Parameter estimation in reactive systems subject to sufficient criteria for thermodynamic stability

• Published in: Chemical engineering science Vol. 197; pp. 420 - 431
• Main Authors: Glass, Moll, Mitsos, Alexander
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 06.04.2019
• Subjects: (e)NRTL; (electrolyte) non-random two-liquid; (G)SIP; (generalized) semi-infinite program; (R)TPC; (reactive) tangent plane criterion; (V)LLE; (vapor-)liquid-liquid equilibrium; bilevel program; BLP; CEOS; Chemical equilibrium constant; cubic equation of state; Data regression; equality constraint; Extent-of-reaction; Gibbs free energy; ionic liquid; Karush-Kuhn-Tucker; KKT; LBD; LBP; least-square errors function; LICQ; linear independence constraint qualification; LLP; lower bound; lower-bounding problem; lower-level problem; mathematical program with equilibrium constraints; MINLP; mixed-integer nonlinear program; MPEC; NLP; nonlinear program; PDH; Pitzer-Debye-Hückel; Reactive tangent plane; UBD; UNIFAC; Universal Quasichemical Functional Group Activity Coefficients; upper bound; Pitzer-Debye-Hückel; (generalized) semi-infinite program; Reactive tangent plane; bilevel program; lower-bounding problem; least-square errors function; (electrolyte) non-random two-liquid; Data regression; Extent-of-reaction; cubic equation of state; lower-level problem; Gibbs free energy; equality constraint; upper bound; lower bound; mathematical program with equilibrium constraints; Karush-Kuhn-Tucker; ionic liquid; (vapor-)liquid-liquid equilibrium; nonlinear program; mixed-integer nonlinear program; (reactive) tangent plane criterion; Chemical equilibrium constant; linear independence constraint qualification; Universal Quasichemical Functional Group Activity Coefficients
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/j.ces.2018.08.035

[Display omitted] •Regression subject to chemical equilibrium constant leads to wrong parameter values.•Wrong parameter values cause erroneous equilibrium conversion in process simulation.•We propose bilevel program for regression that leads to correct parameter values.•Illustrative single-phase dimerization using Margules and NRTL is considered. For process simulation involving chemical reactions, thermodynamically accurate model parameters for chemical equilibrium are indispensable. We demonstrate that regression subject to the well-known chemical equilibrium constant entails violation of the sufficient conditions for thermodynamic stability. As a consequence, erroneous values of the equilibrium conversion are obtained upon use of the respective parameter values in, e.g., process simulation. In order to alleviate the problem, we propose a methodology for estimating parameters subject to necessary and sufficient criteria for thermodynamic stability. In particular, we propose an extension of Mitsos et al. (2009) to parameter estimation in reactive systems; an upper-level model-experiment mismatch is minimized subject to several lower-level minimization problems (LLP), which ensure the fulfilment of the reactive tangent plane criterion (RTPC) of Smith et al. (1993), along with other desired behavior of the Gibbs free energy. A fictitious single-phase dimerization reaction employing Margules and NRTL as Gibbs free energy models illustrates the thermodynamic guarantees provided by the proposed formulation, when the conventional ones fail. Our formulation conceptually allows any type of phase equilibrium, e.g., VLLE, as well as any type of activity coefficient model. The subproblems of the bilevel algorithm pose challenges to state-of-the-art commercial solvers.