Multiphase Multiphysics Modeling Framework for Nonlinear Predictive Control of Particulate Polysilicon Reactor Systems

Fluidized-bed reactors (FBRs) for silane pyrolysis offer an efficient and operationally advantageous approach for producing solar-grade silicon compared to traditional methods. However, controlling these systems poses significant challenges due to the intricate interactions between gas and solid phases. To address these complexities, a predictive modeling framework has been developed to facilitate real-time optimization and control of silicon production in FBRs. The gas-phase dynamics are described using a two-phase flow regime model, enabling accurate representation of the silane pyrolysis reaction and precise prediction of the deposition rate driving particle growth. A discrete population balance equation is employed to estimate the particle size distribution based on the predicted deposition rate. Leveraging this predictive model, a nonlinear model predictive control method is implemented to maintain optimal operating conditions, ensuring effective output tracking and improved economic performance. Closed-loop simulations demonstrate the effectiveness of the proposed framework in achieving desired operational objectives.