Handling Uncertainty in Kinetic Parameters in Optimal Operation of a Polymerization Reactor

Abstract

In deterministic optimization of the epoxy polymerization system, kinetic parameters for the assumed reaction scheme, once tuned with experimental data during the model building exercise, are assumed constant henceforth during the entire course of optimization studies. However, the important fact that these parameters are subjected to experimental and regression errors and thereby some level of uncertainty are embedded in them has been ignored by assuming them as constants. This further leads to emergence of suboptimal solutions that cannot fully utilize the true potential of the situation in hand. It is, therefore, realistic to consider the uncertainty associated with these parameters. Different methodologies from the paradigm of optimization under uncertainty have been generally used to formally tackle these problems 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 trade-off between solution optimality and robustness. Chance constrained programming (CCP) is one such methodology and is adopted here to carry out an analysis in determining optimal performance of a semibatch epoxy polymerization reactor under uncertainty in kinetic parameters. This multiobjective optimal control study aims to find out the trade-off among optimal growth of the desired species, solution robustness, and productivity of the reactor achieved through optimal discrete addition rates of different manipulated variables, e.g., bisphenol-A, epichlorohydrin, and sodium hydroxide. Various system requirements on the control variables are expressed in terms of bounds on number average molecular weight, polydispersity index, and other constraints that express the experimental conditions realistically.