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.     

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.     

High-pressure phase behaviour of binary (CO2 + nicotine) and ternary (CO2 + nicotine + solanesol) mixtures

This work paper presents vapour–liquid equilibrium (VLE) data for binary (CO₂ + nicotine) and ternary (CO₂ + nicotine + solanesol) mixtures, at 313.2 K and 6, 8 and 15 MPa. The (CO₂ + nicotine) system exhibits three phases (L₁L₂V) in equilibrium at 8.37 MPa. It is estimated that this system most likely follows the type-III phase behaviour. In the ternary system, the presence of solanesol in the vapour phase was detected only at the pressure of 15 MPa. At this pressure, partition coefficients and separation factors for solanesol/nicotine were calculated for different initial nicotine/solanesol compositions and a strong influence of composition was found. The results were modelled using the Peng–Robinson equation of state (PR EOS) coupled with the Mathias–Klotz–Prausnitz (MKP) mixing rule (PR–MKP model). Good correlations of the binary data, particularly in the case of the (CO₂ + nicotine) mixture, were obtained. However, the model could not correlate the ternary data.     

Critical points of hydrocarbon mixtures with the Peng–Robinson,SAFT, and PC-SAFT equations of state

The phase behavior of fluids at high pressures can be rather complex, even for mixtures of relatively simple molecules, such as hydrocarbons. In this work, we use the Hicks and Young algorithm to calculate mixture critical points, comparing five modeling options: Peng–Robinson EOS: (1) original and (2) with parameters fitted from molar volume and vapor pressure data; (3) SAFT EOS; and PC-SAFT EOS: (4) original and (5) with refitted parameters to match pure component critical data. Calculations were carried out for binary hydrocarbon mixtures and 29 multicomponent mixtures. The SAFT EOS provided the worst representation of the systems tested and, interestingly, the conventional cubic EOS provided, in general, the best representation.     

Isothermal vapor–liquid equilibrium data for the binary mixture difluoromethane (HFC-32) + ethyl fluoride (HFC-161) over a temperature range from 253.15 K to 303.15 K

Isothermal vapor–liquid equilibrium data of difluoromethane (HFC-32) + ethyl fluoride (HFC-161) mixture in the range of temperatures from 253.15 K to 303.15 K have been measured in the wide range of compositions. The experimental method used for this work is the single-cycle type. Using Peng–Robinson (PR) equation of state, combined with the first Modified Huron-Vidal (MHV1) mixing rule and Wilson model, the vapor–liquid equilibrium data are correlated. The correlation results have a good agreement with the experiment results. The average absolute vapor composition deviation is within 0.0125, and its largest absolute deviation of the vapor composition is 0.0568; the average relative pressure deviation is within 0.76% and its largest relative pressure deviation is 2.87%. In addition, the results reveal that there is no azeotrope in the binary system, and their temperature glides are small.     

High-pressure vapor–liquid equilibria for CO2 + alkanol systems and densities of n-dodecane and n-tridecane

An apparatus based on the static-analytic method was used to measure the vapor–liquid equilibria (VLE) for CO₂ + alkanol systems. Equilibrium measurements for the CO₂ + 1-propanol system were performed from 344 to 426 K. For the case of the CO₂ + 2-propanol system, measurements were made from 334 to 443 K, and for the CO₂ + 1-butanol were obtained from 354 to 430 K. VLE data were correlated with the Peng–Robinson equation of state using the classical and the Wong–Sandler mixing rules. Moreover, compressed liquid densities for the n-dodecane and n-tridecane were obtained via a vibrating tube densitometer at temperatures from 313 to 363 K and pressures up to 25 MPa. The Starling and Han (BWRS), and The five-parameter Modified Toscani-Swarcz (MTS) equations were used to correlate them. The experimental density data were compared with those from literature, and with the calculated values obtained from available equations for these n-alkanes.     

