Prediction Of Vapor-liquid Equilibria Research Articles

Three-phase crystallization for purification of acrylic acid from acrylic/propionic acid mixture

A new separation technology, three-phase crystallization (TPC), was utilized to purify acrylic acid (AA) from a binary liquid mixture comprising AA and propionic acid (PA). The solid–liquid equilibrium data of AA/PA mixture reported in the literature were adopted to recover the activity coefficients of the liquid mixture; and, subsequently, the vapor–liquid equilibrium conditions of AA/PA mixture were predicted using Raoult’s law and the Wilson equations for the recovered activity coefficients. The reported solid–liquid equilibrium data and the predicted vapor–liquid equilibrium conditions were coupled to determine the three-phase transformation conditions of AA/PA mixture, which were employed to conduct the batch TPC experiments. Upon conclusion of the TPC, the yield and purity were measured to estimate the amount of the AA crystals and volume of the liquid mixture retained in the overall final product, respectively.

Isothermal (vapor ＋ liquid) equilibrium measurements and correlation of the binary mixture 3,3,3-trifluoropropene (R1243zf) ＋ isobutane (R600a) at temperatures from [formula omitted] to [formula omitted] K

The restrictions set by the F-gas Regulation and the Kigali Amendment to the Montreal Protocol have pushed an extensive research into alternatives for fluorinated greenhouse gases in air conditioning and refrigeration. Hydrofluoroolefins (HFOs) are emerging as promising substitutes for hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs) in HVAC and refrigeration. Amongst these, R1243zf raised interests as low-GWP substitutes for R134a. The pursuit of low GWP refrigerants has also led to the examination of hydrocarbons (HCs), like propane (R290) and isobutane (R600a), due to their efficiency, low charge, and affordability, despite their flammability. The mixtures of R1243zf and isobutane could be of interest for medium temperature heat pump applications. Moreover, blending HFOs with HCs usually leads to azeotropic mixtures. While HCs benefit of a wide range of data and reliable Equations of State (EoS), HFOs, and in particular their mixtures, lack comprehensive information. This study reports vapor–liquid equilibrium (VLE) measurements for the 3,3,3-trifluoropropene (R1243zf) + isobutane (R600a) binary system in the temperature range between 283.15 K and 323.15 K. The measurements have been carried out by means of a vapor-recirculation apparatus combined with gas-chromatographic analysis. This work reports 53 experimental data with an expanded uncertainty (k=2) of 0.003 mol mol−1. The reported data, along with the data available in the literature, have been used to developed two new mixture models based on the Helmholtz free energy EoS, both leading to a significant improvement in the VLE prediction, with RMSE values lower than 0.005 mol mol−1 for both the liquid and the vapor phase composition.

Prediction of vapor-liquid equilibrium and pvTx properties of mixtures containing HFOs, HFCs, HCs, and CO2 using polar PC-SAFT model

In this work, the polar perturbation chain statistical associated fluid theory (PC-SAFT) was utilized to determine model parameters of HFOs pure working fluid. Subsequently, a predictive equation for the binary interaction parameters of mixtures containing HFOs was constructed, allowing for the prediction of the vapor-liquid equilibrium (VLE) and pressure-volume-temperature-composition (pvTx) properties of mixtures comprising of HFOs, HFCs, HCs, and CO2. For 9 pure working fluids of HFOs, the average deviations of the polar PC-SAFT model in calculating saturated vapor pressure, saturated liquid phase density, and saturated vapor phase density were 1.2 %, 0.7 %, and 0.9 %, respectively. For the VLE properties of 35 binary mixtures containing HFOs, the average absolute relative deviation of pressure (AARD(p)) and average absolute deviation of vapor phase compositions (AAD(y)) predicted by the polar PC-SAFT were 2.4 % and 0.008, respectively. When directly using the parameters of binary subsystems to predict the VLE properties of ternary mixtures by the polar PC-SAFT model, the predicted AARD(p) and AAD(y) were 2.2 % and 0.011 for 8 ternary mixtures containing HFOs. For the pvTx properties, the predicted average absolute relative deviation of density (AARD(ρ)) was 0.9 % for 12 liquid binary mixtures containing HFOs, and the AARD(ρ) was 1.3 % for 16 vapor binary mixtures containing HFOs. The model established in this work has good predictive effects on the VLE and pvTx properties of binary mixtures containing HFOs, and can also be extended to multicomponent mixtures.

