Wong Sandler Mixing Rules Research Articles

Phase behavior of mixture of supercritical CO2 + ionic liquid: Thermodynamic consistency test of experimental data

Various models have been applied composed of the Peng‐Robinson equation of state (PR‐EoS) and the Soave‐Redlich‐Kwong equation of state (SRK‐EoS) associated with three mixing rules including the following: Wong‐Sandler (WS), van der Waals one (vdW1), and van der Waals two (vdW2) for phase behavior modeling of mixtures of supercritical CO2 + different ionic liquids in vapor–liquid equilibrium (VLE) region. It has been found that the PR EoS implying the WS mixing rule can be used as a reliable thermodynamic model to perform a thermodynamic consistency test on the experimental data of phase behaviors of the supercritical CO2 + ionic liquid systems (19 commonly‐used ionic liquids have been studied). The results show that 40% of the experimental data seem to be thermodynamically consistent, 55.5% seem to be thermodynamically inconsistent, and 4.5% seem to be not fully consistent. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3892–3913, 2013

Isothermal vapor–liquid equilibrium data for the decafluorobutane (R3110) + 1,1,1,3,3-pentafluorobutane (R365mfc) system at temperatures from 333 K to 441 K

The organic Rankine cycle (ORC) is one solution to recover energy from high temperature hot sources. It requires working fluid with high critical coordinate values. It is named for its use for an organic high molecular masse fluid with a liquid-vapor phase change. The knowledge of phase diagram of working fluid is a crucial task in refrigeration process. In this context, a new mixture of decafluorobutane (R3110) and 1,1,1,3,3-pentafluorobutane (R365mfc), is studied by means of experimental measurements and modeling procedures. The purpose is to obtain the isothermal vapor-liquid equilibrium data (R3110 + R365mfc) of binary system ranging from (333.26 to 441.61) K temperature, and (0.2016 to 3.0927) MPa pressure. The data were obtained with accurate within u(T, k = 2) = 0.02 K, u(P, k = 2) = 0.0003 MPa and u(z) = 0.004 for molar composition. In the present work, the static analytic method is another time investigated to achieve a high quality data as it was largely demonstrated previously by the team of our laboratories. The experimental data are correlated using the classical equations: Peng-Robinson equation of state, the Mathias-Copeman alpha function, and the Wong-Sandler mixing rules involving the NRTL model. The predicted critical line is well reproduced.

High pressure solubility of CO2 in non-fluorinated phosphonium-based ionic liquids

High pressure solubility of carbon dioxide in three phosphonium-based ionic liquids has been measured experimentally. A synthetic method was used to measure vapor–liquid, vapor–liquid–liquid and liquid–liquid equilibria of carbon dioxide in the ionic liquids trihexyltetradecylphosphonium bromide [thtdp][Br], trihexyltetradecylphosphonium dicyanamide [thtdp][dca] and trihexyltetradecylphosphonium bis(2,4,4-trime-thylpentyl)phosphinate [thtdp][phos] for a temperature range of 271–363 K and up to 90 MPa. Furthermore, the densities and viscosities of these ILs have been measured in a temperature range of 293–363 K. The solubility of carbon dioxide in these ILs is (on mole fraction basis) significantly larger than most of the commonly used fluorinated imidazolium ionic liquids. The latter statement, however, does not hold for the [Br] and [dca] based IL if the solubility is compared on molality (mole/mass solvent) basis, where the solubility differences among physical ILs tends to vanish indicating a strong molecular weight effect. The solubility of carbon dioxide in [thtdp][phos], both on mole fraction and molality basis, is among the highest compared to all the other physical ILs reported so far in the literature. The Peng–Robinson equation of state in combination with Wong–Sandler mixing rules incorporating the NRTL Gibbs excess energy model was applied to represent the experimental data with acceptable accuracy.

Correlation of Viscosity of Aqueous Solutions of Alkanolamine Mixtures Based on the Eyring's Theory and Wong-Sandler Mixing Rule

A viscosity model, based on Eyring's absolute rate theory combined with a cubic PR equation of state and Wong-Sandler mixing rule, has been proposed in order to correlate viscosities of aqueous solutions of alkanolamine mixtures at atmospheric pressure and different temperatures. In the proposed method, the energy and size parameters in studied Equation of State (EoS) have been obtained using the Wong - Sandler (WS) mixing rule combined with the NRTL and Wilson Gibbs equations. The NRTL and Wilson parameters for aqueous solutions of alkanolamine mixtures have been correlated using measured viscosity data at atmospheric pressure and different temperatures. The overall average deviation between the experimental and calculated viscosities of studied aqueous solutions of alkanolamine mixtures using Wilson model is 0.92%.

