Van Der Waals One-fluid Mixing Research Articles

Experimental validation on the phase separation for the 2-(Diisopropylamino)ethyl methacrylate and Poly[2-(diisopropylamino)ethyl methacrylate] in supercritical CO2

Using an intense pressure flexible volume apparatus, the phase transition equilibrium of the two-component mixture consisting of 2-(diisopropylamino)ethyl methacrylate (2DIPAEMA) + supercritical carbon dioxide (Sc CO2), as well as poly(2-(diisopropylamino)ethyl methacrylate) [P(2DIPAEMA)] with various co-solvents (propylene, propane, 1-butene, butane, and dimethyl ether), was investigated. Additionally, the three-component system P(2DIPAEMA) + 2DIPAEMA (0.0, 0.0245, 0.0523, 0.1036 mol fraction) + Sc CO2 was studied at a specific temperature range of 313.2 K to 454.5 K and an upper-pressure limit of 171.03 MPa. The dew-point, critical-point, and bubble-point equilibria data for the 2DIPAEMA + Sc CO2 binary system at a temperature interval of 313.2–393.2 K and a pressure limit of 21.61 MPa were measured. At low co-solvent concentrations, the solubility transition curve in the three-component P(2DIPAEMA) + Sc CO2 + co-solvent system (comprising propylene, propane, 1-butene, butane, and dimethyl ether) shows a cloud pressure curve that increases as temperature decreases. However, at higher concentrations, cloud pressure decreased rapidly, but a minor change in cloud pressure with temperature was recorded, indicating a homogeneous single-phase behavior resembling a type-I phase diagram. The van der Waals one-fluid mixing rule was employed to compare the experimentally calculated data with the computed and modelled data of the Peng–Robinson mathematical equation. It was discovered that the computed values were consistent with the experimental values. The RMSD for the (Sc CO2 + 2DIPAEMA) system was 4.37 % at five different temperatures. The critical parameter of the pure component, 2DIPAEMA, was estimated using the Joback-Lyderson approach.

Excess molar enthalpies in the binary system of carbon dioxide + ethyl lactate at 298.15 and 303.15 K and 5.0–7.0 MPa

This paper presents an experimental determination of the excess molar enthalpies (HE) for the binary system of carbon dioxide (CO2) + ethyl lactate at temperatures of 298.15 and 303.15 K and pressures in the range of 5.0–7.0 MPa. A maximum exothermic value of approximately 7.4 kJ mol−1 was found, similar to the exotherms observed in our previous work for other binary systems such as CO2 + ester or ether. We discussed this exothermic behavior based on the change-of-state contribution, strong CO2-ester interactions, and unusual intra- and intermolecular hydrogen bonding of ethyl lactate. The experimental HE data correlated well with a composition-dependent equation and the Peng–Robinson equation of state with the van der Waals one-fluid mixing rule.

Vapor Equilibrium Data for the Binary Mixtures of Dimethyl Carbonate and Ethyl Methyl Carbonate in Compressed Carbon Dioxide

Phase equilibrium data (p, T, y) for the binary systems of carbon dioxide + dimethyl carbonate and carbon dioxide + ethyl methyl carbonate were obtained. All systems were measured for isotherms ranging from 298.2 K to 328.2 K with pressure ranging between 0.13 MPa and 10.6 MPa. A static equilibrium technique was established with samples quantified using an offline method. The results were modeled using the Peng–Robinson equation of state with van der Waals one-fluid mixing rules.Graphical

CO2 Solubility in 1,1,2,2-Tetrafluoroethanesulfonate Anion-Based Ionic Liquids: [EMIM][TFES], [BMIM][TFES], and [BNMIM][TFES

