Vapor-liquid Equilibrium Properties Research Articles

Transferable Water Potentials Using Equivariant Neural Networks.

Machine learning interatomic potentials (MLIPs) have emerged as a technique that promises quantum theory accuracy for reduced cost. It has been proposed [J. Chem. Phys. 2023, 158, 084111] that MLIPs trained on solely liquid water data cannot accurately transfer to the vapor-liquid equilibrium while recovering the many-body decomposition (MBD) analysis of gas-phase water clusters. This suggests that MLIPs do not directly learn the physically correct interactions of water molecules, limiting transferability. In this work, we show that MLIPs using equivariant architecture and trained on 3200 liquid water structures reproduces liquid-phase water properties (e.g., density within 0.003 g/cm3 between 230 and 365 K), vapor-liquid equilibrium properties up to 550 K, the MBD analysis of gas-phase water cluster up to six-body interactions, and the relative energy and the vibrational density of states of ice phases. We show that potentials developed using equivariant MLIPs allow transferability for arbitrary phases of water that remain stable in nanosecond long simulations.

Vapor-liquid equilibrium and thermodynamic properties of saturated argon and krypton from Monte Carlo simulations using abinitio potentials.

Vapor-liquid equilibria and thermodynamic properties of saturated argon and krypton were calculated by semi-classical Monte Carlo simulations with the NpT + test particle method using abinitio potentials for the two-body and nonadditive three-body interactions. The NpT + test particle method was extended to the calculation of second-order thermodynamic properties, such as the isochoric and isobaric heat capacities or the speed of sound, of the saturated liquid and vapor by using our recently developed approach for the systematic calculation of arbitrary thermodynamic properties in the isothermal-isobaric ensemble. Generally, the results for all simulated properties agree well with experimental data and the current reference equations of state for argon and krypton. In particular, the results for the vapor pressure and for the density and speed of sound of the saturated liquid and vapor agree with the most accurate experimental data for both noble gases almost within the uncertainty of these data, a level of agreement unprecedented for many-particle simulations. This study demonstrates that the vapor-liquid equilibrium and thermodynamic properties at saturation of a pure fluid can be predicted by Monte Carlo simulations with high accuracy when the intermolecular interactions are described by state-of-the-art abinitio pair and nonadditive three-body potentials and quantum effects are accounted for.

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.

Theoretical study on formation mechanism of acetic acid associating configurations and their distributions under saturated conditions.

The vapor-liquid equilibrium (VLE) properties of acetic acid systems generally behave strong non-ideality due to the associating interaction among acetic acid molecules. Theoretical study of the associating mechanism will provide guidance for the VLE property prediction, which is crucial for the designing on the separation process of the acetic acid systems. In this work, the association conformers and their distribution on acetic acid molecules in saturated gas and liquid phase were firstly studied. The proportions of the acetic acid monomer and multimers were obtained, which will contribute to the foundation for the vapor-liquid equilibrium simulations. The association mechanism on acetic acid molecules was then investigated by comparing among the structures and non-bonded interaction energies of different dimers. The structure of the cyclic dimer containing two OC-HO hydrogen bonds, may be found probably when acetic acid molecules approached. Electronic properties of different acetic acid dimers showed that the electrons around carbonyl oxygen atoms were deflected by the attraction of hydrogen atoms in the other molecule, which polarized the acetic acid molecules when the hydrogen bonds between acetic acid molecules were formed, providing theoretical basis for the polarized acetic acid molecular model. In this work, the molecular dynamics (MD) simulations and DFT calculations were conducted through the software GROMACS and Gaussian 09, respectively. For the MD simulations, the OPLS-AA force field was used as the atomic force field, with the cubic simulation cells constructed by Packmol program. For the DFT calculations, the M06-2X functional was employed for the optimization of the associating structures with the 6-311G** basis sets. Hydrogen bonding energies of dimers were corrected for the basis set superposition error (BSSE) and the deformation energies of monomers. Furthermore, the energy decomposition analysis was conducted at DFT/M06-2X/def-tzp level by the ADF software, and the wave function analysis was conducted by the Multiwfn software including the atom in molecule (AIM) topology analysis, the electronic potential analysis, and the electron density difference analysis.