Vapor–liquid equilibria of the carbon dioxide (CO2) + 2,2-dichloro-1,1,1-trifluoroethane (R123) system and carbon dioxide (CO2) + 1-chloro-1,2,2,2-tetrafluoroethane (R124) system

Binary vapor–liquid equilibrium data were measured for the carbon dioxide (CO₂) + 2,2-dichloro-1,1,1-trifluoroethane (R123) system and the carbon dioxide (CO₂) + 1-chloro-1,2,2,2-tetrafluoroethane (R124) system at temperature from 313.15 to 333.15 K. These experiments were carried out with a circulating-type apparatus with on-line gas chromatography. The experimental data were correlated well by Peng–Robinson equation of state using the Wong–Sandler mixing rules.     

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.     

Fluid phase equilibria in the binary system trifluoromethane + 1-phenyloctane

Vapour–liquid, liquid–liquid and liquid–liquid–vapour equilibria in the binary system consisting of trifluoromethane (refrigerant R23) and 1-phenyloctane were determined in the temperature range T = 250–400 K and at pressures up to 15 MPa. The experiments were carried using a Cailletet apparatus according to the synthetic method. The investigated system exhibits type III phase behaviour according to the classification of van Konynenburg and Scott. Modelling of the equilibrium data was done with the Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) equations of state coupled with classical van der Waals mixing rules. In order to predict the global phase behaviour of the system, one single set of binary parameters was used. The topology of the phase behaviour was correctly reproduced.     

Estimation of solubility parameter by the modified ER equation of state

The applications of the solubility parameter in chemical, petroleum and polymer engineering industries have been cleared up along the past 50 years. In this article, the Hildebrand solubility parameter of over 250 substances were calculated by the modified ER (Esmaeilzadeh–Roshanfekr) equation of state and some others (the Peng–Robinson, Soave–Redlich–Kwong, Patel–Teja and Schmidt–Wenzel) and compared with the experimental data. Once the less average errors of the mER method predictions were satisfied in subcritical and some supercritical fluids region, a correlation based on this EOS was presented in order to calculate the total HSP (Hansen solubility parameter) of various types of organic components categorized in 13 distinct groups including paraffins, olefins, aromatics, naphthenes, alcohols, aldehydes, ketones, ethers, esters, amines, carboxylic acids and two petroleum sub-fractions (resins and asphaltenes). The optimal values of the model parameters were obtained applying the DE (differential evolution) optimization method. The absolute average deviations of the proposed correlations results from the experimental ones lied between 0.09 and 6%.     

Vapor–liquid equilibrium in the n-butane + methanol system,measurement and modeling from 323.2 to 443.2 K

New experimental vapor–liquid equilibrium (VLE) data for the n-butane + methanol binary system are reported over a wide temperature range from 323.2 to 443.2 K and pressures up to 5.4 MPa. A static–analytic apparatus, taking advantage of two pneumatic capillary samplers, was used. The phase equilibrium data generated in this work are in relatively good agreement with previous data reported in the literature. Three different thermodynamic models have been used to represent the new experimental data. The first model is the cubic-based Peng–Robinson equation of state (EoS) combined with the Wong–Sandler mixing rules. The two other models are the non-cubic SAFT-VR and PC-SAFT equations of state. Temperature-dependent binary interaction parameters have been adjusted to the new data. The three models accurately represent the new experimental data, but deviations are seen to increase at low temperature. A similar evolution of the binary parameters with respect to temperature is observed for the three models. In particular a discontinuity is observed for the k_ij values at temperatures close to the critical point of butane, indicating the effects of fluctuations on the phase equilibria close to critical points.     

Vapor–liquid equilibria and phase densities at saturation of carbon dioxide + 1-butanol and carbon dioxide + 2-butanol from 313 to 363 K

Experimental vapor–liquid equilibria for the systems carbon dioxide + 1-butanol and carbon dioxide + 2-butanol were obtained from 313 to 363 K via a static-analytic set-up. A vibrating U-tube densitometer was coupled to this apparatus to perform simultaneous measurements of both saturated densities of the vapor and liquid phases. The suitability of this apparatus was checked by comparing the experimental vapor–liquid equilibrium and saturated density results with the literature data. The experimental vapor–liquid equilibrium data were correlated using the Peng–Robinson equation of state coupled to the Wong–Sandler mixing rules with good agreement; however densities using the same model were not satisfactorily represented.     