The solubility of carbon dioxide (CO2) in three different ionic liquids (ILs): 1-ethyl-3-methylimidazolium 1,1,2,2-tetrafluoroethanesulfonate ([EMIM][TFES]), 1-butyl-3-methylimidazolium 1,1,2,2-tetrafluoroethanesulfonate ([BMIM][TFES]), and 1-benzyl-3-methylimidazolium 1,1,2,2-tetrafluoroethanesulfonate ([BNMIM][TFES]) were measured. Measurements were done at temperatures ranging from 303.2 to 373.2 K (323.2 to 373.2 K for [BNMIM][TFES]) at pressures from 0.80 to 36.80 MPa. Measured data show that pressure, temperature, and characteristics of cation of ILs ([EMIM], [BMIM], and [BNMIM]) affect its CO2 solubility. We determined the CO2 solubility of fixed CO2 mole fractions for three ionic liquids. Among the three ILs, CO2 solubility intensity was ranked [BMIM][TFES] > [EMIM][TFES] ≈ [BNMIM][TFES]. The Peng–Robinson equation of state, the conventional van der Waals one-fluid mixing rule, and the modified Lydersen–Joback–Reid method were used to correlate the experimental data. The average absolute deviations of pressure were 0.0164 for CO2 + [EMIM][TFES], 0.0361 for CO2 + [BMIM][TFES], and 0.0251 for CO2 + [BNMIM][TFES] systems.

Mercury solubility measurements in natural gas components at high pressure

Saturated vapor pressure of elemental mercury (Hg) and Hg solubility in compressed gaseous methane, ethane, and carbon dioxide were investigated. The apparatus designed for this study was based on a flow method and equipped with a cold vapor atomic absorption survey meter to measure Hg concentration in gas phase. The saturated Hg vapor pressure ranged from 4.579 × 10−2 to 2.757 × 10−1 Pa at 278–298 K. The Hg solubility was measured up to 6.042 MPa for methane, 3.533 MPa for ethane, and 2.070 MPa for carbon dioxide at 268–303 K. The Hg mole fraction ranged from 4.842 × 10−9 to 8.683 × 10−7 in the vapor phase. The Hg solubility decreases with increasing pressure, and the pressure dependencies are similar in the three gases. The activation energy of Hg solubility was determined from the Arrhenius plot at the 1.55 and 3.55 MPa isobars. The activation energy at 1.55 MPa is about 60 kJ/mol·K for the three gases, similar to that at the saturated Hg vapor pressure. At 3.55 MPa the activation energy has the same value for methane but decreases to around 60 kJ/mol·K for ethane. The Peng–Robinson equation of state (PR-EOS) was used to correlate the saturated Hg vapor pressure and the Hg solubility in the vapor phase. The attractive parameter in the PR-EOS was fitted with the saturated Hg vapor pressure, and its temperature dependence was investigated using the van der Waals one-fluid mixing rule. The average absolute deviations were 0.322, 0.265 and 0.197 % for Hg solubility in gaseous methane, ethane and carbon dioxide, respectively. This investigation contributes to predicting mercury partitioning in natural gas processing facilities.

Measurement and modelling of isothermal solubility of methane in methanol from 213.15 K to 273.15 K

The isothermal solubility of methane in methanol was measured at temperatures from 213.15 K to 273.15 K and pressures from 1.0580 MPa to 6.9947 MPa. The static analytical method was used in the experiment, which was carried out by sampling from an equilibrium cell using a heated sample cylinder connected to a gas chromatograph and loading the sample into the chromatograph. The Soave–Redlich–Kwong equation of state with the van der Waals one-fluid mixing rule applying the Wilson activity coefficient model with Henry’s constant was used to describe the equilibrium behaviour of vapour and liquid phase in the system for (methane + methanol) binary mixture. The measurements were correlated with the SRK-vdW-Wilson-Henry model. The calculated results indicate that the model not only matches well with the measurements but also predicts optimally VLE data of the system from 213.15 K to 273.15 K below 7.0000 MPa.

