Adjustable Binary Interaction Parameters Research Articles

Extended thermodynamic model for high salinity produced waters

To support the development of desalination processes for high salinity produced waters, we developed a comprehensive thermodynamic model that reliably predicts the thermodynamic properties and phase behavior of produced water. This study extends a previously developed thermodynamic model for the aqueous hexary oceanic salt system by incorporating the Sr2+ and Ba2+ ions. Based on the electrolyte nonrandom two-liquid theory, the model requires two adjustable binary interaction parameters for each water-electrolyte and electrolyte-electrolyte pair that has a common ion. The binary interaction parameters for the electrolyte-electrolyte pairs involving Sr2+ and Ba2+ ions were identified using thermodynamic and salt solubility data. The model was validated for temperatures from 273.15 K to 473.15 K and electrolyte concentrations from infinite dilution to salt saturation. Extension of the model to include HCO3−, CO32−, and CO2 is currently in progress.

An Electrolyte Non-random-UNIQUAC Model for Thermodynamic Modeling of Binary and Multicomponent Aqueous Electrolyte Systems

An Electrolyte non-random-UNIQUAC (NR-UNIQUAC) local composition model is developed for calculation of the excess Gibbs energy and activity coefficients for binary and the multicomponent electrolyte solutions. A new expression for the energies of the reference cells in the random state is used and a modified version of the UNIQUAC model is provided. The high efficiency of the presented model is demonstrated through the correlation of the available experimental data for various electrolyte solutions. Obtained results are compared with those of Electrolyte-UNIQUAC-NRF model. The correlation of data was carried out using two different approaches, the single system correlation and the global optimization of the interaction parameters. In the single fitting approach, two adjustable binary interaction parameters of the model are regressed using the experimental mean activity coefficient data of binary solutions. In the global approach, the anion-water and cation–anion interaction energy parameters of different ions are calculated via simultaneous correlation of the mean activity coefficient data of the forty-nine binary electrolyte solutions. In both approaches, the adjustable parameters are calculated in a wide range of electrolyte concentrations and at different temperatures, so that these parameters can be used to predict the osmotic coefficient data of many binary systems. Moreover, the solubility and osmotic coefficient data of ternary electrolyte solutions were predicted using the previously obtained binary parameters. Using the present model, the predicted data for the binary and multicomponent electrolyte solutions are in good agreement with the experimental data. When compared to Electrolyte-UNIQUAC-NRF model, the present model is more accurate. Additionally, the presence of salt–salt interaction parameters in the electrolyte-NR-UNIQUAC model can further improve its efficiency when experimental data for a ternary system is available.

Phase behaviors for the poly(2-phenylethyl methacrylate) in supercritical fluid solvents: Experiment and PC-SAFT EoS

In this work, the experimental cloud-points in the binary and ternary mixtures for poly(2-phenylethyl methacrylate) [P(2-PEMA)] solutions containing supercritical solvents (i.e., carbon dioxide, propylene, 1-butene, dimethyl ether (DME)) are carried out up to 473K and 224MPa. According to the amount of cosolvent (i.e., DME), the cloud-point curves for ternary mixtures of P(2-PEMA) in supercritical solvents (i.e., carbon dioxide, propylene, 1-butene) show the changes from upper critical solution temperature (UCST) behavior to lower critical solution temperature (LCST) behavior. The PC-SAFT equation of state is applied to correlate the phase behaviors of all experimental systems, and the calculated results are shown as a reasonable agreement with experimental data. According to the amount of DME (i.e., cosolvent), the UCST- and LCST-type phase behaviors are described exactly by PC-SAFT EoS with one adjustable binary interaction parameter on which the effect of temperature and/or cosolvent amount is not considered.

