(508a) Dynamic Modeling and Recipe Optimization of Semibatch Polymerization Processes

Y. Nie L.T. Biegler

Department of Chemical Engineering

Carnegie Mellon University

C.M. Villa J.M. Wassick

The Dow Chemical Company

Dynamic modeling and optimization techniques offer advantages for the design and improvement of process recipes. In this study, a mathematical model is first developed to describe the dynamic behavior of a polymerization process, based on first-principles including the heat and mass balances, reaction kinetics and vapor-liquid equilibrium (VLE). Next, a dynamic optimization strategy based on the direct transcription method is applied to optimize the process recipe, where the residence time is minimized, given a target product molecular weight as well as requirements on byproduct formation and reactor temperature.

The polymerization reaction can be carried out in conventional stirred- tank reactors with heat exchangers, following a semi-batch manner. The raw materials are first formed by mixing with catalysts in the reactor tank, and then monomer is continuously fed into the tank to form homopolymers. Each polymer chain undertakes the initiation, propagation, exchange and proton transfer reactions. There are two major considerations during the operation of the reactor. First, impurities are generated, which are undesired. Second, the unreacted monomer concentration should be limited to ensure safe operations in case of losing the cooling capacity. To deal with both issues, the monomer feed rate and the coolant flow rate need to be well controlled, and the concept of the adiabatic end temperature is introduced as a safety criteria with a specified upper limit.

The developed polymer process model is complicated by a large set of differential algebraic equations (DAEs) due to the population balances written with respect to chains of the same number of repeating units. Therefore, the optimization formulation is in the form of a dynamic optimization problem. The direct transcription method serves as an efficient tool for solving such problems. In this method, the DAEs are fully discretized into nonlinear algebraic equations at collocation points over finite elements and thus the dynamic optimization problem is translated into a large-scale nonlinear program (NLP) that can be handled by the off-the-shelf nonlinear solvers such as IPOPT. In this study, we model and solve the translated NLP in GAMS with IPOPT. From the simulation results, the batch time is significantly reduced compared to industrial data.