Peng-Robinson-based association equation of state for mixtures of hydrofluorocarbon refrigerants

The objective of this work was to extend to mixtures of hydrofluorocarbon refrigerants a recently developed Peng-Robinson plus association equation of state for those compounds. In that equation of state, two terms constituted the residual dimensionless Helmholtz energy: the first was a substance-specific dimensionless form of the conventional Peng-Robinson equation while the second was the association term from the Statistical Associating Fluid Theory. The extension to mixtures consisted of the conventional Peng-Robinson equation to mixtures, i.e. the expressing the mixture attractive parameter as a van der Waals one-fluid mixing rule with a binary interaction parameter at the unlike-interaction term. The systems of interest were the mixtures systems (HFC-32 + HFC-125), (HFC-32 + HFC-134a), (HFC-125 + HFC-134a), (HFC-125 + HFC-143a), (HFC-134a + HFC-143a), and (HFC-134a + HFC-152a); and the ternary systems (HFC-32 + HFC-125 + HFC-134a) and (HFC-125 + HFC-134a + HFC-143a). For the important number of 98000 data, the percentage overall average absolute deviations obtained were 1.44 in pρT; 53.9 in isochoric heat capacities, 34.8 in isobaric heat capacities, 0.183 in speeds of sound, and 1.27 in bubble-point vapour pressures; and an overall average absolute difference in second virial coefficients of 41.4 cm3.mol−1. Those results compared favourably with those obtained with the standard Pang-Robinson equation, with a substance-specific version of the Pang-Robinson equation, and with a cubic plus association equation.

A four parameter cubic equation of state with temperature dependent covolume parameter

Abstract A four-parameter, Ghoderao–Dalvi–Narayan 2 cubic equation of state (GDN2 CEOS), is presented which incorporates the following: 1. The experimental value of the critical compressibility factor has been used as a fixed input parameter for calculations; 2. All the parameters (a, b, c, d) of CEOS are temperature dependent functions in the subcritical region and are temperature independent functions in the supercritical region and; 3. A new α function is introduced with two compound specific parameters which are estimated by matching saturated vapor pressure at two fixed temperature points Tr = 0.5, 0.7. Our formalism enables us to cast three of the four parameters of the CEOS as a function of the remaining parameter. The proposed CEOS is used to predict properties of 334 pure compounds, including saturated vapor pressure and liquid density, compressed liquid density, heat capacities at the constant pressure and volume, enthalpy of vaporization, sound velocity. To calculate thermodynamic properties of a pure compound, the present CEOS require the critical temperature, the critical pressure, the Pitzer's acentric factor, the critical compressibility factor, and two parameters of the alpha function. The saturated liquid density predictions for pure fluids are very accurate when compared with GDN1 (Ghoderao–Dalvi–Narayan 1), MPR (Modified Peng–Robinson), and PT (Patel–Teja) equations of state. Unlike MPR EOS, the proposed temperature dependent covolume parameter b in the present work satisfies all the constraints mentioned in the literature to avoid thermodynamic inconsistencies at the extreme temperature and pressure. Using van der Waals one-fluid mixing rule, the present CEOS is further used to predict bubble pressure and the vapor mole fraction of binary mixtures.

Solubility Measurement and Correlation of Carbon Monoxide (CO) in Butyraldehydes: n-Butyraldehyde and iso-Butyraldehyde

The solubility of carbon monoxide (CO) in two isomeric butyraldehydes, n-butyraldehyde and iso-butyraldehyde, which are the products of a hydroformylation reaction in which CO is used as a reactant, was measured by using a variable-volume view cell equilibrium apparatus. The CO solubility was determined by measuring the bubble or cloud point pressures of various CO mole fractions at 10 K intervals from 303.15 to 373.15 K. We found that the solubilities of CO increased with increasing pressures and temperatures and that CO was more soluble in the iso-form (iso-butyraldehyde) than in the n-form (n-butyraldehyde). The measured data was calculated with the PR-EoS incorporated with the conventional van der Waals one-fluid mixing rule. Our measured data showed relatively good agreement with the calculated results with an AAD-p (%) of 2.38% for CO + n-butyraldehyde and 1.57% for the CO + iso-butyraldehyde system.

