Modified Soave-Redlich-Kwong equations of state applied to mixtures containing supercritical carbon dioxide

The well-known equation of state Soave-Redlich-Kwong and two of its modifications are applied to describe vapor-liquid equilibrium in binary asymmetric mixtures, which contain supercritical carbon dioxide and a heavy component. Several mixing rules including the classical van der Waals mixing rules with one and two interaction parameters, non-quadratic mixing rules, and the used of a Gibbs free energy model, are used with these equations. Seven mixtures containing supercritical carbon dioxide are considered in the study. The experimental data were obtained from literature sources and the adjustable parameters were found by minimizing the errors between predicted and experimental data of the concentration of the solute in the liquid phase. The work allows concluding on the advantages, disadvantages and expected accuracy of these equations of state and mixing rules for correlating vaporliquid equilibrium data in asymmetric systems as those studied.     

Solubility of chemical warfare agent simulants in supercritical carbon dioxide: experiments and modeling

Solubility data are reported for ethyl phenyl sulfide (EPS) and 2-chloroethyl ethyl sulfide (CEES) in CO₂ at temperatures from 25 to 100 °C. These two sulfide-based compounds are homomorphs for chemical warfare agents (CWAs). Both sulfide–CO₂ mixtures exhibit type-I phase behavior. The maximum in the 100 °C isotherm is approximately 2600 psia for the CEES–CO₂ system and approximately 3400 psia for the EPS–CO₂ system. The Peng–Robinson equation of state (PREOS) is used to model both sulfide–CO₂ mixtures as well as the phase behavior of the 2-chloroethyl methyl sulfide (CEMS)–CO₂ system previously reported in the literature. The Joback–Lydersen group contribution method is used to estimate the critical temperature, critical pressure, and acentric factor for the sulfides. Semi-quantitative estimates of the phase behavior are obtained for the CEES–CO₂ and EPS–CO₂ systems with a constant value of k_ij, the binary interaction parameter, fit to the 75 °C isotherms. However, very poor fits are obtained for the 2-chloroethyl methyl sulfide–CO₂ system regardless of the value of k_ij. On the basis of the high solubility of EPS and CEES in CO₂, supercritical fluid (SCF)-based technology could be used to recycle or recover chemical warfare materials.     

Equation of state for the systems containing aqueous salt: Prediction of high pressure vapor-liquid equilibrium

An equation of state (EOS), which is based upon contributions to the Helmholtz energy, is presented for systems containing aqueous electrolyte solutions at high pressure. The Peng-Robinson equation of state is used to provide the Helmholtz energy of a reference system. The electrolyte terms consist three terms containing a modified Debye-Hückel term for long-range electrostatic interactions, the Born energy contribution for electrostatic works and a Margules term for short-range electrostatic interactions between ions and solvents. The binary and ternary interaction parameters of the equation of state are obtained by experimental osmotic coefficient data. Systems that were studied here are (water+ NaCl+SC-CO₂), (water+NH₄Cl+SC-CO₂), (water+Na₂SO₄+SC-CO₂) and (water+methanol+NaCl+SC-CO₂). It is found that the proposed equation of state is able to accurately represent the experimental data over a wide range of pressure, temperature and salt concentration.     

Thermodynamic modeling of vapor-liquid equilibria and excess properties of the binary systems containing diethers and n-alkanes by cubic equation of state

A comparison of the performances of two different approaches of cubic equations of state models, based on a classical van der Waals and mixing rules incorporating theG ^E equation, was carried out for correlation of Vapor-Liquid Equilibria (VLE), H^E and C _P ^E data alone, and simultaneous correlation of VLE+H^E, VLE+C _P ^E , H^E +C _P ^E and VLE+H^E +C _P ^E data for the diethers (1,4-dioxane or 1,3-dioxolane) with n-alkane systems. For all calculations the Peng-Robinson-Stryjek-Vera cubic equation of state (PRSV CEOS) was used. A family of mixing rules for the PRSV CEOS based on the Modified van der Waals one-fluid mixing rule (MvdW1) and two well-known CEOS/G^E mixing rules (MHV1 and MHV2), was considered. The NRTL equation, as the G^E model with linear or reciprocal temperature dependent parameters, was incorporated in the CEOS/G^E models. The results obtained by the CEOS/G^E models exhibit significant improvement in comparison to the MvdW1 models.     