Vapor–liquid equilibrium data for the binary systems in the process of synthesizing diethyl carbonate

Vapor–liquid equilibrium data for the binary systems of carbon monoxide (CO) + diethyl carbonate (DEC) and carbon monoxide + ethyl acetate (EA) were measured at temperatures of 293.2 K, 313.2 K and 333.2 K and the elevated pressures up to 12.00 MPa. The measurements were carried out in a cylindrical autoclave with a moveable piston and an observation window. The experimental data were correlated using the Peng–Robisom (PR) equation of state (EOS) and Peng–Robinson–Stryjek–Vera (PRSV) equation of state with the two-parameter van der Waals II or Panagiotopoulos–Reid mixing rule. The interaction parameters were obtained while correlating. The comparison between calculation results and experimental data indicated that the method of PRSV equation of state with van der Waals II produced the better correlated results.     

Extension of the group-contribution lattice-fluid equation of state

This work focuses on the extension of the numbers of group parameters and application of the group-contribution lattice-fluid equation of state (GCLF EOS). The new group parameters of the GCLF EOS were evaluated by means of the volume translated Peng–Robinson equation of state (VTPR EOS) and the UNIFAC model. Values for 20 main groups and 33 subgroups are added into the current parameter matrix. The procedure used in this work can also be used to evaluate group parameters for the groups not present in the current matrix. Some examples are given to show the reliability of the new group parameters. Two new applications of the GCLF EOS are present: the effect of polymeric additive to solvents in extractive distillation and prediction of the crystallinity of polymers in the presence of gas.     

Evaluation of co-volume mixing rules for bitumen liquid density and bubble pressure estimation

The Peng–Robinson cubic equation of state (CEOS) is widely used to predict thermodynamic properties of pure fluids and mixtures. The usual implementation of this CEOS requires critical properties of each pure component and combining rules for mixtures. Determining critical properties for components of heavy asymmetric mixtures such as bitumen is a challenge due to thermolysis at elevated temperatures. Group contribution (GC) methods were applied for the determination of critical properties of molecular representations developed by Sheremata for Athabasca vacuum tower bottoms (VTB). In contrast to other GC methods evaluated, the Marrero–Gani GC method yielded estimated critical properties with realistic, non-negative values, followed more consistent trends with molar mass and yielded normal boiling points consistent with high temperature simulated distillation data. Application of classical mixing rules to a heavy asymmetric mixture such as bitumen yields saturated liquid density and bubble pressure estimates in qualitative agreement with experimental data. However the errors are too large for engineering calculations. In this work, new composite mixing rules for computing co-volumes of asymmetric mixtures are developed and evaluated. For example, composite mixing rules give improved bubble point predictions for the binary mixture ethane + n-tetratetracontane. For VTB and VTB + decane mixtures the new composite mixing rules showed encouraging results in predicting bubble point pressures and liquid phase densities.     

Phase equilibria of imidazolium ionic liquids and the refrigerant gas, 1,1,1,2-tetrafluoroethane (R-134a)

A number of applications with ionic liquids (ILs) and hydrofluorocarbon gases have recently been proposed. Detailed phase equilibria and modeling are needed for their further development. In this work, vapor–liquid equilibrium, vapor–liquid–liquid equilibrium, and mixture critical points of imidazolium ionic liquids with the hydrofluorocarbon refrigerant gas, 1,1,1,2-tetrafluoroethane (R-134a) was measured at temperatures of 25 °C, 50 °C, 75 °C and pressure up to 143 bar. The ionic liquids include 1-hexyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)amide ([HMIm][Tf₂N]), 1-hexyl-3-methyl-imidazolium hexafluorophosphate ([HMIm][PF₆]), and 1-hexyl-3-methyl-imidazolium tetrafluoroborate ([HMIm][BF₄]). The effects of the anion and cation on the solubility were investigated with the anion having greatest impact. [HMIm][Tf₂N] demonstrated the highest solubility of R-134a. The volume expansion and molar volume were also measured for the ILs and R-134a. The Peng–Robinson Equation of State with van der Waals 2-parameter mixing rule with estimated IL critical points were employed to model and correlate the experimental data. The models predict the vapor–liquid equilibrium and vapor–liquid–liquid equilibrium pressure very well. However, the mixture critical points predictions are consistently lower than experimental values.     

