Isothermal Vapor Liquid Equilibrium Research Articles

Estimation of excess Gibbs free energy of multicomponent biofuel mixtures of Butan-1-ol using machine learning methods based on modified Raoults law models

In biofuels, the excess Gibbs free energy of mixing is a very important thermodynamic property as it is used in evaluating the efficiency and sustainability in terms of energy conversion. Multiple biofuel systems containing butan-1-ol were examined with oxygenate ether additives such as MTBE and DIPE using isothermal vapour-liquid equilibrium data at different temperatures (298.15K, 313.15K, 318.15K). Two activity coefficient models, Wilson and van Laar model were compared by determining the bubble pressure and vapor mole fractions of each system using Modified Raoults Law and Machine Learning techniques. Besides, mole fractions and activity coefficients were used to identify the excess property. Results showed that Wilson model is appropriate for all the biofuel systems when using the Artificial Neural Network (ANN) resulting in an MSE of 3.2010e-09, 4.6792e-10, 1.6186e-10, and 5.3461e-07. In addition, van Laar model is more acceptable when Rational Quadratic GPR or Fine Tree algorithm were used with an average RMSE of 0.005820.01 and 0.020950.03 respectively. Lastly, the generated data for both activity coefficient models were also used to estimate the systems excess Gibbs free energy of mixing across varying mole fraction of its components.

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

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

Isothermal Vapor–Liquid Equilibrium Data for a Binary System of (−)-α-Pinene + (−)-Limonene and a Quaternary System of (−)-α-Pinene + (−)-Limonene + Water + Ethephon at 313.2, 323.2, and 333.2 K

Isothermal Vapor–Liquid Equilibrium Data for a Binary System of (−)-α-Pinene + (−)-Limonene and a Quaternary System of (−)-α-Pinene + (−)-Limonene + Water + Ethephon at 313.2, 323.2, and 333.2 K

Thermodynamic Behavior of (2-Propanol + 1,8-Cineole) Mixtures: Isothermal Vapor-Liquid Equilibria, Densities, Enthalpies of Mixing, and Modeling.

Vapor pressures and other thermodynamic properties of liquids, such as density and enthalpy of mixtures, are the key parameters in chemical engineering for designing new process units, and are also essential for understanding the physical chemistry, macroscopic and molecular behavior of fluid systems. In this work, vapor pressures between 278.15 and 323.15 K, densities and enthalpies of mixtures between 288.15 and 318.15 K for the binary mixture (2-propanol + 1,8-cineole) have been measured. From the vapor pressure data, activity coefficients and excess Gibbs energies were calculated via the Barker's method and the Wilson equation. Excess molar volumes and excess molar enthalpies were also obtained from the density and calorimetric measurements. Thermodynamic consistency test between excess molar Gibbs energies and excess molar enthalpies has been carried out using the Gibbs-Helmholtz equation. Robinson-Mathias, and Peng-Robinson-Stryjek-Vera together with volume translation of Peneloux equations of state (EoS) are considered, as well as the statistical associating fluid theory that offers a molecular vision quite suitable for systems having highly non-spherical or associated molecules. Of these three models, the first two fit the experimental vapor pressure results quite adequately; in contrast, only the last one approaches the volumetric behavior of the system. A brief comparison of the thermodynamic excess molar functions for binary mixtures of short-chain alcohol + 1,8-cineole (cyclic ether), or +di-n-propylether (lineal ether) is also included.

Isothermal vapor-liquid equilibria for binary liquid mixtures of ethylmercaptan and propylmercaptan with some common solvents

Isothermal vapor-liquid equilibria for binary liquid mixtures of ethylmercaptan and propylmercaptan with some common solvents

Modeling of the Vapor-Liquid Equilibria Properties of Binary Mixtures for Refrigeration Machinery