Prediction of Vapor Liquid Equilibrium of Binary CO2-Contained Mixtures for Carbon Capture and Sequestration using Artificial Intelligence

Prediction of Vapor Liquid Equilibrium of Binary CO2-Contained Mixtures for Carbon Capture and Sequestration using Artificial Intelligence

Prediction of vapor-liquid equilibrium of ternary system at high pressures

Prediction of vapor-liquid equilibrium of ternary system at high pressures

Isobaric Vapor–Liquid Equilibrium Prediction from Excess Molar Enthalpy Using Cubic Equations of State and PC-SAFT

Isobaric Vapor–Liquid Equilibrium Prediction from Excess Molar Enthalpy Using Cubic Equations of State and PC-SAFT

Modelling of the isothermal vapor-liquid equilibrium of alternative refrigerants: Determination of phase diagrams (high-pressure/low-pressure) and optimized binary interaction parameters

In this work, a thermodynamic model for prediction of Vapor-Liquid Equilibrium (VLE) at moderate pressures (up to 19 bar) and different temperatures (288-323 K) is developed by using Soave-Redlich-Kwong (SRK) and Peng-Robenson (PR) equations of state (EoS) in combination with the classical van der Waals (vdW) mixing rules. Four refrigerant binary systems have been considered in this study (R134a+ R1336mzz (E)), (R600a+R1234ze (Z)), (R600a+R1243zf), (R744+R152a). Also, a new method was used to improve binary interaction parameters (kij). A comparison of experimental phase equilibrium data in the literature with the predicted results showed very good representation for some mixing rules.

Simulation prediction and experimental study of phase equilibria of Bi–Sb and Bi–Sb–Cd alloys in vacuum distillation

In this study, experimental determination and model prediction of the vacuum distillation vapor-liquid equilibrium (VLE) values of Bi–Sb binary alloy and Bi–Sb–Cd ternary alloy at different temperatures were undertaken under a vacuum of 1–5Pa. The experimental result shows that Bi and Sb were separated effectively from Bi–Sb binary alloy and Cd in Bi–Sb–Cd ternary alloy preferentially volatilized and entered the vapor phase completely. Combined with the above two-step experiments, the segmented distillation can purify crude antimony. The molecular interaction volume model (MIVM) was used to predict both the activity of each alloy element of Bi–Sb, Bi–Cd and Sb–Cd and VLE values. The average relative deviation of activity was <±5.19% compared with the adopted experimental values, and the VLE values were consistent with the trend of the experimental values. The MIVM was further used to predict the activity and VLE values of Bi–Sb–Cd ternary alloy, and the result corresponds with the experimental values. This combination of experiment and model prediction not only verified the reliability of the MIVM in predicting the activity and VLE values of antimony-based alloys, but also optimized their process parameters of vacuum distillation, providing theoretical guidance for vacuum distillation purification of crude antimony and further industrial experiments.

Net zero Flow Assurance - Validation of various equations of state for the prediction of VLE and density of CO2-rich mixtures for CCUS applications

Carbon dioxide management is becoming a major topic of interest in the energy industry and carbon capture is part of this process. Carbon capture utilization and storage is considered a promising technique to mitigate the impact of the hard-to-abate industries. Despite the high level of accuracy of predictions of the thermodynamic behaviour of pure CO2, there are still several uncertainties when dealing with CO2-rich mixtures. The impact of impurities in the captured stream can impact considerably the sizing and the design of components such as pipelines and related costs. The scope of this work is to assess the capabilities of the most acknowledged Equations of State (EoS) in the energy industry to predict CO2-rich mixtures behaviour. In this work we assess their accuracy in the prediction of Vapour-Liquid Equilibrium (VLE) and density validating numerical results with detailed experimental data available in literature. A quantitative estimation of deviations from experimental data is provided for density and bubble points. The results show that, based on experimental data available, multi-parameters Equations of State, such as GERG-2008 and CSMA, are generally more accurate in the description of both VLE and density if compared with cubic EoS.

