Vapor-liquid Equilibrium Research Articles

Vapor-liquid phase equilibria behavior prediction of binary mixtures using machine learning

Basic thermodynamic data plays an important role in chemical applications. However, the traditional acquisition of thermodynamic data through experiments is laborious. Thermodynamic data prediction is considered as an alternative to the experiments, especially when qualitative analysis is needed prior to experimental studies. In this work, we report a successful machine-learning based approach to predict the fundamental thermodynamics characteristics of vapor–liquid equilibrium (VLE). A new dataset of the VLE experimental data of 210 binary mixtures with screened descriptors was constructed. The obtained results show that the VLE characteristics of the target system can be fully revealed by machine learning methods and random forest has more excellent predictive ability on the VLE behavior than the neural network. This work provides a new approach to the prediction of VLE data and useful information for the mechanistic study on the VLE phenomenon.

Nucleation of a Vapor Phase and Vapor Front Dynamics Due to Boiling-Up on a Solid Surface

The effect of temperature and pressure on the nucleation of the vapor phase and the velocity of the vapor front in the initial stage of activated boiling-up of n-pentane on the surface of a quartz fiber was studied. Using a developed approach combining the “pump-probe” and laser Doppler velocimetry methods, this velocity was tracked in the course of sequential change in the degree of superheating with respect to the liquid–vapor equilibrium line. The studied interval according to the degree of superheating was 40–100 °C (at atmospheric pressure). In order to spatiotemporally localize the process, the activation of boiling-up at the end of the light guide was applied using a short nanosecond laser pulse. A spatial locality of measurements was achieved in units of micrometers, along with a time localization at the level of nanoseconds. An increase in temperature at a given pressure was found to lead to an increase in the speed of the transition process with a coefficient of about 0.2 m/s per degree, while an increase in pressure at a given temperature leads to a decrease in the transition process speed with a coefficient of 25.8 m/s per megapascal. The advancement of the vapor front velocity measurements to sub-microsecond intervals from the first signs of boiling-up did not confirm the existence of a Rayleigh expansion stage with a constant velocity.

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

A Numerical Study of Vapor–Liquid Equilibrium in Binary Refrigerant Mixtures Based on 2,3,3,3-Tetrafluoroprop-1-ene

The binary refrigerant mixtures containing 2,3,3,3-Tetrafluoroprop-1-ene are considered as excellent substitutes for traditional refrigerants. Weak hydrogen bonds exist in hydrofluorocarbons and hydrofluoroolefins. However, for several recently published binary refrigerant mixtures, there is no Vapor–Liquid Equilibrium calculation study considering hydrogen-bonding associations. This work presents a calculation work of the saturated properties of nine pure refrigerants using the Cubic-Plus-Association Equation of State, considering the hydrogen-bonding association in refrigerant fluids. The average relative deviations of the saturated vapor pressure, liquid, and vapor density are less than 1.0%, 1.5%, and 3.5%, respectively. The Vapor–Liquid Equilibrium of ten binary refrigerant mixtures containing 2,3,3,3-Tetrafluoroprop-1-ene is also calculated using the Cubic-Plus-Association Equation of State with the van der Waals mixing rule. The average relative deviations of the liquid-phase and vapor-phase mole fractions are less than 1.0% and 2.0%, respectively. Moreover, the Vapor–Liquid Equilibrium data and the model’s adaptability are analyzed and discussed.

Implementation of PC-SAFT for Predicting thermodynamic properties of pure refrigerants and vapor-liquid equilibria of refrigerants binary mixtures.

A new approach to evaluate PC-SAFT molecular parameters based on pure components critical properties was proposed in our previous paper. In this study, the performance of the proposed approach is verified through its application to the calculation of vapor pressure, saturated density, saturated enthalpy, heat of vaporization, isobaric heat capacity, and speed of sound for propane, butane, isobutane, R22, R23, R32, R116, R125, R134a, R143a, and R1234yf. In general, the results have shown that the new approach is better than the existing one when applied in predicting second-order thermodynamic derivative properties, and it has much less overall percent average absolute deviations than the existing method. However, the main limitation on the accuracy is that underestimated liquid densities. The PC-SAFT is also applied to predict vapor-liquid equilibria of eleven binary refrigerant mixtures, including R23 – R22, R23 – R134a, R23 – R143a, R23 – R227ea, R32 –Isobutane, R32 – Propane, R116 – Butane, R116 – 134a, R116 – R143a, R125 – R1234yf, and Propane – R227ea. The obtained results show that the new approach provides very good predictions of the vapor-liquid equilibria and the critical properties of mixtures, while the existing approach tends to overestimate these quantities.

