Vapor-liquid Equilibrium Relations Research Articles

Study on thermodynamic parameters of volatile components in polydimethylsiloxane and polystyrene

In polymer production, devolatilization is an important unit operation that separates low molecular weight components from the polymer system. The presence of volatile matter not only reduces the quality of the product, but may also cause harm to users and the environment. The Henry’s coefficient is the most fundamental parameter in the vapor–liquid equilibrium relationship. The Henry’s coefficient of n-pentane, n-hexane, and n-octane for polydimethyl siloxane (PDMS) and polystyrene (PS) were measured using the pressure difference method. The influence of different operating conditions on Henry’s coefficient has been studied. The results indicate that as the experimental temperature increases, the Henry’s coefficient of volatile matter gradually increases. The viscosity of polymers has little effect on the Henry’s coefficient. Under the same volatile matter conditions, when the viscosity increases from 50 cst to 5000 cst, the maximum growth rate of the Henry’s coefficient is only 5%. As the number of carbon atoms increases, the Henry’s coefficient decreases. This work provides theoretical guidance for polymer devolatilization processes in industry.

Vapor-liquid equilibrium in methanol + water system and modeling from 298.15 to 373.15 K

Vapor-liquid equilibrium (VLE) relationships are needed in the solution of many engineering problems. The required data can be found by performing an experiment. But such measurements are not so easy, even for binary systems. The fundamental idea of a solution- of- groups model is to utilize existing phase equilibrium data for predicting phase equilibria of systems for which no experimental data are available. The popular predictive method of industries called the UNIFAC (Universal Quasi-Chemical Functional Group Activity Coefficient) group contribution model has been found to be successful to represent the available experimental data of VLE for wide variety of mixtures at various values of temperatures and pressures. In this work, the vapour-liquid equilibrium (VLE) for the methanol (1) + water (2) system has been investigated at temperatures ranging from 298.15 K to 373.15 K. The VLE data of methanol (1) + water (2) mixture for this temperature range have been also regressed using UNIFAC model available in data pro ii. The thermodynamic consistency test of experimental data such as point test has been also performed. The phase equilibrium data generated in this work are relatively good in agreement with previous data reported in the literature.

Numerical modelling and investigation of microwave heating and boiling phenomena in binary liquid mixtures using OpenFOAM

To understand Microwave (MW) heating and boiling of binary liquid mixtures, a new multiphysics model was developed. The new model solves Maxwell's equations for the electromagnetic field distribution. Concerning the coupled dispersed and segregated vapor-liquid flow during MW boiling, it was modelled based on a hybrid Two-Fluid-Volume-of-Fluid method. As for the modelling of heat and mass transfer, Two-fluid energy and species conservation equations were solved, with new dispersed and segregated interphase heat and mass transfer closures formulated using appropriate interface jump conditions combined with vapor-liquid equilibrium relations. The new model showed reasonably good agreement with the experimental data. The capability of the model to simulate MW heating, superheating, superboiling, and interphase transfer phenomena in methanol-water mixture (heated in a multi-mode MW cavity) was demonstrated, and the associated physics was investigated. The simulation results revealed three underlying mechanisms that lead to superheating (up to 9.5°C at 300 W) in binary mixtures, namely limited bubble nucleation, inefficient mixing, and higher interfacial saturation temperature compared to that in bulk liquid (about 2°Chigher). Besides, the results also showed that the increase of heating time mainly increases the amount of superheat rather than the superheat temperature. It was also found that MW superheating tends to reduce the mass fraction of the lighter component in the released vapor (by up to 2%). In the subsequent study, the effects of several operating conditions were examined. The simulation results generally showed that higher liquid methanol concentration, higher MW power, rectangular sample geometry, and smaller sample volume lead to higher superheat intensity, but poorer methanol concentration in the vapor released. The new model and findings could open up new avenues for the design and improvement of processes such as MW-assisted synthesis, extraction, biodiesel production, and distillation.

