(659d) On the Identification of Meta-Models for the Optimization of Grade Transition in Polymerization Processes

An accurate mathematical model is essential in optimizing the grade transition in polymerization processes. Due to the complexity of the processes, large-scale knowledge-driven models consisting of Differential Algebraic Equations (DAE) have been developed to describe the process behaviours [1, 2]. Industrial models are expected to be more complex than the ones in the open literature. The grade transition problem is usually solved using model-based optimization approaches [3, 4] explicitly utilizing the available knowledge-driven models. There are two major limitations in this approach. Firstly, it might require substantial computational resources, especially when the detailed knowledge-driven models are very complex and when one needs to simultaneously schedule multiple plants and multiple grade transitions. Secondly, there is always a model-plant mismatch that needs to be taken into account. Adapting the highly complex and nonlinear knowledge-driven model through parameter re-estimation to match the plant 100% does not appear to be an easy task.

We approach the problem by first developing a meta-model of the detailed knowledge-driven model and quantify its performance in the grade transition optimization problem, from the prediction accuracy and the needed computational time points of view. A set of systematically selected in silico experiments, using the Design of Experiments approach [5, 6], is used to generate data for estimating the parameters of the Response Surface Model, the meta-model. The parameter estimation task aims to match the detailed modelâ??s predictions to those of the meta-model in the desired regions of operation. Analysis of variance concepts are used to assess the accuracy of the meta-model.

The optimal operating conditions, depending on the Hydrogen feeding profile, and leading to minimum amount of the off-spec product are determined using the detailed knowledge-driven model and its meta-model approximation. We compare the meta-model predictions against those of the knowledge-driven model concerning the amount of off-spec product and the needed time for transition. This is done in six grade transition examples covering the entire range of desired polymer grades. In all six transitions, the differences between the meta-model predictions and the knowledge-driven modelâ??s calculations are within 3%. More importantly, the computational time for the optimization using the meta-model is, on the average, 50 times smaller than the computational time required for solving the same problem using the knowledge-driven model. We also discuss how such a meta-model can be complemented to fit the plantâ??s behaviour more accurately utilizing historical data on the expected and achieved plant behaviours.

References

1. Zacca, J.J. and W.H. Ray, Modeling of the liquid-phase polymerization of olefins in loop reactors. Chemical Engineering Science, 1993. 48(22): p. 3743-3765.

2. Dunnebier, G., et al., Optimization and control of polymerization processes. Chemical Engineering & Technology, 2005. 28(5): p. 575-580.

3. Shi, J., L.T. Biegler, and I. Hamdan, Optimization of grade transitions in polyethylene solution polymerization processes. Aiche Journal, 2016. 62(4): p. 1126-1142.

4. Cervantes, A.M., et al., Large-scale dynamic optimization for grade transitions in a low density polyethylene plant. Computers & Chemical Engineering, 2002. 26(2): p. 227-237.

5. Box, G.E.P. and N.R. Draper, Response Surfaces, Mixtures, and Ridge Analysis. 2007, Hoboken, NJ: Wiley.

6. Montgomery, D.C., Design and Analysis of Experiments. 8 ed. 2013, New York: Wiley. 729.