A Numerical Algorithm for Calculating Critical Points and Its Application to Predictive Mixture Models and Binary CO$$_2$$ Mixtures

The use of supercritical fluids in technical applications requires an accurate knowledge of their critical points. For mixtures, these can deviate significantly and without a linear dependency from the critical points of its individual pure components. Since even small amounts of admixture can have noticeable effects, this not only concerns blends of targeted compositions, but also unintentional mixtures for example caused by impurities. Within this work, a method for the calculation of critical points is presented which focuses on numerical robustness promoting a fast and reliable generation of results. Implemented into the thermodynamic property software TREND, with its mixture modeling capabilities, the method allows a flexible combination of different equations of state and mixture models which also includes predictive approaches. Against the background of an increasing relevance of mixtures based on supercritical CO $$_2$$ 2 (sCO $$_2$$ 2 ) for energy applications, critical lines are calculated and compared against experimental results for selected sCO $$_2$$ 2 -based mixtures recently considered for power plant applications. Herein, several combinations of equations of state (EoS) and mixture models are compared. Critical lines are calculated for the first time in this work with the combination of the multi-fluid mixture model with excess Gibbs energy ( $$g^\text {E}$$ g E ) models. It was found that the critical lines calculated with the combination of the multi-fluid mixture model with the $$g^\text {E}$$ g E -model COSMO-SAC yields good predictive results for the investigated CO $$_2$$ 2 mixtures.