Liquid Equilibrium Properties Research Articles

A new method to combine high-pressure vapor–liquid equilibrium and thermophysical property measurements for low-volatility liquids and a gas

Vapor-liquid equilibria measurements involving liquids with low volatility, such as many types of lubricants, ionic liquids, and various solvents are essential for process research and development in a wide variety of fields. State–of–the–art methods to measure these phase equilibria, e.g. thermogravimetric analysis or equilibrium cells, generally cannot be combined with instruments measuring thermophysical properties, e.g. density, transport properties, spectroscopic properties, etc. A novel approach was developed to measure simultaneously vapor–liquid equilibrium and thermophysical properties involving a single gas dissolved in one or more low-volatility liquids. The method is based upon a mass balance measuring liquid phase density, total masses in the system, and volumes. The governing equations of the novel approach are derived, and a detailed uncertainty analysis is presented. As an example, the solubility, density, and viscosity are measured with the new apparatus for a system of a non-volatile ionic liquid solvent saturated with the compressed hydrofluorocarbon gas, pentafluoroethane (R-125), at 25 °C and 75 °C and pressures to ∼ 3.1 MPa. The solubility data are validated by comparison to previously published literature data using a high precision gravimetric microbalance. The combination of vapor–liquid equilibria and thermophysical properties in a single experiment can significantly accelerate scientific and engineering studies.

Modelling the thermodynamic properties of the mixture of water and polyethylene glycol (PEG) with the SAFT-[formula omitted] Mie group-contribution approach

The SAFT-γ Mie group-contribution (GC) equation of state (EoS) is employed to describe the thermodynamic properties of aqueous mixtures of polyethylene glycol (PEG), a polyether of great industrial and scientific interest. This prototypical system is chosen due to the intrinsic complexity of hydrogen-bonding polymers, and represents a critical test of the theory. Water is modelled as a single Mie segment with four association sites and PEG as a linear heteronuclear chain of three types of segments: the associating hydroxymethyl end group (CH2OH); the associating oxygen (cO); and the modified methylene group (CH2OE), which incorporates the effects that the proximity of an electronegative atom has on the electronic environment of the methylene group. The SAFT-γ Mie model parameters characterizing the newly-defined group interactions are estimated to reproduce the liquid–liquid equilibrium (LLE) closed-loop miscibility gaps observed in the orthobaric phase diagram of PEG + water mixtures. The resulting model allows one to predict miscibility gaps in a temperature range between 350 K and 600 K, capturing both the UCST and the LCST within a 2% error with a close description of the overall phase behaviour. The predictive capability of the model is assessed by comparing the calculations with the experimental density of pure PEG, the enthalpy of mixing, and vapour–liquid equilibrium properties of PEG + water mixtures, with a good overall agreement. By coupling the present SAFT model with a recent thermodynamic model describing solubility in semi-crystalline polymers, the solubility of water in PEG below its melting point is semi-quantitatively captured both in the low- and high-humidity regimes. In particular, deliquescence – the melting of semi-crystalline PEG at high relative humidity – is predicted by simply accounting for the melting enthalpy of PEG crystals.

Vapor-liquid equilibrium measurement and heating performance modeling on eco-friendly zeotropic blends of CO2/R1234ze(Z) and CO2/R1336mzz(E)

In the context of sustainable development, CO2 and hydrofluoroolefins (HFOs) are regarded as promising refrigerant candidates. Despite recognition of application potential, the knowledge of their blends is insufficient. In this paper, vapor–liquid equilibrium (VLE) properties of two eco-friendly zeotropic CO2/HFO blends, namely CO2/R1234ze(Z) and CO2/R1336mzz(E), were measured at temperature from 253.15 K to 333.15 K at CO2 concentration from 0 to 1. Peng-Robinson (PR) model and Soave-Redlich-Kwong (SRK) model are identified as suitable models for describing VLE of CO2/HFO with deviation less than 4.5%, whereas Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) model is shown to have larger deviation. Furthermore, a heat pump water heater is modelled to demonstrate the working potential of CO2/HFO in terms of thermodynamics and safety, while the newly fitted binary interaction parameter kij being used. Both CO2/R1234ze(Z) and CO2/R1336mzz(E) show more than 150% advantage in volumetric heating capacity and comparable heating efficiency compared to R134a. The optimal concentration of CO2 is higher than 0.6, eliminating the flammability of mixture. Additionally, the operating pressures of CO2/HFO are reduced to lower than 3.2 MPa at typical working condition due to HFO addition. The results contribute to the accurate VLE description of CO2/HFO and further investigation on the applications of eco-friendly refrigerants.

