Parameters estimation and VLE calculation in asymmetric binary mixtures containing carbon dioxide + n-alkanols

In the present work, the estimation of the parameters for asymmetric binary mixtures of carbon dioxide + n-alkanols has been developed. The binary interaction parameter k₁₂ of the second virial coefficient and non-random two liquid model parameters τ₁₂ and τ₂₁ were obtained using Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules. In all cases, Levenberg–Marquardt minimization algorithm was used for the parameters optimization employing an objective function based on the calculation of the distribution coefficients for each component. Vapor–liquid equilibrium for binary asymmetric mixtures (CO₂ + n-alkanol, from methanol to 1-decanol) was calculated using the obtained values of the mentioned parameters. The agreement between calculated and experimental values was satisfactory.     

Thermodynamic consistency of experimental VLE data for asymmetric binary mixtures at high pressures

A thermodynamic consistency of isothermal vapor–liquid equilibrium data for 9 non-polar and 8 polar binary asymmetric mixtures at high pressures has been evaluated. A method based on the isothermal Gibbs–Duhem equation was used for the test of thermodynamic consistency using a Φ–Φ approach. The Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules were used for modeling the vapor–liquid equilibrium (VLE) within the thermodynamic consistency test. The VLE parameters calculations for asymmetric mixtures at high pressures were highly dependent on bubble pressure calculation, making more convenient to eliminate the data points yielding the highest deviations in pressure. However the results of the thermodynamic consistencies test of experimental data for many cases were found not fully consistent. As a result, the strategies for solving these problems were discussed in detailed.     

Vapor–liquid equilibrium measurement and modeling for the difluoromethane + pentafluoroethane + propane ternary mixture

Vapor–liquid equilibrium data for the difluoromethane (R32) + pentafluoroethane (R125) + propane (R290) ternary mixture were measured at 5 isotherms between 263.15 K and 323.15 K. The measurement was carried out using a circulation-type apparatus recently developed, which was validated with binary mixtures. With binary interaction parameters obtained for the three corresponding binary mixtures, VLE modeling and prediction were performed for the ternary mixture using the Peng–Robinson equation of state with the classical mixing rules and MHV1 mixing rules. Hou's group contribution model for VLE of new refrigerant mixtures was further tested with the experimental data for the ternary system. The predicted pressure and vapor phase composition were compared with experimental ones.     

Modeling of high-pressure vapor–liquid equilibrium in ionic liquids + gas systems using the PRSV equation of state

Ionic liquids are environmentally friendly solvents composed of large organic cations and relatively small inorganic anions, whose melting point is below T = 373.15 K. This is an arbitrary limit defined in order to organize the dramatically increasing number of possible applications in chemical processes. These compounds are regarded as potentially environmentally benign solvents due to their almost negligible vapor pressure, which essentially eliminates emission to the atmosphere; besides, they present a wide range of liquid existence. Ionic liquids are applicable in separation processes, such as recovery of valuable products and remotion of polluting agents in effluents 1, 2, 3 and 4 and are a new and exciting class of compounds that have the potential to overcome many of the problems associated with current CO₂-capture techniques. In this work, high-pressure vapor–liquid equilibrium (VLE) of 17 binary mixtures ionic liquid + gas has been modeled with the Peng–Robinson/Stryjek–Vera (PRSV) 5 and 6 equation of state (EoS) applying the Wong–Sandler (WS) [7] mixing rules, including the van Laar (VL) model for the excess Gibbs free energy [8] for the gamma–phi approach and the one-fluid van der Waals (VDW) mixing rules for the phi–phi approach. Critical properties and acentric factor of ionic liquids [pmim][Tf₂N] and [hmmim][Tf₂N] were determined using the extended group contribution method by Lydersen–Joback–Reid [9], while, for the other ionic liquids, these properties are available in the literature 10 and 11. Experimental data were obtained from literature 12, 13, 14, 15, 16, 17 and 18 and the adjustable parameters were fitted by minimizing the errors between predicted and experimental bubble pressure. van Laar and binary interaction parameters were regarded as temperature-dependent. The results, in terms of main deviations between experimental and calculated pressures for the 17 binary systems, are reasonably satisfactory (3.62% and 2.59% for the gamma–phi and phi–phi approaches, respectively).     