Supercritical carbon dioxide solubility in hydrophobic ionic liquid mixtures: Experimental determination and thermodynamic modeling

The solubility of supercritical carbon dioxide (scCO2) in the pure ionic liquids (ILs): 1-hexyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate, [hmim][eFAP], and trihexyltetradecylphosphonium bis(trifluoromethylsulfonyl)imide [P6,6,6,14][Tf2N], and mixtures formed by mixing these ILs with trihexyltetradecylphosphonium tetraphenylborate ([P6,6,6,14][BPh4]), was experimentally measured by means of an equilibrium cell that was designed and assembled to allow obtaining the solubility using small amounts of ILs. This equilibrium cell was first tested using previously published experimental data where long times were necessary to reach equilibrium. However, good agreement with literature data was found. Thus, for pure [hmim][eFAP], the experimental data showed high solubility, which means molalities between 5.96 and 9.12, approximately (mole fractions between 0.78 and 0.85). However, mixing these ILs with 1% w/w [P6,6,6,14][BPh4], decreased or increased CO2 solubility depending on interactions between the ILs. The obtained experimental data was modeled using the vapor-liquid equilibrium relations by means of the Peng-Robinson equation of state and a two-parameter Van der Waals mixing rule, showing excellent agreement. Finally, the information obtained in this work could enable the study of the liquid-liquid phase microextraction with ionic liquids where the dissolution of CO2 in ILs could create an enhanced phase for the microextraction.

Mathematical modeling and optimization of carbon dioxide stripping tower in an industrial ammonia plant

In the present study, performance of an industrial regeneration tower has been examined and validated for stripping of carbon dioxide from diethanolamine (DEA)-promoted hot potassium carbonate solution. The applied model employs a comprehensive non-linear rate-based method to take into account the coupling between material and energy balances, thermodynamic vapor-liquid equilibrium (VLE) relations and chemical kinetics. VLE relations are used to model the flash section located on the top of tower. The penetration theory provides an appropriate desorption rate and enhancement factor for the chemical desorption which incorporates an extensive set of important reactions. The model predictions were compared with the operating data obtained from ammonia plant of a petrochemical complex. The impact of parameters such as steam temperature, potassium carbonate concentration, inlet temperature of rich solution, promoter concentration and column pressure on the tower performance have been examined and optimized. Acceptable agreements have been attained between the simulation and measured industrial data. The optimum conditions were found to be 2.5wt%, 1.6 barg, 401 and 378K for promoter concentration, column pressure, steam temperature, and inlet temperature of rich solution which demonstrate a good compatibility in comparison to optimum operational conditions.

다성분 염화물계 진공 증류의 잔류 액체 거동 계산

파이로 공정은 사용후핵연료 관리 이슈 해결과 유용자원 재활용 제고의 목적으로 개발되고 있다. 파이로 공정 중 전해환원 공정은 LiCl을 전해질로 사용하여 산화물을 금속으로 전환시키는 공정으로 금속 전환체에 잔류염이 포함되므로 후속 공정이 요구된다. 진공 증류 공정은 다양한 용융염계에서 적용되어 왔으며 금속 전환체에서도 활용될 수 있다. 전해환원 금속 전환체 잔류염은 LiCl과 알카리 및 알카리토 금속 염화물을 포함한다. 본 연구에서는 이들 염화물들의 증기압을 추산하여 진공 증류 공정에서 잔류 액체의 조성변화를 계산하였다. 증류된 기체가 일정하게 제거되는 조건에서 물질수지와 기-액 평형식을 결합한 모델을 개발하였으며 증기압을 이용하여 무차원 시간에 대한 액체 조성 변화를 계산하였다. 공정 조건 변화 모사를 위해 온도와 용융염 조성을 변화시켜 거동을 비교하였다. 잔류염의 증류는 주성분인 LiCl에 의해 지배되었으며 LiCl 보다 증기압이 높은 CsCl은 쉽게 제거될 것이 예상되었다. 증기압이 유사한 RbCl은 LiCl과 일정한 조성이 유지되었다. 반면 증기압이 낮은 <TEX>$SrCl_2$</TEX>와 <TEX>$BaCl_2$</TEX>는 시간에 따라 농축되며 초기 조성이 높은 경우 증류 과정에서 석출될 가능성이 있는 것으로 예상되었다. Pyroprocessing has been developed for the purpose of resolving the current spent nuclear fuel management issue and enhancing the recycle of valuable resources. An electrolytic reduction of the pyroprocessing is a process to reduce oxides into metals using LiCl as an electrolyte and requires a post-treatment process due to the inclusion of residual salt in porous metal products. A vacuum distillation has been adopted for various molten salt systems and could be applied to the post-treatment process of the electrolytic reduction. The residual salt in the metal products includes LiCl, alkali chlorides, and alkaline earth chlorides. In this paper, vapor pressures of chlorides have been estimated and the composition changes on the residual liquid during the vacuum distillation process have been calculated. A model combining a material balance and vapor-liquid equilibrium relations has been proposed under a constant vapor discharging flow rate and liquid composition changes have been calculated using the vapor pressures with respect to a dimensionless time. The behaviors have been compared with temperature and molten salt composition changes to simulate the process condition variation. The distillation of the residual salt has been dominated by LiCl which is the main component of the salt and CsCl of which vapor pressure is higher than that of LiCl would be readily removed. RbCl exhibits similar vapor pressure with LiCl and maintains its composition. However, <TEX>$SrCl_2$</TEX> and <TEX>$BaCl_2$</TEX> of which vapor pressures are much lower than that of LiCl are concentrated with time and expected to be possibly precipitated during the distillation when the initial compositions are increased.

