Vapor-liquid Equilibrium Behavior Research Articles

Predicting Mixture Phase Equilibria and Critical Behavior Using the SAFT-VRX Approach

The SAFT-VRX equation of state combines the SAFT-VR equation with a crossover function that smoothly transforms the classical equation into a nonanalytical form close to the critical point. By a combinination of the accuracy of the SAFT-VR approach away from the critical region with the asymptotic scaling behavior seen at the critical point of real fluids, the SAFT-VRX equation can accurately describe the global fluid phase diagram. In previous work, we demonstrated that the SAFT-VRX equation very accurately describes the pvT and phase behavior of both nonassociating and associating pure fluids, with a minimum of fitting to experimental data. Here, we present a generalized SAFT-VRX equation of state for binary mixtures that is found to accurately predict the vapor-liquid equilibrium and pvT behavior of the systems studied. In particular, we examine binary mixtures of n-alkanes and carbon dioxide + n-alkanes. The SAFT-VRX equation accurately describes not only the gas-liquid critical locus for these systems but also the vapor-liquid equilibrium phase diagrams and thermal properties in single-phase regions.

Measurement and prediction of vapor–liquid equilibria of ternary systems containing ionic liquids

For the first time vapor–liquid equilibrium (VLE) data for ternary systems containing ionic liquids are reported. The data were measured by means of a computer-operated static VLE apparatus at 353.15 K with the ionic liquids 1-ethyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)imide [EMIM] +[(CF 3SO 2) 2N] − and 1-butyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)imide [BMIM] +[(CF 3SO 2) 2N] − and acetone, 2-propanol and water. The experimental VLE data of the binary systems were correlated using the Wilson, NRTL and UNIQUAC models. The errors using Wilson, NRTL, and UNIQUAC are 3.92%, 1.45%, and 1.53%. The g E-model parameters of the binary systems were used to predict the VLE behavior of the ternary systems and the predictions were compared to the experimental datasets. The errors using Wilson-, NRTL-, and UNIQUAC-parameters are 5.61%, 7.22%, and 5.02%.

Gibbs Ensemble Simulations of Vapor/Liquid Equilibrium Using the Flexible RWK2 Water Potential

Gibbs ensemble Monte Carlo simulations of water vapor/liquid equilibrium (VLE) using the flexible fixed charge RWK2 water-water potential are reported. The equilibrium densities, saturation pressures, and critical parameters calculated with this potential are in better agreement with experimental data than are values obtained from the SPC, MSPC/E, TIP4P, and TIP5P rigid fixed charge potentials as well as from polarizable interactions, such as those of the PPC, KJ, SPC/P, TIP4P/P, and SPCDP potentials. The agreement between predicted and experimental phase coexistence phase density versus temperature variation in the critical region is similar to that obtained from the SPC/E and the polarizable SPC-pol-1 potentials. However, the variation of the saturation pressure and heat of vaporization with temperature and the critical pressure predicted by the RWK2 potential are closer to experiment than predictions from SPC/E interaction and similar (for lower temperatures) to those of the MSPC/E potential. The water structure predictions of the RWK2 potential are substantially better than those from the SPC-pol-1 interaction. VLE data are not used to parametrize the RWK2 potential. Nevertheless, predictions for coexistence temperature versus phase density and saturation pressure versus temperature are similar to those of the recent potential of Errington and Panagiotopoulos (EP potential), which is adjusted to reproduce the VLE behavior of water. MD simulations using the RWK2 potential show much better agreement with the room-temperature liquid structure and second virial coefficient data than does the EP potential. Fixing the bond lengths and HOH angle in the RWK2 interaction at their isolated molecule minimum energy values leads to significant deterioration of the VLE predictions obtained.

Adsorption of ethylene on graphitized thermal carbon black and in slit pores: a computer simulation study.

In this paper, we studied vapor-liquid equilibria (VLE) and adsorption of ethylene on graphitized thermal carbon black and in slit pores whose walls are composed of graphene layers. Simple models of a one-center Lennard-Jones (LJ) potential and a two-center united atom (UA)-LJ potential are investigated to study the impact of the choice of potential models in the description of VLE and adsorption behavior. Here, we used a Monte Carlo simulation method with grand canonical Monte Carlo (GCMC) and Gibbs ensemble Monte Carlo ensembles. The one-center potential model cannot describe adequately the VLE over the practical range of temperature from the triple point to the critical point. On the other hand, the two-center potential model (Wick et al. J. Phys. Chem. B 2000, 104, 8008-8016) performs well in the description of VLE (saturated vapor and liquid densities and vapor pressure) over the wide range of temperature. This UA-LJ model is then used in the study of adsorption of ethylene on graphitized thermal carbon black and in slit pores. Agreement between the GCMC simulation results and the experimental data on graphitized thermal carbon black for moderate temperatures is excellent, demonstrating that the potential of the GCMC method and the proper choice of potential model are essential to investigate adsorption. For slit pores of various sizes, we have found that the behavior of ethylene exhibits a number of features that are not manifested in the study of spherical LJ particles. In particular, the singlet density distribution versus distance across the pore and the angle between the molecular axis and the z direction provide rich information about the way molecules arrange themselves when the pore width is varied. Such an arrangement has been found to be very sensitive to the pore width.