Molecular Simulation Studies on the Vapor-Liquid Equilibrium of CO2 + 3,3,3-Trifluoropropene (R1243zf) Binary Mixtures.

As fourth-generation refrigerants with great development prospects, hydrofluoroolefins (HFOs) can be mixed with other refrigerants, such as carbon dioxide (CO2), to form refrigerant mixtures with low global warming potential (GWP) and zero ozone depleting potential (ODP) while retaining the advantages of each component. Refrigerants can work together to achieve complementary benefits. Combinations of CO2 and HFOs can strengthen the thermodynamic properties of CO2 while inhibiting the flammability of HFOs. At present, relatively few studies have been conducted on the CO2 + 3,3,3-trifluoropropene (R1243zf) mixture. Besides experimental approaches, molecular simulation has grown in importance as a way to determine thermodynamic and transport properties in recent years. In this study, the Gibbs Ensemble Monte Carlo (GEMC) method was used to simulate the vapor-liquid equilibrium (VLE) properties of the CO2 + R1243zf binary mixture in the temperature range of 273.15 to 313.15 K, in which the three-site rigid TraPPE force field and a fully flexible transferable all-atom force field were selected to describe CO2 and R1243zf, respectively. By comparing the GEMC simulation results with the experimental data, it was found that the average deviation of pressure is 2.33%, the average deviation of liquid phase molar fraction Δx is 0.0099, and the mean deviation of gaseous phase molar fraction Δy is 0.0204. The simulation results accord well with the experimental data and the fitting data of the correlation model in the literature, indicating that the molecular models used for CO2 and R1243zf can reliably predict the VLE properties. Finally, the critical parameters of the mixture at a temperature of 313.15 K were predicted, and the radial distribution functions (RDFs) of pure R1243zf and the mixture at 273.15 K and 3.5 MPa were calculated and analyzed by molecular dynamics (MD) simulation.

Neural Network Water Model Based on the MB-Pol Many-Body Potential.

The MB-pol many-body potential accurately predicts many properties of water, including cluster, liquid phase, and vapor-liquid equilibrium properties, but its high computational cost can make applying it in large-scale simulations quite challenging. In order to address this limitation, we developed a "deep potential" neural network (DPMD) model based on the MB-pol potential for water. We find that a DPMD model trained on mostly liquid configurations yields a good description of the bulk liquid phase but severely underpredicts vapor-liquid coexistence densities. By contrast, adding cluster configurations to the neural network training set leads to a good agreement for the vapor coexistence densities. Liquid phase densities under supercooled conditions are also represented well, even though they were not included in the training set. These results confirm that neural network models can combine accuracy and transferability if sufficient attention is given to the construction of a representative training set for the target system.

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.

First-Principles-Based Machine Learning Models for Phase Behavior and Transport Properties of CO2

In this work, we construct distinct first-principles-based machine-learning models of CO2, reproducing the potential energy surface of the PBE-D3, BLYP-D3, SCAN, and SCAN-rvv10 approximations of density functional theory. We employ the Deep Potential methodology to develop the models and consequently achieve a significant computational efficiency over ab initio molecular dynamics (AIMD) that allows for larger system sizes and time scales to be explored. Although our models are trained only with liquid-phase configurations, they are able to simulate a stable interfacial system and predict vapor-liquid equilibrium properties, in good agreement with results from the literature. Because of the computational efficiency of the models, we are also able to obtain transport properties, such as viscosity and diffusion coefficients. We find that the SCAN-based model presents a temperature shift in the position of the critical point, while the SCAN-rvv10-based model shows improvement but still exhibits a temperature shift that remains approximately constant for all properties investigated in this work. We find that the BLYP-D3-based model generally performs better for the liquid phase and vapor-liquid equilibrium properties, but the PBE-D3-based model is better suited for predicting transport properties.

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%.

