a b s t r a c tModels of chemical reaction systems can be quite complex as they typically include information regarding the reactions, the inlet and outlet flows, the transfer of species between phases and the transfer of heat. This paper builds on the concept of reaction variants/invariants and proposes a linear transformation that allows viewing a complex nonlinear chemical reaction system via decoupled dynamic variables, each one associated with a particular phenomenon such as a single chemical reaction, a specific mass transfer or heat transfer. Three aspects are discussed, namely, (i) the decoupling of reactions and transport phenomena in open non-isothermal both homogeneous and heterogeneous reactors, (ii) the decoupling of spatially distributed reaction systems such as tubular reactors, and (iii) the potential use of the decoupling transformation for the analysis of complex reaction systems, in particular in the absence of a kinetic model.

A novel method is presented for the rigorous propagation of uncertainties in initial concentrations and in dosing rates into the errors in the rate constants fitted by multivariate kinetic hard-modelling of spectroscopic data using the Newton-Gauss-Levenberg/Marquardt optimisation algorithm. The method was successfully validated by Monte-Carlo sampling. The impact of the uncertainties in initial concentrations and in the dosing rate was quantified for simulated spectroscopic data based on a second and a formal third order rate law under batch and semi-batch conditions respectively. An important consequence of this study regarding optimum experimental design is the fact that the propagated error in a second order rate constant is minimal under exact stoichiometric conditions or when the reactant with the lowest associated uncertainty in its initial concentration is in a reasonable excess (pseudo first order conditions). As an experimental example, the reaction of benzophenone with phenylhydrazine in THF was investigated repeatedly (17 individual experiments) by UV-vis and mid-IR spectroscopy under the same semi-batch conditions, dosing the catalyst acetic acid. For all experiments and spectroscopic signals, reproducible formal third order rate constants were determined. Applying the proposed method of error propagation to any single experiment, it was possible to predict 80% (UV-vis) and 40% (mid-IR) of the observed standard deviation in the rate constants obtained from all experiments. The largest contribution to this predicted error in the rate constant could be assigned to the dosing rate. The proposed method of error propagation is flexible and can straightforwardly be extended to propagate other possible sources of error.

h i g h l i g h t s" Extent-based incremental identification models extents computed from concentrations. " Calorimetry is related to extents of reaction and mass transfer via enthalpies. " Extents are computed by augmenting rank-deficient concentrations with calorimetry. " Extents computed from full-rank conc. allow estimating enthalpies from calorimetry. " These concepts are illustrated via homogeneous and gas-liquid reaction systems. a r t i c l e i n f oArticle history: Available online 21 July 2012 Keywords:Reaction kinetics Mass-transfer rates Extents of reaction Extents of mass transfer Incremental identification Calorimetry a b s t r a c t Extent-based incremental identification uses the concept of extents and the integral method of parameter estimation to identify reaction kinetics from concentration measurements. The approach is rather general and can be applied to open both homogeneous and gas-liquid reaction systems. This study proposes to incorporate calorimetric measurements into the extent-based identification approach for two main purposes: (i) to be able to compute the extents in certain cases when only a subset of the concentrations is measured and (ii) to estimate the enthalpies when all concentrations are measured. The two approaches are illustrated via the simulation of a homogeneous and a gas-liquid reaction system, respectively.

Hard-modelling Concentration matrix Rank deficiency and augmentation A priori information and experimental designA novel method is presented for the systematic identification of the minimum requirements regarding mathematical pre-treatment, a priori information, or experimental design, in order to allow optimising rate constants and pure component spectra associated with a kinetic model via multivariate kinetic hardmodelling of spectroscopic data. Rank deficiencies in the kinetic concentration matrix represent a major problem for the calibration free method developed by Maeder and Zuberbühler, as its pseudo-inverse, required for the optimisation process, is not defined. In this contribution, the underlying linear dependencies in the concentration profiles are systematically elucidated and appropriate strategies are discussed in order to break them. Also, conditions are predicted for which full spectral resolution can be expected. The method is based on the kernel of a time invariant augmented matrix covering potential rank deficiency due to stoichiometry and rate laws, also relevant for the concentration matrix. Compared to employing the full concentration matrix, this augmented matrix does not require a numerical integration of the differential equations describing the kinetic model and thus can easily be set up. The kernel can be calculated numerically by Singular Value Decomposition (SVD) or determined in a symbolical way, the latter allowing the detection of particular stoichiometric conditions leading to spectral resolution of species. The capabilities of the method are demonstrated analysing three kinetic mechanisms of increasing complexity covering consecutive and parallel reactions.