Simultaneous prediction of the critical and sub-critical phase behavior in mixtures using equations of state II. Carbon dioxide-heavy n-alkanes

In the present study we present the final development of the Global Phase Diagram-based semi-predictive approach (GPDA), which requires only 2-3 key data points of one homologue to predict the complete phase behavior of the whole homologues series. The ability of GPDA to predict phase equilibria in CO₂-heavy n-alkanes is compared with the equations of state LCVM and PSRK. It is demonstrated that both LCVM and PSRK are more correlative rather than predictive because their parameters are evaluated by the local fit of a considerable amount of VLE experimental data. In addition, these models fail to predict accurately the VLE of systems, which have not been considered in the evaluation of their parameters. They are also particularly inaccurate in predicting LLE and critical lines. In contrast, GPDA is reliable in the entire temperature range and for all types of phase equilibria. It yields an accurate prediction of the global phase behavior in the homologues series and their critical lines. Moreover, increasing asymmetry does not affect the reliability of GPDA; it predicts very accurately even the data of the heaviest homologues of the series.     

Fluid-phase equilibria in binary systems containing an ionic liquid. Application of the Percus-Yevick-van der Waals equation of state

Following some simplifications to reduce the computational effort, the Percus-Yevick-van der Waals equation of state is used to calculate the isothermal total pressure of a binary liquid system containing one volatile nonelectrolyte liquid and one nonvolatile ionic liquid. Pure-component parameters a and b are found from pure-component enthalpy-of-vaporization and liquid-density data. The single binary parameter a₁₂ is obtained from Henry's constant for the nonelectrolyte in the ionic liquid. For 10 binary systems, calculated total pressures are in good agreement with experiment although in a few systems observed total pressures are slightly higher than those calculated in the region where the ionic liquid is dilute. Brief attention is given to a few binary systems with a miscibility gap.     

Modeling the phase equilibria of asymmetric hydrocarbon mixtures using molecular simulation and equations of state

Monte Carlo simulation (MC) is combined with equations of state (EoS) to develop a methodology for the calculation of the vapor–liquid equilibrium (VLE) of multicomponent hydrocarbon mixtures with high asymmetry. MC simulations are used for the calculation of the VLE of binary methane mixtures with long n-alkanes, for a wide range of temperatures and pressures, to obtain sufficient VLE data for the consistent fitting of binary interaction parameters (BIPs) for the EoS. The Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), and Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT) EoS are considered. The ability of each EoS to correlate the VLE data is assessed and the selected ones are used to predict the VLE of multicomponent gas condensate mixtures. MC simulations proved to be very accurate in predicting the VLE in all conditions and mixtures considered. The BIPs regressed from the simulation dataset lead to equally accurate modeling results for multicomponent mixtures, compared to those regressed from experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 65: 792–803, 2019     

Correlation of high-pressure phase equilibria in the retrograde region with three common equations of state

Phase equilibria in the retrograde regions were calculated for the methane — n-decane binary system and for a realistic natural-gas system (methane - Kensol-16). Calculations were performed using three equations of state (EOS): Peng-Robinson, Redlich-Kwong-Soave and Perturbed-Hard-Chain; calculations were compared to experiment. Liquid-drop-out curves and pressure-temperature diagrams were calculated between 301 and 369 K and pressures to 90 MPa. The binary system was represented best by the Peng-Robinson EOS. For the natural-gas system, the Perturbed-Hard Chain equation yielded the best results, although all equations of state showed appreciable deviations. Good results could only be obtained when binary coefficients were fitted to the experimental retrograde data.     