Isothermal Vapor–Liquid Equilibrium Data and Modeling for the Ethane (R170) + Perfluoropropane (R218) System at Temperatures from (264 to 308) K

Isothermal vapor–liquid equilibrium data are presented for the ethane (R170) + perfluoropropane (R218) binary system. Measurements were performed at five isotherms ranging from (264.05 to 308.04) K, with pressure ranging from (0.298 to 4.600) MPa. The measurements were undertaken using a “static-analytic” type apparatus, with sampling of the equilibrium phases via a mobile capillary sampler (ROLSI). The uncertainties in the measurements were within 0.06 K, 0.9 kPa, and less than 0.006 for temperature, pressure, and mole fraction, respectively. The full set of isothermal vapor–liquid equilibrium data was successfully correlated with the Peng–Robinson equation of state, incorporating the Mathias–Copeman alpha function, and the Wong–Sandler mixing rule with the Non-Random Two-Liquid (NRTL) activity coefficient model.

Isothermal vapor–liquid equilibrium of R170 + n-perfluorooctane at 308–338 K: Measurement, equation of state modelling, and molecular simulation

Isothermal vapor–liquid equilibrium data are presented for the R170 + n-perfluorooctane system. Measurements were performed at five isotherms ranging from 308.45 to 338.43 K and were undertaken using a “static-analytic” type apparatus, with sampling of the equilibrium phases via a moveable capillary sampler (ROLSI™). The uncertainties in the measurements of temperature, pressure, and phase compositions were within 0.036 K, 0.0058 MPa, and less than 0.02 mol mol−1 respectively. The VLE data were correlated with the Peng–Robinson equation of state, incorporating the Mathias–Copeman α function. The Wong–Sandler mixing rule with the non-random two-liquid (NRTL) activity coefficient model and the classical one-fluid mixing rule were used. The Wong–Sandler mixing rule represents the experimental data more accurately than the classical mixing rule. These measurements have also been compared to results obtained from isobaric–isothermal Gibbs ensemble Monte Carlo molecular simulations. Very good agreement between experiment and simulation was obtained, although systematic under-estimation of the experimental vapor compositions was observed. The simulations further validate the transferability of an existing optimum Lennard–Jones cross-parameter set. Radial distribution functions for the liquid phase were calculated and show that R170 molecules tend to cluster around each other, while the CF2 groups on n-perfluorooctane molecules show the least preference for mutual proximity.

Vapor–liquid and liquid–liquid equilibrium for binary systems ester + a new protic ionic liquid

This study reports the synthesis of a new protic ionic liquid, bis(2-hydroxyethyl)ammonium butyrate (2-HE2AB), performed by a Bronsted acid–base reaction between butanoic acid and bis(2-hydroxyethyl)ammonia. The new ionic liquid was characterized by 1D hydrogen NMR spectrum. The ionic liquid shows complete solubility in water, methanol, and ethanol, and is partially soluble in methyl acetate, ethyl acetate, and propyl acetate, while it is not soluble in some alkanes. Density, refractive index, and vapor–liquid equilibrium were measured for the binary system 2-HE2AB + methyl acetate at atmospheric pressure. Furthermore, density, refractive index, and liquid–liquid equilibrium were measured for the binary systems 2-HE2AB + ester (methyl acetate, ethyl acetate, or propyl acetate) at 293.2 K. The Peng-Robinson equation of state, coupled with the Wong-Sandler mixing rule, was used in the thermodynamic modeling of density, vapor–liquid, and liquid–liquid equilibrium data. The COSMO-SAC activity coefficient model was used to calculate the activity coefficient within the Wong-Sandler mixing rule. The calculations show deviations for density, for the vapor–liquid equilibrium, and for the non-polar and polar phases of the liquid–liquid equilibrium within 13.0, 0.1, 132.5, and 23.8 %, respectively.

