Problem 1 (Elkem ASA, Kristiansand, Norway)

Mathematical Modelling of Silicon Carbide (SiC) Reactor for the Optimization of Industrial Design Parameters

Elkem is developing a new method to eliminate all direct CO₂ emissions from silicon (Si) production. The innovative approach uses carbon looping, where carbon oxides in the process off-gases are captured, converted into solid carbon, and reused in the process. If successful, this could revolutionise the global silicon industry. The process has several unique challenges including high-temperature conditions, solid to solid reaction, solid to gas reaction, solid and gas flow dynamics, and material properties changes due to reaction.

The modelling problem focuses on a high-temperature process where silicon carbide (SiC) is produced from solid carbon (C) and quartz (SiO₂) at temperatures around 1750℃, with CO as a byproduct. Elkem has studied this process in a pilot shaft reactor in Kristiansand, Norway the last year. At ESGI 171 in 2023, we presented a problem on modelling this SiC pilot reactor. The resulting report provides a detailed understanding of the process, including heat and material transfer and chemical reactions in the pilot shaft reactor, and will serve as a starting point for this study group task.

A packed-bed shaft SiC reactor faces significant scale-up issues due to radial heat transfer limitations. We are exploring alternative solutions for industrialisation, such as an electrical rotary kiln. This kiln uses electric heating elements to heat materials, providing efficient heat transfer, better temperature control, and producing non-combusted CO off-gas.

The task involves developing a mathematical model for the SiC pilot shaft reactor, using the previous model as a starting point. This model will be adapted to the framework of a rotary kiln. It should allow to simulate different kiln design configurations and operating parameters. This will help determine which configurations meet the requirements for SiC production while providing necessary control over the off gases produced in the process.

Problem 2 (Statnett, Oslo)

Optimization in power system markets

In the European power system, price coupling algorithms are applied to find the equilibrium market price from bids in the day-ahead spot market and markets for system stability services. To be able to forecast future market energy prices months and years ahead, stochastic simulation models are applied. Usually the stochastic part is related to variation in inflow, wind and solar production. Later development points to a more volatile and unpredictable market due to geopolitical circumstances and variation in availability and price of fossil fuels used for electricity generation.

The green transition will see the inclusion of new resources as wind and solar power. These renewables are more volatile and there is a need for system services to maintain system balance and stability. New markets will be applied to exchange system services. To be able to maximize the socio-economic surplus of production and flexibility resources, the physical system and its capabilities and restrictions must be modelled. An optimization over time must take into account the future volatility and uncertainty.

Challenge: Apply stochastic optimization methods to maximize the socio-economic surplus and market utilization of production and flexibility resources in an market for electric energy.