Critical temperature shift modeling of confined fluids using pore-size-dependent energy parameter of potential function

The behavior and critical properties of fluids confined in nanoscale porous media differ from those of bulk fluids. This is well known as critical shift phenomenon or pore proximity effect among researchers. Fundamentals of critical shift modeling commenced with developing equations of state (EOS) based on the Lennard–Jones (L–J) potential function. Although these methods have provided somewhat passable predictions of pore critical properties, none represented a breakthrough in basic modeling. In this study, a cubic EOS is derived in the presence of adsorption for Kihara fluids, whose attractive term is a function of temperature. Accordingly, the critical temperature shift is modeled, and a new adjustment method is established in which, despite previous works, the bulk critical conditions of fluids are reliably met with a thermodynamic basis and not based on simplistic manipulations. Then, based on the fact that the macroscopic and microscopic theories of corresponding states are related, an innovative idea is developed in which the energy parameter of the potential function varies with regard to changes in pore size, and is not taken as a constant. Based on 94 available data points of critical shift reports, it is observed that despite L–J, the Kihara potential has sufficient flexibility to properly fit the variable energy parameters, and provide valid predictions of phase behavior and critical properties of fluids. Finally, the application of the proposed model is examined by predicting the vapor–liquid equilibrium properties of a ternary system that reduced the error of the L–J model by more than 6%.

Phase equilibria and interface properties of hydrocarbon propellant–oxygen mixtures in the transcritical regime

Vapor–liquid equilibria and fluid interface properties of binary mixtures containing either methane or cyclohexane representing fuel and nitrogen or oxygen are reported. The mixtures are studied at different temperatures and pressures, which are chosen such that the temperature of the fuel component is subcritical, while that of the gaseous component is mainly supercritical. Data are obtained from molecular dynamics (MD) simulation, as well as density functional theory and density gradient theory in combination with the PC-SAFT equation of state (EOS). The studied interface properties include surface tension, interface thickness, enrichment, and relative adsorption. Furthermore, bulk vapor–liquid equilibrium properties are computed with two distinct MD methods as well as the PC-SAFT EOS. All approaches are compared to data from highly accurate empirical EOS. Despite the fundamental differences between these methods, very good agreement between the results of MD, density functional theory, and density gradient theory and EOS data is observed for the phase equilibria and interface properties, reinforcing the present predictions. It is found that the equivalence of nitrogen to oxygen is rather limited, in particular for the methane propellant. The disparities are particularly pronounced for low temperatures, where the compositions of the bulk phases differ significantly. As a result, enthalpy of vaporization as well as surface tension attains much higher values for mixtures containing oxygen.

Study of the Liquid–Liquid Equilibrium and Extraction Properties of Deep Eutectic Solvents Based on Choline Chloride for the Separation of the Ethanol–Ethyl Formate System for Potential Use in Biofuel Production

Study of the Liquid–Liquid Equilibrium and Extraction Properties of Deep Eutectic Solvents Based on Choline Chloride for the Separation of the Ethanol–Ethyl Formate System for Potential Use in Biofuel Production

The viscosity of liquid ethene: Measurement and molecular dynamic simulation

This work reports new experimental data and detailed equilibrium molecular dynamics (EMD) simulations of viscosity for liquid ethene. The measurements were carried out by using an improved vibrating-wire viscometer for temperatures from (173.150 to 233.150) K and pressures up to 5.5 MPa, with a combined expanded relative uncertainty of 5.3 % (k = 2). The experimental data were compared with the values calculated by the correlation of Holland et al. (with an uncertainty of 10 % for liquid), the deviations vary from − 7.2 % to 0.8 % and the AARD is 3.6 %. Furthermore, the Assael and Dymond scheme based on the hard-sphere model was used to correlate the experimental results with an AARD of 0.1 %. For understanding the structure and properties of liquid ethene at the molecular level, a comprehensive evaluation of ten different ethene force fields with four types of molecular configurations (two-site, three-site, four-site, and six-site models) was then performed to predict density and viscosity at a wide temperature range from (133.150 to 233.150) K and pressure of 5 MPa. The selected force fields were generally developed for the vapor–liquid equilibrium properties, without explicit consideration of viscosity and other transport properties. Overall, three rigid two-site force fields (SET, TraPPE-UA, and AUA4) gave the best predictions with the AARD within 0.32 % for density and 8.5 % for viscosity comparing with the correlations of Smukala et al. and Holland et al., separately. Mie force field with 16–6 potential and TraPPE-UA2 force field with two negative partial charges can accurately predict density but severely overestimate viscosity greater than 20 %. The larger intermolecular repulsion and electrostatic interaction may have contributed to the overestimation of viscosity especially at low temperatures.

