VLE Data Research Articles

Vapor–liquid phase equilibrium prediction for mixtures of binary systems using graph neural networks

AbstractVapor–liquid phase equilibrium (VLE) plays a crucial role in chemical process design, process equipment control, and experimental process simulation. However, experimental acquisition of VLE data is a challenging and complex task. As an alternative to experimentation, VLE data prediction offers great convenience and utility. In this article, an artificial intelligence network is proposed to predict the temperature and the vapor phase composition of binary mixtures. We constructed a graph neural network (GNN) and designed an uncertainty‐aware learning and inference mechanism (UALF) in the prediction process. The model was tested on both a self‐constructed dataset and a publicly available dataset. The results demonstrate that the proposed method effectively reveals the phase equilibrium properties of the target data. This work presents a novel approach for predicting vapor–liquid phase equilibrium in binary systems and proposes innovative ideas for investigating phase equilibrium mechanisms and principles.

Performance Evaluation of CO2 + SiCl4 Binary Mixture in Recompression Brayton Cycle for Warm Climates

This work demonstrates the potential of CO2 + SiCl4 binary mixture as a working fluid for power generation cycle. Recompression Brayton cycle configuration is considered due to its proven record of high performance for medium- to high-temperature sources. The objective of this study is to assess the thermodynamic performance of a recompression Brayton cycle using a CO2 + SiCl4 binary mixture as a working fluid, particularly under warm climate conditions. The cycle is simulated using the Peng–Robinson equation of state in Aspen Hysys (v11) software, and the model is validated by comparing VLE data against experimental data from the literature. The analysis involves the assessment of cycle’s thermal efficiency and exergy efficiency under warm climatic conditions, with a minimum cycle temperature of 40 °C. The results demonstrate a notable improvement in the cycle’s thermodynamic performance with CO2 + SiCl4 binary mixture compared to pure CO2. A small concentration (5%) of SiCl4 in CO2 increases the thermal efficiency of the cycle from 41.7% to 43.4%. Moreover, irreversibility losses in the cooler and the heat recovery unit are significantly lower with the CO2 + SiCl4 binary mixture than with pure CO2. This improvement enhances the overall exergy efficiency of the cycle, increasing it from 62.1% to 70.2%. The primary reason for this enhancement is the substantial reduction in irreversibility losses in both the cooler and the HTR. This study reveals that when using a CO2 + SiCl4 mixture, the concentration must be optimized to avoid condensation in the compressor, which can cause physical damage to the compressor blades and other components, as well as increase power input. This issue arises from the higher glide temperature of the mixture at increased SiCl4 concentrations and the limited heat recovery from the cycle.

Partial molar and microstructural properties of binary propane + o-toluidine system near the critical point of pure solvent based on the VLE measurements and modeling with CP-PC-SAFT and mg-SAFT equation of states

The isothermal VLE properties (PTxy relationship) of a binary supercritical (SC) C3H8 + o-toluidine mixture was measured by means of static-analytic method with fluid phase sampling at equilibrium conditions. The measurements were made at three temperatures of (393.15, 433.15, and 473.15) K and pressures up to 10.41 MPa. An experimental VLE apparatus, a high-temperature and high-pressure optical cell, has been used to measure the phase equilibrium properties (PTxy) of the binary SC C3H8 + o-toluidine mixture. The combined expanded absolute and relative uncertainties of the temperature, pressure, and the phase concentration measurements at 0.95 confidence level with a coverage factor of k = 2 is estimated at 0.15 K, 0.5 %, 4.2 % (for x) and 4.8 % (for y), respectively. The critical curve data, TC−x,PC-x, and PC− TC projections, have been derived based on the measured VLE data. The measured VLE and the derived critical curve data were used to estimate the theoretically important and physical meaning of Krichevskii parameter, ∂P∂xTCVC∞. Thermodynamic (partial molar properties, V¯2∞,H¯2∞,C¯P2∞, and distribution equilibrium constant KD), and microstructural (cluster’s size, Nexc∞) properties of infinite-dilute C3H8 + o-toluidine mixture near the critical point of pure solvent (C3H8) were calculated based on the derived Krichevskii parameter and pure solvent (SC C3H8) properties. CP-PC-SAFT and mg-SAFT equation of state (EoS), with zero interaction parameter, k12 = 0, for both models (pure prediction models, no adjustable parameters) were successfully applied to the present PTxy phase equilibria for the SC C3H8 + o-toluidine mixture. The present measured VLE data for C3H8 + o-toluidine system along with the reported pure compound properties of pure propane and o-toluidine have been used to examine the predictive capabilities of the theoretically based CP-PC-SAFT and mg-SAFT models of EoS. It was demonstrated that mg-SAFT is superior in predicting VLE of the C3H8 + o-toluidine system with k12 = 0.

