Adjustable Binary Interaction Parameters Research Articles

Prediction of vapor–liquid equilibrium in water–alcohol–hydrocarbon systems with the dipolar perturbed-chain SAFT equation of state

It is well known that water–alcohol–hydrocarbon systems are very difficult to model due to the existence of hydrogen bonding interactions, permanent dipole–dipole interactions and induced dipole–permanent dipole interactions. Although the statistical association fluid theory (SAFT) which is a successful model to describe hydrogen bonding interactions has been employed for such systems before, neglecting some intermolecular interactions necessitates the introduction of an adjustable binary interaction parameter to reproduce the VLE data. This of course limits the SAFT as a predictive tool. Among these interactions which may influence the phase behavior and have not been considered in the original form of the SAFT are the dipole–dipole interactions. Recently, three approaches, namely, Jog and Chapman, Gross and Vrabec, and Economou have been proposed to incorporate such interactions in SAFT. In this study, water–alcohol–hydrocarbon systems are modeled by the inclusion of the three dipolar theories to the perturbed-chain statistical association fluid theory (PC-SAFT) where different classes of alcohols are considered including glycols. A comparison of the performance of the three approaches is presented by using data from 53 binary systems. Finally, it is demonstrated that binary data are not necessarily needed to estimate pure component parameters.

Ethane as an alternative solvent for supercritical extraction of orange peel oils

The objective of this study was to investigate the superiority of ethane in comparison to CO 2 as a supercritical extraction solvent for deterpenating citrus oils. A rigorous computer code was developed that optimized extraction column operating conditions to minimize solvent recirculation. The SRK equation of state was used as the thermodynamic model after globally optimizing its adjustable binary interaction parameters to a combination of different literature data sets consisting of binary isothermal P– x, y, ternary constant composition P– T, and ternary isothermal isobaric x– y data. An investigation of the effects of different process variables on the degree of extraction revealed complicated and interconnected relations among the variables and extraction efficiencies. However, since the process of deterpenation, in particular, benefits from higher solubility more than from higher selectivity, increases in temperature, pressure, solvent-to-feed ratio, and reflux rate all seem to favor the separation. To compare the performance of ethane and carbon dioxide for orange oil deterpenation, selectivities of separation between the terpene and aroma fractions were calculated and compared for the two solvents. Compared to CO 2, ethane is the better solvent for citrus constituents. This results in decreased solvent/feed mass ratio for ethane when the processes are compared at the same reduced pressure. However, these are not the only benefits of ethane over CO 2. As the critical pressure of ethane is lower, the absolute operating pressures of ethane columns can be lower.

Experimental P−T−ρ Measurements of Supercritical Mixtures of Carbon Dioxide, Carbon Monoxide, and Hydrogen and Semiquantitative Estimation of Their Solvent Power Using the Solubility Parameter Concept

The P−T−ρ behavior of the CO2−CO−H2 system was studied in the supercritical region under operative conditions close to those adopted to perform hydrogenation and hydroformylation reactions in dense CO2, thus providing new interesting information on this fluid mixture. Experiments were performed in a fixed volume reactor in the temperature range from 298 K to 343 K changing the density and the composition of the fluid phase. The one-component (Hildebrand) solubility parameter of the mixture was estimated from experimentally measured P vs T profiles, and its dependence on the density and composition of the system was analyzed to study the antisolvent effect of the permanent gases. We have found that, under adopted operative conditions, the Peng−Robinson equation of state (PR-EOS) can be used to predict with good accuracy the values of the Hildebrand solubility parameter of the binary and ternary mixtures without using adjustable binary interaction parameters. The PR-EOS was eventually used to calculate the dependence of the solubility parameter of CO2-containing mixtures on the composition, pressure, and density. By this approach, it seems that the antisolvent effect of CO and H2 is mainly due to the reduction of the density of the fluid phase, at fixed T and P, when the mole fraction of syn-gas components is increased.

Solubility of Carbon Dioxide in Aqueous Solutions of Methanol. Predictions by Molecular Simulation and Comparison with Experimental Data

The solubility of carbon dioxide in pure methanol, and in aqueous solutions of methanol, was computed using the Gibbs ensemble Monte Carlo (GEMC) technique for 313, 354, and 395 K at pressures up to 9 MPa. Three solvent mixtures (of methanol and water) with methanol mole fractions of 10, 50, and 75 mole percent (in the gas-free solvent mixture) were studied. The Monte Carlo simulations were conducted in an isothermal-isobaric ensemble applying effective pair potentials for the pure components from literature. Common mixing rules without any adjustable binary interaction parameters were used to describe the interactions between the mixture components. Overall, a good agreement between simulation results and recently published experimental data is achieved.