The presence of both critical and azeotropic states in the vapor-liquid equilibria (VLE) is a very important issue in the chemical and refrigeration engineering. The knowledge of the phase behavior (subcritical phase/supercritical phase) of refrigerant allows designing and optimizing the refrigeration industrials processes. However, it is rare to find data for this information, which poses a great challenge for researchers to develop predictive and correlative thermodynamic models. The present study proposes the computation of the compositions and pressures of critical and azeotropic points of the isothermal VLE as well as the correlation of experimental VLE data. Firstly, experimental data (PTxy) was used to predict the vapor-liquid phase of both critical and azeotropic behaviors and to determine their properties using the relative volatility model. Secondly, the thermodynamic model (PR-MC-WS-NRTL) was applied to correlate the data of the binary refrigerant systems and describe their isothermal (VLE) behavior. The results proved that there is good agreement between predicted values obtained by the developed model and the experimental reference data. The relative error of both critical and azeotropic properties does not exceed 4.3 % for the molar fraction and 7.5 % for the pressure using relative volatility model. On other hand the relative deviation is respectively less than 2.60 % and 2.58 % for the liquid and vapor mole fractions using (PR-MC-WS-NRTL) model. This shows the ability of these models to give a reliable solution to predict and modulate the phase behavior of the binary refrigerant systems.

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.

Measurement and prediction of isothermal vapor–liquid equilibrium of α-pinene + camphene/longifolene + abietic acid + palustric acid + neoabietic acid systems

The vapor-liquid equilibrium (VLE) data of α-pinene + camphene + [abietic acid + palustric acid + neoabietic acid] and α-pinene + longifolene + [abietic acid + palustric acid + neoabietic acid] systems at 313.15 K, 333.15 K and 358.15 K were measured by headspace gas chromatography (HSGC). These data was compared with the predictions value by Conductor-like screening model for realistic solvation (COSMO-RS). Moreover, the calculated data of COSMO-RS and NRTL（Nationally Recognized Testing Laboratory） models showed good agreement with the experimental data. It was found that the three resin acids inhibits the volatility of α-pinene, camphene and longifolene and resulted in the decrease of total pressure. Moreover, H E (HB) contributes the most to the excess enthalpy and the hydrogen bonding interaction is the dominant intermolecular force of α-pinene, camphene and longifolene with the three resin acids. In addition, the geometric structures optimization and binding energy were obtained by the DFT to further illustrate the hydrogen bonding interaction and the effects of the addition of the three resin acids on the isothermal VLE.

Measurements of Isothermal Vapor–Liquid Equilibrium and Critical Point-Based Perturbed-Chain Statistical Association Fluid Theory Phase Behavior Modeling of the Propane + Phenol and Tetracosane + Propane/n-Butane Mixtures

The isothermal vapor–liquid equilibrium (VLE, pressure, temperature, and composition of coexisting vapor and liquid phases, PTxy) was directly determined using a high-pressure optical cell for binary propane + phenol and ternary tetracosane + propane/n-butane systems. Measurements were carried out at three selected isotherms of 383.15, 403.15, and 423.15 K at pressures from 0.94 to 14.5 MPa for propane + phenol and 403.15, 423.15, and 443.15 K at pressures up to 7.5 MPa for tetracosane + propane/n-butane systems. The critical property data (TC and PC) for both mixtures have been derived from the measured VLE data. Based on the initial slopes of the critical lines (shape of the critical lines), the qualitative behavior (pure- and mixture-like behavior) of the isochoric heat capacity (CVx, weak singular property), isobaric heat capacity (CPx), and isothermal compressibility (KTx, strong singular property) of the propane + phenol binary mixture near the critical point has been studied. It is demonstrated that the simplest version of critical point-based perturbed-chain statistical association fluid theory neglecting the complex molecular background of phenol yields reasonably accurate predictions of its pure compound properties. With the value of k12 obtained by fitting the present data of propane + phenol, this model yields reliable predictions for VLE in the systems of other n-alkanes, benzene, carbon monoxide, and nitrogen.

Isothermal Vapor–Liquid Equilibrium of the Binary Mixture of Octafluoropropane (R218) + Tetrafluoromonochloroethane (R124) at Temperatures from 283.15 to 323.15 K

Isothermal Vapor–Liquid Equilibrium of the Binary Mixture of Octafluoropropane (R218) + Tetrafluoromonochloroethane (R124) at Temperatures from 283.15 to 323.15 K

Research of a Thermodynamic Function (∂p∂x)T, x→0: Temperature Dependence and Relation to Properties at Infinite Dilution

