Isothermal Vapor-liquid Equilibrium Data 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.

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

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 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.

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.

Solubility measurements of refrigerants in polyolesters lubricants at temperature from 323.K to 383.K

In refrigeration systems and heat pumps, lubricant selection is important to avoid issues that can lead to a breakdown of the compressor and the entire system. Daniel plots are a great tool to make the selection. Half of the graph is the solubility of refrigerant in lubricating oil. Isothermal vapor-liquid equilibrium (VLE) data are measured for five refrigerants in four oils. Refrigerants include HFC-32 (dichlorofluoromethane), HFC-134a (1,1,1,2-tetrafluoroethane), HFO-1234yf (2,3,3,3-tetrafluoropropene), HFO-1336mzz(Z) (cis-1,1,1,4,4,4-hexafluoro-2-butene) and HCFO-1233zd(E) (trans-1‑chloro-3,3,3-trifluoroprop-1-ene) in four oils named POE 80, SE 55, SE 170 and SE 220, based on their viscosity grade. The experimental technique used is based on static synthetic methods. All of the data are correlated with the cubic equation of state developed by Yokozeki.

Isothermal vapour-liquid equilibrium of (difluoromethane + trifluoroiodomethane) at temperatures ranging from 253.150 K to 293.150 K

In this paper, the isothermal vapour-liquid equilibrium (VLE) data for pure difluoromethane (R32) and trifluoroiodomethane (R13I1) and their binary mixtures have been measured based on a vapour – phase single recirculation method. The data were collected for five temperatures from 253.150 K to 293.150 K. The experimental VLE data were regressed by PR-MHV2-NRTL model and PR-vdW model. The deviation curves of pressures and vapour compositions for the binary system between experimental and calculated values were given. The results indicated that the maximum mean absolute relative deviation of pressure (MARDp) for PR-MHV2-NRTL is 0.54%, which shows a better fit than PR-vdW with a maximum MARDp of 2.73%. The maximum mean absolute deviation of vapour phase mole fraction (MADy) for PR-MHV2-NRTL and PR-vdW are 0.013 and 0.010, respectively. The azeotropic behaviours were found at T = (253.150, 263.150, 273.150) K, while the zeotropic behaviours were found at 283.150 K and 293.150 K.

Vapour-liquid equilibria for the binary systems of pentafluoroethane {(R125) + 2,3,3,3-tetrafluoroprop-1-ene (R1234yf)} and {trans-1,3,3,3-tetrafluoropropene R1234ze(E)}

In this work, isothermal vapour-liquid equilibrium (VLE) data for the binary mixtures of pentafluoroethane (R125) + 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and trans-1,3,3,3-tetrafluoropene (R1234ze(E)) have been investigated. The experimental measurements were carried out by using the AnTLcirCapValVis analytical method over the temperature range from 283.15 K to 323.15 K. The standard uncertainties of temperature, pressure and mole fractions are 10 mK, 0.5 kPa and 0.005, respectively. The Peng-Robinson (PR) equation of state (EoS) and its modifications from Stryjek and Vera (PRSV and PRSV2) combined with Wong-Sandler (WS) mixing rule and the non-random two-liquid activity coefficient model (NRTL) were employed to correlate the parameters of binary mixtures, respectively. The PRSV2 + WS + NRTL model shows the best consistency with the experimental VLE data compared with the other two models (PR + WS + NRTL and PRSV + WS + NRTL). The average absolute relative deviation of pressure (AARD(p)) and average absolute deviation of vapour phase mole fraction (AAD(y)) are 0.10% and 0.0012 for R125 + R1234yf, 0.16% and 0.0014 for R125 + R1234ze(E), respectively. Both the experimental data and the calculated results imply that R125 + R1234yf and R125 + R1234ze(E) are zeotropic binary mixtures over the studied temperatures.

Vapor-liquid equilibrium measurements for 5 binary mixtures involving HFO-1336mzz(E) at temperatures from 313 to 353 K and pressures up to 2.735 MPa

Performances of systems using refrigerants are highly dependent on the selection of the working fluids. In order to guide this choice, the thermophysical properties of these fluids need to be correctly correlated. Experimental data are required for models to work; The knowledge of thermophysical properties of working fluids is required for designing ORC and High Pump (HP) systems. Isothermal vapor-liquid equilibrium (VLE) data for the HFO-1336mzz(E) (trans-1,1,1,4,4,4-hexafluoro-2-butene) binary mixture with HFC-290 (Propane), HFC-134a (1,1,1,2-tetrafluoroethane), HFC-152a (1,1-difluoroethane), HFC-227ea (1,1,1,2,3,3,3-heptafluoropropane) and HFO-1234ze(E) (trans-1,3,3,3-tetrafluoropropene) were measured at 313 K, 333 K and 353 K. The experimental technique used is based on static analytic methods. All of the data (P-x-y) were well correlated with the Peng-Robinson equation of state, associated with a Mathias-Copeman alpha function and classical mixing rules. The results of such modeling are in good agreement with the measured data.