A Helmholtz Free Energy Equation of State of CO2-CH4-N2 Fluid Mixtures (ZMS EOS) and Its Applications

An equation of state (EOS) of CH4-N2 fluid mixtures in terms of Helmholtz free energy has been developed by using four mixing parameters, which can reproduce the pressure-volume-temperature-composition (PVTx) and vapor-liquid equilibrium (VLE) properties of CH4-N2 fluid mixtures. The average absolute deviation of all the PVTx data available up to 673.15 K and 1380 bar from this EOS is 0.38%. Combining this EOS of CH4-N2 fluid mixtures and the EOS of CH4-CO2 and CO2-N2 fluid mixtures in our previous work, an EOS of CO2-CH4-N2 fluid mixtures has been developed, which is named ZMS EOS. The ZMS EOS can calculate all thermodynamic properties of ternary CO2-CH4-N2 fluid mixtures and the average absolute deviation of the PVTx data from the ZMS EOS is 0.40% for the CO2-CH4-N2 system. The ZMS EOS can be applied to calculate excess enthalpies of CO2-CH4-N2 fluid mixtures, predict the solubility of CO2-CH4-N2 fluid mixtures in brine and water, and quantitatively estimate the impact of the impurities (CH4 and N2) on the CO2 storage capacity in the CO2 capture and storage (CCS) processes. The ZMS EOS can also be applied to calculate the isochores of CO2-CH4-N2 system in the studies of fluid inclusions. All Fortran computer codes and Origin drawing projects in this paper can be obtained freely from the corresponding author.

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.

A "short blanket" dilemma for a state-of-the-art neural network potential for water: Reproducing experimental properties or the physics of the underlying many-body interactions?

Deep neural network (DNN) potentials have recently gained popularity in computer simulations of a wide range of molecular systems, from liquids to materials. In this study, we explore the possibility of combining the computational efficiency of the DeePMD framework and the demonstrated accuracy of the MB-pol data-driven, many-body potential to train a DNN potential for large-scale simulations of water across its phase diagram. We find that the DNN potential is able to reliably reproduce the MB-pol results for liquid water, but provides a less accurate description of the vapor-liquid equilibrium properties. This shortcoming is traced back to the inability of the DNN potential to correctly represent many-body interactions. An attempt to explicitly include information about many-body effects results in a new DNN potential that exhibits the opposite performance, being able to correctly reproduce the MB-pol vapor-liquid equilibrium properties, but losing accuracy in the description of the liquid properties. These results suggest that DeePMD-based DNN potentials are not able to correctly "learn" and, consequently, represent many-body interactions, which implies that DNN potentials may have limited ability to predict the properties for state points that are not explicitly included in the training process. The computational efficiency of the DeePMD framework can still be exploited to train DNN potentials on data-driven many-body potentials, which can thus enable large-scale, "chemically accurate" simulations of various molecular systems, with the caveat that the target state points must have been adequately sampled by the reference data-driven many-body potential in order to guarantee a faithful representation of the associated properties.

A new heat transfer model based on non-equilibrium film theory for annular flow condensation of binary zeotropic mixtures

In recent years, zeotropic mixtures have been widely used as substitutes for pure fluids. Accordingly, their condensation properties have attracted increasing attention. However, it is a challenge to accurately describe the heat transfer performance of zeotropic mixtures in condensation, which is limited by the estimation of mixture effects, especially the mass transfer resistance therein. Focusing on this issue, the mass transfer due to the axial and radial concentration gradients in the vapor phase was considered, and a new heat transfer model for the annular flow of binary zeotropic mixtures in horizontal tubes was developed based on non-equilibrium film theory. In this model, the boiling point difference was introduced to approximate the effect of concentration gradients by combining with the vapor-liquid phase equilibrium properties of binary zeotropic mixtures. Secondly, equivalent specific heat capacities were defined for an analogy with single-phase heat transfer, which further simplifies the form of the model. The simplified model was evaluated with a consolidated database of 11 mixtures from 13 sources. The results show that the predictions of the model are in good agreement with the experimental results, with a mean absolute relative deviation (MARD) of 15.88 and 91.14% of points falling in the ±30% deviation band. Predictions were also performed for excluded data from other sources and satisfactory results were obtained with a MARD of 13.47%. Moreover, the mechanism of mixture effects is elaborated. It indicates that besides the commonly mentioned heat transfer degradation, there is also heat transfer enhancement for binary zeotropic mixtures condensation due to the opposite effects of the axial and radial concentration gradients.

