(4aa) Multi-Scale Modeling and Optimal Design Of Particulate Processes With Application To Solar Grade Silicon Production

My research interest in particle technology and particulate processes was motivated by an industrial application of solar grade silicon production in a fluidized bed reactor. We completed a multi-scale model by integrating three modules to capture the complex dynamics along different temporal and spatial coordinates. The integrated model has the capability to predict the silicon yield in the bed. By collaborating with our industrial partners from Renewable Energy Corporation, we validated the model against actual experimental data. The model was used to scale up and optimal design the demonstration scale reactor and is continued to be used for operation of the commercial system. A multi-scale model predicts silicon production yield and powder loss in a fluidized bed reactor for solar silicon production. The reaction module calculates the silicon vapor deposition and powder scavenging rates used by a population balance model that calculates the particle mass distribution functions. The model results are validated against industrial data. Furthermore, we conduct a sensitivity analysis to investigate the effect of gas flow rate and inlet Silane concentration.

New findings of my work show that an inherent instability exists in population balance as long as small particles are present in the particulate processes. An analytical expression was derived to explain how the critical size for stability of the particle size distribution function depends on physical properties and control parameters of the process. The mass distribution function of particles at steady state is derived and serves as the stationary equilibrium point of the population balance. I developed a discretization scheme which requires negligible computing effort. The discretized population balance is formulated in a network representation and a modified Tellegen's theorem is developed to provide an equivalent stability condition for the discrete form.

I pursued research in the control structure design in the context of reactive systems involving population balance. A systematic approach to choose process measurements and controlled outputs for nonlinear control systems was developed.  The exponential stability and strict passivity of closed-loop control systems are guaranteed if the control structure is selected properly. I applied it to the abovementioned fluidized bed reactor, which only has a few degrees of freedom to manipulate. The proposed control strategy is proposed to maintain the process at the desired operating condition.