Experimental and modeling study of isothermal VLE properties of the supercritical C3H8 + benzylamine mixture

BackgroundsFor the design and development of a method utilizing SC C3H8 for the chemical synthesis like the production of active pharma ingredients (pharmaceutical applications) and crop protection agents, it is essential to understand the solubility and other properties of benzylamine as an industrial important compound in the SC C3H8. MethodsA high-temperature and high-pressure optical cell has been used to measure the phase equilibrium properties (PTxy) of the binary SC C3H8 + benzylamine mixture. The experimental and modeling studies of the isothermal VLE properties (solubility, PTxy relationship) of benzylamine in the supercritical (SC) C3H8 along the four selected constant temperatures of (393.15, 413.15, 433.15, and 473.15) K over the pressure range from (0.9 to 9.5) MPa have been performed in the present work. Significant FindingsIt was found the Perturbed-Chain Statistical Association Fluid Theory (PC-SAFT) is less accurate than its Critical Point-based revision (CP-PC-SAFT) in predicting the new VLE data in the C3H8 + benzylamine binary system with k12 = 0. Both models substantially deviate from the bubble point data at pressures below 2 MPa.

Effect of Variation between Different Experimental VLE Data Sets on Thermodynamic Model and Separation Predictions: NRTL Correlation of the Ethanol + Water System

Effect of Variation between Different Experimental VLE Data Sets on Thermodynamic Model and Separation Predictions: NRTL Correlation of the Ethanol + Water System

An efficient polar cubic equation of state for predictive modeling of phase behavior and critical phenomena of mixtures

AbstractA polar cubic equation of state (EOS) is developed by incorporating the dipolar theory of Jog and Chapman into the Soave‐Redlich‐Kwong (SRK) EOS. We propose simplifying assumptions in the dipolar term of Jog and Chapman to reduce the double and triple sums in the theory to single sums. The simplified version of the dipolar theory can significantly improve computational speed and can be used with either Cubic EOS or SAFT‐based EOS. The proposed model, which we call Simplified Polar SRK (SP‐SRK), is parametrized in a similar fashion to classical cubic EOS to exactly reproduce , and will self‐consistently reduce to the base SRK EOS in the absence of polar interactions. Binary VLE data with a non‐polar reference hydrocarbon is used to extract the polarity of the respective functional group. The model shows superior performance in capturing the phase behavior of polar mixtures compared to the base SRK.

Experimental investigation of the CO2+SiCl4 mixture as innovative working fluid for power cycles: Bubble points and liquid density measurements

Supercritical CO2 is recognized as a promising working fluid for next-generation of high temperature power cycles. Nevertheless, the use of CO2 mixtures with heavier dopants is emerging as a promising alternative to supercritical CO2 cycles in the recent years for air-cooled systems in hot environments. Accordingly, this work presents an experimental campaign to assess the thermodynamic behaviour of the CO2+SiCl4 mixture to be used as working fluid for high-temperature applications, conducted in the laboratories of CTP Mines Paris PSL. At first, bubble conditions of the mixture are measured in a variable volume cell (PVT technique), then liquid densities are measured with a vibrating tube densimeter, for molar composition in the range between 70 % and 90 % of CO2. The Peng Robinson EoS was fine-tuned on the bubble points obtained, resulting in a satisfactory accuracy level. Finally, a non-conventional methodology has been developed to measure bubble points with the vibrating tube densimeter, whose results are consistent with the VLE data obtained with the standard PVT technique. Thermodynamic analysis in next-generation concentrated solar power plant, at 700 °C turbine inlet, confirms the mixture overcomes 50 % thermal efficiency, providing +4.2 % net electrical output over pure supercritical CO2 at equal thermal power from the solar field.