A new three-parameter cubic equation of state for calculation physical properties and vapor–liquid equilibria

A new three-parameter cubic equation of state is presented by combination of a modified attractive term and van der Waals repulsive expression. Also a new alpha function for the attractive parameter of the new EOS is proposed. The new coefficients of alpha function and the other parameters of the attractive term are adjusted using the data of the saturated vapor pressure and liquid density of almost 60 pure compounds including heavy hydrocarbons. The new EOS is adopted for prediction of the various thermophysical properties of pure compounds such as saturated and supercritical volume, enthalpy of vaporization, compressibility factor, heat capacity and sound velocity. Following successful application of the new EOS for the pure components, using vdW one-fluid mixing rules, the new EOSs are applied to prediction of the bubble pressure and vapor mole fraction of the several binary and ternary mixtures. The accuracy of the new EOS for phase equilibrium calculation is demonstrated by comparison of the results of the present EOSs with the PT, PR, GPR and SRK cubic EOSs.     

Vapour–liquid equilibrium for β-myrcene and carbon dioxide and/or hydrogen and the volume expansion of β-myrcene or limonene in CO2 at 323.15 K

Vapour–liquid equilibrium measurements for binary and ternary (carbon dioxide + β-myrcene and carbon dioxide + β-myrcene + hydrogen) systems have been carried out at 323.15 K and pressures in the range from 7 MPa to the critical pressure of the binary mixture and at pressures from 10 to 14 MPa for the investigated ternary systems. Samples from the coexisting phases were taken, and compositions were determined experimentally. Results were correlated using the Peng–Robinson and the Soave–Redlich–Kwong equations of state with the Mathias–Klotz–Prausnitz mixing rule. The set of interaction parameters for the employed equations of state and applied mixing rule for the system of CO₂ + β-myrcene and of CO₂ + β-myrcene + H₂ were obtained. Additionally, the volume expansion of the liquid phase for the binary mixtures (carbon dioxide + β-myrcene and carbon dioxide + limonene) were measured at 323.15 K and at pressures from 4 MPa up to very close to the critical pressure of the mixture. The ratio of liquid phase total volumes at the given pressure and at 4 MPa was calculated.     

Experimental measurements of vapor–liquid equilibria at low pressure: Systems containing alcohols,esters and organic acids

In this work the vapor–liquid equilibria for nine binary mixtures (methanol + acetic acid, methanol + methyl acetate, methanol + water, methyl acetate + acetic acid, water + acetic acid, ethyl acetate + acetic acid, ethanol + acetic acid, ethanol + ethyl acetate and ethanol + water) at subatmospherical pressure (580 mmHg) is presented. Peng–Robinson Stryjek–Vera equation of state coupled with the Wong–Sandler mixing rules were used for predicting phase equilibria of these mixtures. The measurements were developed using an apparatus with recirculation that can also be employed for liquid–vapor equilibrium with chemical reaction.     

Calculation of the critical point for mixtures using mixture models based on Helmholtz energy equations of state

This paper mainly focuses on refrigerant mixtures with relatively simple critical behavior, and presents a practical and useful method for the critical point calculation for the mixtures using mixture models based on Helmholtz energy equations of state. The expression for critical point criterion suitable for this objective is derived first. Numerical manipulations to obtain a physically correct solution are described in detail. For four binary refrigerant mixtures of difluoromethane (R-32) + pentafluoroethane (R-125), R-125 + 1,1,1,2-tetrafluoroethane (R-134a), R-125 + 1,1,1-trifluoroethane (R-143a), and R-32 + propane (R-290), the critical temperatures and critical molar volumes are calculated applying the presented method. The calculation results are compared with experimental values, and the capabilities of the mixture models for the mixtures in the critical region are discussed.     

Crossover Peng-Robinson equation of state with introduction of a new expression for the crossover function

In this research, we use the original Peng-Robinson (PR) equation of state (EOS) for pure fluids and develop a crossover cubic equation of state which incorporates the scaling laws asymptotically close to the critical point and it is transformed into the original cubic equation of state far away from the critical point. The modified EOS is transformed to ideal gas EOS in the limit of zero density. A new formulation for the crossover function is introduced in this work. The new crossover function ensures more accurate change from the singular behavior of fluids inside the regular classical behavior outside the critical region. The crossover PR (CPR) EOS is applied to describe thermodynamic properties of pure fluids (normal alkanes from methane to n-hexane, carbon dioxide, hydrogen sulfide and R125). It is shown that over wide ranges of state, the CPR EOS yields the thermodynamic properties of fluids with much more accuracy than the original PR EOS. The CPR EOS is then used for mixtures by introducing mixing rules for the pure component parameters. Higher accuracy is observed in comparison with the classical PR EOS in the mixture critical region.     

