Incremental Identification of Reaction and Mass-Transfer Rates In Gas-Liquid Reaction Systems Using Tendency Modeling
The identification of reliable reaction and mass-transfer rates is important for building first-principles models of gas-liquid reaction systems. The identification of these rates involves the determination of a model structure (reaction stoichiometry, rate expressions for the reactions and mass transfers) and of the corresponding parameters. The identification of these rate expressions from measured concentrations is a challenging task because of the direct coupling between the reactions and the transfer of reactants and products between the two phases. The identification task can be performed globally in one step by choosing the model structure and estimating the model parameters via the comparison of model predictions and measured data. The approach is termed simultaneous identification since all reactions and mass transfers are identified simultaneously. The procedure needs to be repeated for all candidate model structures. Hence, the simultaneous identification can be computationally costly when several candidate rate expressions are available for each reaction and mass transfer. Furthermore, since the global model is fitted so as to reduce the least-squares error, structural mismatch in one rate expression of the model will typically result in errors in all the parameters. Finally, it is often difficult to come up with suitable initial parameter values, which may lead to convergence problems. An incremental identification approach has recently been proposed, which decomposes the identification task into the following two steps [1, 2]: (i) computation of the extents of reaction and mass transfer from measured concentrations without knowledge of the reaction and mass-transfer rates, and (ii) for each rate individually, identification of the rate expression and its parameters from the computed extents. The fact that each reaction and mass-transfer rate is treated individually in the incremental approach helps reduce considerably the number of model candidates, thereby reducing the computational effort. Although the proposed incremental approach provides an efficient framework for the identification of gas-liquid reaction systems, a systematic way of selecting the appropriate rate expressions from several candidate expressions is needed in Step (ii). Recently, the so-called generalized tendency modeling (GTeMoC) method has been proposed to select appropriate rate expressions from a large number of rate expression candidates [3, 4]. In the GTeMoC methodology, a stepwise linear regression is used as a tool to select appropriate rate expressions. Moreover, the statistical metrics are developed to discriminate rate expression candidates and avoid collinearity in rate parameters. However, the effect of mass transfer rates is not treated explicitly in the GTeMoC method, and lumped rate expressions containing the effect of reactions and mass transfers are identified. This work combines the incremental approach and the GTeMoC methodology so that the reaction and mass-transfer rates can be identified individually. Hence, the resulting incremental approach proceeds in three steps: (i) computation of the extents of reaction and mass transfer from measured concentrations without knowledge of the reaction and mass-transfer rates, (ii) computation of the reaction and mass-transfer rates through differentiation of the corresponding computed extents, and (iii) for each rate individually, identification of the rate expression and its parameters using the GTeMoC method. The proposed incremental identification approach combines the strengths of the incremental approach (can handle each reaction and each mass transfer individually) and the GTeMoC method (can efficiently select the rate expression from several candidate expressions). The approach will be illustrated via the simulation of the chlorination of butanoic acid.