Maths model could ‘improve nuclear safety’

Utilising data taken from its model, the research team at the University of Leeds aims to reduce the number of potentially dangerous manual inspections of nuclear waste containers.

“It’s a wonderful example of how complex mathematical models can have everyday applications,” said Duncan Borman, from the School of Civil Engineering at the University of Leeds, and co-author of the study.

“The modelling tool can be applied to a range of ’fouling’ type applications such as [industrial boilers, refining plants, and within large laboratory equipment such as fume cupboards],” Borman said.

“This includes heat exchangers where there are regular issues of deposits building up which block and reduce performance.”

According to Borman, the model can also be used to understand the way these deposits will form so that interventions can be made to minimise them.

Originally approached by the National Nuclear Laboratory (NNL) and nuclear management firm Sellafield, Borman’s team was tasked with predicting the shapes that precipitate from nuclear process solutions that can form in containment chambers.

Daniel Lesnic, from the School of Mathematics at the University of Leeds and co-author of the study, said: “Our first thought was to find a suitable analogy in nature. At first we looked at how lava flows from a volcano to the ocean, but the formation of stalagmites in caves mimics the process much more closely.

“Geologists have well-established models for the formation of stalagmites. So we are taking models from one field of science and applying them to a completely different discipline.”

Within the nuclear industry, hazardous salt solutions can arise within industrial containment vessels. The salt solution precipitates out, forming structures with morphologies that bear a resemblance to stalagmites, the researchers said.

According to the researchers, if left unchecked, there is a potential for these solutions to multiply, which increases the hazard risk within a nuclear containment chamber.

The nuclear model, which was based on an existing model for predicting stalagmite growth, was adapted to include the chemical and physical properties of the particular salt solution of interest to the nuclear industry; a more realistic fluid flow; and to consider the sensitivity of results to varying temperature.

Mike Dawson from the School of Chemical and Process Engineering at the University of Leeds and study leader, said: “It took many months of intensive research to develop the model. The big test came when we tested the model against real data from the National Nuclear Laboratory.

“Our model stood up to the test. For the first time it was possible to predict the morphology of these complex crystallising flows reliably.”

The research team said that its model provides a “new tool” for the NNL and Sellafield, with the potential to “save both money and continue to ensure they are at the forefront of world-leading safety technology”.

Looking ahead, the research team will continue to work alongside the NNL and Sellafield to adapt the model to a range of processes.

This includes boilers and evaporators, but also safety related systems, the researchers said.

A full account of the study has been published in the journal Computers & Chemical Engineering.