Vapor Phase PvTx Measurements of Binary Blends of 2,3,3,3-Tetrafluoroprop-1-ene + Propane and cis-1,2,3,3,3-Pentafluoroprop-1-ene + Propane

The paper presents 86 PvTx measurements in the vapor phase for blends of 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and propane and 62 PvTx measurements in the vapor phase for blends of cis-1,2,3,3,3-pentafluoroprop-1-ene (R1225ye(Z)) and propane. The R1234yf and propane blends were measured along four isochores (0.047, 0.048, 0.072, 0.095) m3·kg–1 for (268 < T < 363) K for four propane mole fractions (0.230, 0.505, 0.611, 0.709) mol·mol–1. The R1225ye(Z) and propane blends were measured along five isochores (0.032, 0.038, 0.042, 0.067, 0.090) m3·kg–1 for (303 < T < 363) K for five propane mole fractions (0.225, 0.516, 0.593, 0.690, 0.855) mol·mol–1. The data are well-predicted when fitted (1) with Fundamental Helmoltz Equations of State (EoS), Peng–Robinson EoS, and Extended Corresponding States EoS when each are coupled with a modified van der Waals one-fluid linear mixing model, and (2) with a truncated Virial EoS.

Phase Behavior for the CO2 + Methyl Methoxyacetate and CO2 + Methyl trans-3-Methoxyacrylate Systems at Pressures from (5 to 20) MPa and Various Temperatures

Acetate and acrylate are compounds with weak polarity which show a nonideal behavior. Phase equilibria of these systems play a significant role as organic solvents in industrial processes. In this work, the solubility behavior for the (CO2 + methyl methoxyacetate) and (CO2 + methyl trans-3-methoxyacrylate) mixtures at pressures from (5 to 20) MPa and various temperatures (313.2, 333.2, 353.2, 373.2, and 393.2 K) are measured in the static method with a variable-volume high pressure view cell. The experimental results obtained in this research are correlated with Peng–Robinson equation of state and van der Waals one-fluid mixing rule containing two adjustable interaction parameters. The critical constants for the Peng–Robinson equation of state were estimated using the group contributions method. The Lee–Kesler method was used to predict the acentric factor.

Bubble-point measurement for the binary mixture of propargyl acrylate and propargyl methacrylate in supercritical carbon dioxide

Acrylate and methacrylate (acrylic acid type) are compounds with weak polarity which show a non-ideal behaviour. Phase behaviour of these systems play a significant role as organic solvents in industrial processes. High pressure phase behaviour data were reported for binary mixture of propargyl acrylate and propargyl methacrylate in supercritical carbon dioxide. The bubble-point curves for the (carbon dioxide+propargyl acrylate) and (carbon dioxide+propargyl methacrylate) mixtures were measured by static view cell apparatus at temperature range from 313.2K to 393.2K and at pressures below 19.14MPa. The (carbon dioxide+propargyl acrylate) and (carbon dioxide+propargyl methacrylate) systems exhibit type-I phase behaviour. The (carbon dioxide+(meth)acrylate) systems had continuous critical mixture curves with maximums in pressure located between the critical temperatures of carbon dioxide and propargyl acrylate or carbon dioxide and propargyl methacrylate. The solubility behaviour of propargyl (meth)acrylate in the (carbon dioxide+propargyl acrylate) and (carbon dioxide+propargyl acrylate) systems increases as the temperature increases at a fixed pressure. The experimental results for the (carbon dioxide+propargyl acrylate) and (carbon dioxide+propargyl methacrylate) systems correlate with the Peng–Robinson equation of state using a van der Waals one-fluid mixing rule. The critical properties of propargyl acrylate and propargyl methacrylate were predicted with the Joback–Lyderson group contribution and Lee–Kesler method.

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.

High-Pressure Phase Behavior of Poly(l-lactic acid), Trichloromethane, and Carbon Dioxide Ternary Mixture Systems

In this study, the phase behavior of a poly(l-lactic acid) (M = 312 000, polydispersity 2.189)–trichloromethane–carbon dioxide ternary system was measured using a variable volume view cell at pressures up to 34.0 MPa and temperatures between (313.15 K and 363.15) K at an interval of 10 K. Bubble and cloud point pressures were determined as functions of the trichlomethane-to-carbon dioxide ratio, concentration of poly(l-lactic acid) (1.0, 2.0, and 3.0 wt %), and temperature. The hybrid equation of state for the supercritical CO2-polymer system combined with the van der Waals one-fluid mixing rule was used for correlation of the experimental results. The three binary parameters of this system were optimized by the simplex method algorithm.