Study on vapor-liquid equilibrium and microscopic properties of DL-proline, L-glutamic acid, and L-serine aqueous solutions.

The vapor–liquid equilibrium (VLE) in aqueous amino acid solutions is essential in chemical production, such as purification, isolation, or crystallization of amino acid intermediates. In this work, VLE of DL-proline, L-glutamic acid, and L-serine aqueous solutions was measured at pressures ranging from 4.82 to 102.58 kPa. The developed model was successfully applied to correlate experimental data with temperatures in the range of 298.15–382.75 K. Model parameters (h, , , , and ) were given. Moreover, the amino acid aqueous solution was investigated by Fourier transform infrared spectroscopy (FTIR). By analyzing infrared spectra, the strength of intermolecular interactions was obtained, and the structure–activity relationship between the microscopic interactions and the VLE was established.

Mechanism analysis of solvent selectivity and energy-saving optimization in vapor recompression-assisted extractive distillation for separation of binary azeotrope

Octane and p-xylene are common components in crude gasoline, so their separation process is very important in petroleum industry. The azeotrope and near azeotrope are often separated by extractive distillation in industry, which can realize the recovery and utilization of resources. In this work, the vapor–liquid equilibrium experiment was used to obtain the vapor–liquid equilibrium properties of the difficult separation system, and on this basis, the solvent extraction mechanism was studied. The mechanism of solvent separation plays a guiding role in selecting suitable solvents for industrial separation. The interaction energy, bond length and charge density distribution of p-xylene with solvent are calculated by quantum chemistry method. The quantum chemistry calculation results and experiment results showed that N-formylmorpholine is the best solvent among the alternative solvents in the work. This work provides an effective and complete solvent screening process from phase equilibrium experiments to quantum chemical calculation. An extractive distillation simulation process with N-formylmorpholine as solvent is designed to separate octane and p-xylene. In addition, the feasibility and effectiveness of the intensified vapor recompression assisted extraction distillation are also discussed. In the extractive distillation process, the vapor recompression-assisted extraction distillation process is globally optimal. Compared with basic process, the total annual cost can be reduced by 43.2%. This study provides theoretical guidance for extractive distillation separation technology and solvent selection.

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.

1-Bromopropane Capture with Hydrophobic Zeolites: Force Field Development and Molecular Simulations

1-Bromopropane is a solvent used in various industrial and commercial applications. United States Environmental Protection Agency recently concluded that 1-bromopropane posed unreasonable risks to human health in several conditions of use. In this work, the adsorption of 1-bromopropane vapors in zeolites was investigated using molecular simulations. First, a united-atom model of 1-bromopropane was developed and the model was validated to reproduce vapor–liquid equilibrium properties of 1-bromopropane by carrying out Gibbs ensemble Monte Carlo simulations. The new model was then used to investigate the capture of 1-bromopropane in hydrophobic zeolites with Monte Carlo simulations in the grand canonical ensemble. The results show that a filtering system that consists of MRE and STW zeolites can capture 1-bromopropane within its ambient concentration range that occurs as a result of 1-bromopropane release in various industrial and commercial applications as identified by the US EPA. While MRE zeolite has the optimal pore size that provides favorable host–guest interactions to capture 1-bromopropane at extremely low concentrations, rapid condensation of 1-bromopropane occurs at relatively higher concentrations in the intersections of narrow helical and straight pores in the STW zeolite.

Transferability of data-driven, many-body models for CO2 simulations in the vapor and liquid phases.

Extending on the previous work by Riera et al. [J. Chem. Theory Comput. 16, 2246-2257 (2020)], we introduce a second generation family of data-driven many-body MB-nrg models for CO2 and systematically assess how the strength and anisotropy of the CO2-CO2 interactions affect the models' ability to predict vapor, liquid, and vapor-liquid equilibrium properties. Building upon the many-body expansion formalism, we construct a series of MB-nrg models by fitting one-body and two-body reference energies calculated at the coupled cluster level of theory for large monomer and dimer training sets. Advancing from the first generation models, we employ the charge model 5 scheme to determine the atomic charges and systematically scale the two-body energies to obtain more accurate descriptions of vapor, liquid, and vapor-liquid equilibrium properties. Challenges in model construction arise due to the anisotropic nature and small magnitude of the interaction energies in CO2, calling for the necessity of highly accurate descriptions of the multidimensional energy landscape of liquid CO2. These findings emphasize the key role played by the training set quality in the development of transferable, data-driven models, which, accurately representing high-dimensional many-body effects, can enable predictive computer simulations of molecular fluids across the entire phase diagram.

