Kinetic Model Building through Simultaneous Optimization with Spectral Data: 1,2-Butylene Oxide Polymerization Case Study

Kinetic parameter estimation from in situ spectroscopic data, such as those from infrared or Raman spectroscopy, remains a challenging and highly active research area. Obtaining accurate predictions of concentrations and pure component spectra from multicomponent mixtures is difficult to decouple. From the dominant pathway of the ring-opening polymerization of 1,2-butylene oxide (BO), initiated by propylene glycol (PG) and catalyzed by KOH, we developed a mechanistic population balance model with global kinetic parameters. Reaction data were previously obtained in a semibatch fashion via in situ attenuated total reflectance Fourier transform infrared spectroscopy (ATR FT-IR) monitoring. Lacking available standards for the broad distribution of possible intermediate oligomer products, we estimate initiation and propagation constants as well as accurate predictions of pure component spectra for various product oligomers. Our results are validated by a separate reference spectrum from previous work. We formulate and solve the population balance model using a nonlinear programming-based simultaneous solution strategy to obtain estimates of global reaction kinetics and spectra. Because of the nonlinear programming formulation, which utilizes exact second derivatives, this approach leads to the direct calculation of 95% confidence regions for all estimates. We also apply the Bayesian notion of probability shares as a methodology for model discrimination among various candidate models.