A modified Patel–Teja cubic equation of state: Part I – Generalized model for gases and hydrocarbons

Abstract A generalized cubic equation of state is proposed for non-polar substances, including heavy hydrocarbons. The new model is based on the Patel–Teja cubic equation of state and the alpha function of Heyen. The proposed equation is compared with the Peng–Robinson, the Peng–Robinson–Gasem, the original Patel–Teja and the translated Peng–Robinson model proposed by Ahlers and Gmehling. Results show that the model proposed in this work is the best of the models evaluated to represent the saturated thermodynamic properties of non-polar substances, especially in the cases of heavy hydrocarbons and hydrogen. The new model improves the capability of the Patel–Teja equation to predict the second virial coefficient and the Boyle temperature of gases and hydrocarbons. Finally, some generalized expressions are developed to predict the vapor liquid equilibria for aromatic/alkane and aromatic/aromatic system using the proposed model and the Wong–Sandler mixing rules.

Thermodynamic modeling of PVTx properties for several water/hydrocarbon systems in near-critical and supercritical conditions

E ) model and the cubic plus association (CPA) equa- tion of state (EoS) are compared in this study with respect to their accuracy in the correlation of PVTx for systems such as water/methanol, water/ethanol, water/benzene, water/toluene, water/methane, water/n-butane, water/n-pentane, water/ n-hexane, water/heptane, and water/octane, in supercritical conditions within temperature and pressure ranges of (573- 698 K) and (7.0-276.0 MPa), respectively. In the proposed EoS/G E model, Peng-Robinson (PR) equation of state, linear combination Vidal-Michelsen (LCVM) and Wong-Sandler (WS) mixing rules in conjunction with UNIQUAC activity coefficient model were used. Correlation of both CPA and EoS/G E models was evaluated by comparing the results with the experimental data. Average absolute relative deviation (AARD) for WS, LCVM, and CPA was found to be 2.99, 11.11 and 5.14%, respectively, indicating better correlation of WS model with the experimental data.

Vapor-liquid equilibrium data concerning refrigerant systems (R3110+R365mfc)

In ORC, the knowledge of phase diagram of working fluid is essential. In this paper isothermal vapor liquid equilibrium data are presented for the R3310 + R365mfc system. Measurement were performed for seven isotherms (three below and four above the critical temperature of C4F10) ranging from 333.26 to 441.61 K, with pressure ranging from 0.2016 to 3.0927 MPa. The measurements were undertaken using a “static-analytic” type apparatus, with sampling of the equilibrium phases via capillary samples (ROLSI TM ). The maximum uncertainties in the measurements were within ± 0.02 K, 0.0003 MPa and less than ± 0.004 for temperature, pressure, and equilibrium phase mole fractions, respectively. The full set of isothermal vapor-liquid equilibrium data were correlated with the Peng-Robinson equation of state, incorporating the Mathias-Copeman alpha function, with the Wong-Sandler mixing rule utilizing the NRTL activity coefficient model.

Modeling the melting temperature depression of ionic liquids caused by supercritical carbon dioxide

Abstract The melting temperature depression (MTD) that happens when an ionic liquid (IL) is pressurized by a soluble gas is modeled using phase equilibrium relations. MTD of hydrocarbons, polymers and lipids has been reported by several authors and the subject has been widely discussed in the literature. However, the phenomenon in ionic liquids (ILs) has received recent attention especially because some ILs that are potentially attractive for organic synthesis could not be used due to their relatively high melting temperatures. When solid is formed from the gas-pressurized liquid, three phase equilibrium in the binary system IL + gas is produced. In this paper the equation of state method is used to model the gas–liquid equilibrium and activity coefficients for representing the solid–gas equilibrium. Thus a consistent set of equations is formulated and solved by an optimization method using available experimental data of pressure, and temperature of IL + gas systems. The Peng–Robinson equation with the Wong–Sandler mixing rules showed to be appropriate for correlating the gas–liquid equilibrium data while the van Laar model for the activity coefficient was appropriate for correlating the solid–gas equilibrium data.

Modeling associating hydrocarbon + alcohol mixtures using the Peng-Robinson equation of state and the Wong-Sandler mixing rules

Abstract The main objective of the study is the accurate modeling of the bubble pressure and of the vapor phase concentration in associating hydrocarbon + alcohol mixtures and the correct comparison with results from the literature. A relatively simple equation of state is used and comparison is done considering various factors that affect the accuracy of the results, so fair and correct conclusions can be drawn. The mathematical complexity of the model, the type and amount of basic properties and the number of adjustable parameters used by the model, among other factors are discussed. The Peng-Robinson equation of state including the Wong-Sandler mixing rules was used. This combination of equations of state and mixing rules have not yet been applied in a systematic way to alcohol + hydrocarbon mixtures at low and moderate pressure, as done in this work, although other complex equation of state models have been used for some selected systems. It is concluded that simple and well-founded models can correlate equilibrium data in these complex mixtures with similar accuracy than other more sophisticated models.

