High-pressure Vapor-liquid Equilibria Research Articles

A new method to combine high-pressure vapor–liquid equilibrium and thermophysical property measurements for low-volatility liquids and a gas

Vapor-liquid equilibria measurements involving liquids with low volatility, such as many types of lubricants, ionic liquids, and various solvents are essential for process research and development in a wide variety of fields. State–of–the–art methods to measure these phase equilibria, e.g. thermogravimetric analysis or equilibrium cells, generally cannot be combined with instruments measuring thermophysical properties, e.g. density, transport properties, spectroscopic properties, etc. A novel approach was developed to measure simultaneously vapor–liquid equilibrium and thermophysical properties involving a single gas dissolved in one or more low-volatility liquids. The method is based upon a mass balance measuring liquid phase density, total masses in the system, and volumes. The governing equations of the novel approach are derived, and a detailed uncertainty analysis is presented. As an example, the solubility, density, and viscosity are measured with the new apparatus for a system of a non-volatile ionic liquid solvent saturated with the compressed hydrofluorocarbon gas, pentafluoroethane (R-125), at 25 °C and 75 °C and pressures to ∼ 3.1 MPa. The solubility data are validated by comparison to previously published literature data using a high precision gravimetric microbalance. The combination of vapor–liquid equilibria and thermophysical properties in a single experiment can significantly accelerate scientific and engineering studies.

High-pressure vapor-liquid equilibrium measurements of methane + water mixtures by nuclear magnetic resonance spectroscopy

The vapor-liquid equilibrium (VLE) of methane + water mixtures has been studied with nuclear magnetic resonance (NMR) spectroscopy. This work had two primary goals. The first goal was to develop methods that broaden the utility of NMR spectroscopy for VLE measurements. In this regard, we report a method by which the liquid-phase and vapor-phase compositions are measured in separate experiments by adjusting the height of the liquid phase in the sample tube. We also report a method for hastening phase equilibration by adding glass beads to the sample and repeatedly inverting the sample tube. The second goal of this work was to collect VLE data on a challenging mixture with real-world importance. Mixtures of methane + water are a useful test case because of their challenging characteristics, including the widely differing vapor pressures of the two components. One use for accurate VLE data on methane + water mixtures is to better predict the formation of harmful liquid phases in natural gas pipelines. Herein we utilize 1H NMR spectroscopy to measure the VLE of methane + water mixtures at temperatures of 299.73, 307.98, and 323.25 K, and pressures ranging from 0.69 MPa to 13.89 MPa. Experiments were carried out with a 600 MHz spectrometer. Mixtures were prepared and equilibrated in a high-pressure zirconia sample tube with an integrated needle valve. NMR-based VLE measurements on the liquid phase are in good agreement with available literature data and with Henry's Law predictions at low pressures. However, the commonly used GERG-2008 model for natural gas systems deviates dramatically from the experimental data for the liquid phase. NMR-based VLE measurements on the vapor-phase resulted in measured water concentrations that are systematically lower than available literature data and models. This systematic offset is likely caused by peak overlap in the NMR spectra.

High-pressure vapor-liquid equilibrium of hydrogen and diesel components: Maximum likelihood implicit estimation of equation-of-state binary parameters

Due to increasing environmental requirements and efforts to improve fuel quality, hydro-processing has attained worldwide importance as a critical oil refining operation. Hydro-processing involve hydrogenation of oil fractions and subsequent separations at high-temperature, high-pressure and high hydrogen fugacity. Thus, effective thermodynamic modeling of hydro-processing systems allows accurate vapor and liquid property calculation to solve mass-energy hydro-processing balances. In this work, experimental data of high-pressure vapor-liquid equilibrium of binary systems consisting of hydrogen and Diesel hydrocarbons were compiled and used to statistically calibrate classical cubic equations-of-state and variants with different alpha functions. To accomplish this, the Maximum Likelihood Principle was used to conduct the implicit estimation of binary interaction parameters of hydrogen and each one of 22 hydrocarbons (paraffin, naphthenic and aromatic hydrocarbons) typical of Diesel fractions. Several statistical estimators were used to evaluate the estimated parameters as well as to test the insertion of a second binary interaction parameter or temperature dependence. In general, the FT Equation-of-State – i.e., the Peng-Robinson Equation-of-State using Fu & Tan alpha function for hydrogen – attained the best adherence to data and this adherence is improved by using two binary interaction parameters per pair or imposing temperature-dependence on the binary interaction parameter.