Systematic evaluation of parameterization approaches for the ePPC-SAFT model for aqueous alkali halide solutions. II. Alkali bromides, iodides, fluorides, and lithium halides

In this work, state-of-the-art ion-specific parameter sets for the ePPC-SAFT model are obtained for 15 aqueous alkali halide solutions based on extensively collected and critically evaluated databases. The association approach, which has been proven the best for accounting for the short-range interactions, is here extended to all the alkali halides. Efforts are made to improve modeling accuracy. The impact of anion association site number on modeling accuracy is investigated. Recommended parameter sets are presented. Only 7 adjustable parameters altogether are needed for the 4 salts with the same anion, e.g., NaBr, KBr, RbBr, and CsBr. It is found that Li+-water dispersion needs to be accounted for to reach the same accuracy for Li+ salts as for the other salts. Thus, 7 parameters altogether are needed for LiCl, LiBr, and LiI. The obtained model and parameter sets are very accurate for correlating the properties included in the regression, mean-ionic activity coefficient, vapor-liquid equilibria, and density, and for predicting the osmotic coefficient. In all cases, maximum deviations are within a few percent. The contributions of the model terms are analyzed.

Vapor-liquid equilibria behavior of binary and ternary polymer-polymer alcoholic solutions

Aiming at scrutinizing the soluting effect occurring in alcoholic systems composed of two polymers (polymer 1 + polymer 2 + alcohol systems), the systematic isopiestic measurements of the vapor-liquid equilibrium behavior were carried out on some ternary ethanolic, propanolic, and butanolic solutions of two polymers at 298.1 K. In order to cover a wide range of hydrophilic and lipophilic behaviors, the polymers: polyethylene glycol 400 (PEG400), polyethylene glycol dimethyl ether 250 (PEGDME250), polyethylene glycol dimethyl ether 500 (PEGDME500), polypropylene glycol 400 (PPG400), polypropylene glycol 1000 (PPG1000) and polyvinylpyrrolidone 10000 (PVP10000) were selected. Deviations of iso-solvent activity lines from the linear isopiestic relation (LIR) were considered as a benchmark to identify the soluting effects of polymer 1 on polymer 2 in these systems. It was found that all the investigated solutions containing PVP show the soluting-in effect (positive deviation from the linear isopiestic relation), and the other solutions including PEG-PPG, PEG-PEGDME, PPG-PEGDME, PEG-PEG, PPG-PPG and PEGDME-PEGDME show the semi-ideal (linear isopiestic relation) behavior. The effect of alcohol type, polymer type, and polymer molar mass on the solvent activity of binary alcohol-polymer solutions as well as on the deviations of ternary systems from the semi-ideal behavior was studied. Finally, the obtained solvent activity data were used to calculate the vapor pressure of solutions as a function of concentration, and the segment-based local composition Wilson model was used to correlate the experimental solvent activity data.

High-pressure vapor-liquid equilibrium of hydrogen and diesel components: Maximum likelihood implicit estimation of equation-of-state binary parameters

Due to increasing environmental requirements and efforts to improve fuel quality, hydro-processing has attained worldwide importance as a critical oil refining operation. Hydro-processing involve hydrogenation of oil fractions and subsequent separations at high-temperature, high-pressure and high hydrogen fugacity. Thus, effective thermodynamic modeling of hydro-processing systems allows accurate vapor and liquid property calculation to solve mass-energy hydro-processing balances. In this work, experimental data of high-pressure vapor-liquid equilibrium of binary systems consisting of hydrogen and Diesel hydrocarbons were compiled and used to statistically calibrate classical cubic equations-of-state and variants with different alpha functions. To accomplish this, the Maximum Likelihood Principle was used to conduct the implicit estimation of binary interaction parameters of hydrogen and each one of 22 hydrocarbons (paraffin, naphthenic and aromatic hydrocarbons) typical of Diesel fractions. Several statistical estimators were used to evaluate the estimated parameters as well as to test the insertion of a second binary interaction parameter or temperature dependence. In general, the FT Equation-of-State – i.e., the Peng-Robinson Equation-of-State using Fu & Tan alpha function for hydrogen – attained the best adherence to data and this adherence is improved by using two binary interaction parameters per pair or imposing temperature-dependence on the binary interaction parameter.

