Bilevel optimization for parameter estimation in thermodynamics

  • Bilevel-Optimierung zur Schätzung thermodynamischer Parameter

Glass, Moll Helene; Mitsos, Alexander (Thesis advisor); Leonhard, Kai Olaf (Thesis advisor)

Aachen (2018, 2019)
Book, Dissertation / PhD Thesis

In: Aachener Verfahrenstechnik Series 4
Page(s)/Article-Nr.: 1 Online-Ressource (xiii, 153 Seiten) : Illustrationen

Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2018


In order to determine thermodynamic interactions in phase equilibria, there is an increasing interest in fully predictive methods. However, parameter estimation using measurement data often is more accurate and thus, still widely applied in the chemical industry. In this thesis, the parameter estimation problems in Mitsos et al. (Chem. Eng. Sci., 2009 (64), 548-559) are reinterpreted as bilevel problem (BLP) formulations and extended to different types of equilibria (phase, mechanical, and chemical reaction equilibria), and finally, solved by means of global deterministic optimization. As an important feature of Mitsos et al. and this thesis, thermodynamic stability is guaranteed to be satisfied for the regressed parameter values and the aforementioned equilibria, while standard regression tools fail. The key to the reliability of the new methods is the fact that they are appropriate for even nonconvex problems which are prevalent for thermodynamics, in that they use the algorithm in Mitsos et al. (J. Glob. Optim., 2008 (42), 475-513), in contrast to methods that perform a posteriori stability checks only, if any. Numerical proofs for the importance of the satisfaction of thermodynamic stability are given, by comparing the BLP formulation to two prevalent specimens of regression tools, namely Aspen Data Regression System and DECHEMA Data Preparation Package. In particular, based on case studies of single-phase reactive systems and various liquid-liquid equilibria using the non-random two-liquid model, it is demonstrated that only the new methods reliably avoid, e.g., spurious phases and spurious liquid-liquid splits, as well as incorrect values for phase compositions and extents-of-reaction. In addition, for parameter estimation involving cubic equations of state models, a continuous criterion to discriminate between multiple roots to cubic equations is introduced in this thesis. In terms of readership, this thesis tries to reach both the developers of said regression tools and process designers as their potential users. Even though the aforementioned case studies are predominantly illustrative in nature due to computational limits of the sub-solvers used, the author believes that they demonstrably highlight the relevance of global optimization to process simulation and optimization in both academia and industry.