The Binary Vapor-Liquid Phase Equilibrium of Citronella Oil under High Vacuum

Citronellal, citronellol and geraniol are the main components of the natural plant citronella oil, and their vapor-liquid phase equilibrium relationship is the critical data to separate, purify the citronella oil and design rectifying column. Citronella oil is a thermo-sensitive material, so the separation under high vacuum conditions could lower its boiling point and maintain its quality. This paper adopts the precise vapor-liquid phase equilibrium instrument to collect the binary system of citronellal-citronellol, citronellal-geraniol and citronellol-geraniol with the absolute pressure of 1.2kPa. Meanwhile, the corresponding phase equilibrium diagrams are drawn, which provide data support for the distillation of citronella oil.

Solubility of ethylene in 2,2,4-trimethylpentane and 1-octene mixture

With a static type equilibrium cell and the pressure decaying method, the solubility of ethylene in a mixture of 2,2,4-trimethylpentane and 1-octene was measured in the temperature range of 323.15–423.15 K, pressure range of 5–25 bar, and 1-octene concentration from 0 to 85 wt%. The experimental results show that the solubility of ethylene in a 2,2,4-trimethylpentane and 1-octane mixture increases with system pressure but decreases with system temperature. The experimental solubility data were also expressed in the vapor–liquid equilibrium relationship and correlated by the bubble pressure calculation using the Peng–Robinson equation of state (PR EOS) incorporated with the van der Waals one-fluid and the Zhong–Masuoka mixing rules. Among the deviations between the experimental and correlated results, the largest value of average absolute relative deviation is 1.73% for pressure at 423.15 K and that of average absolute deviation is 0.0024 mol fraction for vapor composition at 373.15 K by the Zhong–Masuoka mixing rule.

The experiments and correlations of the solubility of ethylene in toluene solvent

Polymer cyclic olefin copolymer (COC) is produced from the reaction of attaching ethyl groups to the norbornene monomer in liquid phase. The first step of process is dissolving ethylene in a liquid phase where toluene is present as a cosolvent. Thus, the solubility of ethylene in liquid toluene is the most important factor affecting the production of COC. In this study, the solubility of ethylene in toluene was measured in the temperature range from 323.15 to 423.15 K and pressure range from 5 to 25 bar. The experiments were conducted by the method of pressure decaying with a newly designed apparatus. The experimental results show that the solubility of ethylene in toluene increases with increasing pressure but decreases with increasing temperature. The experimental solubility data were expressed in the vapor–liquid equilibrium relationship and correlated fairly well by the bubble–pressure calculation with the Peng–Robinson equation of state (PR EOS) incorporated with the van der Waals one-fluid and the Zhong–Masuoka mixing rules with the consideration of binary interaction parameters. The results showed the van der Waals (vdW-1) mixing rule is slightly better than the Z–M mixing rule for pressure correlation but the Z–M mixing rule is slightly better for vapor composition correlation. A semi-empirical solubility equation with four parameters for the present binary system was proposed in this study. This proposed model estimates the solubility easier and as accurate as the PR EOS does for the present system.

