Thermodynamic modeling of poorly specified mixtures using NMR fingerprinting and group-contribution equations of state

Mixtures of which the composition is only partially known are ubiquitous in chemical and biotechnological processes and pose a significant challenge for process design and optimization since classical thermodynamic models require complete speciation, which cannot be obtained with reasonable effort in many situations. In prior work, we have introduced a framework combining standard nuclear magnetic resonance (NMR) experiments and machine-learning (ML) algorithms for the automated elucidation of the group composition of unknown mixtures and the rational definition of pseudo-components and have applied the results together with group-contribution (GC) models of the Gibbs excess energy. In the present work, we extend this approach to the application of group-contribution equations of state (GC-EOS), enabling the predictive modeling of basically all thermodynamic properties of such mixtures. As an example, we discuss the application of the SAFT-$\gamma$ Mie GC-EOS for predicting the CO${}_2$ solubility in several test mixtures of known composition. However, the information on their composition was not used in applying our method; it was only used to generate reference results with the SAFT-$\gamma$ Mie EOS that were compared to the predictions from our method. In addition, the CO${}_2$ solubility in the test mixtures was also determined experimentally by NMR spectroscopy. The results demonstrate that the new approach for modeling poorly specified mixtures also works with GC-EOS, which further extends its applicability in process design and optimization.