In this work, we propose the idea of considering (∂p∂x)T, x→0 as an infinite dilution thermodynamic function. Our research shows that (∂p∂x)T,x→0 as a thermodynamic function is closely related to temperature, with the relation being simply expressed as: ln(∂p∂x)T, x→0=AT+B. Then, we use this equation to correlate the isothermal vapor−liquid equilibrium (VLE) data for 40 systems. The result shows that the total average relative deviation is 0.15%, and the total average absolute deviation is 3.12%. It indicates that the model correlates well with the experimental data. Moreover, we start from the total pressure expression, and use the Gibbs−Duhem equation to re-derive the relationship between (∂p∂x)T,x→0 and the infinite dilution activity coefficient (γ∞) at low pressure. Based on the definition of partial molar volume, an equation for (∂p∂x)T,x→0 and gas solubility at high pressure is proposed in our work. Then, we use this equation to correlate the literature data on the solubility of nitrogen, hydrogen, methane, and carbon dioxide in water. These systems are reported at temperatures ranging from 273.15 K to 398.15 K and pressures up to 101.325 MPa. The total average relative deviation of the predicted values with respect to the experimental data is 0.08%, and the total average absolute deviation is 2.68%. Compared with the Krichevsky−Kasarnovsky equation, the developed model provides more reliable results.

Vapor–Liquid Equilibrium Measurements for Aqueous Mixtures of NH3+ MDEA + CO2and KOH + MDEA

Isothermal vapor–liquid equilibrium measurements were performed for aqueous solutions containing N-methyl diethanolamine (MDEA), MDEA + ammonia (NH3), MDEA + potassium hydroxide (KOH), MDEA + carbon dioxide (CO2), NH3 + CO2, and MDEA + NH3 + CO2. The experiments were carried out between 310 and 390 K and 0.07 and 34 bar using a static synthetic apparatus. Overall, 202 data points are reported in terms of total volume, total number of moles, temperature, and pressure. The experimental results for MDEA(aq), NH3(aq) + CO2(aq), and MDEA(aq) + CO2(aq) are in good agreement with the calculations done using the Extended UNIQUAC model within the studied range. The data presented in this work are also comparable to previously published measurements. This work reports for the first time VLE measurements for aqueous mixtures of MDEA + NH3 and MDEA + KOH. These data suggest that the interactions between MDEA(aq) and NH3(aq) or K+(aq) ions have a minor effect on the equilibrium pressures. Consequently, other physical properties are needed to describe the thermodynamic state of these systems, such as heat capacity, heat of dilution, and other phase equilibrium measurements. The isothermal VLE measurements for solutions containing NH3(aq) showed a pressure minimum that was confirmed by model estimates and by other works done in similar conditions. As a consequence, it is not possible to estimate the partial pressure of CO2 based on the difference between the pressure at equilibrium conditions and the partial pressure of the lean solvent. This paper demonstrates that this common approach to determining the partial pressure of gases may introduce a bias in these values. The dissolution of CO2 into MDEA(aq) + NH3(aq) mixtures changes the speciation of the system, leading to an increase in the concentration of their protonated species (MDEAH+(aq) and NH4+(aq), respectively). For this reason, the interaction between these charged species must be determined in order to perform reliable phase equilibrium calculations. Ultimately, the measurements reported in this work can be used for thermodynamic modeling of CO2 capture solvents to ensure accurate results in process simulation.

Isothermal Vapor–Liquid Equilibrium for the Tetrafluoromethane (R14) + Octafluoropropane (R218) Binary Mixture at Five Temperatures from 173.150 to 213.150 K

Tetrafluoromethane (R14) and octafluoropropane (R218) are essential nonflammable refrigerants for mixed-refrigerant Joule Thomson refrigerators. In this paper, the vapor–liquid equilibrium (VLE) data were acquired for the R14 + R218 binary mixture from 173.150 to 213.150 K by a vapor-phase single-cycle method. The VLE data were regressed by the Soave–Redlich–Kwong (SRK) equation of state plus van der Waals (vdW) mixing rule model (SRK-vdW) and the Soave–Redlich–Kwong (SRK) equation of state combined with modified Huron–Vidal first-order (MHV1) mixing rule plus non-random two liquids (NRTL) activity coefficient model (SRK-MHV1-NRTL). The maximum average absolute relative deviation of pressure (AARDp) and the maximum average absolute deviation of vapor-phase mole concentration (AADy) are 2.42% and 0.0019 for the SRK-vdW model, respectively. A better correlation result was obtained by the SRK-MHV1-NRTL model, and the maximum AARDp and AADy are 1.04% and 0.0019, respectively. Based on the experimental and calculated results, a strong non-azeotropic behavior was found.