Thermophysical Property Formulations for R32/R134a Mixtures

This paper deals with the thermophysical properties of R32/R134a mixtures. A computer code has been developed based on widely acceptable correlations for property predictions. The fundamental problem of the vapor-liquid equilibrium relationship is solved by using related activity and fugacity coefficients. All results are in good agreement with available experimental and computational data. This paper was presented at the ECOS’98 Conference in Nancy, June 8-10, 1998

Effect of Dissolved Salts on the Vapor-Liquid Equilibrium Relationships of Three Miscible Binary Systems at the Pressure of 101.3 kPa.

The effect of the salts sodium chloride, calcium chloride and zinc chloride on the vapor-liquid equilibria (VLE) of three miscible binary system viz., benzene-pyridine, water-pyridine and methanol-benzene has been experimentally investigated at atmosphere pressure using a Smith and Bonner type of equilibrium still. The salts were dissolved in the solvent in which they are preferentially soluble, to concentrations upto 20 percent by weight wherever possible. In the case of benzene-pyridine system, the salts calcium chloride and zinc chloride cause the “salting out” of benzene. As for the azeotropic system, water-pyridine, while sodium chloride increases the pyridine content in the vapor phase, calcium chloride and zinc chloride bring about “salting out” of water and “phase splitting”. In respect of the third binary, methanol-benzene which is also azeotropic, shift in the azeotropic composition and ‘crossover effect’ are observed upon addition of calcium chloride and zinc chloride. The experimental VLE data have been correlated using Wilson and NRTL models after ascertaining their thermodynamic consistency.

Optimal operation policy for multi-effect batch distillation system

The optimal operation policy which minimizes the total batch time is derived for a new type of separation system called “Multi-Effect BAtch Distillation system (MEBAD).” The MEBAD consists of a set of batch distillation columns connected sequentially and separates (M+1) components by M columns simultaneously. The feature of this system is that only the first column has a reboiler and only the final column has a condenser. The results of optimizations show that the feature of the optimal holdup policy depends mainly on the vapor liquid equilibrium relationship. In most cases, especially when the relative volatilities among the components are constant, the following strategy minimizes the total batch time: First, almost all of the raw material is fed to the reboiler, and the holdups of remaining vessels are gradually increased up to the final holdup. The optimization results of ten example problems show that by optimizing the vessel holdups with respect to time, a 47 % reduction on average of the total batch time is achieved.

Salt Effect of Potassium Acetate on Vapor-Liquid Equilibria of Ethanol-Water and Methanol-Ethanol Systems.

The activities of methanol, ethanol or water in potassium acetate solutions and the vapor-liquid equilibrium relations of methanol-ethanol-potassium acetate and ethanol-water-potassium acetate systems were determined by use of a flow-type apparatus at 298.15 K. The activity data are presented for single solvent and vapor-liquid equilibrium data are shown for mixed solvents. Salting-out and salting-in effects of potassium acetate were shown for ethanol-water and methanol-ethanol systems, respectively. Further, the experimental data were correlated by using the model of Chen et al.

Heterogeneous nucleation characteristics of mixed vapor of benzene and cyclohexane on a cold substrate.

The heterogeneous phase transition of mixed benzene and cydohexane vapors on a cold copper substrate was observed by slowly cooling the substrate under reduced pressure conditions. In the conversion of the vapor to the condensed phase, vapor-to-liquid or vapor-to-solid phase transitions occurred depending on the mixing ratio of both vapors. By measuring the critical vapor pressure and temperature, corresponding critical supersaturation ratios were determined for various mixing ratios of both vapors. The critical pressure for the formation of solid benzene from mixed vapor agreed closely with that of pure vapor having higher composition. The critical pressure for the formation of solid cyclohexane from mixed vapor decreased from 6 to 9% compared with that from pure vapor. Liquid condensate was formed at critical supersaturation ratios of almost unity. A phase diagram was constructed by solving a non-linear simultaneous equation derived from vapor-liquid equilibrium and critical pressure-temperature relationships. It agreed in a practical sense with the observed results.