Research on the thermodynamic properties of binary mixtures containing R1234ze(E) based on Helmholtz model

R1234ze(E) has excellent environmental protection properties, but the unsatisfactory latent heat of vaporization and volumetric cooling capacity impede its application. A mixture with excellent thermophysical properties and environmental performance can be obtained through blending R1234ze(E) with other working fluids. In this paper, the vapor-liquid equilibrium data of R1234ze(E)/R32, R1234ze(E)/R152a, R1234ze(E)/R290, and R1234ze(E)/R161 were correlated by Helmholtz equation of state combined with the mixing rule, and the calculation model of thermodynamic properties was established. On this basis, temperature glides, latent heats of vaporization, saturated vapor pressures, and other thermodynamic properties of binary mixtures containing R1234ze(E) were calculated and compared. The results indicate that the standard boiling points and critical temperatures of the four binary mixtures containing R1234ze(E) were similar to those of R22 in most mass concentration ranges. And their saturated vapor pressures at 298.15 K were all lower than that of R22 except for R1234ze(E)/R32 mixed in a few proportions. The latent heat of vaporization and specific heat capacity at a constant pressure of the four mixtures were larger than those of R1234ze(E) and adding the four pure refrigerants with excellent thermodynamic properties into R1234ze(E) helps to improve the latent heat of vaporization and specific heat capacity of the binary mixtures. Among the four mixtures, R1234ze(E)/R290 is an azeotropic mixture and R1234ze(E)/R152a is a non-azeotropic mixture. Finally, the recommended mixing ratios of R1234ze(E)/R32, R1234ze(E)/R152a, R1234ze(E)/R290, and R1234ze(E)/R161 to replace R22 were in the range of 0.56/0.44∼0.76/0.24, 0.58/0.42∼0.71/0.29, 0.27/0.73∼0.85/0.15, and 0.58/0.42∼0.84/0.16.

Measurement and Correlation of the Isobaric Vapor–Liquid Equilibria of Methanol + Dimethyl Carbonate + 1-Butyl-3-Methylimidazolium Hexafluorophosphate at 101.3 kPa

Measurement and Correlation of the Isobaric Vapor–Liquid Equilibria of Methanol + Dimethyl Carbonate + 1-Butyl-3-Methylimidazolium Hexafluorophosphate at 101.3 kPa

Separation of methyl ethyl ketone - methanol azeotrope by ionic liquids: Thermodynamic and molecular mechanism

In this work, three ionic liquids (ILs) based on acetate, namely tetraethylammonium acetate ([N2222][Ac]), 1-hexyl-2,3-dimethylimidazolium acetate ([HMMIM][Ac]), and tributylmethylammonium acetate ([N4441][Ac]) were selected to separate the methyl ethyl ketone - methanol azeotrope. The vapor–liquid equilibrium (VLE) data of the binary system (methyl ethyl ketone + methanol) and the ternary systems (methyl ethyl ketone + methanol + IL) were measured at 101.3 kPa. It was found that all the experimental data were thermodynamically consistent and the three ionic liquids could effectively eliminate the azeotropic phenomenon at a specific concentration. The separation ability of the three ionic liquids is [N2222][Ac] > [HMMIM][Ac] > [N4441][Ac]. The NRTL model was used to correlate the VLE data and was found to have an excellent quality of fit. Moreover, the quantum chemical calculations, COSMO-RS model, and FT-IR analysis were used synergistically to provide microscopic insights into the separation mechanism of ionic liquids.

The use of equations of state of pure components in pore fluid and fluid inclusion research: Computer program Pures (software package FLUIDS)

Fluid inclusions and pore fluids seldomly contain pure fluids, i.e. single component, and the properties of these natural fluids must be investigated with complex equations of state for fluid mixtures. However, the properties of nearly-pure fluids can be modelled with equations of state for pure gas components, including an insignificant error. Occasionally, fluid inclusions are observed that can be modelled according to these considerations. The program “Pures” has been developed to calculate properties of pure gases: H2O, CO2, CH4, N2, C2H6, O2, NH3, CO, H2, D2O, Ar, C3H8, SO2, H2S, and He. These fluid components belong to the most abundant volatile species that are observed in fluid inclusions in quartz and other host minerals in rock. The thermodynamic properties of these fluids are calculated with highly accurate Helmholtz energy functions that cover both the liquid and vapour. Viscosity and surface tension are calculated with additional purely- and semi-empirical equations. Stand-alone applications can be operated in Macintosh-, Windows-, and Linux-based operated computer systems, and contain algorithms that are designed with BASIC language within the XOJO programming environment. A series of twelve self-instructive interfaces (modules) are leading the user through the complex calculation procedures. The modules include the calculation of pressure, temperature, molar volume, isochores, isotherms, fugacity, homogenization conditions, liquid-vapour equilibria, thermodynamic state properties, viscosity, and surface tension. Fluid densities in quartz-confined inclusions can be corrected for temperature- and pressure-dependent volume changes of the host crystal. Fluid modelling in the program “Pures” is not restricted to fluid inclusion research, and can also be applied to other research fields that involve a fluid phase. “Pures” is included in the software package FLUIDS.

