Control of a Titania Aerosol Reactor

Abstract

Titania powder finds a major use as a white pigment in paints and in absorbents, and is commercially produced by two main processes: the gas phase oxidation of titanium tetrachloride, resulting in micron sized particles which are used as white pigments, and the gas phase hydrolysis of titanium tetrachloride, resulting in nanometer sized particles, which are used as UV absorbants. The pigmentary properties of titania, such as the opacity and gloss, depend heavily on the particle size. This fact suggests the design and implementation of advanced model-based feedback control schemes on titania aerosol reactors to produce powders with desired size distributions. The development of mathematical models for aerosol reactors that accurately describe the evolution of key variables that characterize the form of the size distribution is usually addressed through application of population balances to the particulate phase (see Akhtar et al., 1991; Kobata et al., 1991 for modeling of titania aerosol reactors). However, the high complexity of the population balances (systems of nonlinear partial integro-differential equations) renders them inappropriate for process simulation and controller design. Fortunately, the fact that most aerosol size distributions can be adequately described by lognormal functions (William and Loyalka, 1991) allows utilizing the method of moments to derive approximations of the population balances that accurately describe the key properties of the aerosol size distribution; such approximate models are suitable for process simulation and controller design.