Hybrid process for separation of morpholine−water mixture: A rigorous design with experimental confirmation based on LLE and VLE data

The separation of morpholine from the aqueous effluent stream is carried out using an efficient hybrid extraction-distillation (HED) system using commercially viable solvents 2-ethyl hexanol and toluene, which makes heteroazeotrope with water. This paper investigated the tie-line, mutual solubility and VLE measurements, and thermodynamic modeling. On comparing the two solvents, 2-ethyl hexanol emerged as an appropriate extractant. The experimental tie-line data regressed by the NRTL model and a deviation of 0.8 indicates a good correlation between experimental and predicted data. Further, the process is designed, simulated, and optimization is performed by minimizing total annual cost (TAC) as the objective function. At extract/solvent to feed ratio S/F of 0.78 mol fraction, number of stages, NT of 28, 99.8% morpholine recovered in the extract phase with TAC of $23.3×104/y. Subsequently, the extract phase is fed to the heteroazeotropic distillation column to remove moisture followed by the final recovery column. Finally, a laboratory-scale experiment was conducted to verify the separation performance in the downscaled (3.5×50 cm) counter-current extraction column.

Solubility of o-toluidine in supercritical carbon dioxide at high-temperatures and high-pressures

In many technological applications the solubility (VLE data) of materials (solid or liquids) in SC CO2 is required. It is essential to understand the solubility and other properties of o-toluidine in the SC CO2 due to their technological importance. This paper presents a new isothermal VLE data for SC CO2 (1)+ o-toluidine (2). Thus, the main purpose of the present work is to experimental study of the VLE properties (solubility, PTxy relationship) of o-toluidine (one of the technologically important compound) in the SC CO2 needs for variety industrial applications. The measurements were made at four selected isotherms of (313.15, 333.15, 353.15, and 373.15) K over the pressure range from (1.24 to 31.44) MPa. A high-temperature and high-pressure optical cell has been used to measure of the phase equilibrium properties (PTxy) of the binary CO2 (1)+ o-toluidine (2) mixture. The combined expanded absolute and relative uncertainty of the temperature, pressure, and the phase concentration measurements at 0.95 confidence level with a coverage factor of k = 2 is estimated at 0.15 K, 0.2 %, and 3 %, respectively. The critical point parameters of the mixture in the PC−TC projection have been estimated using the measured VLE data. The shape of the critical curve behavior indicates that CO2 (1) + o-toluidine (2) mixture belongs to the Type III according to the Konynenburg and Scott classification. PR and PC-SAFT equation of state (EoS) were successfully applied to model the phase equilibria (qualitative point of view) for the SC CO2 (1) + o-toluidine (2) mixture at the measured experimental temperatures. From a quantitative point of view, the best choice (among the models used) was PR EoS. The critical curves predicted with PR and PC-SAFT EoS confirmed that the mixture is classified as Type III phase behavior.

Measurement and Correlation of Isobaric VLE Data for 1-Propanol + Water + 1-Butyl/Decyl-3-methylimidazole Bromide/Nitrate ILs at 101.33 kPa

Measurement and Correlation of Isobaric VLE Data for 1-Propanol + Water + 1-Butyl/Decyl-3-methylimidazole Bromide/Nitrate ILs at 101.33 kPa

Flash point and safety evaluation of binary mixture of diphenyl ether + biphenyl: A commonly utilized heat transfer fluid

The binary mixture of diphenyl ether and biphenyl finds wide applications in various industries. Notably, it is widely utilized in renewable energy systems such as concentrated solar power (CSP) facilities. This study addresses the lack of research on the flash point (FP) behavior of this blend, crucial due to high operating temperatures in related processes, especially when used as a heat transfer fluid. This study fills the research gap by analyzing the entire composition range, using experimental measurements, and a unique mathematical method based on SLE data; unlike the conventional method that relies on VLE data. The FP prediction results demonstrated satisfactory outcomes when compared to the experimental data. The findings of this study can be employed to mitigate the fire and explosion risks associated with processes using the binary mixture of diphenyl ether + biphenyl.

