Steady-State and Dynamic Modeling for New Product Design for the Solid-State Polymerization of Poly(Ethylene Terephthalate)

We model an entire poly(ethylene terephthalate) (PET) solid-state polymerization (SSP) process with precrystallizers, crystallizers, SSP reactors, and dryers using a unified cell approach. This approach builds complex unit-operation models using individual cells, or continuous-stirred-tank reactor (CSTR) models. Each cell considers the essential physical properties, phase equilibrium, polymerization kinetics, mass transfer through the polymer and into the carrier gas, and crystallization kinetics. Our model development involves fundamental chemical engineering principles and advanced software tools, such as Polymers Plus and Aspen Custom Modeler. We analyze both reaction and diffusion in each cell, considering two options: (1) to model diffusion using a second-order partial differential equation (PDE) or a simplified two-film theory and (2) to include or ignore crystallization kinetics. Performing best is the model with a PDE for diffusion and with equations describing crystallization and its effect on reaction and diffusion. We validate the model using commercial plant data of intrinsic viscosity, degree of crystallinity, and acetaldehyde concentration. We are unable to find a suitable set of parameters for other simpler models to represent accurately the plant data in its entirety. After validating our SSP model, we apply it to study the sensitivity of our SSP process on temperature and pellet geometry. For pellets with cross-sectional dimensions of 3.2 mm × 3.2 mm, we vary the length from 1.5 to 3.5 mm and predict the intrinsic viscosity. The model suggests only a mild dependence of intrinsic viscosity on the pellet length. In contrast, our model suggests that, for an increase in temperature of 12 °C, intrinsic viscosity rises by almost 0.1 dL/g. Last, we use our validated model to predict the process changes required to produce a high-viscosity product (1 dL/g). Our model suggests that, with appropriate increases in both reactor temperature and residence time, we can make this product.