Simultaneous prediction of the critical and sub-critical phase behavior in mixtures using equations of state IV. Mixtures of chained n-alkanes

The present study compares the ability of two semi-predictive approaches, namely the global phase diagram approach (GPDA) and the predictive Soave-Redlich-Kwong model (PSRK), for describing the experimental data in the binary homologous series of n-alkanes. A method to expand the application of the GPDA model to the heavy n-alkanes, absent in the Design Institute for Physical Property Data (DIPPR) data base, is proposed. Since both models do not implement the binary data of the systems under consideration for evaluation of their parameters, they appear here as entirely predictive. It is shown that both models are reliable in predicting the data of symmetric systems and they yield deviations that do not significantly exceed the possible experimental uncertainties. The robustness and reliability of GPDA in comparison with PSRK becomes evident predicting the data of asymmetric systems. PSRK tends to overestimate the liquid-liquid immiscibility range and as a result it over predicts the phase equilibria pressures and fails to describe the global phase behavior. In contrast, GPDA describes the global phase behavior exactly and yields accurate predictions of both the critical and the sub-critical data even for very asymmetric systems, such as propane—n-hexatetracontane.     

Estimations of the viscosities of binary mixtures with different equations of state and mixing rules

In this study, the Eyring's kinematic viscosity model was applied with the consideration that the activation free energy of flow was related to the excess free energy of mixtures and estimated with the equation of state (EOS). The effects of the equation of state, mixing rule, and interaction parameter on the viscosity estimations were considered.     

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

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 (G^ex) 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.     

On the information and methods for computing phase equilibria and thermodynamic properties

The Helmholtz free energy or an equation of state relating temperature, pressure, volume and composition plays a key role in the calculation of phase equilibria and thermodynamic properties. Such information is usually available for vapor, partially available for liquids, and rarely available for solids. Depending on the information available, different methods are used for properties calculation. In this study, various methods were systematically presented and their relations with available information were comprehensively discussed.     

A general treatment of polar-polarizable systems for an equation of state

In this work, a general theory to account for any kind of polarization arising from polar as well as ions induced interactions in fluid mixtures is proposed. The general treatment is based on the self-consistent mean field theory (SCMF) that was originally proposed and applied for pure components using integral equation theories and molecular simulation studies. The extended SCMF is consistent with theory-based equations of state applied to hard chain mixtures. The theory is extended to mixtures and compared to molecular simulation data. The comparison to molecular simulation data shows good to excellent results for phase co-existence properties, energy and effective dipole moment. The validity of the theory is demonstrated by studying VLE of highly non-ideal mixtures of aldehyde and ketones using statistical association fluid theory.     

Experimental determination and modeling of the phase behavior for the direct synthesis of dimethyl carbonate from methanol and carbon dioxide

This study focuses on the investigation of the phase behavior of mixtures relevant to the direct synthesis of dimethyl carbonate from methanol and carbon dioxide. The bubble points of corresponding quaternary mixtures of varying composition were experimentally determined. The Cubic-Plus-Association (CPA) equation of state was applied to model the phase behavior of the experimentally studied systems. In this regard, the CPA binary interaction parameters were estimated based on experimental data for the corresponding binary systems available in the literature, and subsequently the model was applied to predict the phase behavior of the multicomponent systems. It was shown that CPA is capable of predicting the phase behavior of such complex systems containing polar and associating components at high temperatures and pressures with reasonable accuracy considering the non-ideality of such mixtures. The results reveal P–T regions where the system can exist in one single phase and where it is multiphase, which can be used for further optimization not only of the chemical reaction itself but also subsequent product separation processes.     

Understanding the chemical reaction and mass-transfer phenomena in a recirculating enzymatic membrane reactor for green ester synthesis in ionic liquid/supercritical carbon dioxide biphasic systems

The synthesis of butyl propionate in a recirculating bioreactor in room temperature ionic liquid/supercritical carbon dioxide biphasic systems at 50 °C and 80 bar was studied. In these systems, α-alumina microporous membranes with immobilized Candida antarctica lipase B were coated with four different ionic liquids based on 1-n-alkyl-3-imidazolium cations and hexafluorophosphate and bis{(trifluoromethyl)sulfonyl}imide anions. Selectivity increased (reaching >99.5%) when room temperature ionic liquid/supercritical carbon dioxide biphasic systems were used rather than in supercritical carbon dioxide alone. To understand the behaviour of the enzyme and the mass-transfer phenomena in these biphasic systems, the reaction was also carried out in ionic liquids and in ionic liquid/hexane biphasic systems, and the ionic liquid/hexane partition coefficients of the compounds involved in the transesterification reaction were determined. It was observed that the activity in room temperature ionic liquid/supercritical carbon dioxide biphasic systems depends on the effect of the ionic liquid media on the enzyme and the diffusional limitations across the IL-layer around the biocatalyst.     