MODELING OF HYDROLYTIC POLYMERIZATION IN A SEMIBATCH NYLON 6 REACTOR

Hydrolytic polymerization of caprolactam to Nylon 6 in a semibatch reactor is carried out by heating a mixture of water and caprolactam. Evaporation of volatiles caused by heating results in a pressure build-up. After the pressure reaches a predetermined value, vapors are vented to keep the pressure constant for some time, and thereafter, to lower the pressure to a value slightly above atmospheric in a preprogrammed manner. The characteristics of the polymer are determined by the chemical reactions and the vaporization of water and caprolactam. The semibatch operation has been simulated and the predictions have been compared with industria data. The observed temperature and pressure histories were predicted with a fair degree of accuracy. It was found that the predictions of the degree of polymerization however are sensitive to the vapor-liquid equilibrium relations. A comparison with an earlier model, which neglected mass transfer resistance, indicates that simulation using the VLE data of Giori and Hayes and accounting for mass transfer resistance is more reliable.

Vapor-liquid equilibria for four binary systems made of alcohol and cyclohexylamine at 100 kPa

Bolling points for four binary systems made of an alcohol (methanol, ethanol, 1-propanol, or 2-propanol) and cyclohexylamine were measured with a flow-type ebulliometer at 100-kPa pressure, and their isobaric vapor-liquid equilibrium relations were determined

Vapor—liquid equilibrium measurements of three binary systems made of formic acid, acetic acid and propionic acid by the dew—bubble point temperature method

Vapor—liquid equilibrium relations were measured for the three binary systems made of acetic acid, formic acid, and propionic acid at 100 kPa pressure by the dew—bubble point temperature method. Combining the experimental dew point temperature curve and the bubble point temperature curve, vapor—liquid equilibrium relationships were obtained. The experimental vapor—liquid equilibrium data were correlated with the Wilson equation, accounting for the dimerization effect of acids between like and unlike molecules in vapor phase.

Vapor-liquid equilibrium prediction with pseudo-cubic equation of state for binary mixtures containing hydrogen, helium, or neon.

A pseudo-cubic equation of state has been previously proposed by the authors. In the present study, the effective critical values of hydrogen, helium, and neon are proposed. Combining the effective critical values proposed in the present study and the pseudo-cubic equation of state proposed, vapor-liquid equilibrium relations can be successfully predicted for quantum gas mixtures without using any binary interaction parameter.

Vapor-liquid equilibria of non-azeotropic halogenated hydrocarbon mixtures under high pressure.

The vapor–liquid equilibrium phase composition of three binary non-azeotropoic halogenated hydrocarbon systems were measured in the following temperature and pressure ranges;chlorodifluoromethane (R22) + 1,2-dichloro-1,1,2,2-tetrafluoroethane (R114): 253, 283, 313, 338 K, 0.08–2.59 MPa,dichlorodifluoromethane (R12) + R114: 253, 283, 313 K, 0.06–0.90 MPa,bromotrifluoromethane (R13B1) + R12: 253, 283, 313 K, 0.21–2.09 MPa.Determination of the equilibrium data was carried out in an apparatus which can circulate vapor and liquid phase alternately.The uncertainties in measurement were less than 50 mK in temperature and 8 kPa in pressure. The uncertainties in the equilibrium composition near 0.5 mole fraction were less than 0.009 mole fraction, and near 0.9 or 0.1 are less than 0.003.Simple consistency tests were applied to check the experimental data. Their results show the reliability of the present experimental data.Two equations of state, the P–R equation and the S–R–K equation, were used to correlate the vapor–liquid equilibrium relationships of these systems. It was found that both equations of state reproduce the experimental data satisfactorily by introducing the binary interaction parameter into the conventional mixing rule.

Ebulliometric measurement of vapor-liquid equilibria for four binary systems: methanol + silicon tetramethoxide, methanol + silicon tetraethoxide, ethanol + silicon tetramethoxide, and ethanol + silicon tetraethoxide

The authors discuss vapor pressures of silicon tetramethoxide and silicon tetraethoxide measured with a small ebulliometer. Boiling points for the four binary systems made of alcohol (methanol and ethanol) and alkoxide (silicon tetramethoxide and silicon tetraethoxide) were further measured at 760 and 450 mmHg pressures, and their vapor-liquid equilibrium relations were determined by using the Wilson equation.