PρT parameterization of SAFT equation of state: developing a new parameterization method for equations of state

Abstract

The lack of a transparent and universal parameterization method is one of the main problems in developing SAFT-type equations of state and it's an obstacle in their way of becoming an industrial equation of state. Usually, vapor-pressure and saturated liquid density data with a local optimization algorithm are used to parameterize SAFT-type equations of state. In addition to the ambiguity in the data selection process, using a local optimization method reduces the accuracy of the estimated parameters. Therefore, in this paper, a new method for calculating the adjustable parameters of SAFT or any equations of state with several parameters is presented. By providing a clear and explicit data selection procedure, including data categorization, comparison, and validation, integrated with the use of a combination of global and local optimization methods, the new methodology achieves the best possible parameters set for the equation of state. The proposed computational program for fitting parameters is based on the use of the Differential evolution algorithm as the main process and the Levenberg-Marquardt algorithm as the post-process along with applying one (or two) hyperparameter. Afterward, a wide range of pressure-temperature-density data has been used to estimate the parameters of 60 non-associating and associating pure compounds. Then, the SAFT equation of state with the new parameters, so-called PρT-SAFT-HR, is applied to predict pressure (P), temperature (T), density (ρ), vapor-pressure (Psat), saturated vapor density (ρvapsat), saturated liquid density (ρliqsat), critical point, isochoric heat capacity (cv), isobaric heat capacity (cP), speed of sound (u), isothermal compressibility (κT), and isobaric thermal expansivity (αP). All properties are calculated with the PρT-SAFT-HR equation of state, and the results are compared with experimental data and SAFT-HR and the average absolute percentage deviation is reported for all of them. In total, 19460 experimental and pseudo-experimental data were used to reparameterization the SAFT equation of state, and more than 74,000 data were validated to calculate thermodynamic properties. The results showed a significant improvement in predicting second-order thermodynamic derivative properties. In general, PρT-SAFT-HR performs better than SAFT-HR, and in some cases, such as pressure, speed of sound, isothermal compressibility, and isobaric thermal expansivity, the results have been significantly improved, and the average absolute deviation of PρT-SAFT-HR has been much less than SAFT-HR.