Assessing optimal growth of desired species in epoxy polymerization under uncertainty

While carrying out optimization studies on kinetic scheme based models of polymerization reactions, there are kinetic parameters that need to be tuned with process data during model building exercise and henceforth assumed constant during the entire course of optimization studies. As these parameters are subjected to experimental and regression errors, some levels of uncertainty are embedded in them. Hence, handling them as constant parameters and thereby neglecting the uncertainty associated with them during the entire course of optimization is not realistic. These problems are handled formally in the paradigm of optimization under uncertainty where uncertainty propagation of these parameters through model equations is reflected in terms of system constraints and objectives that facilitate a designer to unveil the tradeoff between solution optimality and robustness. Chance constrained fuzzy simulation based approach is one such methodology that merges the facets of chance constrained programming and fuzzy logic and is adopted here to carry out an analysis in determining optimal performance of a semi-batch epoxy polymerization reactor under uncertainty in kinetic parameters used for model building. The aim of this study is to find out the tradeoff among optimal growth of the desired species, solution robustness and productivity achieved through optimal discrete addition rates of different ingredients, e.g. bisphenol-A, epichlorohydrin and sodium hydroxide while maintaining the constraints on the control variables that are expressed in terms of bounds on Mn, PDI and other constraints reflecting the experimental conditions realistically. The deterministic multiobjective optimization model of Majumdar et al. [11] forms the basis of this work on which various effects of uncertain parameters are shown and analyzed in a Pareto fashion using real coded fuzzy chance constrained NSGA II.