In this work, we present a multi-scale modeling approach for solar grade silicon production in fluidized bed reactor (FBR) by thermal decomposition of silane. The FBR process has been commercialized by several companies and promises to deliver poly-silicon at reasonable and stable price. Silane decomposes to form hydrogen and silicon and seed particles grow by heterogeneous chemical vapor deposition and by scavenging silicon powder produced in homogeneous gas phase reaction. The subsequent particle growth process is represented by a discretized version of population balance. The model uses ordinary differential and algebraic equations to track particle movement through discrete size intervals to simulate changes in the size distribution. The dynamics of gas phase is modeled Computational Fluid Dynamics (CFD) model. The CFD module shows the hydrodynamics via momentum balance, mass and heat transfer between different phases. The volume fraction of phase, concentration of each components and temperature of the bed is generated and are imported into the population balance. The particle size distribution calculated by population balance is used as the input of the CFD module and thus the complex interplay between particulate phase and continuous phase is captured by integrating those two modules.
Based on the multi-scale model, a novel method is proposed to derive the global stability condition to guarantee the stable operation of FBR. The resulting analytical stability condition will be verified by numerical simulations. The particulate process in FBR is complex and typically has very few measurements, inventory control is a simple method for control of complex systems and thus has potential for industrial application. We apply inventory control strategy to control particle size distribution to improve the performance of the silicon production process. Due to the lack of knowledge of the reaction coefficient, which is used in population balance to describe the mass transfer rate from gas phase to dispersed phase, an on-line estimator based on adaptive mechanism will be developed to track experimental behavior more accurately and in addition to enhance robustness of the inventory control system.
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