Measurements and modeling of the vapor–liquid equilibrium properties of low-global-warming-potential refrigerant R32/R1234yf/R1123 ternary mixtures

There is an urgent need to replace existing refrigerants that have significant greenhouse effects with next-generation, low-global-warming-potential refrigerants. Various multi-component refrigerant mixtures are potential candidates to reduce the flammability and/or toxicity and improve the compatibility with lubricating oils while preserving the refrigerant performance. In this study, for R1123/R1234yf/R32 ternary mixtures, we performed two types of accurate measurements of the vapor–liquid equilibrium properties and attempted to verify the reliability of two types of thermodynamic property models. Measurements were conducted at temperatures from 303.15 to 328.15 K and at saturation pressures of up to 3.7 MPa. The expanded uncertainties (k = 2) of the temperature, pressure, and composition measurements were estimated to be less than 0.03 K, 1.4 kPa, and 0.43 mol%, respectively. Two of the models used were the well-known and well-established Helmholtz free energy equations of state. We used these equations of state to predict the vapor–liquid equilibrium data of the ternary mixtures. The predicted values and measured results of the ternary mixtures were systematically compared, and the most reliable numerical values of the vapor–liquid equilibrium properties for these ternary mixtures and the necessity for improvement of the recent models were clarified.

Solubility determination and prediction for FOX-7 in three binary solvents at different temperatures

ABSTRACT The solid–liquid equilibrium and thermodynamic properties of FOX-7 in three binary mixed solvents (N-methyl pyrrolidone-water, N,N-dimethylacetamide-water and 1,4-Butyrolactone-water) are studied by focused beam reflectance measurement (FBRM) dynamic detection method and the solubility is predicted by conductor-like screening model for real solvents (COSMO-RS) under atmospheric pressure from 298.15 to 343.15 K. The results show that the solubility of FOX-7 increase with the increasing temperature and the mole fraction of N-methyl pyrrolidone, N,N-dimethylacetamide and 1,4-Butyrolactone. The solubility data can be well correlated by Apelblat, van’t Hoff and Yaws equation. The data of hybrid thermodynamic parameters (including the hybrid enthalpy, entropy, and Gibbs energy) show that the dissolution process is endothermic, non-spontaneous and enthalpy driven. In addition, COSMO-RS can accurately predict the increasing trend of solubility with increasing of temperature and mole fraction of solvent. However, the COSMO-RS overestimates solubility in three binary solvents except for x NMP = 0.1575, the average mean squared quadratic error becomes larger with an increasing mole fraction of water. Solubility data and thermodynamic parameters can lay a foundation for the crystallization and spheroidization modification of FOX-7.

Molecular dynamics of liquid-liquid equilibrium and interfacial properties of aqueous solutions of methyl esters.

In this work, the liquid-liquid phase equilibria and interfacial properties of methyl ester + water binary mixtures are determined at atmospheric pressure and from 278 to 358 K combining the direct coexistence technique and molecular dynamics simulations. Methyl esters are modelled using new parametrizations based on the united atom TraPPE model force field proposed recently by us [E. Feria, J. Algaba, J. M. Míguez, A. Mejía, P. Gómez-Álvarez and F. J. Blas, Phys. Chem. Chem. Phys., 2019, 22, 4974-4983] that are able to predict the vapour-liquid interfacial properties of pure methyl esters with high accuracy. In the case of water, we consider the well-known TIP4P/2005 model, the most popular rigid and non-polarizable model to describe the interfacial properties of pure water. The simulations are performed using the direct coexistence technique in the isothermal-isobaric or NPzT ensemble in combination with molecular dynamics. We obtain density profiles, temperature-densities and temperature-composition projections of the phase diagrams, and interfacial tensions. The liquid-liquid interfacial tension is calculated from the normal and tangential components of the pressure tensor according to the mechanical virial route. We pay attention particularly to the ability of the molecular models in predicting the experimental behavior of the systems. Simulation results are able to account for the liquid-liquid phase equilibria of these binary mixtures, in good agreement with the experimental data taken from the literature. Unfortunately, experimental values for interfacial tensions are substantially overestimated by predictions from computer simulations in all cases. To our knowledge, this is the first time that the liquid-liquid phase equilibrium and interfacial properties of methyl ester + water mixtures have been predicted from computer simulations.

