(255cf) Industrial Production of Styrene-Butadiene Rubber: Dynamic Modeling, Process Intensification, Sensitivity and Uncertainty Analysis

Styrene-butadiene rubber (SBR) is a synthetic elastomer with wide range of industrial applications, mainly as an essential component of car tires. Production of SBR latex by cold emulsion polymerization is usually carried out continuously in the cascade of six to fourteen tank reactors. Description of this process by means of mechanistic mathematical modeling is quite scarce in the literature, due to limited understanding of underlying phenomena, e.g. the influence of emulsifiers on the quality of produced copolymer, and the description of the thermodynamics of polymer particle swelling.

This contribution is focused on dynamic modeling of continuous SBR production by cold emulsion polymerization in the train of up to twelve tank reactors of industrial scale. The model is used by SBR manufacturer for deeper investigation of the production line behavior and mainly for off-line optimization of the production process[1]. The principal objectives of the developed simulation software are: (i) minimization of the off-spec product amount during transitions between different SBR grades, (ii) study of production line behavior with respect to varying quality of incoming monomers, (iii) investigation of possible technological improvements of the SBR production, and (iv) determination of reasons for undesirable quality of produced latex.

Reaction mechanism of free-radical copolymerization of styrene and butadiene[2] was processed by the moments of chain-length and chain-branching distributions (i.e., the polymer moments), allowing prediction of important characteristics of produced latex, such as conversion of monomers, copolymer composition, number-average and weight-average molar weight of copolymer. The last two mentioned quantities are empirically correlated to the most important characteristics of SBR latex, the Mooney viscosity[3].The developed model is represented by a set of differential-algebraic equations (DAE) and validated by plant data both in the steady-state (profiles of important process/product characteristics along the reactor train) and in the dynamic regime (evolution of SBR characteristics during transition between different product grades). Strategy for optimum grade transition trajectory is suggested.

The study includes also sensitivity and uncertainty analysis of the optimization problem with respect to the feed composition and parameters of the copolymerization kinetics. A Monte Carlo technique with Latin Hypercube Sampling and correlation control (Iman Conover) is used for the uncertainty analysis, which is complemented by Morris screening and first order sensitivity index, Si (Sobolâ??s method) for sensitivity analysis[4,5].^ The results provide importance ranking of feed versus kinetic model parameter uncertainty for model-based polymer process optimisation.

[1] A. Zubov, J. Pokorny, J. Kosek: Styrene-butadiene rubber (SBR) production by emulsion polymerization: Dynamic modeling and intensification of the process, Chem. Eng. J., 207 (2012), 414-420.

[2] S. Saldivar, P. Dafniotis, W.H. Ray: Mathematical modeling of emulsion copolymerization reactors. I. Model formulation and application to reactors operating with micellar nucleation, J. Macromol. Sci., Rev. Macromol. Chem. Phys., 38 (1998), 207-325.

[3] O. Kramer, W.R. Good: Correlating Mooney viscosity to average molecular weight, J. Appl. Polym. Sci., 16 (1972), 2677-2684.

[4] J.C. Helton, F.J. Davis: Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems, Reliab. Eng. Syst. Safe, 81 (2003), 23-69.

[5] G. Sin, K.V. Gernaey, M.B. Neumann, M.C. van Loosdrecht,W. Gujer: Global sensitivity analysis in wastewater treatment plant model applications: prioritizing sources of uncertainty, Water Research, 45 (2011), 639-651.