Thermodynamic modeling of the vapor–liquid equilibrium of the CO2/H2O mixture

In order to evaluate the feasibility of CO₂ sequestration in geological formations detailed knowledge of the mutual solubilities of the CO₂/H₂O system is required. In this work we employ three models, which all involve the well-known Peng–Robinson equation of state, to study the CO₂/H₂O phase equilibrium, with emphasis on the solubility of CO₂ in the aqueous phase and the solubility of H₂O in the CO₂-rich phase. The considered models include the Peng–Robinson equation of state coupled with the conventional van der Waals one fluid mixing rules or the universal mixing rules, and the cubic-plus-association equation of state that uses the Peng–Robinson equation of state in order to account for the usual attractive and repulsive forces and an extra association term to account for the strong hydrogen bonding interactions. The required model parameters are calibrated using experimental data up to 1500 bar for pressure, and up to 673 K for temperature. To improve the accuracy of the proposed models we consider two temperature ranges. Temperatures lower than 373 K are of interest to the geological CO₂ sequestration, while higher temperatures are of interest to fluid-inclusion studies. Good agreement is obtained between the experimental and the correlated solubilities.     

Solid–liquid equilibrium and hydrogen solubility of trans-decahydronaphthalene + naphthalene and cis-decahydronaphthalene + naphthalene for a new hydrogen storage medium in fuel cell system

Solid–liquid equilibrium was measured for benzene + cyclohexane, trans-decahydronaphthalene + naphthalene and cis-decahydronaphthalene + naphthalene under the atmospheric pressure in the temperature range from 226.69 to 353.14 K. The apparatus was specially designed in this study, and it was based on a cooling method. The phase diagram with the complete immiscible solids was observed for the three systems, and the eutectic point was found at x₂ = 0.2709 and T_eu = 232.11 K for benzene + cyclohexane, x₂ = 0.9816 and T_eu = 241.98 K for trans-decahydronaphthalene + naphthalene, and x₃ = 0.9822 and T_eu = 225.74 K for cis-decahydronaphthalene + naphthalene, respectively. Hydrogen solubility was also measured for the two pure substances, trans-decahydronaphthalene and cis-decahydronaphthalene, and the three mixtures, trans-decahydronaphthalene + cis-decahydronaphthalene, trans-decahydronaphthalene + naphthalene, and cis-decahydronaphthalene + naphthalene, in the pressure range from 1.702 to 4.473 MPa at 303.15 K. Considering the solid–liquid equilibrium data, mole ratio of trans-decahydronaphthalene:cis-decahydronaphthalene was set to 50:50, and those of trans-decahydronaphthalene + naphthalene, and cis-decahydronaphthalene + naphthalene to 85:15. The hydrogen solubility increased linearly with the pressure following the Henry's law for all systems. The experimental solubility data were correlated or predicted with the Peng–Robinson equation of state [D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59–64; R. Stryjek, J.H. Vera, Can. J. Chem. Eng. 64 (1986) 323–333].     

Vapor–liquid equilibrium measurements and modeling of the n-butane + ethanol system from 323 to 423 K

Vapor–liquid equilibrium (VLE) data are presented for the n-butane + ethanol system in the temperature range from 323 to 423 K. Measurements were performed using a “static-analytic” apparatus, equipped with two electromagnetic ROLSI™ capillary samplers, and thermally regulated via an air bath. This work presents vapor compositions which have not been explicitly measured previously. The modeling of the data was performed using two models: the Peng–Robinson equation of state with the Wong and Sandler mixing rule and NRTL excess function (PR/WS/NRTL); and the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. To assess the effect of dipole–dipole interactions present, a dipolar contribution developed by Jog and Chapman (1999) [20] was tested with the second model. Temperature dependent binary interaction parameters have been adjusted to the new data. The PR/WS/NRTL equation of state shows good correlation with the results, while the PC-SAFT is slightly less accurate.