(126b) Robust Online Optimization for Grade Transitions in Polyethylene Solution Polymerization

There are various grades of linear low-density polyethylene (LLDPE) 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. In certain instances, complex transitions rely heavily on operator/expert experience. 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 smarter way such that the transition time as well as the off-grade product could be minimized.

In this study, we consider a mathematical model capturing the dynamics of the solution polymerization process carried out in a CSTR. Besides the mass and heat balance equations, the whole model adopts the molecular weight moment model for the prediction of product properties and incorporates a simple, yet accurate, vapor-liquid equilibrium (VLE) model derived from rigorous calculation. As described in Shi et al. (2013), the model is validated via input step responses and then simultaneous dynamic optimization approach is applied to solve the problem. Two optimization formulations, single stage and multistage optimization, have been developed 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 compared with step change simulation. Also, the multistage formulation designed for problems with specification bands outperforms the single stage formulation as the former one leads to more aggressive control profiles and allows oscillations within the bands. Another advantage of multistage formulation is that it’s capable to minimize the transition time and off-grade production directly.

The offline dynamic optimization demonstrates the potential in dealing with grade transition problems, but its performance can deteriorate in the presence of uncertainties, disturbances and model mismatch. In order to assess the impact, different transitions under various uncertainty levels are performed and robust optimization strategies for grade transitions are taken into account to obtain optimal policies which can be applied to systems with different uncertainty levels.  This talk describes two complementary approaches to deal with these uncertainties. The first deals with the development of a robust, multi-scenario optimization approach. As detailed in Huang et al. (2009) and Lucia, Finkler and Engell (2013), a multi-scenario dynamic optimization problem is posed and solved on-line. Next, we consider a model-based state estimator that provides an estimate of the uncertainties to feed into the model-based on-line optimizer.  Finally, we develop an optimization formulation that combines both strategies and we demonstrate improved performance of this synergistic strategy, over implementations of either strategy by itself.

References

Shi, J., Hamdan, I, Munjal, S., & Biegler, L. T. (2013) Model-Based Control for Optimal Transitions in Polyethylene Solution Polymerization. AIChE Annual Meeting. Presentation.

Lucia, S., Finkler, T., & Engell, S. (2013). Multi-stage nonlinear model predictive control applied to a semi-batch polymerization reactor under uncertainty.Journal of Process Control, 23(9), 1306-1319.

Huang, R., Patwardhan, S. C., & Biegler, L. T. (2009). Multi-scenario-based robust nonlinear model predictive control with first principle models. Computer Aided Chemical Engineering, 27, 1293-1298.