Modification of the predictive capability of the PRSV-2 equation of state for critical volumes of binary mixtures

The predictive capability of the Peng–Robinson–Stryjek–Vera (PRSV-2) equation of state for critical properties of binary mixtures showing continuous critical lines has been investigated. The procedure adopted by Heidemann and Khalil and discussed by Abu-Eishah et al., in a previous paper, has been followed. The effect of using the pure-component parameters of the PRSV-2 equation of state (κ₁, κ₂ and κ₃), new values of κ₁, revised values of κ₁, or giving zero values for these parameters have been investigated. The effect of using zero values or optimized values for the binary interaction parameter on the PRSV-2 predictive capability of critical properties have also been investigated. The standard and the average of the absolute relative deviations in critical properties are included. The predicted critical temperature and pressure for the 20 nonpolar and 18 polar systems studied here agree well with experimental data, and are always better than those predicted by the group-contribution method. A correction has been introduced here to the critical volume predicted by PRSV-2 equation of state that makes the average deviations between the predicted and experimental values very close to or even better than those predicted by the group-contribution method.     

Peng-Robinson equation of state for vapor-liquid equilibrium calculations for carbon dioxide + hydrocarbon mixtures

Lin, H.-M., 1984. Peng-Robinson equation of state for vapor-liquid equilibrium calculations for carbon dioxide + hydrocarbon mixtures. Fluid Phase Equilibria, 16: 151–169.Binary interaction parameters δ_ij in the Peng-Robinson equation of state have been determined from vapor-liquid equilibrium data for binary mixtures of carbon dioxide with a variety of hydrocarbons. A constant value of δ_ij ? 0.125 appears to represent the experimental data well in most cases. Comments are made on the recent work of Kato, Nagahama and Hirata, who correlated δ_ij as a function of temperature for CO₂ + n-paraffin binary mixtures.     

The Effect of Functional Groups on the Phase Behavior of Carbon Dioxide Binaries and Their Role in CCS

In recent years we have focused our efforts on investigating various binary mixtures containing carbon dioxide to find the best candidate for CO₂ capture and, therefore, for applications in the field of CCS and CCUS technologies. Continuing this project, the present study investigates the phase behavior of three binary systems containing carbon dioxide and different oxygenated compounds. Two thermodynamic models are examined for their ability to predict the phase behavior of these systems. The selected models are the well-known Peng–Robinson (PR) equation of state and the General Equation of State (GEOS), which is a generalization for all cubic equations of state with two, three, and four parameters, coupled with classical van der Waals mixing rules (two-parameter conventional mixing rule, 2PCMR). The carbon dioxide + ethyl acetate, carbon dioxide + 1,4-dioxane, and carbon dioxide + 1,2-dimethoxyethane binary systems were analyzed based on GEOS and PR equation of state models. The modeling approach is entirely predictive. Previously, it was proved that this approach was successful for members of the same homologous series. Unique sets of binary interaction parameters for each equation of state, determined for the carbon dioxide + 2-butanol binary model system, based on k₁₂–l₁₂ method, were used to examine the three systems. It was shown that the models predict that CO₂ solubility in the three substances increases globally in the order 1,4-dioxane, 1,2-dimethoxyethane, and ethyl acetate. CO₂ solubility in 1,2-dimethoxyethane, 1.4-dioxane, and ethyl acetate reduces with increasing temperature for the same pressure, and increases with lowering temperature for the same pressure, indicating a physical dissolving process of CO₂ in all three substances. However, CO₂ solubility for the carbon dioxide + ether systems (1,4-dioxane, 1,2-dimethoxyethane) is better at low temperatures and pressures, and decreases with increasing pressures, leading to higher critical points for the mixtures. By contrast, the solubility of ethyl acetate in carbon dioxide is less dependent on temperatures and pressures, and the mixture has lower pressures critical points. In other words, the ethers offer better solubilization at low pressures; however, the ester has better overall miscibility in terms of lower critical pressures. Among the binary systems investigated, the 1,2-dimethoxyethane is the best solvent for CO₂ absorption.     