High-Pressure Phase Behavior of Poly(lactic-co-glycolic acid), Dichloromethane, and Carbon Dioxide Ternary Mixture Systems

Phase behavior measurements of the (poly(lactic-co-glycolic acid) + dichloromethane + carbon dioxide) ternary system were taken using a variable-volume view cell at temperatures between 313.15 K and 363.15 K and at pressures up to 340 bar in poly(lactic-co-glycolic acid) weight fraction = 1.0 %, 2.0 %, and 3.0 %, respectively. To explain these systems, the hybrid equation of state (Peng–Robinson equation of state + SAFT equation of state) was applied with the van der Waals one-fluid mixing rule. The binary interaction parameters were obtained from the simplex method.

Isothermal (vapor + liquid) equilibria for the binary mixtures of (propylene oxide + ethanol) and (propylene oxide + 1-propanol) at several temperatures

Isothermal (vapor+liquid) equilibrium data for the binary mixtures of (propylene oxide+ethanol) and (propylene oxide+1-propanol) were measured using a static apparatus at three different temperatures ranging from (303.15 to 333.15)K at an interval of 15K. The measured data were correlated using Peng–Robinson–Stryjek–Vera equation of state (PRSV EOS) combined with van der Waals one-fluid mixing rule for the vapor phase and with Wong-Sandler mixing rule involving a non-random two liquid (NRTL) model, universal quasi-chemical (UNIQUAC) model and Wilson model for the liquid phase. The experimental data are in good agreement with the correlation results.

Vapor–liquid equilibrium measurements of the binary mixtures CO2 + acetone and CO2 + pentanones

Vapor–liquid equilibrium (VLE) data of the binary mixtures carbon dioxide (CO2)+acetone and CO2+pentanones (i.e. all C5-ketones, which are 3-methyl-2-butanone, 2-pentanone, and 3-pentanone) are measured at 313.15K, 333.15K, and 353.15K up to a pressure of 11.8MPa using a high pressure view cell technique based on the synthetic method. The VLE measurement results of CO2+acetone are compared to the available experimental data from the literature in order to validate the employed experimental apparatus. In case of binary CO2+pentanone mixtures, only for CO2+3-methyl-2-butanone and CO2+2-pentanone at 313.15K experimental data are available in the literature. The present measurements thus complete the literature database for binary VLE of CO2+pentanones. All present data are compared to the results from the Peng–Robinson equation of state (PR EOS) with the van der Waals one-fluid mixing rule and from the combination of the PR EOS with the UNIQUAC model through the Huron–Vidal mixing rule.

Calculations of vapor–liquid equilibria of the H2O-N2 and H2O-H2 systems with improved SAFT-LJ EOS

The SAFT-LJ equation of state (EOS) improved by our previous study, which introduces a multi-polar term to explicitly account for the contribution of multi-polar interactions (including the dipole–dipole, dipole–quadrupole and quadrupole–quadrupole interactions), is applied to the H2O-N2 and H2O-H2 systems. N2 and H2 are modeled as chain molecules with evenly distributing quadrupole moments. The van der Waals one-fluid mixing rule was used to calculate parameters for mixtures and two binary parameters for the interactions of H2O-N2 and H2O-H2 pairs were evaluated from mutual solubility data of binary water–gas systems. Comparison with the experimental data shows that this molecular-based EOS can well represent vapor–liquid equilibria of H2O-N2 and H2O-H2 systems over a wide P–T range (273–623K and 0–1000bar). In addition, the effect of the dipole moment of H2O and quadrupole moments of N2, H2 and CO2 on VLE of the CO2-N2, H2O-N2 and H2O-H2 systems was checked. It was found that the SAFT-LJ model without any polar term gives good prediction (without any binary parameters) for vapor compositions of the CO2-N2, H2O-N2 and H2O-H2 systems except in the critical region and taking account of the contribution of multi-polar interactions does not improve the prediction of this EOS any more. However, taking account of multi-polar interactions indeed significantly improves the prediction of this EOS for compositions of liquid phase. We argue that it is the reason why this EOS can quantitatively represent VLE of highly non-ideal water–gas systems. Comparison of calculations of this EOS with experimental VLE data of the ternary CO2-N2-H2O system confirms the prediction capability of this EOS for thermodynamic properties of multi-component systems.

