PhD Studentship: Energy Storage Bed Dynamics - The Ever-expanding Magnesium Bed Conundrum

University of Nottingham - Mathematical Sciences

Location: University Park

Supervised by John King (Maths), Gavin Walker (Engineering) and Richard Wheatley (Chemistry)

The Project:

In order to facilitate high penetration of renewable energy in to the grid, energy storage is needed in order to better manage supply and demand for the grid. Hydrogen offers a high energy density solution and, rather than storing the hydrogen as a gas at high pressures, solid state storage of hydrogen in a metal like magnesium offers a low pressure and low cost technology. The hydrogenation of magnesium is very exothermic (74.5 kJ mol-1) and the material is also being investigated as a thermal energy store (i.e. using the exotherm of hydrogenation to liberate the stored thermal energy back as heat at 400C).

A fear was that cycling a magnesium bed at high temperatures would lead to sintering and loss of void space. However, the startling result was that the powdered magnesium bed when cycled at temperatures of 350-400C, rather than losing porosity, gained porosity. The form of the bed had changed from a loose powder to a metal porous plug which had swelled in dimensions to fill the available head space in the vessel. Further cycling at temperature below 350C results in the bed resorting back to a more densely packed loose powder.

The intriguing question is to uncover the fundamental mechanism(s) behind this process and to develop a predicative model based on the physical and chemical processes occurring. For the application, understanding these processes will enable optimisation of the porous structure for heat and mass flow; moreover, there is also concern the expanding bed may exert significant stress on the wall of the storage vessel eventually leading to failure of the vessel.

This challenging project will develop new mathematical models based on the chemical and physical processes occurring in order to develop a model that simulates the expanding porous bed phenomenon. Some of these processes include: nucleation, growth of the metal hydride phase, crystal lattice expansion leading to defect formation, decrepitation, atomic diffusion and surface energy minimisation, annealing. The models developed will thus need to encompass a wide range of physical phenomena; the focus will be on partial-differential-equation/moving-boundary formulations, building on the established sintering literature but, for the reasons described above (specifically, to generate increased, rather than decreased, porosity), of necessity raising significant additional challenges.The project will accordingly equip the student with an unusually wide experience of experimental and modelling questions and of mathematical techniques, as applied in a context with clear energy and sustainability implications.

Summary: UK/EU students - Tuition Fees paid, and full Stipend at RCUK rate, £14,600 per annum. The scholarship length will be 3.5 years, the successful applicant will be part of the Energy Research Accelerator at the University of Nottingham (

Entry Requirements: Starting October 2018, we require a graduate with a 1st class degree in Mathematics or relevant discipline, preferably at Masters level, or an equivalent overseas degree (2:1 in exceptional circumstances).



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Midlands of England