Control of Emulsion Polymerisation Processes: A Control-Relevant Model for Particle Size Distribution
Advancing the chemical engineering fundamentals
Polymer Science & Engineering - II (T2-12b)
Keywords: emulsion polymerisation, population balance model, particle size distribution, model reduction, feedback control
Emulsion polymerisation is a commercially important technology to produce polymeric materials for both conventional and novel applications. In this paper, firstly, an analysis will be presented identifying an inferential control scheme for the emulsion polymerisation process. Secondly, a control-relevant model will be described that is computationally less demanding, and thereby ideally suited for on-line applications. This model will serve as a useful complement for a more detailed population balance model that is imperative for off-line purposes such as open-loop optimisation. These two aspects are elaborated in the rest of the abstract.
In emulsion polymerisation, the polymer is produced within particles that span the sub-micron size range. The particle size distribution (PSD) plays a strong role in determining several end-use properties of the emulsion polymers. In particular, the PSD determines the rheology of the emulsion polymers by influencing the maximum packing factor of the particles in the latex. Thus, in addition to the conversion of the monomers and the polymer content of the latex, the PSD constitutes the most crucial control variable in the process. The PSD itself is determined by three particle-level phenomena, namely, nucleation, growth and coagulation, which interact with each other through an integrated internal feedback mechanism, resulting in a highly nonlinear process. The inferential control of rheology through PSD control facilitates the complex and non-convex rheology control problem by providing a guarantee for the identification of a control move that would lead to the desired rheology. It is also clear that the identification of the target PSD that would lead to the desired rheology will be strongly influenced by the process imposed reachability restrictions as well as interactions among the process variables.
Typical industrial operation of emulsion polymerisation reactors is in the batch mode. A detailed model of PSD in emulsion polymerisation is obtained through the use of population balances, which is the ideal basis for the open-loop optimisation of (semi-)batch operation, to determine the operating conditions and feed policies. For on-line feedback control using a model-based control framework, a less-extensive model would be preferable. Such a model could be formulated based on a lumping approximation using simpler material balances, instead of the population balances. While the population balances consider the time evolution of the particle population distribution over the size range of about 5 nm to 500 nm, the lumped material balances consider the time evolution of the total number of particles over the entire size range and their average size. The lumped model proposed here, which is computationally substantially simpler than the population balance model, retains all the features of the more intensive population balance model, including phase partitioning of monomers, surfactants and other reagents; kinetics and associated balances in the aqueous and particle phases; and the major particle phenomena of nucleation, growth and coagulation. However, all size-dependent properties are calculated based on the average particle size. The differences in the predictions of the simple lumped model and the comprehensive population balance model for two classes of PSD of interest have been studied (unimodal monodisperse PSD, and bimodal PSD). It is seen that the primary difference is in the prediction of the secondary nucleation while considering bimodal PSD classes. Thus, it is clear that this simpler model can be used for on-line control purposes, when combined with a state/parameter estimator. The estimator would use on-line measurements to implement a lumped correction to the model with regard to the nucleation parameters, and thereby produce a better prediction of any secondary nucleation for control of PSD. This holds better promise than the use of the comprehensive distributed model for on-line control purposes. As part of future work, it is of interest to study the ability of this lumped model to predict the oscillatory dynamics exhibited by continuous emulsion polymerisation reactors.
Presented Tuesday 18, 09:45 to 10:05, in session Polymer Science & Engineering - II (T2-12b).