Isothermal vapor-liquid equilibria for the binary systems of ethylene glycol monopropyl ether with 2,2-dimethylbutane and 2,3-dimethylbutane

Isothermal vapor liquid equilibria for the binary system of ethylene glycol monopropyl ether with 2,2-dimehylbutane and 2,3-dimethylbutane were measured in a circulating water bath at 303.15, 318.15, and 333.15 K. The apparatus was in-house designed and manufactured. Consistency testing of the apparatus was done by comparing the measured vapor pressures to the calculated vapor pressures from the Antoine equation. The measured systems were correlated with a Peng-Robinson equation of state (PR) combined with Wong-Sandler mixing rule for the vapor phase, and NRTL, UNIQUAC, and Wilson activity coefficient models for the liquid phase. All the measured systems showed good agreement with the correlation results.

Use of a hybrid optimization method to reduce vapor–liquid equilibrium data of maverick systems: The case of carbon dioxide with 2-methoxyethanol and 2-ethoxyethanol using cubic equations of state

Abstract Using a hybrid of the Genetic Algorithm (GA) and the Fmincon optimization techniques is proposed for reducing vapor liquid equilibrium (VLE) data of systems formed by a subcritical and a supercritical compound. As an example, this hybrid technique is used with advantage for evaluation of binary parameters required by cubic equations of state for the correlation of VLE data of binary mixtures containing carbon dioxide with 2-methoxyethanol and 2-ethoxyethanol. Four cubic equations of state (modified Van der Waals, Soave–Redlich–Kwong, Peng–Robinson, and Peng–Robinson–Stryjek–Vera), coupled with four mixing rules (conventional one-binary parameter, Margules-type, Huron–Vidal and the reformulated Wong–Sandler) were used. The Peng–Robinson–Stryjek–Vera EoS coupled with the Margules-type mixing rule gave the best correlation of vapor phase composition and combined with the reformulated Wong–Sandler mixing rule gave the best correlation of equilibrium pressure. The latter combination gave the best overall fit of the data. The binary interaction parameters were found to be independent of temperature.

Vapor–Liquid Equilibrium Measurements and Modeling for the Ethane (R-170) + 1,1,2,3,3,3-Hexafluoro-1-propene (R-1216) Binary System

Novel isothermal (p–x–y) vapor–liquid equilibrium data are reported for ethane (R-170) + 1,1,2,3,3,3-hexafluoro-1-propene (R-1216) mixtures at five temperatures in the (282.93 to 322.89) K range, at pressures up to about 4.6 MPa. The experimental data were measured using an apparatus based on the “static-analytic” method taking advantage of two electromagnetic capillary samplers for repeatable and reliable equilibrium phase sampling and handling. The experimental data are well-correlated with the “PR-MC-NRTL-WS” model constituted by the Mathias–Copeman α function, nonrandom two-liquid (NRTL) local composition model, and Wong–Sandler mixing rule introduced in the Peng–Robinson equation of state. The studied system did not exhibit azeotropic behavior nor liquid–liquid immiscibility over the range of investigated temperatures. Mixture critical points have been estimated from the experimental vapor–liquid equilibrium data via the extended scaling laws and the “PR-MC-NRTL-WS” model and are found to be in good agreement with the experimental isothermal phase envelopes.

Vapor–liquid equilibria of ethylene (C2H4) + decafluorobutane (C4F10) at 268–298 K from experiment, molecular simulation and the Peng–Robinson equation of state

Abstract Isothermal vapor–liquid equilibrium (VLE) data are presented for the system ethylene + decafluorobutane. Measurements are performed for four isotherms around the critical temperature of ethylene, i.e. in the temperature range from 268.13 to 298.13 K. The measurements are undertaken using a “static-analytic” type apparatus, sampling the phases in equilibrium via a moving capillary sampler (ROLSITM). The uncertainties of the present measurements of temperature, pressure and mole fraction are within 0.036 K, 0.0058 MPa and 0.02 mol/mol, respectively. The VLE data are correlated with the Peng–Robinson equation of state (PR EOS), incorporating the Mathias–Copeman alpha function. Both, the Wong–Sandler mixing rule with the non-random two-liquid (NRTL) activity coefficient model and the quadratic Van der Waals one-fluid mixing rule are used. In addition, a new rigid force field model for decafluorobutane is developed and molecular simulations are carried out. The simulation results are compared to the present experimental data for the binary system. Furthermore, pure component properties of decafluorobutane are predicted and compared to experimental data from the literature and the PR EOS.