Prediction of Phase Equilibria and Transport Properties Using ASOG and PRASOG Group Contribution Methods: A Review

Half century has passed since the first version of Analytical Solution of Groups (ASOG) model was proposed. Now the ASOG model is well known as a group contribution method as well as UNIFAC. Although the ASOG model was designed for prediction of vapor-liquid equilibrium around the atmospheric pressure, the applications are extended to not only the phase equilibria in the wide temperature and pressure ranges but also the transport properties. The function forms in the ASOG model, basically composed of Flory-Huggins equation and Wilson equation, can be applied for the prediction of the phase equilibria (vapor-liquid, liquid-liquid, solid-liquid and vapor-solid) and the transport properties (kinematic viscosity, thermal conductivity) of the mixtures with some modifications.

Group Contribution Based Graph Convolution Network: Predicting Vapor–Liquid Equilibrium with COSMO-SAC-ML

Group Contribution Based Graph Convolution Network: Predicting Vapor–Liquid Equilibrium with COSMO-SAC-ML

Improving water–hydrocarbon equilibrium calculations using multi objective optimization

The addition of chemical terms to Cubic Equations of State to improve polar components Vapor–Liquid Equilibrium prediction overestimates the critical point. In this paper, we analyze the mathematical behavior of these equations and propose a new methodology based on multi-objective optimization with four independent functions, saturation pressure, saturated liquid volume, and two critical points constraints to estimate the pure component parameters for the equation of state. The effect of different parameters sets on the phase equilibrium prediction and binary interaction coefficient for some binary water–hydrocarbon systems is presented and discussed, showing the improvement of the proposed technique.

Vapor-liquid equilibrium predictions of refrigerant systems using COSMO based Gex-EoS methods

Combining COSMO-based excess Gibbs free energy models with the Peng-Robinson (PR) equation-of-state (EoS) via mixing rules has recently been shown as a promising method for satisfied VLE predictions on refrigerant systems by Mambo-Lomba and Paricaud. An extension is provided in this work for more systematic and dedicated evaluations focusing on a significantly larger refrigerant database and comparisons between different VLE modeling approaches. In particular, the COSMO-SAC-dsp model is combined with via the original Huron-Vidal (HVO), the modified Huron-Vidal (MHV1) and the Wong-Sandler (WS) mixing rules. Comprehensive model evaluation is performed on the basis of 447 vapor-liquid-equilibrium (VLE) experimental datasets for 233 refrigerant pairs. The results show that the combination of the COSMO-SAC-dsp with the PR yields satisfied and comparable prediction accuracy on the VLE in most cases comparing to the well-established group-contribution based Gex-EoS methods VTPR and PSRK. The performance of the three mixing rules on the studied database follows a decreasing order of MHV1 > HVO > WS but without qualitative difference. Large VLE prediction errors can appear between halogenated hydrocarbons and hydrocarbons. Moreover, errors become more significant and the VLE calculation cannot converge at all for mixtures involving R717 and R744 respectively. Improved predictive accuracy can be achieved by re-optimizing the atomic dispersion parameters of F and =O to 35.5 and 74.0 respectively.

Interfacial Properties of Linear Alkane/Nitrogen Binary Mixtures: Molecular Dynamics Vapor-Liquid Equilibrium Simulations.

Molecular dynamics simulations were used to investigate the vapor-liquid equilibria (VLE) and interfacial properties of binary mixtures of N2 with either ethane, propane, n-decane, or n-dodecane. Alkanes and N2 were modeled by using the TraPPE-UA and Rivera force fields, respectively. The typically used Lorentz-Berthelot combining rules resulted in liquid phases that are too N2-rich compared to experiment. To improve the accuracy of VLE predictions, the hydrocarbon-nitrogen interactions were fine-tuned, and these improved parameters were used to investigate interfacial properties. Scaling the interaction strength between nitrogen and -CH3 and -CH2- groups by factors of 0.95 and 0.85, respectively, relative to the Lorentz-Berthelot value, was found to minimize error in pressure-composition phase diagrams. These scaling parameters gave excellent agreement with experimental phase diagrams for mixtures of N2 with ethane, propane, or n-dodecane over a range of state points. For ethane/N2 and n-decane/N2 mixtures, trends in surface tension as a function of temperature and pressure are correctly reproduced, although the simulated values are slightly too high compared to experimental values. To assess how the accuracy of hydrocarbon-N2 interaction strength impacts interfacial property predictions, we have compared density profiles and surface tension using several different scaling factors. Using the Lorentz-Berthelot combining rules rather than optimized parameters gave the same qualitative trends, although some quantitative results, such as liquid-phase N2 mole fraction, were found to differ by a factor of ∼1.5. Using the optimized interaction parameters, interfacial behavior was examined by calculating density and free energy profiles. Nitrogen molecules preferentially adsorb at the interfacial region between the liquid and vapor phases. This interfacial adsorption becomes less energetically favorable as either the temperature, pressure, or length of the alkane chain increases.

