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.

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.

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The identification of kinetic models for multiphase reaction systems is complex due to the simultaneous effect of chemical reactions and mass transfers. The extentbased incremental approach simplifies the modeling task by transforming the reaction system into variant states called vessel extents, one for each rate process. This transformation is carried out from the measured numbers of moles (or concentrations) and requires as many measured species as there are rate processes. Then, each vessel extent can be modeled individually, that is, independently of the other dynamic effects. This paper presents a modified version of the extent-based incremental approach that can be used to identify multiphase reaction systems in the presence of instantaneous equilibria. Different routes are possible depending on the number and type of measured species. The approach is illustrated via the simulated example of the oxidation of benzyl alcohol by hypochlorite in a batch reactor.

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