Solubility of diazepam in water + tert-butyl alcohol solvent mixtures: Part 2. Correlation using Scatchard-Hildebrand and combined Scatchard-Hildebrand/Flory-Huggins excess Gibbs energy models

The aim of this work is to evaluate the performances of two excess Gibbs energy models, namely the Scatchard-Hildebrand model and the combined Scatchard-Hildebrand/Flory-Huggins model, in correlating the composition and temperature dependence of the solubility of diazepam in water + tert-butyl alcohol solvent mixtures. The dependence of the pure component properties required as input data to the models on temperature was considered as well as that of the adjustable binary interaction parameters. For this purpose, a set of twenty-seven model versions containing from three up to six adjustable parameters and differing from one another by the dependence of at least one binary interaction parameter on temperature was generated for the two excess Gibbs energy models investigated. To rank and weight among these different model versions, second-order Akaike's information criterion corrected for small sample size was used. The correlative performances of the most parsimonious versions of the Scatchard-Hildebrand and combined Scatchard-Hildebrand/Flory-Huggins models selected from this approach were then evaluated, compared and discussed.

High-pressure phase behaviour of poly(d-lactic acid), trichloromethane, and carbon dioxide ternary mixture systems

The high pressure phase behaviour of poly(d-lactic acid) (Mw=359,000), trichloromethane, and carbon dioxide ternary mixture systems is presented in this study. Cloud and bubble point pressures were measured using a variable volume view cell at temperatures (313.15 to 363.15)K and pressures up to 33.6MPa. The hybrid equation of state for the polymer-carbon dioxide system was used to correlate the experimental results. The van der Waals one-fluid mixing rule with three adjustable binary interaction parameters was used for all correlations. The binary parameters were optimised using the simplex method algorithm.

The study of binary interaction parameters on VLE for alternative refrigerant mixtures

AbstractThe vapor–liquid equilibrium (VLE) data for hydrofluorocarbons (HFCs) + hydrocarbons (HCs) and HFCs + dimethyl ether (DME) are correlated by the Soave–Redlich–Kwong, Peng–Robinson, and Carnahan–Starling–DeSantis, respectively, with one adjustable binary interaction parameter kij, and each equation can represent the satisfactory results. For the three equations, the obtained optimum interaction parameter kij is almost the same for the binaries containing the same HFC component in the same class, and when the kij of the lack‐of‐data mixtures are needed, it just needs to know the kij of any binary in the same class on the basis of the phenomena and law. Moreover, a new equation for kij is developed that enables the three equations of state to predict the VLE properties for such mixtures within reasonable accuracy. © 2015 Curtin University of Technology and John Wiley & Sons, Ltd.

Prediction of Vapor-Liquid Equilibrium of Polypropylene Oxide Solution Systems by Cubic Equations of State

In this research, vapor-liquid equilibrium behavior of Polypropylene oxide (PPO)/solvent and Polypropylene glycol (PPG)/solvent were calculated using cubic equation of states. Eight models containing PRSV and SRK CEOS with four mixing rules namely vdW1, vdW2, Wong-Sandler (WS), and Zhong-Masuoka (ZM) were applied to calculations of bubble point pressure. For the better prediction, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results of absolute average deviations (%AAD) between predicted and experimental bubble point pressure were calculated and presented. The PRSV+vdW2 model was the best predictive model with the highest accuracy (AAD=1.021%) between other models.

Modeling Solubilities of Gases in the Ionic Liquid 1-Ethyl-3-methylimidazolium Tris(pentafluoroethyl)trifluorophosphate Using the Peng–Robinson Equation of State

In this paper, vapor–liquid equilibrium (VLE) data of binary mixtures containing gases such as carbon dioxide (CO2), methane, ethane, propane, or butane in the ionic liquid 1-ethyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate ([emim][FAP]) have been modeled using the Peng–Robinson equation of state (PR-EoS), combined with quadratic mixing rules. The calculations were performed at various temperatures. All calculations were performed with only one adjustable binary interaction parameter except in the system with CO2. In that case, two adjustable binary interaction parameters were used. The results showed a temperature dependence of the adjustable parameters. In all cases, the calculated results have been found to be in good agreement with the experimental data. A total absolute average deviation in the bubble-point pressures of less than 3% was established over a wide temperature range (293–363 K) and pressures up to 11 MPa.