Solubility of anthraquinone derivatives in supercritical carbon dioxide

Abstract Solubility data of 1-amino-4-hydroxyanthraquinone and 1-hydroxy-4-nitroanthraquinone in supercritical carbon dioxide have been measured at the temperature of 323.15, 353.15 and 383.15 K and over pressure ranges 12.5–25.0 MPa by a flow – type apparatus. The solubility of 1-amino-4-hydroxyanthraquinone was significantly higher than that of 1-hydroxy-4-nitroanthraquinone. It was found that amino group in 1-amino-4-hydroxyanthraquinone can enhance the solubility of anthraquinone derivatives in supercritical carbon dioxide compared with nitro group in 1-hydroxy-4-nitroanthraquinone. The experimental results were correlated satisfactorily by four types of the density-based models, namely, Mendez-Santiago–Teja, Kumar–Johnston, Chrastil, and Sung–Shim. Moreover accurate representation of the solubility of anthraquinone dyestuffs was obtained by the regular solution model with the Flory–Huggins theory as well as the Peng–Robinson equation of state modified by Stryjek and Vera with the van der Waals one-fluid mixing rule.

Effect of cosolvent on the phase behavior of binary and ternary mixture for the poly(2-dimethylaminoethyl methacrylate) in supercritical solvents

Cloud-point behaviors at pressure up to 230MPa and temperatures up to 463K were measured for poly(2-dimethylaminoethyl methacrylate) [P(2-DMAEMA)] in CO2 (carbon dioxide), C3H8 (propane), C3H6 (propylene), C4H10 (butane), C4H8 (1-butene), and CH3OCH3 [dimethyl ether (DME)], as well as for the P(2-DMAEMA)+2-dimethylaminiethyl methacrylate (2-DMAEMA) (or DME) in supercritical CO2. The phase behavior for the P(2-DMAEMA)+CO2+2-DMAEMA mixture was measured in changes of the pressure–temperature (p, T) slope and with 2-DMAEMA mass fraction of 0.0 wt%, 5.5 wt%, 11.6 wt%, 21.2 wt% and 48.1 wt%. With 51.4 wt% and 60.4 wt% 2-DMAEMA to the P(2-DMAEMA)+CO2 solution, the cloud point curves take on the appearance of a typical lower critical solution temperature (LCST) boundary, liquid+liquid transition and liquid+vapor transition. The cloud point curves for the P(2-DMAEMA)+CO2+(0.0–95.0) wt% DME systems change the (p, T) curve from upper critical solution temperature region to lower critical solution temperature region as the DME mass fraction increases. The phase behavior curves for P(2-DMAEMA) in alkane hydrocarbons were about 50–60K higher than P(2-DMAEMA)+alkene hydrocarbons curves, at a fixed pressure of about 70.0MPa. Also, the impact by 2-DMAEMA and DME mass fraction for the P(2-DMAEMA)+propane+2-DMAEMA+DME system was measured at temperatures to about 453K and a pressure range of 4.3–192.9MPa.The experimental data was presented for the CO2+2-DMAEMA system at temperatures ranging from 313.2 to 393.2K and pressures up to 19.07MPa. The CO2+2-DMAEMA system exhibits type-I phase behavior with a continuous critical mixture curve and was correlated with Peng–Robinson equation of state using a van der Waals one-fluid mixing rule including two adjustable parameters. The property of 2-DMAEMA was obtained by Constantinou-Gani group contribution method.