Vapor-liquid equilibrium for binary systems containing n-alkanes and cycloalkanes

In this study, VLE data for five binary systems comprising n-octane, n-nonane, methylcyclopentane, and methylcyclohexane were measured using the total pressure method at 393.15 K, 433.15 K, and 473.15 K. The NRTL-HOC and the UNIQUAC-HOC models were used to successfully correlate all VLE data and determine binary interaction parameters. No azeotropic behavior was observed in any of the binary systems under the operating conditions. The predictive UNIFAC-DMD and COSMO-SAC models were implemented to predict binary VLE phase diagram and unveiled the mechanism of the separation efficiency of alkanes–cycloalkanes. Through the examination of the COSMO-SAC based molecular surface charge profile (σ-profile), the variance in non-hydrogen bonding segments within the σ-profiles of the analyzed alkanes determines both the strength of electrostatic interactions and the temperature-dependent VLE separation behaviors. The results indicate that σ-profile could be suggested as a good indicator to assess operating conditions of the alkanes VLE separation.

Development of the NRTL functional activity coefficient (NRTL-FAC) model using high quality and critically evaluated phase equilibria data. 2

One of the most significant models based on the local composition concept in advanced thermodynamics, is the non-random two-liquid (NRTL) model. Many studies have been conducted to enhance its applicability to various systems. Among these studies, the development of the NRTL model for electrolytic systems, polymer systems, and systems containing special chemical associations has been particularly significant. However, the NRTL model and its developed forms are based on the concept of local composition, and the dependency of these models on the experimental data for regressing NRTL interaction parameters limits their applicability of the NRTL model. Accordingly, to overcome this limitation, the NRTL functional activity coefficient model (NRTL-FAC), which is a group contribution model, was developed (https://doi.org/10.1016/j.fluid.2021.113088). The current study aims to extend the NRTL-FAC model. To achieve this, 15 new main groups have been added to the previous ones, and 266 new interaction parameters have been optimized. A total of 374 isothermal/isobaric VLE data sets, including 7115 data points, were used. The quality of the experimental VLE data was assessed using various thermodynamic consistency tests, including the Herington test, Van Ness test, point test, infinite dilution test, EoS test, and endpoint test. The NRTL-FAC model can accurately predict the VLE of binary systems, with results in good agreement with experimental data at different temperature and pressure ranges. This accuracy was observed for both azeotrope systems and ideal systems with positive or negative deviation from Raoult's law. Unlike the UNIFAC-DMD model, which restricts a portion of its interaction parameters to consortium members, the NRTL-FAC model interaction parameters are publicly accessible. Therefore, the NRTL-FAC model can be confidently used as a preliminary estimate to predict VLE behavior in process design when experimental data is not available.

The a priori screening of potential organic solvents using artificial neural networks

A QSPR model using artificial neural networks was constructed to estimate the binary interaction parameters for the temperature-dependant form of the NRTL model with the objective of using it as a supplement to assist limitations of group contribution methods in the screening of potential solvents for liquid-liquid extraction processes. Parameters were regressed using experimental LLE and VLE data and checked for consistency. Molecule structures were drawn and descriptors determined with the use of Materials Studio. The QSPR model uses 31 descriptors as input and produced absolute average deviations of 0.23 and 0.19 for each pair of binary interaction parameters respectively. The development of this model is shown to be effective in improving the robustness of solvent screening processes.

