Peng-Robinson equation of state: 40 years through cubics

Abstract In the 21st century, the mission of chemical engineering is to promote innovative technologies that reduce or eliminate the use or generation of hazardous materials in the design and manufacture of chemical products. The sustainable use of renewable resources, complying with consumer health and environmental requirements, motivates the design, optimisation, and application of green benign processes. Supercritical fluid extraction is a typical example of a novel technology for the ecologically compatible production of natural substances of high industrial potential from renewable resources such as vegetable matrices that finds extended industrial application. The present review is devoted to the stage of development of supercritical fluid extraction from vegetable material in the last 20 years. Without the ambition to be exhaustive, it offers an extended, in comparison with previous reviews, enumeration of extracted plant materials, discusses the mathematical modelling of the process, and advocates a choice for the appropriate model that is based on characteristic times of individual extraction steps. Finally, the attention is focussed on the elements of a thermodynamic modelling framework designed to predict and model robustly and efficiently the complex phase equilibria of the systems solute+supercritical fluid.

Supercritical fluid extraction from vegetable materials

Comparison the capability of artificial neural network (ANN) and EOS for prediction of solid solubilities in supercritical carbon dioxide

No one can ever deny the significance of calculations of solubilities of industrial solid compounds in supercritical CO2 in separation processes. In this work, the Peng–Robinson (PR) and the Esmaeilzadeh–Roshanfekr (ER) equations of state (EoS) along with several mixing rules including the Wong–Sandler (WS), the covolume dependent (CVD) and the van der Waals one (VDW1) and two (VDW2) fluid mixing rules are applied to evaluate the solubilities of 52 mostly used solid compounds in supercritical carbon dioxide. Besides, the Van-Laar excess Gibbs energy (Gex) model is applied in phase behavior calculations by the WS mixing rule. The optimal values of the proposed thermodynamic model parameters are evaluated using the DE (differential evolution) optimization strategy. The absolute average deviations of the model results from 1776 experimental data points and the optimal values of the adjustable parameters of the model are reported to investigate the capabilities of combinations of each equation of state with different mixing rules in calculations of the solubilities. The results indicate that the combination of the ER EoS with the WS mixing rule leads to more accurate results (AAD = 9.0%) compared with other ones.

Thermodynamic modeling of solubilities of various solid compounds in supercritical carbon dioxide: Effects of equations of state and mixing rules

Solubilities of p-hydroxybenzoic acid (p-HBA) and mixtures of the para and ortho isomers have been determined in supercritical carbon dioxide at 318 and 328 K for pressures in the range 101−203 bar. The solubility of p-HBA in carbon dioxide (p-HBA/CO2 binary system) is 2 orders of magnitude lower than the binary system solubility of o-HBA. However, measurements undertaken with an equilibrium chamber of mixed para and ortho isomers demonstrate a strong enhancement in the solubility of p-HBA. Furthermore, the enhancement was found to be independent of the composition of the equilibrium chamber. The binary and ternary (p-HBA/o-HBA/CO2) solubility data were correlated using a modified form of the Peng−Robinson equation of state. Covolume-dependent mixing rules were also used with the Peng−Robinson model in an attempt to improve the correlation of solubility data. Conventional supercritical fluid (SCF) extraction of a mixture of the isomers is capable of producing an extract which is 99% pure o-HBA in one extr...

Influence of matrix composition on the solubility of hydroxybenzoic acid isomers in supercritical carbon dioxide

Inclusion of a covolume dependent mixing rule for the energy parameter enables the prediction of solubility of solids in supercritical fluids. This approach avoids the use of difficult-to-obtain critical properties and acentric factors and involves simple characteristic properties, namely the van der Waals volume and the heat of sublimation of the solid. These properties are predicted using the molecular structure and the Bondi's group contribution method. The predictions of solubilities by the proposed model, including those not employed in the development of the model, are found to be in good agreement with the experimental data on solubilities of a range of solids in supercritical carbon dioxide, ethane, and ethylene.

Solid solubilities in supercritical fluids from group contributions

Improved solubility data predictions by the Peng-Robinson equation-of-state (PR-EOS) for supercritical fluid-solid systems are obtained for asymmetric systems by employing the covolume dependency in the mixing rule for the attraction parameter, a , along with the corresponding states approach for both like and unlike pair parameters of the EOS. This method reduces the sensitivity of solubility predictions to variations in the value of the interaction parameter and allows the binary interaction parameter to be correlated in terms of the pure component properties with small sacrifice in accuracy. The solubility data predictions using the developed correlation for supercritical carbon dioxide and hydrocarbon solvents compare well with the experimental results.

V.S. Gangadhara Rao

Papers

Solid solubilities in supercritical fluids from group contributions

Effect of covolume dependency of the energy parameter on the predictability of SCFE data using the Peng-Robinson equation of state