(226c) Optimal Control of Particle Size Distribution in Semi-Batch Emulsion Polymerisation Processes: Recipe Optimisation and Experimental Validation

The talk will describe open-loop optimisation studies aimed at the determination of the optimal feed policies and operating conditions for semi-batch emulsion polymerisation to attain a target particle size distribution (PSD). A detailed population balance model is used for this purpose. Experimental validation of the identified optimal policies will be discussed. Emulsion polymerisation is used in industry to produce a wide range of products, such as adhesives, paints, coatings, synthetic rubbers and cosmetics. Emulsion polymerisation is a free-radical chain polymerisation and a heterogeneous process, in which polymer particles are dispersed in an aqueous phase. Surfactant is used to stabilise the particles. If excess monomers are supplied to the system, monomer droplets can form in the bulk and be used as reservoir, with monomers diffusing from them into the particles through the aqueous phase. Because it uses water as solvent, emulsion polymerisation is seen as an environmentally friendly alternative to solution polymerisation. Gelation problems, common in bulk polymerisation, are subdued due to segregation of the growing polymer chains inside the polymer particles. Moreover, in contrast with other polymerisation processes, in emulsion polymerisation molar mass and polymerisation rate can be simultaneously incremented. Low viscosity of the bulk and high heat transfer coefficient of the water also contributes, together with the above listed features, to the success of this widely used industrial process. The focus of our research is the control of the particle size distribution (PSD) of emulsion latexes. The importance of controlling this parameter resides in the strong influence of PSD on some relevant properties of the final latex, such as mechanical strength and film forming, optical and rheological properties. Different attempts to control a few average properties of the distribution [1, 2] and the full distribution [3, 4] are reported. The control of the entire PSD has been addressed only in recent times as a direct consequence of the advancement in the technologies used for the online measurements of PSD, which guarantee faster and more accurate estimation. The importance of controlling the full PSD resides in the fact that different distributions can have same moments, but show different end-use properties [5]. Nucleation of particles by homogeneous and/or micellar nucleation, continuous growth of the polymer chains inside the polymer particles and discrete growth by particle coagulation are the three major phenomena that drive the PSD of the emulsion latex. For control purposes, an accurate model of the PSD dynamic evolution, which accounts for the complex interactions between these phenomena, is needed. The model is formulated using population balance equations, natural framework to embed nucleation, growth and coagulation rates. In our studies we refer to the mechanistic population balance model of Immanuel et al. [6]. Different work can be found in the literature on the control of particulate processes described by population balance equations [7, 8, 9]. The process under study is the semi-batch emulsion copolymerisation of Vinyl Acetate (VAc) and Butyl Acrylate (BuA). The use of both ionic and non-ionic surfactants, as well as of redox and thermal initiators, was considered. A jacketed half-litre pilot reactor with multiple feeds was used for experimental validations and a Capillary Hydrodynamic Fractionator (CHDF) for PSD measurements. Dynamic optimisation studies were performed on the process to determine operating policies that lead to better matches of target PSDs. The manipulated variables optimised are the feed policies of surfactant and VAc (i.e. feed rates and duration of time interval in a piece wise constant feed profile). Different formulations of the underlying optimisation were considered ranging from single objective to multi-objective optimisation based on hierarchical process considerations. The multi-objective optimisation is a å-constrained optimisation strategy. In this, the minimisation of the error between end-point and target weight-averaged PSD is coupled with that of other two objective functions that account for the error on the solids content and total number of particles profiles. While the PSD is optimised to the target, the other two objective functions are subject to upper constraints with an increasing penalty. The correlation between the three parameters guarantees enhanced optimiser performances. Moreover, both solids content and number of particles profiles are optimised at different times along the batch, which makes them suitable for the use in a potential online feedback control of the process. A Sequential Quadratic Programming (SQP) package from Fortran NAG library is used as optimisation routine. Although non convexity in the optimisation problem and discontinuities in the process could enforce the use of a global optimisation technique, we saw that the implementation of gradient based techniques, such as SQP, give excellent results in terms of match between targets and simulated distributions. Experimental validation of the optimisation results suggested possible enhancements of the original model. A more prolonged coagulation phenomena and a possible error in the range of stable particles were observed experimentally. The micellar nucleation phenomena is captured well by the model in the first part of the batch. The growth rate (i.e. solids content) seems to be also well reproduced.

References

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