Modelling chemical and transfer processes in a silicon carbide reactor

Thesis

Traditional refining of silicon generates carbon dioxide emissions that are released into the atmosphere. An alternative pathway under experimental exploration processes quartz and carbon into silicon carbide. We present mathematical models for the chemical and transfer processes within a silicon carbide reactor. We consider both a single pellet model and multiphase model. We then optimize the the multiphase model for silicon~yield.

We first examine a quartz particle coated in a layer of porous carbon as the raw material. We derive governing equations for the key chemical species silicon monoxide, carbon monoxide, and carbon dioxide, along with conservation laws on the surface of the quartz. We reduce our model to an industrially relevant distinguished limit and identify two distinct behaviours: reaction-limited and diffusion-limited. We find that the diffusion-limited regime obtains higher silicon yield and carbon utilization.

We then develop a multiphase model for a homogenous bed of quartz and carbon particles in a laboratory-scale crucible. We model the phases of carbon, silicon carbide, quartz, and the gas mixture. We also consider the motion of the solid, and model the gas flow with Darcy's law. Both analytical and numerical methods are employed to explore the effects of the dimensionless parameters on system behaviour. The dependence of silicon yield, carbon utilization, and maximum pressure on dimensionless parameters is understood through parameter sweeps. We find that a high silicon yield is primarily achieved by balancing the relative speed of the reactions, while maintaining a safe gas pressure requires balancing the ratio of transport to reaction speed.

Finally, we focus on optimizing the multiphase model to maximize silicon yield while maintaining safe pressures. We further examine the parameter space around the optimum point with parameter sweeps and sensitivity analysis. We find that maximizing the speed of the silicon carbide reaction most significantly contributes to a high silicon yield. We then explore the effect of dimensional parameters, such as the initial bed height, on the maximum silicon yield achievable within an industrially relevant timeframe.

Authors: Metherall, B

• DOI: 10.5287/ora-xqpv95bay
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: multiphase modelling; gas dynamics; porous media; silicon production
• Subjects: Applied mathematics