Atomistic simulation framework for molten salt vapor-liquid equilibrium prediction and its application to NaCl.

Knowledge of the vapor-liquid equilibrium (VLE) properties of molten salts is important in the design of thermal energy storage systems for solar power and nuclear energy production applications. The high temperatures involved make their experimental determination problematic, and the development of both macroscopic thermodynamic correlations and predictive molecular-based methodologies are complicated by the requirement to appropriately incorporate the chemically reacting vapor-phase species. We derive a general thermodynamic-based atomistic simulation framework for molten salt VLE prediction and show its application to NaCl. Its input quantities are temperature-dependent ideal-gas free energy data for the vapor phase reactions and density and residual chemical potential data for the liquid. If these are not available experimentally, the former may be predicted using standard electronic structure software, and the latter may be predicted by means of classical atomistic simulation methodology. The framework predicts the temperature dependence of vapor pressure, coexisting phase densities, vapor phase composition, and vaporization enthalpy. It also predicts the concentrations of vapor phase species present in minor amounts (such as the free ions), quantities that are extremely difficult to measure experimentally. We furthermore use the results to obtain an approximation to the complete VLE binodal dome and the critical properties. We verify the framework for molten NaCl, for which experimentally based density and chemical potential data are available in the literature. We then apply it to the analysis of NaCl simulation data for two commonly used atomistic force fields. The framework can be readily extended to molten salt mixtures and to ionic liquids.

Vapor-liquid equilibrium (VLE) prediction for dimethyl ether (DME) and water system in DME injection process with Peng-Robinson equation of state and composition dependent binary interaction coefficient

Dimethyl ether (DME) is arousing attention as a novel water-soluble additive in oil industry. The accurate prediction of phase behavior of DME and water system is crucial important for DME-based research. An equation of state has been a powerful tool for solving phase equilibrium problem, which is based on an ideal molecular force model with binary interaction coefficients reflecting the deviation of a non-ideal system. However, the current knowledge of interaction coefficient is limited by obtaining from backward by using phase equilibrium data. This leads to the unclear meaning of the interaction coefficients, insufficient response to the molecular force interaction relationship at the molecular level and no ability to predict phase equilibrium properties without primary use of experimental data. To overcome this, in this study a correction by combining an activity coefficient and a linear solvation energy relationship (LSER) has been proposed to address the solubility deviation from an idealized model. This deviation at the micro level indicates the deviation of nonideal molecular forces from the ideal Raoult's law. Based on this novel correction, binary interaction coefficients have been obtained with a more practical molecular interaction relationship, which leads to more consistent results with experimental data from the literature. Moreover, in asymmetric phase systems, concentration-dependent binary interaction coefficients have been proposed based on previous discussion to represent intermolecular forces in non-ideal phase systems. Furthermore, partitioning coefficients, which lead to a potential criterion for solvent selection for heavy oil recovery, have been discussed from the perspective of intermolecular forces. This study provides new insights into non-ideal phase behavior. By combining a LSER and activity coefficients, a quantitative analysis on non-ideal molecular behavior and related complex phase problems becomes possible.