Investigation of Thermodynamic Consistency Test of Carbon Dioxide (CO2) in Room-Temperature Ionic liquids using Generic van der Waals Equation of State

Thermodynamic consistency test of isothermal vapor-liquid equilibrium (VLE) data of various binary systems containing Carbon dioxide (CO2)/Room temperature ionic liquids (RTILs) have been investigated in wide ranges of pressures in each isotherm precisely. In this paper Generic van der Waals (GvdW) equation of state (EoS) coupled with modified van der Waals Berthelot mixing rule has successfully been applied for correlating P-T-x binary data. The optimum parameters were obtained by minimizing the average relative deviation between modeled and experimental data based on the bubble pressure algorithm. Modeling is highly shown satisfactory in all cases which means that deviations in correlated data are low subsequently can prove that the flexibility and capability of the proposed model for thermodynamic consistency. Results of the consistency test represented ten isothermal experimental data set to be thermodynamically consistent, fourteen were declared to be not fully consistent and just four isothermal experimental data sets were represented to be thermodynamically inconsistent.

Volumetric, enthalpic and VLE studies of binary mixtures of isomers of butyl chloride with cyclohexane at 298.15 K

Excess molar volumes (VmE), excess molar enthalpy (HmE) and isothermal vapor-liquid equilibrium data for n-, sec- and tert-butyl chloride (A) + cyclohexane (B) systems were measured at 298.15 K. Excess molar Gibbs free energy (GmE) for these systems were calculated by Barker's method. The VmE and HmE for these mixtures follow the sequence: n- > sec- > tert-butyl chloride while it is reverse for GmE. Prigogine-Flory-Patterson theory (PFP) predicts the experimental VmE and HmE data for these systems quite well except for HmE of n-butyl chloride (xA>0.5) mixtures and tert-butyl chloride mixtures for xA<0.5. The activity coefficients γA and γB of the components in binary (A+B) mixtures were also predicted by Singh and Maken activity coefficient model employing limited experimental activity coefficient data.

Vapour-liquid equilibria of n-butane and ethyl mercaptan: Experiments and modelling

Design of debutaniser in fractionation train in gas processing requires accurate knowledge of phase equilibrium properties of n-butane with sulphur compounds like mercaptan. In this paper, we report high-quality isothermal vapour–liquid equilibrium data for n-butane + ethyl mercaptan (or ethanethiol) between 298.14 K and 388.18 K and pressures up to 2.0029 MPa. An equipment whose experimental technique is based on static-analytic method was considered. The equipment is composed by an agitated equilibrium cell with two online micro samplers connected to a Gas Chromatograph. The data was correlated with the Peng Robinson equation of state with classical alpha function. A comparison was also performed with two predictive models, PPR78 and PSRK UNIFAC.

Excess properties and isothermal vapour-liquid equilibrium data for the ((toluene + pyridine)) system from 343 K to 383 K

Isothermal vapour-liquid equilibrium (VLE) data for the ((toluene + pyridine)) system has been measured at four temperatures from approximately 343 K to 383 K, using a dynamic-analytic apparatus. The densities of ((toluene + pyridine)) mixtures were also measured from 298 K to 363 K using an Anton Paar DMA-5000 densitometer. The vapour-liquid phase equilibrium data were modelled by the γ-Φ approach and the Non-Random Two-Liquid and UNIQUAC activity coefficient models. The consistency of the experimental isothermal VLE data were checked by the area and point tests. The experimental density data were modelled using an 8-parameter empirical correlation which allowed for the simultaneous representation of temperature and liquid composition. The experimental data were used to determine the excess properties for volume, Gibbs energy, enthalpy and entropy. The excess volume was modelled using Redlich-Kister polynomials.