Isothermal vapor-liquid equilibrium measurements and PC-SAFT, PR78, and CPA phase behavior modeling of n-tricosane + SC CO2 mixtures

This study reports the isothermal VLE (PTxy) data of n-tricosane (heavy n-alkane, n-C23H48) in supercritical (SC) CO2 at two selected temperatures of (323 and 343) K over the pressure range from (1.66 to 34.88) MPa. The measurements were made using a high-temperature and high-pressure VLE optical cell. The combined expanded uncertainty of the temperature, pressure, and phase concentration measurements at 0.95 confidence level with a coverage factor of k = 2 is estimated to be 0.2 K, 0.22 %, and 3.5 %, respectively. The measured VLE data has been used to estimate the critical parameters (TC, PC, xC) of the binary n-tricosane + CO2 mixture. The derived L-G critical properties data of the binary n-tricosane + CO2 mixture are: TC = 323.15 K, PC = 34.02 MPa, xC=0.060 mole fraction of n-tricosane; and TC = 343.15 K, PC = 40.14 MPa, xC=0.071 mole fraction of n-tricosane. The measured solubility data for the mixture has been used to estimate the physical meaning Krichevskii parameter ∂P∂xTCVC∞=-75.93MPa. Based on the derived Krichevskii parameter the thermodynamic (partial molar volumes, V¯2∞,H¯2∞,C¯P2∞) and structural (cluster size,Nexc∞) properties of the infinite dilution mixture of n-tricosane + CO2 near the critical point (CP) of pure solvent (CO2) have been calculated. The measured vapor – liquid equilibrium data for n-tricosane + CO2 was modeled using three equations of state (PC-SAFT, PR78, and CPA). The best prediction option with PC-SAFT was obtained with kij=0.12, while kij=0 was the best using PR78 and CPA EoS.

Study on the Separation of M-Xdi Products by Non-Phosgene Pyrolysis System

m-Xylylene diisocyanate (m-XDI) is a raw material wildly used in the manufacture of high value-added polyurethane products and others. m-XDI is a heat-sensitive and easily polymerized substance, and obtaining high-purity m-XDI in industry is challenging, difficult and costly. In this paper, a coupling process of crystallization distillation was proposed to meet the challenge. First, an experiment was carried out to produce a simulated liquid close to the actual pyrolysis liquid components by the reaction of XDI and ethanol. Secondly, two key factors, the final crystallization temperature and the concentration of the m-XDI reaction liquid, which have great effect on the crystallization process of the m-XDI reaction liquid, are studied. Combined with m-XDI saturated vapor pressure and m-XDI-TLB VLE data, the process of m-XDI separation by crystallization distillation coupling was simulated (as shown in the Figure 1), and the process was compared with that of m-XDI separation by distillation alone. The purity of 99.1% m-XDI was obtained by the coupled process of crystal distillation.

Experimental study and modeling of the isothermal VLE properties of ethylbenzene in supercritical solvents (CO2 and C3H8)

The isothermal VLE properties (PTxy) of two binary mixtures of ethylbenzene+CO2 and ethylbenzene+C3H8 at temperatures of (313.15, 333.15, 353.15) K, (393.15, 413.15, 433.15) K and at pressures up to 13 MPa and 6.4 MPa, respectively, were measured in the present work using a high-temperature and high-pressure optical cell VLE apparatus based on the static-analytic method. The combined expanded absolute uncertainty of the temperature, and the relative uncertainty of pressure, and concentration measurements at 0.95 confidence level with a coverage factor of k = 2 is estimated to be 0.15 K, 0.002 (or within 0.002–0.02 MPa, depending on temperature and pressure ranges), and 0.03, respectively, and 0.035 (or within 0.0001–0.028 mol fraction depending on temperature and pressure ranges), respectively. The critical parameters (TC, PC, xC) of the both mixtures were determined based on the measured isothermal phase equilibrium VLE data. Using the derived and reported critical property data (initial slopes of the critical curves at the solvent critical point, CO2 and C3H8) for ethylbenzene+CO2 and ethylbenzene+C3H8 mixtures, the values of the physical meaning (theoretically important) Krichevskii parameter have been calculated. The effect of the critical solvent (CO2 and C3H8) on the value of the Krichevskii parameter is studied. Pure- and mixture- like thermodynamic behavior (Fisher’s renormalization of the critical behavior of dilute mixtures) and structural properties (cluster sizes) of the infinite dilute mixture near the critical point of pure solvents (CO2 and C3H8) have been studied based on the Krichevskii parameter and initial slopes of the critical curves. Accuracies of the Perturbed-Chain Statistical Association Fluid Theory (PC-SAFT) and its Critical Point-based revision (CP-PC-SAFT) models in estimating the measured VLE data with the zero value of the binary adjustable parameter k12 were compared with E-PPR78 (Enhanced Predictive Peng–Robinson, 1978) approach.