Mathematical modelling of phase equilibria for supercritical CO2 and polyethylene glycol of various molecular weights

The Sanchez–Lacombe equation of state and the Statistical Associating Fluid Theory were applied for modelling the phase equilibrium for the polyethylene glycol–CO₂ systems. The Aspen Plus software was used and polyethylene glycol with various molecular weights was investigated. The results were compared with previously obtained experimental values for solubility. The phase equilibrium was calculated at a temperature of 343 K, in the pressure range of 10–30 MPa and for polyethylene glycol molecular weights from 1000 to 100,000 g/mol. The binary interaction parameters for the models were optimized in order to obtain the best fit between the estimated and the experimental gas solubility data. The results suggest that both models are reliable in describing the phase equilibrium of the polyethylene glycol–CO₂ systems at the proposed conditions. Moreover, the molecular weight of the polymer affects the behaviour of the system, as observed from the variation of solubility values and of binary interaction coefficients.     

Extended UNIQUAC model for correlation and prediction of vapor-liquid-liquid-solid equilibria in aqueous salt systems containing non-electrolytes. Part B. Alcohol (ethanol, propanols, butanols)-water-salt systems

The Extended UNIQUAC model for electrolyte solutions is an excess Gibbs energy function consisting of a Debye-Hückel term and a term corresponding to the UNIQUAC equation. For vapor-liquid equilibrium calculations, the fugacities of gas-phase components are calculated with the Soave-Redlich-Kwong equation of state. The model only requires binary, temperature-dependent interaction parameters. It has previously been used to describe the excess Gibbs energy for aqueous electrolyte mixtures and aqueous electrolyte systems containing methanol. It has been found to be an adequate model for representing solid-liquid-vapor equilibrium and thermal property data for strongly non-ideal systems. In this work, the model is extended to aqueous salt systems containing higher alcohols. The calculations are based on an extensive database consisting of salt solubility data, vapor liquid equilibrium data, and liquid-liquid equilibrium data for solvent mixtures and for mixed solvent-electrolyte systems.The application of this model to represent the vapor-liquid-liquid-solid equilibria in aqueous systems containing various non-electrolytes (ethanol, 1-propanol, 2-propanol, 1-butanol, 2- butanol, 2-methyl 1-propanol, 2-methyl 2-propanol) and various ions (Na⁺, K⁺, NH₄⁺, Cl⁻, NO₃⁻, SO₄²⁻, SO₃²⁻, HSO₃⁻, CO₃²⁻, and HCO₃⁻) shows the capability of the model to accurately represent the phase behavior of these kinds of systems.     

Application of the simplex simulated annealing technique to nonlinear parameter optimization for the SAFT-VR equation of state

A non-equilibrium simplex simulated annealing algorithm is applied as a global optimization method to parameter optimization for an equation of state based on the generalized statistical associating fluid theory incorporating potentials of variable range. The parameters are determined by optimizing the calculated phase behaviour of a number of pure solvents, such as water and alcohols, and aqueous electrolyte solutions. The optimized parameters obtained via the simulated annealing algorithm are compared to those obtained using the simplex method and, for the electrolyte solutions, a gradient-based quasi-Newton method. In the case of the pure solvents, the lowest values of the objective function have been obtained using the simulated annealing technique in six out of the seven studied systems, while for the electrolyte solutions the method results in the lowest values in nine systems out of 11; in the other systems the local methods have resulted in lower values of the objective function. It is observed that both for the solvents and the solutions considered the parameters obtained using the annealing technique are theoretically justifiable, follow physically meaningful trends, and can more easily be generalized; such results provide a measure of confidence that the annealing method does converge to the global minimum in the majority of the studied systems. For pure solvents a simple generalization of parameters leads to accurate predictions for other solvents in the same homologous series. In the case of the electrolyte systems correlations among parameters obtained via simulated annealing can be qualitatively identified, and a simple correlation is proposed which simplifies the molecular models. This is generally not the case for the two local minimization methods considered which, except for a few specific cases, lead to parameters showing no general trends, despite the calculated phase behaviour being almost identical.