Applicability of cubic equation of state mixing rules on correlation of excess molar volume of non-electrolyte binary mixtures – Part II

The excess molar volume (V?^E) data of the 24 binary highly non-ideal mixtures containing dicyclic ethers (593 data points) were correlated by the Peng–Robinson–Stryjek–Vera (PRSV) cubic equation of state (CEOS) coupled with two different classes of mixing rules: (i) the composition dependent van der Waals (vdW) mixing rule and (ii) the excess free energy mixing rules (CEOS/G?^E) based on the approach of the Gupta–Rasmunssen–Fredenslund (GRF), as well as the Twu–Coon–Bluck–Tilton (TCBT) mixing rule; both rules with the NRTL equation as the G?^E model. The results obtained by these models show that the type of applied mixing rules, including the number and position of interaction parameters are of great importance for a satisfactory correlation of V?^E data. The GRF mixing rules gave mostly satisfactory results for V?^E correlation of the non-ideal binary systems available at one isotherm of 298.15?K, while for the correlation in temperature range from 288.15 to 308.15?K the TCBT model can be recommended.     

Equation of state for square-well chain molecules with variable range II. Extension to mixtures

An equation of state (EOS) developed in our previous work for square-well chain molecules with variable range is further extended to the mixtures of non-associating fluids. The volumetric properties of binary mixtures for small molecules as well as polymer blends can well be predicted without using adjustable parameter. With one temperature-independent binary interaction parameter, satisfactory correlations for experimental vapor–liquid equilibria (VLE) data of binary normal fluid mixtures at low and elevated pressures are obtained. In addition, VLE of n-alkane mixtures and nitrogen + n-alkane mixtures at high pressures are well predicted using this EOS. The phase behavior calculations on polymer mixture solutions are also investigated using one-fluid mixing rule. The equilibrium pressure and solubility of gas in polymer are evaluated with a single adjustable parameter and good results are obtained. The calculated results for gas + polymer systems are compared with those from other equations of state.     

New isothermal vapor–liquid equilibria for the CO2 + n-nonane,and CO2 + n-undecane systems

Experimental vapor–liquid equilibria (VLE) for the CO₂ + n-nonane and CO₂ + n-undecane systems were obtained by using a 100-cm³ high-pressure titanium cell up to 20 MPa at four temperatures (315, 344, 373, and 418 K). The apparatus is based on the static-analytic method; which allows fast determination of the coexistence curve. For the CO₂ + n-nonane system, good agreement was found between the experimental data and those reported in literature. No literature data were available for the CO₂ + n-undecane system at high temperature and pressure. Experimental data were correlated with the Peng–Robinson equation of state using the classical and the Wong–Sandler mixing rules.     

Isothermal vapor–liquid equilibrium data for the binary mixture ethyl fluoride (HFC-161) + 1,1,1,2,3,3,3-heptafluoroproane (HFC-227ea) over a temperature range from 253.15 K to 313.15 K

Vapor–liquid equilibrium (VLE) data for the refrigerant mixture ethyl fluoride (HFC-161) + 1,1,1,2,3,3,3-heptafluoroproane (HFC-227ea) are reported in the temperature range from 253.15 K to 313.15 K with a single-phase circulation vapor–liquid equilibrium still. The results of the correlation for the vapor–liquid equilibrium data with Peng–Robinson (PR) equation of state (EOS), combined with the first Modified Huron-Vidal (MHV1) mixing rule and Wilson model, are presented. These results are in a good agreement with experimental data. The average and maximum derivations of vapor molar composition are within 0.0130 and 0.0295 respectively, and the average and maximum relative derivations of pressure are within 1.04% and 2.96%, respectively. The model parameters, determined from these binary data, are given to predict the phase behavior for a later ternary system. The binary system HFC-161 + HFC-227ea is a non-azeotropic mixture and exhibits a negative deviation from Raoult's law.     

New analytic apparatus for experimental determination of vapor–liquid equilibria and saturation densities

A new experimental apparatus for performing simultaneous determination of high-pressure vapor–liquid equilibria (VLE) and saturated densities was developed in this work. The experimental methodology was verified by measuring these properties for the carbon dioxide + 1-propanol and carbon dioxide + 2-propanol systems from 313 to 363 K. The apparatus is based on the static-analytic method for VLE determinations and was slightly modified by coupling a vibrating U-tube densitometer to obtain saturated densities for both vapor and liquid phases. VLE measurements agreed with previous literature data and were correlated with the Peng–Robinson equation of state coupled to the Wong–Sandler mixing rules. Saturation densities at temperatures above 313 K have not been published up to now.     