Erratum to: Thermodynamic modeling of vapor–liquid equilibrium for binary polyethylene glycol/solvent solutions using cubic equations of state: optimization and comparison of CEoS models

The cubic equation of state (CEoS) is a powerful method for calculation of (vapor + liquid) equilibrium in polymer solutions. Using CEoS for both the vapor and liquid phases allows one to calculate the non-ideality of polymer solutions based on a single EoS approach. In this research, vapor–liquid equilibrium calculations of Polyethylene glycol(Polyethylene oxide)/solvent solutions were carried out. In this approach eight models containing PRSV and SRK CEoS separately combined with four mixing rules namely one-parameter van der Waals one-fluid, two-parameter van der Waals one-fluid (vdW2), Wong–Sandler, and Zhong–Masuoka were applied to calculations of bubble point pressure. For the better prediction, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results were very acceptable and satisfactory. The results of absolute average deviations between predicted results and experimental bubble point pressure data were calculated and presented. Although the capability of two cubic equations of state had a good agreement with experimental data and predict the correct type of phase behavior in all cases, the performance of the PRSV+vdW2 was more reliable than the other models.

Application of cubic equation of state models in prediction of vapor–liquid equilibria for binary polyvinyl acetate/solvent solutions

ABSTRACTThe cubic equation of state (CEoS) is a powerful method for calculation of (vapor + liquid) equilibrium (VLE) in polymer solutions. Using CEoS for both the vapor and liquid phases allows one to calculate the non‐ideality of polymer solutions based on a single EoS approach. In this research, vapor–liquid equilibria calculations of polyvinyl acetate (PVAc)/solvent solutions were performed. In this approach, eight models containing PRSV and SRK CEoS separately combined with four mixing rules namely vdW1, vdW2, Wong–Sandler (WS), and Zhong–Masuoka (ZM) were applied to calculations of bubble point pressure. For the better prediction, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results were very acceptable and satisfactory. Absolute average deviations (%AAD) between predicted results and experimental bubble point pressure data were calculated and presented. The capability of two cubic equations of state had a good agreement with experimental data and predict the correct type of phase behavior in all cases, but the performance of the PRSV + vdW2 was more reliable than the other models with 2.65% in AAD for total of solution systems. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40651.

Modeling of vapor-liquid equilibrium for binary polypropylene glycol/solvent solutions using cubic equation of state models: optimization and comparison of CEoS models

Abstract The cubic equation of state (CEoS) is a powerful method for calculation of the vapor-liquid equilibrium (VLE) in polymer solutions. Using CEoS for both the vapor and liquid phases allows one to calculate the non-ideality of polymer solutions based on a single EoS approach. In this research, VLE calculations of polypropylene glycol (polypropylene oxide) [PPG(PPO)]/solvent solutions were carried out. In this approach, eight models containing Peng-Robinson-Stryjek-Vera (PRSV) and Soave-Redlich-Kwong (SRK) CEoS separately combined with four mixing rules, namely van der Waals one-fluid mixing rule with one adjustable parameter (vdW1), van der Waals one-fluid mixing rule with two adjustable parameters (vdW2), Wong-Sandler (WS), and Zhong-Masuoka (ZM) were applied to calculations of bubble point pressure. For a better correlation, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results were very acceptable and satisfactory. The results of absolute average deviations (%AAD) between computed results and experimental bubble point pressure data were calculated and presented. Although the capability of two CEoS had a good agreement with experimental data and illustrated the correct type of phase behavior in all cases, the performance of the PRSV+vdW2 was more reliable than the other models.

Solubilities of 3-acetylpyridine in supercritical carbon dioxide at several temperatures and pressures: Experimental and modeling

3-Acetylpyridine (methyl 3-pyridyl ketone) is one of the important compounds to impart flavor and fragrance in various food products. In this work, the solubility data of 3-acetylpyridine in supercritical carbon dioxide (SC-CO2) were experimentally measured at several temperatures (313.15K, 323.15K, 333.15K, and 343.15K) and pressures from 10MPa to 26MPa under static mode. The experimental solubilities over the measurement range were correlated using Chrastil and Del Valle and Aguilera density-dependent models while phase equilibrium behavior of the studied system was interpreted by Peng–Robinson equation of state (PR-EoS) incorporated with quadratic and Stryjek–Vera mixing rules. The agreement between the model predictions and experimental solubilities was assessed in respect to root-mean-square deviation (RMSD) and consistency of physical meaning of model parameters. Concerning phase equilibria of the studied supercritical system, PR-EoS incorporated with quadratic mixing rule was superior to PR-EoS incorporated with Stryjek–Vera mixing rule and capable to describe the dependency of adjustable binary interaction parameters with temperature.