Sensitivity of the Non-Equilibrium Approach for Mixture Condensation to Heat and Mass Transfer Correlations and Thermophysical Properties

Abstract The prediction of mixture condensation is still complex due to the coupled heat and mass transfer and insufficient data of thermophysical mixture properties. This article analyzes the impact of various heat and mass transfer correlations on the non-equilibrium approach for mixture condensation in a vertical plain tube. Furthermore, the influence of thermophysical properties from different databases is investigated. The results are shown for ethanol-water, but allow conclusions to other fluid mixtures. They indicate that the liquid heat transfer coefficient in the non-equilibrium approach dominates the qualitative behavior of the condensation process, but the vapor mass transfer coefficient can only decrease or increase the quantitative level of the effective heat transfer with minor impact. More importantly, the logarithm in the vapor mass transfer term is central for the prediction of the condensation heat transfer. As this logarithm contains vapor-liquid equilibrium (VLE) data, it proves that there is a strong connection between VLE and overall prediction of mixture condensation. A demonstration of available data for thermophysical mixture properties of ethanol-water shows significant deviations, which affect the calculations as well. Besides, data from our own experiments are presented for mixture viscosity of ethanol-water. It is recommended to focus not only on improved heat and mass transfer correlations but also on thermophysical properties and VLE data for a precise prediction of mixture condensation.

A comparative study of thermodynamic models to describe the VLE of the ternary electrolytic mixture H2O–NH3–CO2

Abstract This study aims to ascertain the influence of the activity coefficient model and equation of state for predicting the vapor–liquid equilibrium (VLE) of the multi-electrolytic system H2O–NH3–CO2. The non-idealities of the liquid phase are described by the eUNIQUAC and eNRTL models. The vapor phase is modeled with the Nakamura equation, which is compared with the ideal gas assumption. The models are validated with experimental data from literature on total pressure and ammonia partial pressure. Results show that the models UNIQUAC and NRTL without dissociation can only reproduce the experimental conditions in the absence of CO2. When the electrolytic term is considered, the eUNIQUAC model is able to reproduce the experimental data with greater accuracy than the eNRTL. The equation of state which describes the vapor phase plays no major role in the accuracy of the VLE prediction in the operational conditions evaluated here. Indeed, the accuracy relies on the activity coefficient, therefore the ideal gas equation can be considered if the non-idealities of the liquid phase are described by a well-tuned model. These findings could be useful for equipment design, flowsheet simulations and large-scale simultaneous optimization problems.

Extractive distillation of the benzene and acetonitrile mixture using an ionic liquid as the entrainer

The benzene and acetonitrile azeotropic mixture was proposed to be separated by extractive distillation using an ionic liquid (IL) as the entrainer. The suitable IL was selected by the COSMO-RS model, and 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF4]) was considered as the suitable entrainer mainly due to its high selectivity, low viscosity, and low price. The experimental vapor pressure data of the IL-containing systems (benzene + [EMIM][BF4] and acetonitrile + [EMIM][BF4]) were measured in the full concentration range. The results show that acetonitrile has a stronger interaction with IL than benzene, and the low deviations between the experimental and UNIFAC predicted values show the reliability of the UNFIAC model. The UNIFAC predicted vapor–liquid equilibrium data of the benzene + acetonitrile + dimethyl sulfoxide (DMSO)/[EMIM][BF4] system show that the relative volatility of benzene to acetonitrile is higher when the entrainer is [EMIM][BF4]. The process simulation results show that [EMIM][BF4] can reduce the material and energy consumptions compared with DMSO.

An improved dispersive contribution for the COSMO-SAC-Phi equation of state

In this work, the COSMO-SAC-Phi equation of state [Fluid Phase Equilib. 488 (2019) 13–26] is refined by the introduction of a new equation to describe dispersive effects. The proposed modification is inspired by the well-known rules of consistency for α-functions, used in cubic equations of state. The results for 38 representative compounds have shown that the proposed modification is able to improve the correlation of pure compound experimental data of saturation pressures and saturated liquid volume, with average deviations of 0.96% and 0.73%, respectively. Densities of pure compounds under conditions beyond the saturation region were also well predicted. Vapor-liquid equilibrium predictions of binary mixtures demonstrated, for most cases, that the modified equation was superior to the original COSMO-SAC-Phi model, PSRK, and Soave-Redlich-Kwong with the classical van der Waals mixing rule. The modified model was also able to produce very good predictions for liquid-liquid equilibrium, being similar to UNIFAC-LLE at low temperatures, but exhibiting a much better performance at higher temperatures (and pressures).