Use of 300,000 pseudo‐experimental data over 1800 pure fluids to assess the performance of four cubic equations of state: SRK, PR, tc‐RK, and tc‐PR

AbstractThe guidelines to constitute a database containing, for 1800 pure fluids, more than 300,000 pseudo‐experimental vapor pressure, liquid density, enthalpy of vaporization, and liquid heat capacity data are described. Such a database provides a tool for a fair assessment of the performances of equations of state to correlate (or predict) the properties of pure components. In this paper, we use it to assess the performance of four cubic equations of state (CEoSs): original Soave–Redlich–Kwong (SRK), original Peng–Robinson (PR), and the translated‐consistent versions of PR (tc‐PR) and RK (tc‐RK). The deviations between calculated and experimental data are compared for the four CEoSs, which make it possible to discuss the influence of the α‐function on the calculated vapor–liquid equilibrium properties and how the volume translation impacts the calculated volumetric properties. Eventually, the 1800 pure components are divided into 1252 non‐self‐associating and 548 self‐associating compounds, and the accuracy of the CEoSs depending on the associating character of the molecules is discussed.

Solid–Liquid Equilibrium and Thermodynamic Properties of 6-Bromo-2-chloro-8-cyclopentyl-5-methylpyrido[2,3]pyrimidin-7(8H)-one in 10 Pure Solvents and 3 Different Miscible Systems at T = (278.15–323.15) K

Solid–Liquid Equilibrium and Thermodynamic Properties of 6-Bromo-2-chloro-8-cyclopentyl-5-methylpyrido[2,3]pyrimidin-7(8<i>H</i>)-one in 10 Pure Solvents and 3 Different Miscible Systems at <i>T</i> = (278.15–323.15) K

Measurement of the vapour–liquid equilibrium properties of binary mixtures of the low-GWP refrigerants R1123 and R1234yf

The vapour–liquid equilibrium properties of binary mixtures of R1123 and R1234yf, which are key components of the next generation of refrigerant mixtures, were measured using a recirculation-type vapour–liquid equilibrium property measurement apparatus. Two sets of measurements were conducted by two different technicians (co-authors Nishida and Saito) using the same apparatus and sample. The first set of measurements were conducted at temperatures that were close to the integer values in absolute temperature, whereas the second set of measurements was taken at temperatures that were close to the integer values in terms of degrees Celsius. Both sets of measurements were based on the ITS-90 temperature scale and were found to be in good agreement at the measurement temperatures (300 and 330 K). These data were compared with the predictions of a Helmholtz-type equation of state, and a systematic deviation of approximately 8% was observed at low temperatures. A regression analysis using the binary interaction parameter kij of the modified Peng–Robinson equation of state more accurately reproduced the experimental measurements.

Impact of solvent properties on post-combustion carbon capture processes: A vapor–liquid equilibrium modelling approach

This paper deals with the effect of solvent vapor liquid equilibrium (VLE) properties on the heat duty in a post-combustion CO2 capture process. The conceptual solvent properties include the absorption heat, absorption performance and cyclic capacity, modeled by a three-parameter VLE equation. There are four processes considered. A conventional process serves as a reference case. An ideal process is used to study the energy saving potential. As typical process improvements, an intercooling and a rich split process are used to analyze the heat duty reduction effect. The optimal solvent in each process is obtained by minimizing the total heat duty. By the sensitive analysis, the solvent with less favorable VLE properties owns a larger energy saving potential and energy saving effect. Results show that the rich split is a more energy-efficient process improvement method than the intercooling configuration for the typical amine solvents.

Generalized equation of state for fluids: From molecular liquids to colloidal dispersions

In this work, a new parameterization for the Statistical Association Fluid Theory for potentials of Variable Range (SAFT-VR) is coupled to the discrete potential theory to represent the thermodynamic properties of several fluids, ranging from molecular liquids to colloidal-like dispersions. In this way, this version of the SAFT-VR approach can be straightforwardly applied to any kind of either simple or complex fluid. In particular, two interaction potentials, namely, the Lennard-Jones and the hard-core attractive Yukawa potentials, are discretized to study the vapor-liquid equilibrium properties of both molecular and complex liquids, respectively. Our results are assessed with Monte Carlo computer simulations and available and accurate theoretical results based on the self-consistent Ornstein-Zernike approximation.