Maximum-Likelihood Parameter Estimation for the Thin-Shell Quasi-Newtonian Model for a Laboratory Blown Film Extruder

While most plastic films are manufactured by blown film extrusion, their first-principles modeling has remained substantially more challenging than for most other chemical engineering unit operations due to its combination of heat transfer, crystallization, and non-Newtonian fluid mechanics. This paper applies maximum-likelihood parameter estimation to characterize the convective heat transfer characteristics from measured spatial radii and temperature profiles for a laboratory-scale blown film process extruding a linear low density polyethylene (LLDPE) polymer. The Pearson and Petrie thin-film extrusion model incorporates (i) a quasi-Newtonian constitutive relation for the effect of temperature and crystallization on the viscosity of the polymer and (ii) a spatial variation of the heat transfer coefficient that is qualitatively consistent with turbulent flow simulations reported in the literature. A single heat transfer expression fit the experimental conditions for a cooling air flow rate of 1.5 m/s, whereas the variation of two parameters was able to fit all but one experimental condition for a cooling air flow rate of 1.0 m/s. The experimental condition that was poorly fit by the model had the highest takeup ratio, which was the operating condition closest to film instability and likely the condition most sensitive to the heat transfer relation. The experimental conditions corresponding to observed stable operations were investigated by linearized stability analysis.