Measurement and correlation of isothermal vapor-liquid equilibrium for (−)-β-caryophyllene + p-cymene with dehydroabietic acid at 313.15, 323.15, and 333.15K

BackgroundBoth rosin and turpentine are extremely abundant and renewable resources in nature. p-Cymene and (−)-β-caryophyllene are components of turpentine and dehydroabietic acid is a component of rosin. The determination of their vapor-liquid equilibrium data can provide more complete basic data for the separation and purification of rosin and turpentine systems. MethodsThe isothermal vapor-liquid equilibrium data of the systems of p-cymene (1) + (−)-β-caryophyllene (2) and p-cymene (1) + (−)-β-caryophyllene (2) + dehydroabietic acid (3) were determined by headspace gas chromatography at resin tapping temperature of 313.15, 323.15, and 333.15 K. Significant findingsThe experimental data showed that the addition of dehydroabietic acid significantly reduced the relative volatility of p-cymene to (−)-β-caryophyllene, and inhibited the separation of (−)-β-caryophyllene and p-cymene. The thermodynamic consistency of binary system was verified by Redlich Kister area test and Van Ness point test, while the thermodynamic consistency of ternary system was verified by Van Ness point test. The experimental data were compared with the calculated value by the NRTL, Wilson, and UNIQUAC models. The average absolute deviation of the vapor phase molar fraction was not more than 0.3%. In addition, the NRTL model was the most appropriate model.

Isothermal Vapor–Liquid Equilibria and Excess Gibbs Energy for Binary Liquid Mixtures of 1,2-Dichloroethane with Some Aliphatic Polyethers

Isothermal Vapor–Liquid Equilibria and Excess Gibbs Energy for Binary Liquid Mixtures of 1,2-Dichloroethane with Some Aliphatic Polyethers

Vapor-liquid equilibrium phase behavior of binary systems of carbon dioxide with dimethyl succinate or dimethyl glutarate

BackgroundTo develop process for separating dimethyl succinate (DMS) and dimethyl glutarate (DMG) with the aid of supercritical carbon dioxide, the vapor-liquid equilibrium (VLE) data of the related mixtures are fundamentally important. The VLE data were determined experimentally and correlated with various thermodynamic models in this study. MethodsThe isothermal VLE data were measured for carbon dioxide + DMS and carbon dioxide + DMG by using a semi-flow and a static types of apparatuses at temperatures from 313.15 K to 413.15 K and pressures up to 20 MPa. These VLE data were correlated with the Krichevsky-Ilinskaya (KI) equation, the Soave-Redlich-Kwong (SRK), the Peng-Robinson (PR) and the Patel-Teja (PT) equations of state incorporating with two-parameter one-fluid van der Waals mixing rules (vdW-2). Significant findingsThe results of this study provide the VLE data of carbon dioxide + DMS and + DMG and reveal the VLE phase transition behavior, especially crossing near critical region. The Henry's constant and critical loci were also estimated. The Peng-Robinson equation of state with the vdW-2 mixing rule yielded the best data correlation results. The optimal values of the binary interaction parameters were also obtained, which can be used in the separation process simulation and design.

Isothermal P, x, y data for the nitrogen + carbon monoxide system at five temperatures from 100 to 130 K and pressures up to 3.4 MPa

Isothermal vapor-liquid equilibrium (VLE) data have been measured for the nitrogen + carbon monoxide binary system at 5 temperatures from 100.01 to 130.07 K, and at pressures from 0.37 to 3.35 MPa. This system had already been studied by different authors. Nevertheless, the existing literature data generally indicate high vapor pressure for pure CO and for the highest CO composition in the N2-CO binary VLE measurements. Our new VLE data have been measured using the “static-analytic” method, taking advantage of two pneumatic capillary samplers (Rolsi®, Armines' patent) coupled to an adapted apparatus able to work at cryogenic temperatures. The new data were compared with the predictions of the GERG equation of state and their consistency was checked by a Van Ness type test. We have observed that the isothermal P, x, y data were well represented with the Peng-Robinson equation of state, especially in the CO rich region.