Thermal decomposition of 1-ethyl-3-methylimidazolium acetate

To realize the potential applications of ionic liquids as working fluids and solvents one should have knowledge about their long-term stability, which depends on their thermally initiated decomposition. However, the possible decomposition pathways are not yet known accurately. 1-Ethyl-3-methylimidazolium acetate ([C2Mim][OAc]) is widely studied and shows potential in cellulose dissolution. In this study, we investigate possible [C2Mim][OAc] decomposition pathways by combining decomposition experiments and ab initio rate constant computations. Both approaches yield activation energies around 135 kJ·mol−1, which significantly deviate from earlier TGA measurements with open surface yielding 100–110 kJ·mol−1 and are probably affected by evaporation. Our study uses an improved TGA measurement protocol with a sealed pan with a tiny hole that fosters measurement of the actual chemical process leading to mass loss. Ab initio computations of this study comprise vapor-liquid equilibria of reactants and products as well as forward and reverse reaction rate constants in the gas and liquid phase. Calculations for the gas phase closely match a first-order analysis of the experiments, but calculations for the liquid phase strongly depend on the quality of solvation modeling. The computations indicate that the SN2 pathway with an activation energy of 142–144 kJ·mol−1 dominates thermal decomposition of [C2Mim][OAc].

Vacuum distillation: A sustainable separation and purification approach for extracting valuable metals from In–Zn, In–Sn, and In–Sn–Zn waste alloys

The vacuum distillation (VD) method was studied for extraction of valuable metals from In–Zn, In–Sn, and In–Sn–Zn waste alloys. The VD studies were carried out between 773 K and 1073 K, at 5 Pa, and for 60 min for the In–Zn alloys. The In content in the residues was greater than 99.999 wt%, and the Zn content in the volatiles was the highest at 99.8962 wt%. For the In-Sn alloys, the VD experiments were carried out from 1323 K to 1573 K at 5 Pa for 540 min for the In–Sn alloys. The Sn content in the residues exceeded 99.9963 wt%, whereas the In content in the volatiles was 99.86 wt%. Further, the In–Sn–Zn VD was carried out between 773 K and 1073 K at 5 Pa for 90 min. The Zn content of the residues decreased from 6.0 wt% to 0.0009 wt%, while the Zn content of the volatiles was 99.79 wt%. Using the M-MIVM and vapor–liquid equilibrium (VLE) theories, the VLE data was predicted and the related phase diagrams for the binary and ternary alloys were displayed. The remarkable similarity between theoretical and experimental VLE phase diagrams demonstrates the reliability of the M-MIVM for In-based alloys.

Effects of electric field on vapor–liquid equilibrium of binary mixture

Effects of electric field on vapor–liquid equilibrium of binary mixture

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.

Unrestricted component count in multiphase lattice Boltzmann: A fugacity-based approach.

Studies of multiphase fluids utilizing the lattice Boltzmann method (LBM) are typically severely restricted by the number of components or chemical species being modeled. This restriction is particularly pronounced for multiphase systems exhibiting partial miscibility and significant interfacial mass exchange, which is a common occurrence in realistic multiphase systems. Modeling such systems becomes increasingly complex as the number of chemical species increases due to the increased role of molecular interactions and the types of thermodynamic behavior that become possible. The recently introduced fugacity-based LBM [Soomro et al., Phys. Rev. E 107, 015304 (2023)2470-004510.1103/PhysRevE.107.015304] has provided a thermodynamically consistent modeling platform for multicomponent, partially miscible LBM simulations. However, until now, this fugacity-based LB model had lacked a comprehensive demonstration of its ability to accurately reproduce thermodynamic behavior beyond binary mixtures and to remove any restrictions in a number of components for multiphase LBM. In this paper we closely explore these fugacity-based LBM capabilities by showcasing comprehensive, thermodynamically consistent simulations of multiphase mixtures of up to ten chemical components. The paper begins by validating the model against the Young-Laplace equationfor a droplet composed of three components. The model is then applied to study mixtures with a range of component numbers from one to six, showing agreement with rigorous thermodynamic predictions and demonstrating linear scaling of computational time with the number of components. We further investigate ternary systems in detail by exploring a wide range of temperature, pressure, and overall composition conditions to produce various characteristic ternary diagrams. In addition, the model is shown to be unrestricted in the number of phases as demonstrated through simulations of a three-component three-phase equilibrium case. The paper concludes by demonstrating simulations of a ten-component, realistic hydrocarbon mixture, achieving excellent agreement with thermodynamics for both flat interface vapor-liquid equilibrium and curved interface spinodal decomposition cases. This study represents a significant expansion of the scope and capabilities of multiphase LBM simulations that encompass multiphase systems of keen interest in engineering.