A critical assessment on two predictive models of binary vapor–liquid equilibrium

A critical assessment on two predictive theoretical models for vapor–liquid equilibrium (VLE) is presented. The first model utilizes molecular dynamics to evaluate interaction energies in liquids. The energy terms are then used as input parameters in activity coefficient models to calculate the vapor–liquid equilibrium and activity coefficients. The second model is based on the recently proposed COSMO-RS to derive VLE diagrams. The assessment was made with 16 binary mixture systems. We show that the hybrid model that combines a predictive method based on molecular dynamics with a correlated method based on activity coefficient methods in general gives qualitatively incorrect results due to the fact that the energy terms used in activity coefficient models do not represent the true intermolecular interaction energies. COSMO-RS on the other hand often predicts VLE behavior with qualitative or semi-quantitative accuracy. However, the current implementations of the method do not allow for a description of non-ideal vapor phases or partially miscible mixtures.

The prediction of vapour–liquid equilibrium behaviour of HFC blend–oil mixtures from commonly available data

This paper addresses the problem of achieving accurate calculations for vapour–liquid equilibrium behaviour in the presence of the (new) oils in use with HFC refrigerants by introducing a correlation which depends only on the gas constant, critical temperature and molecular weight of the blend constituent and the molecular weight of the oil; i.e. the method depends on commonly available data and not a specialised measurements. The work is believed to be of value to plant designers and research workers.

Phase behaviors of ammonia/R-125 mixtures

Hydrofluorocarbons (HFCs) are known to have specific intermolecular interactions (hydrogen bonding) as well as large permanent electric dipole moments. The peculiar vapor–liquid equilibria (VLE) behavior (double azeotropes) observed in ammonia/R-125 mixtures led us further to study the phase behaviors of this binary system. The experimental VLE ( PTx) data were measured from 205 to 248 K for six concentrations. Single gaseous phase PTVx properties for four concentrations were measured using a constant volume cell: densities of 100, 102, 146, and 224 kg m −3 at temperature ranges of 333–385 K. The experimental data, combined with the previously reported data, were analyzed with a cubic equation of state, where non-conventional mixing rules were required in order to fit the experimental VLE data satisfactorily. The VLE phase behavior is discussed with ammonia mixtures with other compounds. There are strong evidences that some of HFCs and HCFCs form complexes (or even react) with ammonia. The complex formation and VLE behavior are elusively related to the number of fluorine atoms and the molecular structure. For ammonia/R-125, it is estimated the enthalpy of complex formation is about −10 kJ mol −1, which is in concordance with those for hydrogen-bonding and/or charge-transfer complexes reported in the literature.

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.

Comparison of the performance of the LCVM model (an EoS/G E model) and the PHCT EoS (the Perturbed Hard Chain Theory Equation of State) in the prediction of the Vapor–Liquid Equilibria of binary systems containing light gases

The purpose of this work is to compare two models, which are able to perform Vapor–Liquid Equilibrium (VLE) predictions. The first one, the LCVM model, is an EoS/G E one and it has been successfully applied in the prediction of the VLE behavior of polar and non-polar systems, as well as, systems of dissimilar component size, such as those containing gases with large n-alkanes. The second one is PHCT, an equation of state based on the perturbed hard chain theory. It has also been successfully applied in binary systems of supercritical fluids and non-polar molecules and in systems containing light gases and large n-paraffins. The comparisons results presented in this paper, proved that the two models are comparable, concerning the ability to predict the VLE, as well as, the volumetric behavior of systems with low to medium component size difference (supercritical fluids with non-polar components up to about 10 carbon atoms). However, as the size difference increases, LCVM performs better, especially in the near critical region of such systems.

