We report the theoretical derivation of a kinetic model for the prediction of average block structures such as number-average blocks, average block length, and average number of linkage points per chain, etc., in chain shuttling polymerization in the presence of dual catalysts based on the proposed mechanism. We further investigate how the chain shuttling rate constant and virgin chain shuttling agent (CSA) feed rate affect the average block structures predicted by this theoretical model for polymers produced in a continuous stirred tank reactor (CSTR). The simulations demonstrate that the coordination of dual catalysts and CSA is the key to enabling a successful chain shuttling polymerization system.

The reactor modeling and recipe optimization of conventional semibatch polyether polyol processes, in particular for the polymerization of propylene oxide to make polypropylene glycol, is addressed. A rigorous mathematical reactor model is first developed to describe the dynamic behavior of the polymerization process based on first‐principles including the mass and population balances, reaction kinetics, and vapor‐liquid equilibria. Next, the obtained differential algebraic model is reformulated by applying a nullspace projection method that results in an equivalent dynamic system with better computational performance. The reactor model is validated against plant data by adjusting model parameters. A dynamic optimization problem is then formulated to optimize the process recipe, where the batch processing time is minimized, given a target product molecular weight as well as other requirements on product quality and process safety. The dynamic optimization problem is translated into a nonlinear program using the simultaneous collocation strategy and further solved with the interior point method to obtain the optimal control profiles. The case study result shows a good match between the model prediction and real plant data, and the optimization approach is able to significantly reduce the batch time by 47%, which indicates great potential for industrial applications. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2515–2529, 2013

We propose a model-based optimization approach for the integration of production scheduling and dynamic process operation for general continuous/batch processes. The method introduces a discrete time formulation for simultaneous optimization of scheduling and operating decisions. The process is described by the resource task network (RTN) representation coupled with detailed first-principles process dynamic models. General complications in scheduling and control can be fully represented in this modeling framework, such as customer orders, transfer policies, and requirements on product quality and process safety. The scheduling and operation layers are linked with the task history state variables in the state space RTN model. A tailored generalized Benders decomposition (GBD) algorithm is applied to efficiently solve the resulting large nonconvex mixed-integer nonlinear program by exploring the particular model structure. We apply the integrated optimization approach to a polymerization process with two parallel semibatch reactors and continuous storage and purification units. The two polymerization reactors share cooling utility from the same source, and the utility price is dependent on the consumption rate. The optimization objective is to design the process schedule and reactor control policies simultaneously to maximize the overall process profit. The case study results suggest improvements in plant profitability for the integrated approach, in contrast to the typical sequential approach, where recipes of the polymerization tasks are individually optimized but the interactions among process units are overlooked.