Phase Behavior of Carbon Dioxide + Isobutanol and Carbon Dioxide + tert-Butanol Binary Systems

In recent years, the dramatic increase of greenhouse gases concentration in atmosphere, especially of carbon dioxide, determined many researchers to investigate new mitigation options. Thermodynamic studies play an important role in the development of new technologies for reducing the carbon levels. In this context, our group investigated the phase behavior (vapor–liquid equilibrium (VLE), vapor–liquid–liquid equilibrium (VLLE), liquid–liquid equilibrium (LLE), upper critical endpoints (UCEPs), critical curves) of binary and ternary systems containing organic substances with different functional groups to determine their ability to dissolve carbon dioxide. This study presents our results for the phase behavior of carbon dioxide + n-butanol structural isomers binary systems at high-pressures. Liquid–vapor critical curves are measured for carbon dioxide + isobutanol and carbon dioxide + tert-butanol binary systems at pressures up to 147.3 bar, as only few scattered critical points are available in the literature. New isothermal vapor–liquid equilibrium data are also reported at 363.15 and 373.15 K. New VLE data at higher temperature are necessary, as only another group reported some data for the carbon dioxide + isobutanol system, but with high errors. Phase behavior experiments were performed in a high-pressure two opposite sapphire windows cell with variable volume, using a static-analytical method with phases sampling by rapid online sample injectors (ROLSI) coupled to a gas chromatograph (GC) for phases analysis. The measurement results of this study are compared with the literature data when available. The new and all available literature data for the carbon dioxide + isobutanol and carbon dioxide + tert-butanol binary systems are successfully modeled with three cubic equations of state, namely, General Equation of State (GEOS), Soave–Redlich–Kwong (SRK), and Peng–Robinson (PR), coupled with classical van der Waals mixing rules (two-parameter conventional mixing rules, 2PCMR), using a predictive method.

Application potential of N-hexylpyridinium bromide for separation azeotrope: Thermodynamic properties measurements

• The thermodynamic behavior of [Hpy]Br was measured by IGC technology. • Obtained the VLE data of [Hpy]Br with solvents and correlated with the NRTL. • The potential of [Hpy]Br as an extractive distillation entrainer was evaluated. A series of thermodynamic parameters of N-hexylpyridinium bromide ([Hpy]Br) ionic liquid (IL) were investigated by inverse gas chromatography (IGC) technique. These parameters included the Flory-Huggins interaction parameters ( χ 12 ), activity coefficients at infinite dilution ( γ 12 ∞ ), molar heat (enthalpy) of probe absorption in the [Hpy]Br ( Δ H 1 S ), molar heat of mixing at infinite dilution between [Hpy]Br and probe ( Δ H 1 ∞ ), and Hildebrand solubility parameters ( δ 2 ). The isothermal vapor-liquid equilibrium (VLE) data of [Hpy]Br and solvents with good solubility at 353.15K were determined from χ 12 and correlated with the NRTL model. The potential of [Hpy]Br as an entrainer for separating benzene (1)/ethanol (2), benzene (1)/isopropanol (2), and benzene (1)/thiophene (2) azeotropic mixture by extractive distillation was explored using the y - x ′ diagram. Results showed that the azeotropy of three binary systems could be broken by adding [Hpy]Br and the reliability of thermodynamic analyses was verified.

Vapor-liquid equilibrium (VLE) measurements of ethanol – heptane at isothermal (363.15, 393.15 and 423.15 K) and isobaric (101.33 kPa) conditions and correlation of liquid viscosity data

Vapor-liquid equilibria (VLE) were measured for ethanol – heptane by a modified Rose-Williams equilibrium still combined with ebulliometer at three isotherms (363.15, 393.15 and 423.15 K) and an isobar (101.33 kPa). The azeotropes were observed in VLE, and the experimental data were correlated with the Peng-Robinson-Stryjek-Vera (PRSV) equation of state. The conventional mixing rule, with kij equal to zero calculates the azeotropic pressure close to the vapor pressure of ethanol. The Adachi-Sugie (AS) mixing rule provides 0.282% average absolute relative deviation (AARD) in temperature for isobaric VLE and 1.711% AARD for isothermal VLE. Eyring theory combined with the PRSV equation enabled an average of 2.810% AARD in correlation of literature liquid viscosity data, which is sufficient for considering biofuel injector. The method will be applied to flow analysis in general process design using mixtures because viscosity can be evaluated from equation of states.