Isothermal Vapor–Liquid Equilibrium Data for the 1,1,2,2-Tetrafluoroethene + 1,1,2,2,3,3,4,4-Octafluorocyclobutane Binary System: Measurement and Modeling from (248 to 283) K

High pressure vapor–liquid equilibrium data are presented for the 1,1,2,2-tetrafluoroethene + 1,1,2,2,3,3,4,4-octafluorocyclobutane binary system. The isothermal measurements were undertaken at (248.3, 263.0, and 282.9) K, with pressures ranging from (0.040 to 2.340) MPa. A static–analytical apparatus was used to carry out the measurements. The liquid and vapor phases were sampled at equilibrium using a movable rapid on-line sampler–injector (ROLSI). The uncertainties in the measurements are less than 0.1 K, 1.5 kPa, and 0.007 for the temperature, pressure, and equilibrium phase mole fractions, respectively. The experimental data were correlated with the Peng–Robinson equation of state incorporating the Mathias–Copeman alpha function, with the Wong–Sandler mixing rule utilizing the nonrandom two-liquid (NRTL) activity coefficient model. The model accurately describes the experimental data.

Measurement of VLE data of carbon dioxide + dimethyl carbonate system for the direct synthesis of dimethyl carbonate using supercritical CO2 and methanol

► VLE data for CO 2 + DMC system were measured from 293.15 to 333.15 K. ► Experimental data were well correlated with PR-EoS using WS-mixing rules. ► AAD-P and AAD-y were 1.325% and 0.3071%, respectively. ► Binary parameters ( k ij ) are independent of temperature and fitted with k ij = 0.38. Isothermal vapor–liquid equilibrium data for the binary system of carbon dioxide + dimethyl carbonate (DMC) were measured at 278.15, 283.15, 293.15, 303.15, 313.15, 323.15 and 333.15 K using a circulation-type equilibrium apparatus in which both vapor and liquid phases were recirculated. The equilibrium compositions of vapor and liquid phases and pressures were reported at each temperature. The measured data were correlated with the Peng–Robinson equation of state (PR-EoS) using the Wong–Sandler mixing rules combined with the NRTL excess Gibbs free energy model and the Peng–Robinson equation of state (PR-EoS) using the Universal mixing rule. Calculated results with these equations can be used to estimate the thermodynamic properties of this binary system of CO 2 (1) + DMC (2).

Vapor-liquid equilibra for cyclohexane+2-propoxyethanol and cyclohexane+2-butoxyethanol systems

2-propoxyethanol (C3E1) and 2-butoxyethanol (C4E1) are nonionic surfactants which are a particularly interesting class of substances due to both inter-molecular and intra-molecular association, related to the presence of O and OH in the same molecule. Binary (vapor+liquid) equilibrium data were measured for cyclohexane+2-propoxyethanol and cyclohexane+2-butoxy ethanol systems at temperatures ranging from 303.15 K to 323.15 K at 10 K intervals. A static apparatus was used in this study. Two systems show positive deviation from Raoult’s law and no azeotrope. The experimental data were correlated well with Peng-Robinson-Stryjek-Vera equation of state using Wong-Sandler mixing rule incorporating the non-random-two-liquid model.

Vapor-liquid Equilibrium Data Concerning Refrigerant Systems (R116 + R143a)

Abstract Development of modern refrigeration systems is critical for the success of new global environmental protection efforts. The binary system of refrigerants: Hexafluoroethane (R116) + 1,1,1- trifluoroethane (R143a), has been studied with the aim of providing PTxy data. Isothermal vapor-liquid equilibrium data have been generated using the “static-analytic” method from 258 to 328 K at pressures from 0.39 to 3.89 MPa. The modelcomposed of the Peng-Robinson equation of state, the Mathias-Copeman alpha function, the Wong-Sandler mixing rules and the NRTL cell theory is applied herein to correlate the data and calculate the critical line.