Modeling CO2 solubility in Aqueous Methyldiethanolamine Solutions by Perturbed Chain-SAFT Equation of State

CO₂ capture by aqueous alkanolamines treating is one of the prevalent methods to reduce carbon dioxide emissions and to help environmental problems. For realizing more the thermodynamics of the CO₂–MDEA–H₂O, the PC-SAFT equation of state was used to simulate the absorption of carbon dioxide by MDEA (methyldiethanolamine). A correlation for temperature-dependent binary interaction parameter were calculated by excess enthalpy data for aqueous MDEA at low temperatures (lower than 350 K), and then this binary interaction parameter used to predict phase equilibria of ternary aqueous mixtures of MDEA with carbon dioxide. Smith–Missen algorithm and PC-SAFT EOS have been used to determine concentration of species in chemical equilibrium and physical equilibrium, respectively. In addition, for determining parameter sets of MDEA, vapor pressure and saturated liquid density data were used and different and probable association schemes were considered in parameter estimations. Results show 4(2:2, 0:0) association scheme for MDEA and 4(2:2) association scheme for water have better agreement with binary and ternary VLE experimental data.     

Correlations for binary phase equilibria in high-pressure carbon dioxide

The high-pressure phase equilibrium in binary mixtures of carbon dioxide and various liquids such as benzene, toluene, m-xylene, chlorobenzene, 1,2-dichlorobenzene, low molecular weight alcohols, amides and a solid, hexachlorobenzene, was modeled using the Peng–Robinson equation of state with quadratic mixing rules. Though the technique of modeling is not new, the key conclusion of the study is that the two adjustable parameters, k_ij and l_ij, vary linearly with the addition of functional groups. In addition, the adjustable parameters are found to be nearly independent of temperature and the same values of k_ij and l_ij can be used for a range of temperatures for the systems considered in the present study.     

Volumetric and compressibility studies on tri-n-butyl phosphate (TBP)-phase modifier (1-octanol, 1-decanol and isodecanol) interactions from T = (298.15 to 323.15) K

Density (ρ) and speed of sound (u) of the binary mixtures of tributyl phosphate (TBP) and alcohols (1-octanol, 1-decanol and isodecanol) were measured at temperatures from T (298.15 to 323.15) K over the entire composition range and at atmosphere pressure. Using these experimentally determined quantities, the excess molar volume (V^E), deviation in isentropic compressibility (Δκ_s), internal pressure (p_i), and adjusted correlation coefficients have been calculated. The excess molar volume has been fitted to a Redlich–Kister type polynomial equation. The positive or negative deviations shown by the excess quantities and the trend shown by the adjusted correlation coefficients have been interpreted in terms of intermolecular interactions and structure of components.     

Phase equilibrium calculations for carbon dioxide + n-alkanes binary mixtures with the Wong–Sandler mixing rules

Phase equilibrium for carbon dioxide + n-alkanes (from methane to n-decane) asymmetric binary systems was calculated using Peng–Robinson Stryjek–Vera equation of state coupled with Wong–Sandler mixing rules. NRTL model was utilized for predicting the excess Helmholtz free energy. The second virial coefficient binary interaction parameter k₁₂ and NRTL model parameters τ₁₂ and τ₂₁ for carbon dioxide + n-alkanes binary systems were optimized trough minimization of two different objective functions: one based on the calculation of the distribution coefficients, and the other one based on the determination of bubble point pressures. Generalized correlations for mixing rule parameters as a function of the n-alkane acentric factor and the equilibrium temperature were obtained from optimal parameters determined by the first objective function. Obtained results using both objective functions were satisfactory, but the estimation of the parameters calculated by the second objective function provided a better accuracy in vapor–liquid equilibrium prediction.     

Modelling of phase equilibria for associating mixtures using an equation of state

In the present work, the group contribution with association equation of state (GCA-EoS) is extended to represent phase equilibria in mixtures containing acids, esters, and ketones, with water, alcohols, and any number of inert components. Association effects are represented by a group-contribution approach. Self- and cross-association between the associating groups present in these mixtures are considered. The GCA-EoS model is compared to the group-contribution method MHV2, which does not take into account explicitly association effects. The results obtained with the GCA-EoS model are, in general, more accurate when compared to the ones achieved by the MHV2 equation with less number of parameters. Model predictions are presented for binary self- and cross-associating mixtures.     

