(53d) Multi-Criteria Optimization of Thermodynamic Models: Describing Water with PCP-SAFT As an Example

Authors: 
Langenbach, K., University of Kaiserslautern
Forte, E., University of Kaiserslautern
Bortz, M., Fraunhofer Institute for Industrial Mathematics (ITWM)
Hasse, H., University of Kaiserslautern
Burger, J., University of Kaiserslautern
Equations of state are important in process engineering for describing thermo-physical properties of the pure components and mixtures. In spite of the effort that has been done in the past years to develop sophisticated physically-sound approaches such as the statistical associating fluid theory (SAFT), the accuracy of the equation of state will ultimately depend on the choice of the model parameters used for describing the pertinent compounds. It is challenging to find appropriate parameter sets which are able to represent various properties at various conditions with the same quality. The parameter estimation is an optimization problem with conflicting objectives representing the deviations of the different properties from experimental data. Typically, a single objective is formulated by weighting of the conflicting objectives resulting in a single set of parameters. In this work, the problem is considered using multi-objective optimization and the calculation of Pareto solutions; i.e., those parameter sets with best compromises between the objectives. Thus, not only one model but a whole set of optimal models is obtained, where optimality means that no improvement in any single objective is possible without deteriorating at least one other objective. By considering and comparing all members of the Pareto set, the decision maker is greatly supported in understanding single solutions in an appropriate context and finding models which are particularly suited for individual applications. To the authorâ??s knowledge this is the first application of such technique for the parameterization of equations of state.

The importance of computing Pareto sets in this field as a powerful tool to support decisions in model development is highlighted. As an example the perturbed-chain polar PCP-SAFT equation of state is used and applied to model the vapor-liquid equilibria of water. The PCP-SAFT equation of state explicitly takes into account the non-sphericity and directional interactions (such as hydrogen-bonding) of molecules; as well as dipole-dipole interactions. The objectives are set to minimize deviations in both the vapor pressure and the liquid density. The equation of state is coupled with an efficient algorithm1 that yields a finite set of Pareto solutions, interpolation of which approximates the whole Pareto set within a given accuracy. PCP-SAFT water models with different levels of molecular detail, and hence different parameters, are studied and discussed against previously published models in the literature. Comparing the Pareto sets obtained for the different models proves to be valuable to assess which molecular features of the models (e.g. number of association sites, polarity, ...) are effectively improving the model quality. For the first time, an overview is given of what can be achieved with PCP-SAFT in its different variants regarding the modeling of different thermodynamic properties of water. Pareto-optimal models are proposed that represent the studied properties of water more accurately than the any existing model from the literature.

(1) Bortz, M.; Burger, J.; Asprion, N.; Blagov, S.; Böttcher, R.; Nowak, U.; Scheithauer, A.; Welke, R.; Küfer, K.-H.; Hasse, H. Multi-Criteria Optimization in Chemical Process Design and Decision Support by Navigation on Pareto Sets. Comput. Chem. Eng. 2014, 60, 354â??363.