A theoretical revision of the derivation of liquid property expressions from an equation of state and its application

The thermodynamic properties of a liquid are generally determined from an equation of state (EOS) through isothermal integration. Kahl (1967. Physical Review, 155, 78–80) and Nitsche (1992. Fluid Phase Equilibria, 78, 157–190) both questioned the validity of performing isothermal integration on a liquid and devised a Kahl's integration path to obtain liquid properties. In this paper, an alternate approach to revise the isothermal integration on liquid was presented. A temperature-dependent revision factor α( T) was introduced to the liquid fugacity coefficient expression derived from traditional isothermal integration, and the vapor pressure of pure liquids can be reproduced. In extension to mixtures, since the vapor–liquid equilibrium (VLE) has been taken into account by the revision factor α( T), simple mixing rules are adequate for EOS parameters even for highly non-ideal systems. Two types of mixing rule have been developed for α( T) depend on the VLE complexity. The proposed revision method and its application were illustrated through a modified Redlich–Kwong (MRK) EOS aiming at improving the description of volumetric properties. The test results on the VLE and PVT behavior of 43 pure substances and 17 binary mixtures are impressive. The comparisons with the widely used Soave–Redlich–Kwong and Peng–Robinson equations of state indicate the advantages of the proposed revision method and the superiority of MRK EOS.

00/03641 Thermodynamic analysis of binary and ternary silicate systems by a structural model

The cubic equation of state/excess Gibbs free energy (CEoS/GE) model is a new idea to predict non-ideal systems. In this study, the Peng-Robinson (PR) EoS combined with the Wong-Sandler (WS) mixing rule and the modified UNIFAC group contribution activity model was used to calculate the vapor liquid equilibrium (VLE) data. The average absolute relative deviations (AARD) of pressure and the average absolute deviations (AAD) of the vapor phase mass fraction between the calculated results and experimental data are 0.87% and 0.005 for fluoroethane (R161) + 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) over the temperature range of (283.15–323.15 K) and at pressures varying from 0.4 MPa to 1.8 MPa, respectively. The liquid and vapor phase mass fraction deviations are within ±0.028 and ±0.025 for difluoromethane (R32) + pentafluoroethane (R125) + 1,1,1,2-tetrafluoroethane (R134a) system at temperatures of (205–350 K), respectively. The VLE behavior for the strongly-zeotropic mixture of 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) + trifluoromethane (R23) + tetrafluoromethane (R14) which is suitable for the three-stage auto cascade refrigeration system was calculated at pressures of (0.2–2.2 MPa) and the corresponding three-dimensional phase diagrams were constructed. It was found that the sliding temperature increases with the decrease of pressure and the maximum predicted sliding temperature reached 73 K.

Vapor–liquid equilibria of novel chemicals and their mixtures as R-22 alternatives

Vapor–liquid equilibrium (VLE) vapor pressures are reported for binary mixtures; octafluoromethylethylether+1,1-difluoroethane (RE218/R152a), trifluoromethylpentafluorosulfur(VI)+1,1-difluoroethane (CF 3SF 5/R152a), hexafluorodimethylthioether+1,1,1,2-tetrafluoroethane (CF 3SCF 3/R134a), and pentafluorodimethylether+1,1,1-trifluorodimethylether (RE125/RE143a). The mixtures; (RE218/R152a), (CF 3SF 5/R152a), and (CF 3SCF 3/R134a) form minimum boiling azeotropes with the normal boiling points; 237.9 K (−35.3°C), 239.7 K (−33.5°C), and 243.0 K (−30.2°C), respectively, and gas–liquid critical temperatures of 353.3 K (80.1°C), 365.7 K (92.5°C) and 368.2 K (95.0°C), respectively. The azeotropic mixtures have sufficiently low boiling points to serve as alternatives for the refrigerant R-22 (CHF 2Cl). The mole fractions of the perfluorinated component of these mixtures at the azeotropic compositions are 0.49, 0.41, and 0.46, respectively. The estimated critical mixing temperatures for liquid–liquid phase separation are 236 K (−37°C), 221 K (−52°C), and 341 K (−68°C), respectively, and are well below the corresponding boiling points. The ether mixtures, (RE125/RE143a), exhibit nearly ideal mixing behavior which contrasts the VLE behavior of mixtures of perfluorinated ether, RE218, with RE143a [I. Kul, D.D. DesMarteau, A.L. Beyerlein, ASHRAE Trans. 106 (1) (1999)]. In addition to binary mixtures, VLE data are reported on four ternary mixtures; RE125(33%)/R134a(33%)/R161(34%), RE125(33%)/RE143a(33%)/R161(34%), RE218(33%)/RE143a(33%)/R161(33%), and RE218(40%)/RE143a(40%)/R161(20%) with boiling points 240.6 K (−32.6°C), 241.6 K (−31.6°C), 236.7 K (−36.5°C), and 238.6 K (−34.6°C), respectively. The boiling points of the ternary mixtures are sufficiently low for a R-22 alternative.