Application of GC-PPC-SAFT EoS to amine mixtures with a predictive approach

The GC-PPC-SAFT equation of state (EoS) is a combination of a group contribution method [S. Tamouza et al., Fluid Phase Equilib. 222-223 (2004) 67-76; S. Tamouza et al., Fluid Phase Equilib. 228-229 (2005) 409-419] and the PC-SAFT EoS [J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 40 (2001) 1244-1260] which was adapted to the polar molecules [D. Nguyen-Huynh et al., Fluid Phase Equilib. 264 (2008) 62-75]. It is here applied to the vapour pressure and liquid molar volume of primary, secondary and tertiary amines and their mixtures with n-alkanes, primary and secondary alcohols, using previously published group parameters. The mixing enthalpy is also evaluated for the binary systems. Binary interaction parameters k_ij are computed using a group-contribution pseudo-ionization energy, as proposed by Nguyen-Huynh [D. Nguyen-Huynh et al., Ind. Eng. Chem. Res. 47 (2008) 8847-8858]. A unique corrective parameter for the cross-association energy between amines and alcohols is used.The agreement with experimental data in correlation and prediction were found rather encouraging. The mean absolute average deviation (AAD) on bubble pressure is about 3.5% for pure amines. The mean AAD on the vapour-liquid equilibria (VLE) are respectively 2.2% and 5.5% for the amine mixtures with n-alkanes and alcohols. The AADs on saturated liquid volume are about 0.7% for the pure compounds and 0.9% for the mixtures. Prediction results are qualitatively and quantitatively accurate and they are comparable to those obtained with GC-PPC-SAFT on previously investigated systems.     

Ternary excess molar enthalpies for the mixtures of methanol and ethanol with tetrahydropyran or 1,4-dioxane at 298.15 K

Ternary excess molar enthalpies, H_m^E, at 298.15 K and atmospheric pressure measured by using a flow microcalorimeter are reported for the (methanol+ethanol+tetrahydropyran) and (methanol+ethanol+1,4-dioxane) mixtures. The pseudobinary excess molar enthalpies for all the systems are found to be positive over the entire range of compositions. The experimental results are correlated with a polynomial equation to estimate the coefficients and standard errors. The results have been compared with those calculated from a UNIQUAC associated solution model in terms of the self-association of alcohols as well as solvation between unlike alcohols and alcohols with tetrahydropyran or 1,4-dioxane. The association constants, solvation constants and optimally fitted binary parameters obtained solely from the pertinent binary correlation predict the ternary excess molar enthalpies with an excellent accuracy.     

Binary and ternary solubilities of disperse dyes and their blend in supercritical carbon dioxide

Binary and ternary solubilities of C.I. Disperse Blue 134 (1,4-bis(isopropylamino)anthraquinone) C.I. Disperse Yellow 16 (3-methyl-1-phenyl-5-pyrazolone) and their dye mixture in supercritical carbon dioxide (SC-CO₂) were measured by a flow-type apparatus. The solubility measurements were carried out at the pressure ranges from 10.0 to 25.0 MPa for the binary systems at the temperatures from 323.15 to 383.15 K and for the ternary system at 383.15 K. An empirical equation was used to correlate the experimental binary solubilities of the dyes in terms of the density of carbon dioxide. To represent accurately the binary solubility of the dyes in terms of temperature and pressure, we used a modified Peng–Robinson–Stryjek–Vera equation of state (PRSV EOS). The ternary solubilities of the dye blend could be predicted successfully from binary parameters with the modified PRSV EOS.     

Vapor–liquid equilibrium data for the carbon dioxide (CO2) + difluoromethane (R32) system at temperatures from 283.12 to 343.25 K and pressures up to 7.46 MPa

Isothermal vapor–liquid equilibrium (VLE) data have been measured for the binary system carbon dioxide (CO₂)+difluoromethane(R32) at eight temperatures between 283.12 and 343.25 K, and at pressures in the range 1.11–7.46 MPa. The experimental method used in this work is of the static-analytic type, taking advantage of two pneumatic capillary samplers (Rolsi™, Armines’ Patent) developed in the Cenerg/TEP laboratory. The data were obtained with uncertainties within ±0.02 K, ±0.002 MPa, and ±1% for molar compositions. The isothermal P, x, and y data are well represented with the Peng–Robinson equation of state (PR EoS) using the Mathias Copeman alpha function and the Wong–Sandler mixing rules involving the NRTL model.     