High-pressure vapor–liquid equilibria of systems containing ethylene glycol,water and methane: Experimental measurements and modeling

This work presents new experimental phase equilibrium measurements of the binary MEG–methane and the ternary MEG–water–methane system at low temperatures and high pressures which are of interest to applications related to natural gas processing. Emphasis is given to MEG and water solubility measurements in the gas phase. The CPA and SRK EoS, the latter using either conventional or EoS/G^E mixing rules are used to predict the solubility of the heavy components in the gas phase. It is concluded that CPA and SRK using the Huron–Vidal mixing rule perform equally satisfactory, while CPA requires fewer interaction parameters.     

Measurement and calculation of vapor–liquid equilibria for methanol + glycerol and ethanol + glycerol systems at 493–573 K

The vapor–liquid equilibria for methanol + glycerol and ethanol + glycerol systems were measured by a flow method at 493–573 K. The pressure conditions focused in this work were 3.03–11.02 MPa for methanol + glycerol system and 2.27–8.78 MPa for ethanol + glycerol system. The mole fractions of alcohol in vapor phase are close to unity at the pressures below 7.0 MPa for both systems. The pressures of liquid saturated lines of the liquid phase for methanol + glycerol and ethanol + glycerol systems are higher than that for the mixtures containing alcohol and biodiesel compound, methyl laurate or ethyl laurate.     

High-pressure phase behavior of CO2 + 1-butyl-3-methylimidazolium chloride system

The phase behavior of carbon dioxide (CO₂) and the ionic liquid (IL) 1-butyl-3-methylimidazolium chloride ([bmim][Cl]) was measured and correlated at high pressures up to ∼40 MPa and at temperatures between 353.15 K and 373.15 K. The solubility data of CO₂ in [bmim][Cl] were obtained by observing the bubble point pressure at specific temperatures. A variable-volume view cell, which is a high-pressure equilibrium apparatus, was used to measure the CO₂ + [bmim][Cl] system solubility under varying pressure and temperature conditions. In addition, liquid–liquid–vapor (LLV) three-phase behavior was investigated using the equilibrium cell to be able to determine the classification of phase-behavior type by Scott and Van Konynenburg. Based on the LLV phase behavior, this system most likely has type III phase-behavior which is common for IL + CO₂ systems. The resulting data showed that CO₂ dissolved well in the IL at low CO₂ concentrations, but that the pressure derivative of CO₂ solubility dramatically decreased as the mole fraction of CO₂ was increased. The experimental data were well fitted by the Peng–Robinson equation of state with a quadratic mixing rule and cubic parameters estimated by the Joback method.     

High-pressure phase equilibria in the carbon dioxide + pyrrole system

Liquid–vapor (LV) and liquid–liquid (LL) phase equilibria in the carbon dioxide + pyrrole system were measured at temperatures between 313 K and 333 K, and pressures between 8.4 MPa and 15.1 MPa. The data were used to predict the overall phase behavior of the system using the Patel–Teja equation of state and the Mathias–Klotz–Prausnitz mixing rules with two temperature-independent parameters. The calculations suggest that the carbon dioxide + pyrrole system may exhibit type IV phase behavior according to the classification of Scott and van Konynenburg.     

A local composition extension of the van der Waals mixing rule for PR cubic equation of state

New mixing rules (VWLC-I and II) capable of connecting van der Waals (VDW) to CEOS/A^E mixing rule models were developed. These models are able to incorporate the same multi-component mixture parameters obtained for the van der Waals and CEOS/A^E models simultaneously. The VWLC mixing rules directly incorporate local compositions into the cubic equations of state (CEOS). The energy parameters required for the local compositions are calculated from the CEOS parameters. The Peng–Robinson (PR) CEOS was used for this study. Binary interactions parameters were obtained by adjusting the vapor pressure of the binary mixture for several low and high-pressure systems. The predictive capabilities of the VWLC mixing rules were tested by vapor–liquid equilibria calculations for low and high-pressure multicomponent systems. The results were compared with the predictions of the VDW mixing rule and a Huron–Vidal (HV) kind of CEOS/A^E-NRTL mixing rule. The VWLC mixing rules are consistent models giving good results in a broad range of pressures and temperatures in binary and multicomponent mixtures. They compare favorably with the CEOS/A^E-NRTL mixing rule for low-pressure systems. In high-pressure ternary systems VWLC-I and II give good predictions, much better, in fact, than the CEOS/A^E-NRTL mixing rule.