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  Solving differential equations in chemical engineering

   Faculty of Engineering and Physical Sciences

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  Dr Jitse Niesen  Applications accepted all year round  Self-Funded PhD Students Only

About the Project

In a compartment model, the total volume in a chemical process is divided in multiple compartments that are assumed to be well mixed. The process is then described as a big system of ordinary differential equations (ODEs) specifying the concentrations of the chemical reactants in each compartment and other quantities like temperature. Prior research led to a tool that construct the ODEs from a high-level description of the chemical process. However, standard implementations of ODE solvers do not work as well as we had hoped.

We have some ideas on potential issues. The vastly different time scales in chemical reactions mean that the ODEs are usually stiff; however, this is quite a classical problem and there are standard methods (implicit solvers) that should be able to handle this. Quantities like concentration and volume can get very small but they have to remain positive throughout the computation, otherwise the equations and results do not make sense. The equations also have discontinuities in them (for instance, an overflow may activate when the volume in a tank exceed some level), which may also require special handling. However, it is not clear at this point which of these is the main bottleneck, or whether it is a combination or even something completely different.

The aim of the project is to investigate the performance issues with standard ODE solvers, identify some ways to resolve them, and incorporate this in our tool. This project requires some knowledge of numerical methods for solving ODEs and some programming experience. An interest in chemistry is also needed.

Engineering (12) Mathematics (25)

Funding Notes

This project is available for Self-Funded Students only

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