Sorption and selective properties of binary liquid-crystalline sorbent based on 4-Methoxy-4′-ethoxyazoxybenzene and a cetylated β-Cyclodextrin

The mesomorphous, sorption, and selective properties of a binary sorbent based on achiral liquid crystal 4-methoxy-4′-ethoxyazoxybenzene and macrocyclic heptakis(2,3,6-tri-O-acetyl)-β-cyclodextrin (10.25 wt %) are investigated. Macrocyclic additive was found to induce the formation of a helically twisted nematic phase (N*). The standard and excess thermodynamic functions of sorption by binary sorbent from gaseous phase are determined for 29 organic compounds (n-alkanes, cycloalkanes, arenes, monoatomic alcohols, heterocycles, optical isomers of camphene, limonene, and butanediol-2,3). The investigated sorbent is found to have high structural selectivity over the wide temperature range of the N* mesophase (α _p/m = 1.11–1.06, 95–120°C) and moderately expressed enantioselectivity within the narrow region of transition from the solid crystalline state to the N* mesophase (α_+/? = 1.024–1.088, 91–100°C).     

Modeling of Liquid-Vapor Equilibrium in Systems Including a Light Oil-Gas Component and Aromatic and Polyaromatic Hydrocarbons

The Victorov-Smirnova's hole lattice quasichemical group-contribution model (HM) is used to simulate the vapor-liquid equilibrium in binary and ternary mixtures systems composed by aromatic (benzene, toluene) and polyaromatic (naphthalene, phenanthrene) hydrocarbons and light oil-gas components (carbon dioxide, hydrogen sulfide, nitrogen, methane, ethane, propane). Eighteen binary and two ternary systems are examined. New group parameters for these systems are estimated. The results of modeling are compared with the experimental data and those predicted by the Peng-Robinson equation of state.     

Phase equilibria in systems containing o-cresol,p-cresol,carbon dioxide,and ethanol at 323.15–473.15 K and 10–35 MPa

Phase equilibria in binary and ternary systems containing o-cresol, p-cresol, carbon dioxide, and ethanol have been investigated experimentally at temperatures between 323.15 K and 473.15 K and pressures ranging from 10 MPa to 35 MPa. The experimental results provide a systematic basis of phase equilibrium data, yielding the effect of temperature on the influence of the position of the methyl groups of cresols that are in phase equilibria with carbon dioxide. Based on the different solubilities of the cresol isomers in carbon dioxide, the separation of o-cresol and p-cresol was investigated. The dependence of the separation factor between both cresol isomers on concentration, temperature, and pressure is obtained from experiments in the ternary system, o-cresol+p-cresol+carbon dioxide. The influence of ethanol added to each of the binary systems, cresol isomer+carbon dioxide, in order to enhance the solubility of the cresols in the carbon dioxide-rich phase is also shown. The experimental data have been correlated using seven different equations of state, whereof four explicitly account for intermolecular association: Statistical Association Fluid Theory (SAFT) by Chapman, Gubbins, Huang and Radosz, the SAFT modification by Pfohl and Brunner for near-critical fluids, a modified cubic-plus-association equation of state (CPA EOS) according to the ideas by Tassios et al., and one of the EOS by Anderko. The mixing rule proposed by Mathias, Klotz, and Prausnitz, with two binary interaction parameters per binary system influencing intermolecular attractive forces, is used for all EOS as a basis for an objective comparison of the EOS.     

High-pressure densities and P–T–x–y diagrams for carbon dioxide+linalool and carbon dioxide+limonene

Liquid and vapor densities for carbon dioxide+linalool, and carbon dioxide+limonene were measured by using a system consisting of two vibrating tube densimeters. The P–T–x–y diagrams and saturated liquid and vapor densities for these two binary mixtures were determined at 313, 323 and 333 K, respectively, as well as at pressures up to 11 MPa. The density of the saturated CO₂ phase increased with increasing pressure. At higher pressure, the density of the liquid phase decreased with increasing pressure, corresponding to an increasing amount of carbon dioxide.     

