In this paper, it is shown that despite the large number of states and equations describing a distillation column the dynamics can be analyzed by lumping the states into a few variables characterizing the total holdup. Changes in holdup are compared to the global mass balance to derive a vector field describing the trajectories of the product compositions. The vector field contains detailed information about the dynamic behavior and is obtained without performing a complete dynamic simulation. Here, the procedure is applied to homogeneous azeotropic distillation, but with appropriate adjustments, it should be applicable to any column.

Recent developments of particle sizing sensors and control algorithms together with a better understanding of the physics of coagulation processes foster the application of advanced control systems to aggregating particulate systems in order to ensure the product quality despite disturbances and model errors. A model containing the main features of coagulation dynamics in shear flows, including aggregation, breakage, and time evolution of the cluster fractal dimension, was introduced and tuned to reproduce experimental data from the literature. Using this model, a set of particulate products, in terms of the mean size and fractal dimension, that can be obtained with different shear rate policies was identified. Finally, a control algorithm, the batch model predictive control, was applied to the system. The algorithm exploits the fact that batch processes are run repetitively and the availability of online measurements. The controller, tested with simulations, was able to guarantee the product quality in terms of the mean radius of gyration by adjusting the shear rate according to the current measurements and the results obtained in previous batches.

We analyze the aggregation process leading to gel formation in colloidal dispersions under quiescent conditions in order to identify possible precursor aggregate distributions for particulate gels. The aggregation process is described with an experimentally validated population balance model, which allows us to calculate how the aggregate mass distribution evolves in time. When the cumulative occupied volume fraction of fractal aggregates reaches a certain limit, the random cluster-cluster aggregation regime crosses over to an interconnection regime, and a gel network forms. The aggregate distribution at the end of the aggregation regime is the precursor for the subsequently formed particulate gel. We demonstrate that, when aggregation proceeds fully in the reaction-limited regime, the precursor aggregate distribution depends only on the solid volume fraction while being insensitive to both the primary particle size and the stability ratio. However, the stability ratio is an important operating parameter controlling the overall aggregation and gelation time. The situation can be significantly changed by entering the diffusion-limited aggregation regime. The interplay among these various factors is illustrated through an example of the optimal design of the precursor aggregate distribution. Primary particle size, solid volume fraction, and stability ratio are used as design parameters, and the objective function is formulated in terms of specific requirements on the precursor cluster mass distribution. These requirements were determined on the basis of qualitative arguments about the relation between the precursor structure and the gel mechanical properties.

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