Predicting vapor-liquid equilibria of CO<sub>2</sub>+HFC binary mixtures by the PR EOS combined with a group contribution model

CO<sub>2</sub>+HFC binary mixtures have good performance and environmental friendliness and are considered good alternative working fluids in cooling and power cycle systems. The vapor-liquid phase equilibrium properties are key to the calculation of the enthalpy and entropy of mixtures, which is critical for the analysis of cooling and power cycle systems. To accurately predict the vapor-liquid equilibrium of CO<sub>2</sub> and HFC (R23, R32, R41, R125, R134a, R143a, R152a, R161, and R227ea) binary mixtures, a group contribution model based on the excess free energy (<i>G</i><sup>E</sup>) mixing rules (PR+MHV1+UNIFAC and PR+LCVM+UNIFAC) is established in this paper. The interaction parameters between groups such as -CO<sub>2</sub>, -Alkane, -CHF, and -CHF<sub>3</sub> are obtained by the vapor-liquid phase equilibrium experiment of CO<sub>2</sub> and HFC refrigerants, and these group parameters are critical for predicting their vapor-liquid phase equilibrium properties (the pressures and vapor phase molar fractions). The AARD<i>p</i> value calculated by the PR+LCVM+UNIFAC model is 5.53%, the value of AAD<i>y</i><sub>1</sub> is 0.0132, and the AARD<i>p</i> and AAD<i>y</i><sub>1</sub> values of the PR+MHV1+UNIFAC model are 7.40% and 0.0229, respectively. However, for the CO<sub>2</sub>+R32 system, the PR+MHV+UNIFAC prediction model can reproduce the experimental data with lower deviations, and the values of AARD<i>p</i> and AAD<i>y</i><sub>1</sub> are 1.53% and 0.0045, respectively. In summary, for CO<sub>2</sub>+HFC binary mixtures, the PR+LCVM+UNIFAC group contribution model can reproduce the experimental data with lower deviations, but for individual CO<sub>2</sub> binary mixtures (such as CO<sub>2</sub>+R32), the PR+MHV1+UNIFAC model also has unique advantages. According to the prediction results of the group contribution model, the PR+LCVM+UNIFAC model has significantly improved the calculation progress compared with the PR+MHV1+UNIFAC model used in the previous system.

Prediction of critical points for carbon dioxide-based binary mixtures by the Heidemann-Khalil approach

Prediction of critical point is of great interest for CO2-based binary mixture being the working fluid of power cycle. Compared with empirical correlation, the critical point of mixture can be calculated based on its rigorous thermodynamic criteria, with limited binary interaction parameters and consistency on vapor-liquid equilibrium and other thermodynamic properties. In this study, the critical points of CO2-based binary mixture, applicable for being working fluid of power cycle, including hydrocarbons, fluorocarbons, dimethyl ether, methanol, water and xenon, were studied based on the Peng-Robinson equation of state (PR EOS) with van der Waals (vdW) mixing rule, according to the Heidemann-Khalil approach. By comparing the predicted results with the experimental data in the literature, the applicability of this method to various mixtures is discussed. The characteristics of critical lines, type of phase diagram, and binary interaction parameters of each mixture were analyzed and discussed, and the results show that the Heidemann-Khalil approach is efficient for critical point calculation and prediction of CO2-based binary mixture.

Prediction of the volumetric and vapor-liquid equilibrium properties of CO2-N2-O2-Ar fluid mixtures with a general Helmholtz equation of state

A general equation of state (EOS) explicit in the form of Helmholtz free energy has been developed to predict the pressure-volume-temperature-composition (PVTx) and vapor-liquid equilibrium (VLE) properties of the CO2N2O2-Ar fluid mixtures. The EOS, which uses four mixing parameters, is based on highly accurate EOS for pure CO2, N2, O2 and Ar fluids and contains a simple generalized departure function presented by Lemmon and Jacobsen (1999). Four mixing parameters are fitted from the experimental PVTx and VLE data of binary systems available. Comparison with experimental data available indicates that the EOS can reproduce the PVTx and VLE properties of CO2N2O2-Ar fluid mixtures up to 453 K and 1000 bar within or close to experimental uncertainties. The general EOS can be used to evaluate the change of density and VLE composition from impurities N2, O2 and Ar during the CO2 capture and sequestration process.