Study on Particle Swarm Optimization Variant and Simulated Annealing in Vapor Liquid Equilibrium Calculation

Phase equilibrium calculation plays a major rule in optimization of separation process in chemical processing. Phase equilibrium calculation is still very challenging due to highly nonlinear and non-convex of mathematical models. Recently, stochastic optimization method has been widely used to solve those problems. One of the promising stochastic methods is Particle Swarm Optimization (PSO) due to its simplicity and robustness. This study presents the capability of particle swarm optimization for correlating isothermal vapor liquid equilibrium data of water with methanol and ethanol system by optimizing Wilson, Non-Random Two Liquids (NRTL), and Universal Quasi Chemical (UNIQUAC) activity coefficient model and also presents the comparison with bare-bones PSO (BBPSO) and simulated annealing (SA). Those three optimization methods were successfully tested and validated to model vapor liquid equilibrium calculation and were successfully applied to correlate vapor liquid equilibrium data for those types of systems with deviation less than 2%. In addition, BBPSO shows a consistency result and faster convergence among those three optimization methods. Keywords: Phase equilibrium, stochastic method, particle swarm optimization, simulated annealing and activity coefficient model

Experimental measurements and correlation of isothermal vapor-liquid equilibria for HFC-32 + HFO-1234ze (E) and HFC-134a + HFO-1234ze (E) binary systems

Currently, refrigeration industry is facing the challenge of developing new highly efficient alternative refrigerants with zero ozone depression potential (ODP) and global warming potential (GWP) lower than 150. Mixtures, composed of hydrofluoro-olefins (HFOs) with either hydrofluorocarbons (HFCs) or natural refrigerants, are of great interest, because they could meet both thermodynamic and environmental requirements. This work investigated the phase behavior of two low GWP binary refrigerants containing trans-1,3,3,3-tetrafluoropropene (HFO-1234ze (E)) and two HFCs. Isothermal vapor-liquid equilibrium (VLE) data for two binary mixtures of difluoroethane (HFC-32) + HFO-1234ze (E) and 1,1,1,2-Tetrafluoroethane (HFC-134a) + HFO-1234ze (E) were measured by a static-analysis apparatus at four temperatures ranging from (283.15 to 323.14) K. The VLE data of HFC-32 + HFO-1234ze (E) system was compared with literature, and good consistence was obtained. The experimental VLE data were correlated by Peng-Robinson (PR) equation of state (EOS) combined with van der Waals (vdW) mixing rules. The binary interaction parameters of two mixtures were obtained, and correlation deviation was acceptable. Our work provides fundamental thermodynamics properties of new mixed refrigerants which are crucial to evaluate their cycle performance and optimize the design of refrigeration system.

VLE measurements and modelling for the binary systems of (CF4 + C6F14) and (CF4+ C8F18)

Isothermal phase equilibrium data were measured for the binary systems of tetrafluoromethane with either perfluorohexane or perfluorooctane to investigate the effect of carbon chain length of the solvent with regards to the solubility of tetrafluoromethane. Both the “static-analytic” and the “static-synthetic” methods were utilized to measure the high-pressure phase equilibrium data. Isothermal measurements were performed within the temperature range of (283.15–303.15) K and at pressures up to 11 MPa. Vapour pressure data for perfluorohexane and perfluorooctane were measured within the temperature range of (283.15–323.15) K. Additionally, isothermal vapour-liquid equilibrium data were measured for the binary system of carbon dioxide + n-hexane at 313.15 K; the data were utilized to validate the experimental method. The experimental data were modeled using the Peng-Robinson equation of state with the Wong-Sandler mixing rule and Non-Random Two-Liquid excess Gibbs energy model. The model provides a satisfactory representation of the experimental data within the measured temperature range.

Vapor–Liquid Equilibrium Data for the Carbon Dioxide (CO2) + 1,1,1,3,3-Pentafluorobutane (R365mfc) System at Temperatures from 283.15 to 337.15 K

Isothermal vapor–liquid equilibrium data for the binary mixture of carbon dioxide (CO2) and 1,1,1,3,3-pentafluorobutane (R365mfc) were measured at six isotherms ranging from 283.16 to 337.16 K, at pressures ranging from 0.7 to 9.1 MPa, and are presented. The measurements were performed using a “static-analytic” apparatus, equipped with two capillary ROLSI samplers, with phase analysis performed via gas chromatography. The measured data were correlated using in-house thermodynamic software based on the Peng–Robinson equation of state with the Mathias–Copeman α function and the Wong–Sandler mixing rules incorporating the nonrandom two liquids model.