Determination and modelling of the high-pressure vapour–liquid equilibrium carbon dioxide–methyl acetate

Experimental data for the high-pressure vapour–liquid equilibrium of the binary system of carbon dioxide and methyl acetate have been measured. Equilibrium data were needed for investigation of acetic acid esterification with methanol. Pressure–composition ( P– x) isotherms were determined at 308, 318 and 328 K and an operation pressure up to 9 MPa. Data were modelled using the Peng–Robinson equation of state. Van der Waals one-fluid mixing rules were used for the temperature-dependent function a and for parameter b in the Peng–Robinson equation. One parameter van der Waals model for the cross coefficient terms a ij and b ij was used, which both contain one adjustable binary interaction parameter k ij and l ij , respectively. In a second modelling method the temperature dependence of k ij and l ij was determined. A comparison of experimental results with calculations obtained from PR equation showed a reasonable accordance of the data over a wide range of composition.

Solubility of CO2, CO, and H2 in the Ionic Liquid [bmim][PF6] from Monte Carlo Simulations

This work reports predictions from molecular simulation results for the solubility of the single gases carbon dioxide, carbon monoxide, and hydrogen in the ionic liquid 1-N-butyl-3-methyl-imidazolium hexafluorophosphate ([bmim][PF6]) at temperatures from 293 to 393 K and at pressures up to 9 MPa. The predictions are achieved by Gibbs ensemble Monte Carlo simulations at constant pressure and temperature (NpT-GEMC). The intermolecular forces are approximated by effective pair potentials for the pure gases and by a quantum-chemistry-based pair potential for [bmim][PF6]. The interactions between unlike groups are described using common mixing rules without any adjustable binary interaction parameter. The simulation results for the solubility of hydrogen agree within their statistical uncertainty with experimental data, whereas the results for carbon monoxide and carbon dioxide reveal somewhat larger deviations.

Solubility of carbon dioxide in dimethylsulfoxide and N-methyl-2-pyrrolidone at elevated pressure

Experimental data on the solubility of CO 2 in dimethylsulfoxide (DMSO) and N-methyl-2-pyrrolidone (NMP) are reported at temperatures of 298, 308 and 318 K and pressures approaching the mixture critical point for each binary system. The corresponding volumetric expansions of DMSO and NMP with CO 2 are also presented. The solubility data are correlated with the Peng–Robinson equation of state (PR-EOS). At a given temperature and pressure, higher solubilities of CO 2 are obtained in NMP compared with DMSO and this trend is consistent with the volumetric expansions of the solvents. A plot of the volumetric expansion data as a function of the solubility of CO 2 in the liquid phase suggests that it is unlikely, as a general rule, that the expansion isotherms for the various systems collapse onto a single expansion curve. The existence of a single expansion curve appears to hold only for a given binary system over a limited range of temperature. The use of two adjustable binary interaction parameters with the PR-EOS provides a superior correlation of the liquid phase composition in comparison with the standard PR-EOS, particularly in the vicinity of the mixture critical point.

High pressure phase behavior of carbon dioxide + heptadecafluorodecyl acrylate and carbon dioxide + heptadecafluorodecyl methacrylate systems

We measured pressure–composition (P–x) isotherms for binary mixtures of carbon dioxide + heptadecafluorodecyl acrylate and carbon dioxide + heptadecafluorodecyl methacrylate using a variable volume view cell at temperatures from 323 K to 353 K and pressure up to 140 bar. Phase behavior of these binary experimental data was modeled with the Peng–Robinson equation of state with two adjustable binary interaction parameters. For the critical constants, we proposed new parameters for –CF2– and CF3– for the Joback group contribution method. These parameters were regressed from normal perfluoroalkane data. We compared this modified Joback group contribution method with the Constantinou–Gani group contribution method for correlation of experimental results.