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.

Vapor-liquid equilibrium measurements and models for the ternary mixtures of R1234yf + R32 + R125 and R1234yf + R32 + CO2

R1234yf as the environmental friendly refrigerant has a low volumetric refrigeration capacity and light flammability. The refrigerant mixtures are expected to achieve excellent thermophysical performance, safety and environmental performance. The vapor-liquid equilibrium (VLE) is one of the most important properties of the mixtures. In this work, the VLE property of R1234yf + R32 + R125 and R1234yf + R32 + CO2 ternary mixtures were measured along 5 isotherms from 273.15 K to 313.15 K by a recirculation analytical apparatus. The Peng-Robinson (PR) equation of state combined with the van der Waals (vdW) mixing rule (PR + vdW), as well as the PR equation of state combined with the Wong-Sandler (WS) mixing rule and the non-random two-liquid (NRTL) activity coefficient model (PR + WS + NRTL) were used to correlate the VLE data. The model parameters were temperature-dependent and could describe the VLE properties of the ternary and binary subsystems. The results showed that the PR + WS + NRTL model was better than the PR + vdW model. The average absolute relative deviation of pressure (AARD(p)) and average absolute deviation of compositions (AAD(y)) of the PR + WS + NRTL model were 0.4% and 0.003 for R1234yf + R32 + R125 ternary mixture, and were 0.7% and 0.007 for R1234yf + R32 + CO2 ternary mixture. Experimental results and model calculations showed that both the ternary mixtures were zeotropic.

Thermodynamic modeling of hydrogen–water systems with gas impurity at various conditions using cubic and PC-SAFT equations of state

Hydrogen (H2) has emerged as a viable solution for energy storage of renewable sources, supplying off-seasonal demand. Hydrogen contamination due to undesired mixing with other fluids during operations is a significant problem. Water contamination is a regular occurrence; therefore, an accurate prediction of H2-water thermodynamics is crucial for the design of efficient storage and water removal processes. In thermodynamic modeling, the Peng–Robinson (PR) and Soave Redlich–Kwong (SRK) equations of state (EoSs) are widely applied. However, both EoSs fail to predict the vapor-liquid equilibrium (VLE) accurately for H2-blend mixtures with or without fine-tuning binary interaction parameters due to the polarity of the components. This work investigates the accuracy of two advanced EoSs: the Schwartzentruber and Renon modified Redlich–Kwong cubic EoS (SR-RK) and perturbed-chain statistical associating fluid theory (SAFT) in predicting VLE and solubility properties of H2 and water. The SR-RK involves the introduction of polar parameters and a volume translation term. The proposed workflow is based on optimizing the binary interaction coefficients using regression against experimental data that cover a wide range of pressure (0.34 to 101.23 MPa), temperature (273.2 to 588.7 K), and H2 mole fraction (0.0004 to 0.9670) values. A flash liberation model is developed to calculate the H2 solubility and water vaporization at different temperature and pressure conditions. The model captures the influence of H2-gas (CO2) impurity on VLE. The results agreed well with the experimental data, demonstrating the model’s capability of predicting the VLE of hydrogen-water mixtures for a broad range of pressures and temperatures. Optimized coefficients of binary interaction parameters for both EoSs are provided. The sensitivity analysis indicates an increase in H2 solubility with temperature and pressure and a decrease in water vaporization. Moreover, the work demonstrates the capability of SR-RK in modeling the influence of gas impurity (i.e., H2–CO2 mixture) on the H2 solubility and water vaporization, indicating a significant influence over a wide range of H2–CO2 mixtures. Increasing the CO2 ratio from 20% to 80% exhibited almost the opposite behavior of H2 solubility compared to the pure hydrogen feed solubility. Finally, the work emphasizes the critical selection of proper EoSs for calculating thermodynamic properties and the solubility of gaseous H2 and water vaporization for the efficient design of H2 storage and fuel cells.

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.