract more information from these complex data sets; for example, to quantify the sand size distribution, volume, shape, and velocity. Armed with this information, UK industry would be able to realise a step-change in its capability to reduce the effects of sand erosion and this would lead to increased production rates, extended well lifetimes, and optimised pipe inspection regimes.


So this is where you come in. You will work in a multi-disciplinary team across two universities and several industry partners. You will develop new mathematical methods and algorithms to tackle this problem. The project is ambitious and transformative and will require mathematical skills to be brought together from topics such as nonlinear dynamical systems, differential equations, and artificial intelligence. Don’t worry however as we will provide all the necessary training. What we need from you is an enquiring mind, a thirst for knowledge, and an excitement about this project.


There will be lots of opportunities to travel to for training and to meet with other PhD students in the different centres, industries and universities involved. Your interactions with the industry partners will provide you with an appreciation of the industrial and commercial opportunities surrounding this research project. This PhD will act as a perfect springboard for a career as a mathematician in industry.


You will be supervised by Prof Tony Mulholland who is the Head of the Department of Mathematics and Statistics at Strathclyde. He has published papers on the mathematics of ultrasonic systems for more than 20 years. He also has published extensively on nonlinear dynamical systems and on combining experimental data with mathematical models (so called inverse problems).

Prof Tony Mulholland

The supervisory team will also include

Prof Philip Aston from the Department of Mathematics at the University of Surrey who has published extensively in areas such as bifurcation theory, symmetry, computation of Lyapunov exponents using spatial integration, and attractor reconstruction methods for analysing time series data.

Prof Philip Aston

Prof Tony Gachagan who is the Director of the Centre for Ultrasonic Engineering; a vibrant, cross-faculty and multi-disciplinary research centre which has world class facilities and a vibrant research environment, including around 70 researchers with backgrounds in engineering, chemistry, biology, mathematics and statistics, physics, material science and computing.

Prof Tony Gachagan

The techniques developed will be tested on data from experimental test facilities both at Strathclyde (Dr Bill Dempster, Weir Advanced Research Centre) and industry, alongside data from computer simulations (Dr Mark Haw, Chemical and Process Engineering, Strathclyde).

Dr Mark Haw

You will work with industry !

Craig Marshall is a Flow Measurement Consultant with 10 years’ experience of USM’s, at TUV-SUD-NEL in East Kilbride, the National Measurement Institute for Flow in the UK.

Craig Marshall

Prof Alistair Forbes is Science Area Leader for Data Analysis and Uncertainty Evaluation at the National Physical Laboratory (NPL) in London.

Prof Alistair Forbes

Dr Daniel Csimszi is a Software Development Engineer with SMS Oilfield in Aberdeen; they supply, install and monitor the ultrasound measurement systems to the oil and gas industry.

Dr Daniel Csimszi

You will have opportunities to visit and interact with these industries on a regular basis throughout your PhD.

Funding Notes

This studentship covers tuition fees and provides an annual tax-free stipend of approx. £14,000 in the first year (typically rising with inflation for subsequent years) - additional support for conference travel is provided. The award is for 3.5 years. To qualify applicants should be UK or EU nationals, or should have been “ordinarily resident” in the UK for the last 3 years. Overseas students can apply but this award only covers the UK/EU fees and so applicants would need to have sufficient additional funds to cover the difference between UK/EU and overseas fees (details can be provided upon request).

How good is research at University of Strathclyde in Mathematical Sciences?

FTE Category A staff submitted: 32.90

Research output data provided by the Research Excellence Framework (REF)

Click here to see the results for all UK universities

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