(71d) Numerical Study of the Evolution of Particle Size and Morphology in an Industrial Titanium Dioxide Reactor

Titanium
dioxide is a ubiquitous industrial product with applications ranging from
pigments to photocatalysts. Particle morphology, which plays a critical role in
controlling optical properties, is determined by the interplay between complex
particle processes such as inception, aggregation and sintering. There is
therefore both scientific and commercial interest in understanding particle
morphology. A stochastic population balance method is used to study the
non-isothermal synthesis of particulate titanium dioxide via the chloride
process under industrial conditions, with a multivariate particle model used to
resolve fine-grained particle structure and inform surface related processes
such as sintering and heterogenous growth. A network of ideal reactors is used
as a modular approximation to the reactor dosing, reaction and cooling zones in
which concentration and temperature gradients exist. Varying the network
topology allows for simultaneous spatial and temporal resolution of particle
aggregate morphology, including size distributions and connectivity of primary
particles in the aggregates. Our model allows us to connect operating
conditions directly to detailed morphology, for example illustrating how the aggregate
collision diameters and the number of constituent primary particles increase as
feed oxygen content increases. The industrial synthesis is performed under
elevated temperatures and pressures, and the precursor concentration and
particle number density are significantly higher than those occurring in
laboratory studies. We discuss computational challenges encountered when
"scaling" population balance modelling techniques to industrially
relevant conditions and accounting for complex reactor geometries while
incorporating multi-dimensional particle structure in the model. Adaptations to
weighted particle methods are developed to address numerical issues encountered
due to the high process rates, temperature exotherm and initial transience. 

Figure
1. Industrial reactor modelled by a network of ideal reactors capable of evolving
individual population balances and particle morphology distributions in each
reactor