Phase behaviour of the ternary mixture system of poly(l-lactic acid), dichloromethane and carbon dioxide

In this study, the high pressure phase behaviour of poly(l-lactic acid) (M=312,000), dichloromethane and carbon dioxide ternary mixtures was studied using a variable volume view cell at temperatures ranging from 313.15K to 363.15K and pressures of up to 30.0MPa as functions of temperature and the CO2/dichloromethane mass ratio at poly(l-lactic acid) weight fractions of 1.0%, 2.5% and 3.0%. The experimental results were correlated with the hybrid equation of state for the CO2-polymer system using the van der Waals one-fluid mixing rule with three adjustable binary interaction parameters.

Correction to High-Pressure Phase Behavior of Carbon Dioxide + Tetrahydrofurfuryl Acrylate and Carbon Dioxide + Tetrahydrofurfuryl Methacrylate Binary Mixture Systems

In this study, the high-pressure phase behavior of carbon dioxide + tetrahydrofurfuryl acrylate and carbon dioxide + tetrahydrofurfuryl methacrylate mixtures was studied using a variable volume view cell at temperatures ranging from (313.15 to 363.15) K and pressures of up to 18 MPa. The experimental results were correlated with the Peng–Robinson equation of state using the van der Waals one-fluid mixing rule with one adjustable binary interaction parameter. We compared the Nannoolal–Rarey and Constantinou–Gani group contribution methods for the correlation of the experimental results.

Predictive Method for the Change in Equilibrium Conditions of Gas Hydrates with Addition of Inhibitors and Electrolytes

Here we present a predictive method for the change in the three-phase (vapor–liquid–hydrate) equilibrium condition of gas hydrates upon the introduction of organic inhibitors and electrolytes. The Peng–Robinson–Stryjek–Vera (PRSV) equation of state, combined with the COSMO-SAC activity coefficient liquid model through the modified Huron–Vidal (MHV1) mixing rule, is used to describe the fluid phase, and the van der Waals and Platteeuw (vdW–P) model is used to describe the hydrate crystalline phase. The temperature-dependent Langmuir absorption constants for the vdW–P model are determined by fitting to the equilibrium condition of pure gas hydrates. Once determined, the method contains no adjustable binary interaction parameters and can be used for prediction of the phase behaviors of gas hydrates with additives that do not enter the cages of the clathrate hydrates (e.g., most inhibitors and electrolytes). We examined the accuracy of this method using five pure gas hydrates, five organic inhibitors, and nine electrolytes, and over ranges of temperature (259.0–303.6 K) and pressure (1.37 × 105–2.08 × 108 Pa). The average relative deviations in the predicted equilibrium temperatures are found to be 0.23% for pure gas hydrates, 0.72% with organic inhibitors, and 0.18% with electrolytes, respectively. We believe that this method is useful for many gas hydrate related engineering problems such as the screening of inhibitors for gas hydrates in flow assurance.

Excess molar enthalpies of binary systems containing 2-octanone, hexanoic acid, or octanoic acid at T = 298.15 K

An isothermal titration calorimeter was used to measure the excess molar enthalpies ( H E) of six binary systems at T = 298.15 K under atmospheric pressure. The systems investigated include (1-hexanol + 2-octanone), (1-octanol + 2-octanone), (1-hexanol + octanoic acid), (1-hexanol + hexanoic acid), {N,N-dimethylformamide (DMF) + hexanoic acid}, and {dimethyl sulfoxide (DMSO) + hexanoic acid}. The values of excess molar enthalpies are all positive except for the DMSO- and the DMF-containing systems. In the 1-hexanol with hexanoic acid or octanoic acid systems, the maximum values of H E are located around the mole fraction of 0.4 of 1-hexanol, but the H E vary nearly symmetrically with composition for other four systems. In addition to the modified Redlich–Kister and the NRTL models, the Peng–Robinson (PR) and the Patel–Teja (PT) equations of state were used to correlate the excess molar enthalpy data. The modified Redlich–Kister equation correlates the H E data to within about experimental uncertainty. The calculated results from the PR and the PT are comparable. It is indicated that the overall average absolute relative deviations ( AARD) of the excess enthalpy calculations are reduced from 18.8% and 18.8% to 6.6% and 7.0%, respectively, as the second adjustable binary interaction parameter, k bij , is added in the PR and the PT equations. Also, the NRTL model correlates the H E data to an overall AARD of 10.8% by using two adjustable model parameters.

