(204a) Online Optimization for Grade Transitions in Polyethylene Solution Polymerization Process

Various grades of linear low-density polyethylene (LLDPE) are tailored to different applications, with each grade defined by specifications of product properties such as melt index and density. Typically, several different grades are produced in the same production line, which requires frequent transitions. Given the large market of LLDPE and the current experience-based transitions, there is a need, and also room for improvement, to perform transitions and to change operation conditions in a way such that the transition time as well as the off-grade product could be minimized.

In our previous study, a mathematical model capturing the dynamics of the solution polymerization process carried out in a CSTR is developed. Besides the mass and heat balance equations, the optimization model for the entire process  adopts the molecular weight moment model for the prediction of product properties and incorporates a simple, yet accurate, data-driven vapor-liquid equilibrium (VLE) model derived from rigorous calculation. Two optimization formulations, single stage and multistage optimization, are proposed to deal with single-value specification and specification bands of product properties, respectively. The results show significant improvement in transition times and off-grade production.

The offline dynamic optimization demonstrates strong potential in handling grade transition problems, but its performance can deteriorate in the presence of uncertainties, disturbances and model mismatch. In order to deal with this problem, an offline optimization strategy based on backoff constraints is taken into account to obtain robust optimal policies which can be applied to systems with different uncertainty levels.

In this talk, we extend the off-line framework described above to include online state estimation and optimal control of the large-scale grade transition problems. As described in Jung et al. (2015), two key components of the framework are state estimator and model predictive controller; both components incorporate the rigorous dynamic model we developed in our previous work. First, a shrinking horizon nonlinear model predictive control (sh-NMPC) is applied to minimize transition time and off-grade product, and to refine the control schemes.  Next, an expanding horizon least squares estimation (eh-LSE) is designed to provide state estimates based on measurements in the past.  At each time step, process measurements are obtained and used in eh-LSE optimization problem. The resulting state estimates serve as the initial value of an updated NMPC problem, which is then solved to reduce the overall transition time and the off-grade product. The resulting control scheme is also applied to the system at each time step so that new measurements are added. The effectiveness of the framework is demonstrated by several case studies in which uncertainties, measurement errors and disturbances are taken into account.

Reference

Tae Y. Jung, Yisu Nie, J. H. Lee, L. T. Biegler, “Model-based On-Line Optimization Framework for Semi-batch Polymerization Reactors,” Proceedings of ADCHEM 2015, Whistler, BC, June, 2015