(370g) Incremental Identification of Polymerization Reaction Kinetics

Estimation of statistically sound kinetic parameters for polymerization reactions is still a difficult task and presents a high computational burden. In order to ensure identifiability, it is generally advantageous to estimate parameters by performing different types of experiments and/or fix some of the model parameters to some nominal value determined in previous experiments. It may however sometimes not be possible to find reliable estimates of the parameters for the system under study. Hence, an integrated approach such as the MEXA (Model-based Experimental Analysis) methodology has to be employed for the systematic identification and validation of mechanistic models.[1] The core of this methodology is IMI, incremental model identification, which relies on decomposition of the estimation problem into a sequence of subproblems. IMI has been successfully applied to the identification of the kinetics of single- and multi-phase reaction systems[2,3]; it is extended in our current work to polymerization reactions in order to complement and hopefully improve on already existing techniques. To this end, a method of moments approach is used to model and approximate the molecular weight distribution of the polymer chains. We will show how the resulting moment model is transformed into more easily identifiable subproblems which can be solved efficiently and robustly using measurements of quantities which are typically monitored in polymerization experiments including  monomer conversion, number average molecular weight and mass average molecular weight. We will demonstrate the computational efficiency of a quasi-global parameter estimation scheme. Further, incremental identification is combined with model-based, optimal experimental design to improve on the reliability of the estimated parameters. The method will be illustrated by means of solution polymerization of acrylic acid which has been chosen as a first exemplary benchmark problem.[4]

[1] Marquardt, W. Model-based experimental analysis of kinetic phenomena in multi-phase reactive systems. Chem. Eng. Res. & Des., 83, 561, (2005).

[2] Brendel M., Bonvin D., Marquardt W., Incremental identification of kinetic models for homogeneous reaction systems. Chem. Eng. Sci., 61, 5404-5420, (2006).

[3] Michalik C., Brendel M., Marquardt W., Incremental Identification of Fluid Multi-Phase Reaction Systems. AlChE Journal, 55(4), 1009-1022, (2009).

[4] Sheibat-Othman N., Peycelon D., Othman S., Suau J.M., Fevotte G. Nonlinear observers for parameter estimation in a solution polymerization process using infrared spectroscopy. Chem.Eng. J., 140, 529-538, (2008).