Multiphase equilibria for binary and ternary mixtures containing propionic acid, n-butanol, butyl propionate, and water

Isothermal vapor–liquid equilibrium (VLE) data were measured for propionic acid + butyl propionate at 373.15 and 393.15 K, and isothermal vapor–liquid–liquid equilibrium (VLLE) data were also measured for n-butanol + water, butyl propionate + water, and water + n-butanol + butyl propionate at temperatures ranging from 323.15 to 393.15 K. No azeotrope was found in propionic acid + butyl propionate. The mutual solubility data of the binary aqueous systems were correlated well with the NRTL model accompanying with temperature-dependent parameters. Improvement on the calculation of saturated vapor compositions has been made by using two-term virial equation with one adjustable binary interaction parameter to represent the non-ideality of the vapor phase. The model parameters determined from the binary VLLE data of n-butanol + water and butyl propionate + water and the binary VLE data of n-butanol + butyl propionate are capable of predicting satisfactorily the VLLE properties for the ternary system of water + n-butanol + butyl propionate.

Multiphase Coexistence for Aqueous Systems with Amyl Alcohol and Amyl Acetate

Phase equilibrium properties were measured with a newly designed apparatus for the mixtures of amyl alcohol + water, amyl acetate + water, and water + amyl alcohol + amyl acetate at vapor−liquid−liquid equilibrium (VLLE) conditions up to 393.15 K. The experimental data form a basis to evaluate the reliability of VLLE calculations with the φ−γ−γ method. It is found that the mutual solubility data can be correlated accurately by the NRTL model with temperature-dependent parameters for the binary aqueous systems over a wide temperature range. The saturated vapor compositions can also be calculated satisfactorily by using a two-term virial equation with one adjustable binary interaction parameter. The model parameters determined from the binary VLLE data of amyl alcohol + water and amyl acetate + water and the binary vapor−liquid equilibrium (VLE) data of amyl alcohol + amyl acetate are applicable to reproducing VLLE properties for the ternary system of water + amyl alcohol + amyl acetate.

Prediction of the vapor–liquid phase equilibrium of hydrogen sulfide and the binary system water–hydrogen sulfide by molecular simulation

NVT- and NpT-Gibbs ensemble Monte Carlo simulations were carried out in order to calculate the vapor–liquid phase equilibrium of hydrogen sulfide (between 203 and 363 K) and of the binary system hydrogen sulfide–water (between 313 and 433 K). Furthermore, the properties of supercritical hydrogen sulfide were determined at pressures between 0.1 and 100 MPa in the temperature range from 383 K to 423 K by NpT-Monte Carlo simulations. Molecular interactions were described using effective pair potential models together with common mixing rules, without any adjustable binary interaction parameters. Good agreement between simulation results and experimental data was found. Simulation of the binary system shows liquid-liquid equilibrium at temperatures below 393 K when pressures are above the vapor pressure of hydrogen sulfide.

Accurate vapour–liquid equilibrium calculations for complex systems using the reaction Gibbs ensemble Monte Carlo simulation method

The reaction Gibbs ensemble Monte Carlo (RGEMC) computer simulation method [J. Phys. Chem. B 103 (1999) 10496] is used to predict the vapour–liquid equilibrium (VLE) behaviour of binary mixtures involving water, methanol, ethanol, carbon dioxide, and ethane. All these mixtures contain molecularly complex substances, and accurately predicting their VLE behaviour is a considerable challenge for molecular-based approaches, as well as for traditional engineering approaches. The substances are modelled as multi-site Lennard–Jones (LJ) plus Coulombic potentials with standard mixing rules for unlike site interactions. No adjustable binary-interaction parameters and no mixture experimental properties are used in the calculations; only readily-available pure-component vapour-pressure data are required. The simulated VLE predictions are compared with experimental results and with those of two typical semi-empirical macroscopic-level approaches. These latter are the UNIFAC liquid-state activity-coefficient model combined with the simple truncated virial equation of state, and the hole quasi-chemical group contribution equation of state. The agreement of the simulation results with the experimental data is generally good and also comparable with and in some cases better than those of the macroscopic-level empirical approaches.

Modeling the Effects of Cosolvent-Modified Supercritical Fluids on Polymers with a Lattice Fluid Equation of State

A single Sanchez−Lacombe lattice fluid equation of state is used to model both phases for a polymer−supercritical fluid−cosolvent system. This method represents well over a wide pressure range both volumetric and phase equilibrium properties for a cross-linked poly(dimethyl siloxane) phase in contact with CO2 modified by a number of cosolvents. A single adjustable binary interaction parameter, obtained from swelling data of the polymer, is used to correlate both polymer dilation and solvent sorption.

