Multivariate kinetic hard-modelling of spectroscopic data: a comparison of the esterification of butanol by acetic anhydride on different scales and with different instruments

For safety, economic efficiency and environmental efficiency understanding and predicting the behaviour of a chemical reaction are of greatest importance in industry. Hard-modelling, the evolution of a chemical reaction by the rate law derived from the molecular mechanism, is a powerful method for this application. Any change in the experimental equipment or conditions does not have an impact on the model and does not require time consuming recalibration or reanalysis. Thus, hard-modelling is suitable for extrapolations of the reaction dynamics to other concentrations and/or temperatures. In this context, the solvent-free esterification of 1-butanol (BuOH) by acetic anhydride (AA) using 1,1,3,3-tetramethylguanidine (TMG) as a base catalyst, to form butyl acetate (BuOA) and acetic acid (AH) has been analysed, in a comparative study, in three different reactors (located in different laboratories) of different volumetric scales (50, 75 mL and 5 L) by mid-IR (50 mL) or near-IR (75 mL and 5 L) spectroscopy. Chemical suppliers and experimenters were also different but the same experimental design (temperatures and initial concentrations) was applied to all measurements. Multivariate kinetic hard-modelling of the spectroscopic signals was applied to the kinetic data sets corresponding to each reactor. The importance of finding the simplest model that sufficiently describes the experimental data is discussed. Compared to previously published results, a non-contradictory but simplified and consistent kinetic model (first order in AA, BuOH and TMG) was found to be optimal to fit the data from all three reactors taken within a temperature range from 30 to 50 °C. The corresponding model parameters, rate constant kref,1 (at reference temperature Tref) and activation energy Ea,1 define a mean-centred Arrhenius equation and were in reasonable agreement considering the different experimental environment, spectroscopic methods, volumetric scales and relatively scarce factorial design of experiments employed; the latter being responsible for a limited definition of Ea,1. For validation of the mechanism, pure component mid-IR spectra have been interpreted and assigned in terms of their characteristic band