A New Mixing Rule for Petroleum Mixture Compositional Processes

Abstract A new mixing rule of a realistic vector form is proposed. It is used for vapor-liquid equilibrium calculations of petroleum mixtures with the commonly used Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) Equations Of State (EOS). The results are compared with those from the conventional calculations with the same EOS and the original matrix form of mixing rule, and the experiment data obtained for the chosen petroleum mixtures with and without added CO2. The new vector form of mixing rule is a successful "transform" of the old matrix form of mixing rule based on the idea of component deviation from their pure-state, vapor-liquid equilibrium behavior when they are present in a petroleum mixture. Such transformation will allow us to eliminate binary interaction coefficients with the more practical component deviation coefficients for petroleum mixture phase equilibrium problems encountered in compositional simulation and relevant chemical engineering calculations. The utilization of the new mixing rule has lead to results with improved computation efficiency, convergence behavior and accuracy for the calculations performed. However, convergence problems cannot be solved completely with the proposed mixing rule as the problem does not stem from there only. Further investigation results in a new critical criterion that has not been satisfied by many EOS, including the PR and SRK EOS, on both analytical and numerical basis for all pure components. Thus, convergence problem has never been really solved no matter how sophisticated mathematical methods have been employed to get the "converged" results. The new critical criterion is established with a newly developed three term cubic EOS, which can be easily reduced to encompass many two term cubic EOS of similar forms as the PR or SRK EOS. A discussion on the new EOS is given. With the new EOS, it becomes obvious that the critical convergence problem is not purely a mathematical one, the EOS models themselves may have some inherent restrictions for the phase equilibrium computation schemes to work for complex mixtures when the critical points are approached. Introduction The PR and SRK EOS have been in use for phase equilibrium calculations for over twenty years since they were published(1,2). However some problems still exist for petroleum mixtures containing more heavy fractions and near critical point conditions or across phase boundaries(3). In some cases, it is even hard to get converged results without considering their accuracy. Because such problems have not been solved with satisfaction, reservoir simulators that use EOS to model reservoir fluid compositional behavior are most likely to inherit the problems. When this happens in simulation, a lot of times, it is not clearly understood. The reason that this is important is because reservoir fluid vapor-liquid equilibrium states reflect its energy and petroleum recovery potential. Another problem with compositional reservoir simulators that use an EOS model is that the computing time and storage requirement increase sharply with the number of components used for each grid and iteration step, and soon become a restriction in a simulation(4). Even with the new generations of computers, this is still the case.

Prediction of vapor–liquid equilibria in mixed-solvent electrolyte systems using the group contribution concept

The LIQUAC model is widely used to predict reliably vapor–liquid equilibria (VLE), osmotic coefficients and mean ion activity coefficients for electrolyte systems. It consists of a Debye–Hückel term, the UNIQUAC term and the osmotic virial equation for the middle-range contribution. The aim of this work is to provide a model based on the group contribution concept that can be used to predict phase equilibria in mixed-solvent electrolyte systems. Therefore, in the LIQUAC model the UNIQUAC equation has been substituted by the original UNIFAC equation and group interaction parameters have been introduced into the middle-range term. With the help of a large data base, 234 group interaction parameters for seven solvent groups, 13 cations and seven anions have been fitted. The model parameters have been used to calculate the VLE behavior, osmotic coefficients and mean ion activity coefficients for a large number of systems with high accuracy.

A simple non-classical equation of state for fluids and fluid mixtures

A method for improving the behavior of classical equations of state (EOS) in the critical region, originally proposed by Fox [J.R. Fox, Fluid Phase Equilibria 14 (1983) 45–53], has been modified in this work for the Patel–Teja (PT) EOS [N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37, 463–473]. The application of the new equation (NPT) for predicting PVT and vapor pressure behavior of pure substances, as well as vapor–liquid equilibrium behavior of binary mixtures, is demonstrated. The NPT equation is simple to use and requires the same input information as the original PT equation. However, it reproduces the correct PVT behavior in the critical region. Limitations of both the PT and NPT equations in calculating the isochoric heat capacity are discussed.