Molecular thermodynamic theory for polymer systems III. Equation of state for chain-fluid mixtures

The equation of state for fluids containing chain-like molecules presented in previous work has been extended to mixtures by using the van der Waals one-fluid theory (vdW1) for the energy parameter responsible for interactions between segments. With an adjustable binary interaction parameter, satisfactory fit for experimental pVT data of binary liquid mixtures including polymer blends, as well as binary vapor-liquid-equilibria data of volatile systems and polymer solutions can be obtained. The potential application for liquid-liquid equilibria is also discussed.

Simulation of Refrigerant Phase Equilibria

Vapor−liquid equilibria for refrigerant mixtures modeled by an equation of state are studied. Phase behavior calculated by the Soave−Redlich−Kwong (SRK) equation with a single adjustable binary interaction parameter is compared with experimental data for binary refrigerant mixtures, two with a supercritical component and one that exhibits azeotropic behavior. It is shown that the SRK equation gives an adequate description of the phase envelope for binary refrigerant systems. The complex domain trust region methods of Lucia and co-workers (Lucia and Xu, 1992; Lucia et al., 1993) are applied to fixed vapor, isothermal flash model equations, with particular attention to root finding and root assignment at the equation of state (EOS) level of the calculations, and convergence in the retrograde and azeotropic regions of the phase diagram. Rules for assigning roots to the vapor and liquid phases in the case where all roots to the EOS are complex-valued are proposed and shown to yield correct results, even in retrograde regions. Convergence of the flash model equations is also studied. It is shown that the complex domain trust region algorithms outperform Newton's method in singular regions of the phase diagram (i.e., at near azeotropic conditions and in the retrograde loop), primarily due to the eigenvalue−eigenvector decomposition strategy given in Sridhar and Lucia (1995). A variety of geometric figures are used to illustrate salient points.

A new predictive quasi-lattice equation of state for high-pressure phase equilibria of pure fluids and mixtures

The recent success of analytical quasi-lattice equation of state (EOS) description of r-mer fluids by the present authors leads us to extend the EOS as a group contribution. With a size parameter for each group and an interaction energy parameter between groups, EOS parameters for pure fluids were calculated. Predicted high-pressure phase equilibrium properties of pure alkanes, cycloalkanes, aromatics, carbon dioxide and their mixtures showed good agreements with experimental data. Especially, the present approach predicts phase equilibria of mixtures without employing any type of adjustable binary interaction parameter. As a result, high-pressure phase equilibrium behaviors of both pure fluids and mixtures can readily be predicted solely from information on functional group interactions.

APPLICATION OF THE SCLC MODEL TO THE SALT EFFECT IN VAPOR-LIQUID EQUILIBRIA

Abstract The ability of the rationalized SCLC model to correlate data on the salt effect in vapor-liquid equilibria is examined in this work. For a system consisting of two miscible solvents the effect of salt in altering the relative volatility is represented by the model with four adjustable binary interaction parameters. The model is shown to correlate vapor-liquid equilibria of several alcohol-water-salt systems satisfactorily.

Model of vapor-liquid equilibria for aqueous acid gas-alkanolamine systems. 2. Representation of hydrogen sulfide and carbon dioxide solubility in aqueous MDEA and carbon dioxide solubility in aqueous mixtures of MDEA with MEA or DEA

A physicochemical model developed in earlier work for representing H 2 S and CO 2 solubility in aqueous solutions of monoethanolamine (MEA) and diethanolamine (DEA) was extended to include the mixtures of methyldiethanolamine (MDEA) with MEA or DEA. Activity coefficients are represented with the electrolyte-NRTL equation treating both long(range electrostatic interactions and short-range binary interactions. Adjustable binary interaction parameters of the model were fitted on binary and ternary system MDEA data reported in the literature. The solubility of CO 2 in aqueous mixtures of MDEA with MEA or DEA was measured at 40 and 80 o C over a wide range of CO 2 partial pressures. Representation of the data by the model is good, especially at low to moderate acid gas loadings

Calculation and prediction of fluid phase equilibria from an equation of state

Liquids or compressed gases consisting of light molecules show deviations from classical mechanics, which are caused by the discontinuity of energy levels. From the assumption that each molecule is confined to a cell with a size depending on the free volume, a quantum correction is derived which extends any van der Waals type equation of state to quantum gases. The correction is applied to a semiempirical equation of state developed by the author. The extended equation yields reasonable critical compressibility factors and gives a better representation of PVT data than the uncorrected equation. Furthermore high pressure phase equilibria in mixtures containing helium and hydrogen have been calculated. Again the agreement with experimental data is improved; the adjustable binary interaction parameters have values close to the Berthelot-Lorentz rules and are less temperature dependent.