Multi‐scale Modeling and Constrained Sensitivity Analysis of Particulate CVD Systems

Abstract

Abstract A finite‐dimensional, state‐space model of the discrete distribution function bypasses discretization of the continuous population balance, and facilitates simple modeling and fast numerical integration. An analytical expression describes the steady‐state, average particle diameter as a function of parameters such as nucleation, agglomeration, breakage, seed rate, and average seed particle diameter. The discrete population balance model is used to evaluate the analytical expression sensitivity to growth and decay phenomena such as nucleation, agglomeration, and breakage. The analytical expression is validated against data obtained from an industrial‐scale, fluidized bed, pilot reactor designed to produce solar‐grade silicon. The results indicate how the analytical expression describes a CVD‐type growth process, and also how the growth process may deviate due to the operating conditions.