(663f) State Observer for Process Monitoring of Melt Polycondensation Reactors

Polycondensation is an important polymerization method for the synthesis of polyesters, polyamides, etc. A commercially important polycondensation product is polyethylene terephthalate (PET), which is mainly used in synthetic fibers, water bottles and molding materials. It is manufactured by a four-stage process which consists of transesterification, prepolymerization, melt polycondensation and solid state polycondensation. The main polycondensation reaction is reversible and thus equilibrium limited [1]. In order to achieve a high molecular weight, byproduct (i.e., ethylene glycol) needs to be removed to favor the forward reaction by applying vacuum to the reactor in the finishing stage. Besides, the product in this stage determines the quality of final product, e.g. purity, melting point, average molecular weight, polydispersity index, etc. Therefore, control and monitoring of the finishing stage is of great importance.

However, lack of fast on-line sensors makes process monitoring of polycondensation very difficult. There is a substantial need to develop soft sensors which can estimate those unmeasured state variables accurately. In this study, a state observer based on exact error linearization with eigenvalue assignment [2,3] is used to reconstruct unmeasured state variables and estimate the degree of polymerization (DP).

Although a detailed kinetic model which includes all the polymeric species can describe the degree of polymerization and molecular weight distribution (MWD) quite accurately, it requires large computational effort and may not be suitable for control problems. For this reason, standard modeling approaches for the finishing stage only account for reactions between functional end groups.

In our work, melt polycondensation of PET in continuous stirred-tank reactor (CSTR) is studied. The four-state reaction-mass transfer model developed by Rafler et al. [4] and verified experimentally, was used throughout the present study. The concentration of ethylene glycol, hydroxyl end group, carboxyl end group and ester group in the melt are the four states of the model. The hydroxyl end group in the melt can be inferred from a model using torque, temperature and stirrer speed, which should be calibrated for the reactor [5]. The concentration of carboxyl end group is measurable by on-line acidimetric titration with addition of an indicator [6,7].

In the CSTR model, the mass transfer parameter is affected by bubbles, geometry of the reactor, and operating condition. Therefore, it needs to be determined from experimental data. Based on the two measurements, an observer was built for estimating the states as well as the mass transfer parameter, which provided fast-converging accurate estimates. After obtaining the mass transfer parameter off-line, we considered the hydroxyl end group as the only measurement in on-line operation. We have found that the concentration of ethylene glycol and ester group can be estimated accurately through a fast-converging state observer. For the carboxyl end group, which is unobservable, an open loop observer was built, whose rate of convergence turned out to be reasonable, even though it is not adjustable. Simulation results indicated that DP is estimated accurately.

References:

[1] Jacobsen, Lance L., and W. Harmon Ray. "Analysis and design of melt and solution polycondensation processes." AIChE Journal 38.6 (1992): 911-925.

[2] Kazantzis, Nikolaos, and Costas Kravaris. "Nonlinear observer design using Lyapunov’s auxiliary theorem." Systems & Control Letters 34.5 (1998): 241-247.

[3] Kazantzis, Nikolaos, Costas Kravaris, and Raymond A. Wright. "Nonlinear observer design for process monitoring." Industrial & Engineering Chemistry Research 39.2 (2000): 408-419.

[4] Rafler, Gerald, et al. "Kinetics of mass transfer in the melt polycondensation of poly (ethylene terephthalate)." Journal of Macromolecular Science—Chemistry 22.10 (1985): 1413-1427.

[5] Appelhaus, Paul, and Sebastian Engell. "Design and implementation of an extended observer for the polymerization of polyethylenterephthalate." Chemical Engineering Science 51.10 (1996): 1919-1926.

[6] Pohl, Herbert A. "Determination of carboxyl end groups in polyester, polyethylene terephthalate." Analytical Chemistry 26.10 (1954): 1614-1616.

[7] Kinniburgh, D. G., C. J. Milne, and P. Venema. "Design and construction of a personal-computer-based automatic titrator." Soil Science Society of America Journal 59.2 (1995): 417-422.