Estimation of Henry's constants for aqueous systems at elevated temperatures

The treatment and removal of dilute organic contaminants from water require methods for estimating the vapor–liquid equilibrium behavior of these mixtures. Highly hydrophobic solutes may exhibit a maximum in Henry's law constant that is difficult to predict using traditional activity coefficient models. This paper examines the application of an activity coefficient model fitted specifically for dilute aqueous systems (UNIFAC-ENV) to make predictions for the infinite dilution activity coefficients at ambient conditions. The use of activity coefficient based mixing rules for equations of state to extend the range of the UNIFAC-ENV predictions to the temperatures typical for steam stripping conditions (80–140°C) is also evaluated. Application of this approach to Henry's law data for trichloroethylene in water indicates that these models require temperature dependent interaction coefficients to accurately predict the highly non-ideal solution behavior observed.

Vapor–liquid equilibria of iso-propanol+iso-butanol and iso-propanol+iso-butanol+calcium chloride at 93.6 kPa

Vapor–liquid equilibrium (VLE) data of iso-propanol+iso-butanol and iso-propanol+iso-butanol+CaCl 2 (at saturation) were measured at a pressure of 93.6 kPa, using a modified Malanowski equilibrium still. The VLE behavior of the salt-free system is nearly ideal with a maximum normalized excess Gibbs energy ( G E/ RT) of 0.01. The salt investigated in this work, i.e. CaCl 2, shows no effect on the phase behavior of iso-propanol+iso-butanol. The experimental results of the salt-free binary were compared with those predicted by the ASOG and UNIFAC models, which predicted the bubble-point temperatures with an RMSD (root mean square deviation) of 1.01 and 1.26 K, respectively. The former model, however, predicted the vapor-phase composition within 0.012 mole fraction while the latter predicted them within 0.016 mole fraction in terms of RMSD. Moreover, two isobaric data sets (at 760 mm Hg) from the literature were analyzed using the above two models.

Statistical regression of binary vapor–liquid equilibrium data for ternary phase equilibrium predictions

High-pressure vapor–liquid equilibrium data of more than 50 binary systems were correlated by a DDLC (density-dependent local-composition) model incorporated into the Soave–Redlich–Kwong equation of state. The Error-Propagation-Law Method based on the maximum likelihood principle and the simple least-squares method were applied to data reduction. Fitting accuracies of the DDLC model by statistical regression were found better than those obtained by the least-squares as well as those of the SRK equation of state by both methods. However, no improvements were obtained for the original SRK equation by the statistical method. Further, vapor–liquid equilibrium behaviors of eight ternary systems were predicted by utilizing the binary interaction parameters of both models obtained from experimental data of the constituent binaries by both statistical and conventional methods, respectively. Results showed that better prediction accuracies were obtained for the DDLC model by statistical regression. Similarly, no improvements were found for the SRK equation of state by statistical regression. In addition, the superiority of the statistical regression over the conventional method was demonstrated by various simulated data.

Modeling fluorocarbon vapor–liquid equilibria using the Wong–Sandler model

Vapor–liquid equilibrium (VLE) data for seven binary fluorocarbon mixtures were modeled using the Wong–Sandler (WS) model. A variety of fluorocarbon azeotropes were chosen for testing the accuracy of the model. The azeotropes tested were CF 2H 2 and CF 3CH 3, CF 2H 2 and CF 3CF 3, CF 2H 2 and CHF 2CF 3, CF 2H 2 and CH 3CH 2CH 3, CF 3H and CF 3CF 3, CF 3CF 3 and CO 2, CHF 2CF 3 and NH 3. Using the WS mixing rule and the nonrandom two-liquid (NRTL) activity coefficient model, a three-parameter fit was calculated for each binary mixture. These parameters were then used to predict the VLE behavior at other temperatures which were compared with experimental data. The results showed that the WS mixing rules with the NRTL activity coefficient model could be accurately fitted to binary fluorocarbon VLE data and used for predictions at other temperatures.

Analysis of excess free energy based equations of state models

AbstractA comparison is made of the capabilities of various equation of state (EOS) + excess free energy (Gex) models in representing the activity‐coefficient models they incorporate. Such EOS models need to reproduce the excess Gibbs free energy behavior of the activity‐coefficient models as closely as possible in order to represent low‐pressure vapor–liquid equilibrium behavior of complex mixtures accurately, and also to make accurate the vapor–liquid predictions at higher temperatures and pressures using only low‐pressure information. It is demonstrated that the EOS models that use the excess Helmholtz free energy instead of the excess Gibbs free energy, and that combine the EOS with activity‐coefficient models at the infinite pressure limit, are successful for calculations of the type just described.