Vapor–Liquid Equilibrium Experiment and Thermodynamic Model Correlation for Ethanol + Isopropyl Acetate with Ionic Liquid at 101.3 kPa

Due to the azeotrope between ethanol and isopropyl acetate, separating them and meeting the separation requirements is challenging. In this study, ethylene glycol (EG), dimethyl sulfoxide (DMSO), and 1-butyl-3-methyl-imidazole acetate ([BMIM][OAC]) were selected as entrainers, and the vapor–liquid equilibrium data of ethanol–isopropyl acetate, ethanol + isopropyl acetate + EG, ethanol + isopropyl acetate + DMSO, and ethanol-isopropyl acetate + [BMIM][OAC] were measured at atmospheric pressure. The thermodynamic NRTL model was able to fit these experimental results. It showed that the model could correctly describe the influence of these entrainers on this azeotropic system. According to the VLE data, three entrainers caused different effects on the relative volatility of ethanol–isopropyl acetate. The azeotropic point would be completely eliminated, while the mole fraction of [BMIM][OAC] added is 0.1, which performs better than EG and DMSO.

Aqueous biphasic systems containing sodium L-tartrate dihydrate and PEG, experimental and application of extended thermodynamic models

In the current study, liquid-liquid equilibrium data of aqueous two-phase systems (ATPS) containing polyethylene glycol at the different molecular weights (1000, 2000, 6000, and 8000) - sodium L-tartrate dihydrate - water at 298.15 K were obtained. Binodal curves of mentioned systems have been determined and the effect of the molecular weight of polymer on binodal curves, tie-lines, and two-phase region sizes was studied. The results showed that increasing the molecular weight of the polymer enhances the biphasic area of the system. Also, an extended UNIQUAC equation and an extended form of Virial expansion models as new models of activity coefficient were examined to predict the phase equilibria of mentioned systems. The fitted binary interaction parameters of the model were reported. Both investigated models were capable to correlate the VLE and LLE data of the pertinent binary and ternary systems successfully. It could be observed that the extended Virial model leads to a better presentation of the data in comparison to the extended UNIQUAC model.

Measurement and Correlation of Isothermal Vapor–Liquid Equilibrium Data for (−)-α-Pinene + (−)-β-Pinene + Water + Phenoxyacetic Acid

Isothermal vapor–liquid equilibrium data of the binary system (−)-α-pinene + (−)-β-pinene and the quaternary system (−)-α-pinene + (−)-β-pinene + water + phenoxyacetic acid were measured at 313.2, 323.2, and 333.2 K using headspace gas chromatography. The experimental data showed that the addition of phenoxyacetic acid and water promoted the separation of (−)-α-pinene and (−)-β-pinene. The experimental data were correlated using the UNIQUAC and NRTL models. The two models showed good correlation for the binary system, whereas the UNIQUAC model gave more accuracy for the quaternary system. Moreover, the COSMO-RS model can be an efficacious method for predicting VLE data of the determined binary and quaternary systems. In addition, the optimal spatial configuration and binding energy between the molecules were obtained by DFT, and the effects on (−)-α-pinene and (−)-β-pinene with the addition of phenoxyacetic acid and water were discussed on the molecular scale.