Data Reconciliation in Reaction Systems using the Concept of Extents

Abstract of the conference paper Concentrations measured during the course of a chemical reaction are corrupted with noise, which reduces the quality of information. Since these measurements are used for identifying kinetic models, the noise impairs the ability to identify accurate models. The noise in concentration measurements can be reduced using data reconciliation, exploiting for example the material balances derived from stoichiometry as constraints. However, additional constraints can be obtained via the transformation of concentrations into extents and invariants, which leads to more efficient identification of kinetic models for multiple reaction systems. This paper uses the transformation to extents and invariants and formulates the data reconciliation problem accordingly. This formulation has the advantage that non-negativity and monotonicity constraints can be imposed on selected extents. A simulated example is used to demonstrate that reconciled measurements lead to the identification of more accurate kinetic models. Extended abstract Reliable kinetic models of chemical reaction systems should include information on all rate processes of significance in the system. Apart from chemical reactions, such models should also describe the mass exchanged with the environment via the inlet and outlet streams and the mass transferred between phases. Model identification and the estimation of rate parameters is carried out using measurements that are obtained during the course of the reaction [1]. Model identification often leads to the combinatorial complexity of identifying simultaneously all rate processes [1]. Alternatively, it can be carried out incrementally by transforming the concentrations to extents and identifying each extent separately [2]. Since measurements are inevitably corrupted by random measurement errors, the identification of kinetic models and estimation of rate parameters are affected by error propagation [3]. Data reconciliation is a technique that uses constraints to obtain more accurate estimates of variables by reducing the effect of measurement errors [4]. Data reconciliation can be formulated as an optimization problem constrained by the law of conservation of mass [5, 6] and positivity of reconciled concentrations. Consequently, model identification can be performed with reconciled concentrations. This paper presents a reformulation of the original reconciliation problem directly in terms of extents. This allows using additional constraints such as the monotonicity of extents. Such a reformulation improves the accuracy of the reconciled extents and hence of concentrations, and leads to better model discrimination and parameter estimation. The advantages derived from the use of reconciled extents are illustrated using a simulated example. References: [1] Bardow et al., Chem. Eng. Sci., 2004, 59, 2673 - 2684 [2] Bhatt et al., AIChE J., 2010, 56, 2873 - 2886 [3] Billeter et al., Chem. Intell. Lab. Syst., 2008, 93, 120 - 131 [4] S. Narasimhan and C. Jordache, Data Reconciliation and Gross Error Detection, Elsevier, 1999 [5] Reklaitis et al., Chem. Eng. Sci., 1975, 30, 243 - 247 [6] Srinivasan et al., IFAC Workshop on Thermodynamic Foundations of Mathematical Systems Theory, Lyon, 2013.