High-pressure phase behaviour measurement of (CO2 + ethylene glycol dimethacrylate) and (CO2 + di-ethylene glycol dimethacrylate) binary mixture systems

Ethylene glycol dimethacrylate (EGDMA) and di-ethylene glycol dimethacrylate (DEGDMA) are two of the most wildly used di-functional monomers in the polymer industry. The EGDMA and DEGDMA are applied to cross-linking polymerisation for improving the physical and chemical properties of synthesized polymers. However, residual and unreacted EGDMA and DEGDMA applied to the synthesis of dental composite and super-absorption polymer poses a health threat. This problem can be solved by using supercritical CO₂, which has high diffusivity and causes polymer swelling. To design and operate the supercritical fluid extraction process using scCO₂, high pressure phase behaviour data are required. The pressure–composition (P–x) isotherms for the (CO₂ + EGDMA) and (CO₂ + DEGDMA) binary mixture systems were measured using the static method with a variable-volume view cell at temperatures ranging from (313.2 to 363.2) K. The experimental data correlation was performed using the Peng–Robinson equation of state (PR-EOS) and the Van der Waals one fluid mixing rule. The critical constants for the PR-EOS were estimated by the Joback method and the Marrero–Gani method. The acentric factor was estimated by the Lee–Kesler method. The Marrero–Gani method showed better correlation results than the Joback method and the EGDMA is more soluble in the supercritical carbon dioxide than the DEGDMA.     

Dew points of binary carbon dioxide + water and ternary carbon dioxide + water + methanol mixtures: Measurement and modelling

Dew points for four carbon dioxide + water mixtures between 1.2×10⁵ and 41.1×10⁵ Pa in the temperature range from 251.9 to 288.2 K, and eight carbon dioxide + water + methanol mixtures between 1.2×10⁵ and 43.5×10⁵ Pa and temperatures from 246.0 to 289.0 K were experimentally determined. The experimental results obtained on the binary and ternary systems were analysed in terms of a predictive excess function–equation of state (EF–EOS) method, which reproduced the experimental dew point temperature data with absolute average deviation (AAD) between 0.8 and 1.8 K for the systems with water, and from 0.0 to 2.7 K for the systems with water and methanol. The experimental results obtained for carbon dioxide + water mixtures, with molar fraction of water lower than 0.00174, at pressure values higher than 5×10⁵ Pa were also compared to a predictive equation of state model. It reproduced experimental dew point temperature data with AAD between 0.2 and 0.6 K.     

Application of the perturbed chain SAFT equation of state to complex polymer systems using simplified mixing rules

A simplified perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state is applied to polymer systems that include a variety of non-associating (esters, cyclic hydrocarbons), polar (ketones) as well as associating (amines, alcohols) solvents. The solvent pure-component parameters that are not available in the literature are estimated by correlating vapor-pressure and liquid-density data. The performance of the simplified PC-SAFT is compared to the original PC-SAFT equation of state for polymer systems of varying complexity. It is shown that the applied simplification is not at the expense of the accuracy of equation of state, while the computational time and complexity are significantly reduced, especially for associating systems. With no binary interaction parameter, simplified PC-SAFT is successfully able to predict vapor–liquid equilibria of polymers with non-associating solvents. In the case of associating solvents, a small binary interaction parameter k_ij is usually needed for the satisfactory correlation of the experimental data.     

High-pressure phase equilibrium for the binary systems of {carbon dioxide (1) + dimethyl carbonate (2)} and {carbon dioxide (1) + diethyl carbonate (2)} at temperatures of 273 K, 283 K,and 293 K

Phase equilibrium data for the binary systems {carbon dioxide (CO₂) + dimethyl carbonate (DMC)} and {carbon dioxide (CO₂) + diethyl carbonate (DEC)} were measured at temperatures of 273 K, 283 K and 293 K in the pressure range of 0.5 MPa to 4.0 MPa. The measurements were carried out in a cylindrical autoclave with a moveable piston and an observation window. The experimental data were correlated with the Peng–Robison (PR) equation of state (EOS) and the Peng–Robinson–Stryjek–Vera (PRSV) equation of state with van der Waals-1 or Panagiotopoulos–Reid mixing rules. The correlations produced reasonable values for the interaction parameters. The comparisons between calculation results and experimental data indicate that the PRSV equation of state coupled with the Panagiotopoulos–Reid mixing rule produced the better correlated results.