Prediction of the critical properties of binary alkanol + alkane mixtures using a crossover CPA equation of state

A crossover Cubic-Plus-Association (CPA) equation of state was derived previously based on the original CPA EOS and renormalization group theory. In this work, the equation was extended to mixtures based on the isomorphism approximation to predict the critical properties of binary alkanol + alkane mixtures. The crossover CPA EOS gave acceptable predictions using van der Waals one-fluid mixing rule without adjustable binary interaction parameter. Since the crossover CPA EOS considers the contributions of both the hydrogen bond and the critical fluctuations, it gives better predictions of all the critical parameters than the SRK and original CPA EOS.

High-Pressure Phase Behavior of Carbon Dioxide + Tetrahydrofurfuryl Acrylate and Carbon Dioxide + Tetrahydrofurfuryl Methacrylate Binary Mixture Systems

In this study, the high-pressure phase behavior of carbon dioxide + tetrahydrofurfuryl acrylate and carbon dioxide + tetrahydrofurfuryl methacrylate mixtures was studied using a variable volume view cell at temperatures ranging from (313.15 to 363.15) K and pressures of up to 18 MPa. The experimental results were correlated with the Peng–Robinson equation of state using the van der Waals one-fluid mixing rule with one adjustable binary interaction parameter. We compared the Nannoolal–Rarey and Constantinou–Gani group contribution methods for the correlation of the experimental results.

Excess molar enthalpies of binary mixtures containing 2-decanone or dipentyl ether with long-chain n-alkanes at T = 298.15 K

Excess molar enthalpies ( H E) of binary mixtures of 2-decanone or dipentyl ether with n-alkanes, including n-dodecane, n-tetradecane, and n-hexadecane, were measured with an isothermal titration calorimeter (ITC) at T = 298.15 K under atmospheric pressure. All the measured H E values are positive over the entire range of composition, indicating that all these mixing processes are endothermic. The H E values varying with composition are found to be nearly symmetric for each binary system. It was also shown that the H E values follow the order of n-hexadecane > n-tetradecane > n-dodecane at a given composition in either the 2-decanone or dipentyl ether binary systems. An empirical Redlich–Kister equation correlated quantitatively these new H E data. The Peng–Robinson and the Patel–Teja equations of state, and the NRTL model were also applied to fit the H E results. Among these tested correlative models, the Patel–Teja equation of state with two adjustable binary interaction parameters generally yielded the best representation.

Equation of state for square-well chain molecules with variable range, extension to associating fluids

The equation of state developed in our previous work for square-well chain molecules with variable range (SWCF-VR EOS) was further extended to associating fluids. The association contribution is directly calculated by Liu et al.’s association equation which was proposed based on the sticky-shield method. For the real pure associating fluids, the SWCF-VR EOS has six temperature-independent model parameters obtained by fitting the saturated pressures and/or liquid molar volumes. The results are satisfactory with the overall average absolute deviations (AADs) of 0.76% and 0.75% for saturated vapor pressures and liquid molar volumes of 78 pure fluids in wide temperature ranges. The heat of vaporization for 17 associating fluids were well predicted using these molecular parameters. The good relations between the molecular parameters and the molecular weights were observed. By using a simple mixing rule with only one adjustable binary interaction parameter k ij for the cross well depth ɛ ij , the SWCF-VR EOS can satisfactorily reproduce the vapor–liquid equilibria (VLE) of binary mixtures at reduced and elevated pressures containing self- and cross-associating interaction. Furthermore, the VLE for ternary mixtures can be successfully predicted by using the obtained binary interaction parameters.