VLE measurement of binary systems 1-butyl-3-methylimidazolium-based ionic liquids and ethanol or water

Experimental vapor–liquid equilibrium (VLE) data for binary systems of ethanol or water with four ionic liquids (ILs) comprising 1-butyl-3-methylimidazolium cation and different anions were measured at atmospheric pressure within a broad region of IL concentrations, IL mole fraction ranging between 0 and 0.7 or even 0.87. Siwoloboff procedure of vapor–liquid phase transition temperature measurement was applied to estimate VLE of the binary mixtures. Obtained t–x data were fitted assuming ideal vapor and non-ideal liquid phase behavior, using the original NRTL equation to calculate component activity coefficients. VLE description results are presented in form of equilibrium diagrams and as the variation of activity coefficients with mixture composition. Quality of the VLE data fitting was assessed based on root mean square deviations and mean deviations in temperature. Some experimental binary t–x data sets were compared to those available in literature (measured in much narrower concentration range) or predicted from ternary VLE data. The selection of ILs in this study was related to the separation of ethanol−water mixture by extractive distillation. Principal IL selection criterium was its ability to affect the ethanol–water relative volatility. Thermodynamic description of the VLE data of IL-containing systems within a wide concentration range is an essential building block of the mathematical model of separation devices, especially in case of regeneration equipment where concentrated IL is present.

Microphase versus macrophase separation in the square-well-linear fluid: A theoretical and computational study.

Due to the presence of competing interactions, the square-well-linear fluid can exhibit either liquid-vapor equilibrium (macrophase separation) or clustering (microphase separation). Here we address the issue of determining the boundary between these two regimes, i.e., the Lifshitz point, expressed in terms of a relationship between the parameters of the model. To this aim, we carry out Monte Carlo simulations to compute the structure factor of the fluid, whose behavior at low wave vectors accurately captures the tendency of the fluid to form aggregates or, alternatively, to phase separate. Specifically, for a number of different combinations of attraction and repulsion ranges, we make the system go across the Lifshitz point by increasing the strength of the repulsion. We use simulation results to benchmark the performance of two theories of fluids, namely, the hypernetted chain (HNC) equationand the analytically solvable random phase approximation (RPA); in particular, the RPA theory is applied with two different prescriptions as for the direct correlation function inside the core. Overall, the HNC theory proves to be an appropriate tool to characterize the fluid structure and the low-wave-vector behavior of the structure factor is consistent with the threshold between microphase and macrophase separation established through simulation. The structural predictions of the RPA theory turn out to be less accurate, but this theory offers the advantage of providing an analytical expression of the Lifshitz point. Compared to simulation, both RPA schemes predict a Lifshitz point that falls within the macrophase-separation region of parameters: in the best case, barriers roughly twice higher than predicted are required to attain clustering conditions.

Flammability of complex hydrocarbon mixtures in air and nitrogen diluted atmosphere at ambient conditions and at elevated pressures

An innovative experimental method was introduced to study flammability limits and limiting oxygen concentration of complex hydrocarbon mixtures simulating crude oil vapour composition. Flammability experiments were conducted in a 10L spherical vessel at 25 °C and initial pressures of 100 kPa, 1100 kPa and 2600 kPa in air with additional nitrogen. Based on the experimental data, applicability of selected empirical methods and two calculated adiabatic flame temperature based methods was validated for ambient initial conditions. The experimental results confirmed relative decrease below 6.5% for lower flammability limit and below 3% for limiting oxygen concentration with increasing pressure within the examined range. The upper flammability limit increased with initial pressure. Vapour-liquid equilibrium was found to be a constraint in the fuel-rich region at elevated pressures to keep the constant initial composition of the vapour phase. At ambient conditions the calculated adiabatic flame temperature based methods were able to approximate the experimental data well. Empirical mixing rules showed accuracy highly dependent on source literature data.