Estimating VLE behavior from SLE data in aqueous mixtures of choline chloride-sorbitol deep eutectic solvents: Experimental investigation and thermodynamic modeling using the e-NRTL model

Knowledge of solid–liquid equilibria (SLE) and vapor–liquid equilibria (VLE) for mixtures containing deep eutectic solvents (DESs) is of paramount importance. We have conducted experiments to obtain additional data for SLE systems and then used the e-NRTL model to predict the VLE behavior in mixtures of DESs comprised of choline chloride (ChCl), sorbitol (S), and water (W). The systems under investigation include three 2-component systems (S/W, ChCl/W, ChCl/S), and one 3-component system (DES/W) where the DES is obtained by mixing ChCl and S at a molar ratio of 1. Using the e-NRTL activity coefficient model, the adjusted binary interaction parameters of the proposed model are determined solely from the experimental SLE data obtained from this work and also those in the literature. There is an excellent agreement between the SLE solubility data and the e-NRTL results. The tuned model is then used to predict the bubble pressure in three aqueous systems (S/W, ChCl/W, and DES/W) with an overall AARD value of 2.21%. The excellent agreement between the experimental and predicted VLE data demonstrates the viability of the proposed thermodynamic modelling framework to represent the equilibrium systems containing DESs. The outcome from our study can be used to relate the SLE and VLE data without the need to perform experiments for both cases for the given system of interest. Compared to the VLE experiments, the SLE tests are much simpler and safer because there is little compressibility and the effect of pressure on solubility is minimal which makes it possible to conduct SLE tests at room conditions (at least for liquids with negligible non-ideality). Therefore, conducting the high-pressure VLE calculations without the need to perform VLE experiments and through SLE experimental data alone will be of practical significance.

Research on Binary Phase Equilibrium for 1-Methylnaphthalene + CO2

High-pressure vapor–liquid equilibrium data for the binary system of 1-methylnaphthalene + CO2 were measured using a set of visible phase equilibrium-measuring apparatus with the analytical isobari...

High-Pressure Vapor–Liquid Equilibria for a CO2 + p-Cymene Binary System at Temperatures from 313.15 to 353.15 K

High-pressure vapor–liquid equilibrium (VLE) data for the carbon dioxide + p-cymene system at 313.15, 333.15, and 353.15 K and pressures up to 12.0 MPa were measured by a flow-type visualization ap...

A comprehensive description of single-phase and VLE properties of cryogenic fluids using molecular-based equations of state

A complete description of fluid-phase thermodynamic properties at cryogenic conditions undoubtedly presents a serious challenge for equations of state (EOSs). This work is focused on comparing the capabilities of two Statistical Associating Fluid Theory-based EoSs, namely PC-SAFT, SAFT + Cubic, and one cubic model, the original PR EOS, in correlating and predicting various thermodynamic properties of 14 main cryogenic fluids (noble gases, light hydrocarbons, nitrogen, oxygen, carbon dioxide, carbon monoxide, and nitrous oxide). Additionally, the available low temperature vapor-liquid equilibrium (VLE) data of their binary and ternary mixtures are also evaluated in this comparative study. It has been found that, apart from the critical and near-critical data, PC-SAFT has a clear advantage in modeling the pure compound properties such the sound velocity and density (with the overall AADs% less than 7%). Nevertheless, the overestimation of the single phase properties in low temperature and high pressure regions and the poor accuracy in modeling the high pressure VLE compositions of binary mixtures are two major drawbacks of PC-SAFT. SAFT + Cubic is less accurate in predicting pure compound properties; however, having small values of binary interaction parameters, it is slightly more accurate than PC-SAFT in modeling various VLE isotherms of mixtures in a predictive manner (with the overall AADs around 3%). At the same time, PR EOS exhibits the most significant deviations from the low temperature experimental data of both pure cryogens and their mixtures. However, it yields particularly accurate predictions of isochoric heat capacities in the liquid phase.

High-Pressure Vapor−Liquid Equilibria of 1-Alkyl-1-Methylpyrrolidinium Bis(trifluoromethylsulfonyl)imide Ionic Liquids and CO2

The high-pressure vapor–liquid equilibrium for the binary systems of carbon dioxide (CO2) and a series of 1-alkyl-1-methyl pyrrolidinium bis(trifluoromethylsulfonyl)imide ionic liquids ([CnC1pyr][N...

Migration and Evaporation Characteristics of Kerosene Droplet in Supercritical Environment

A one-dimensional full transient droplet evaporation model was established under consideration of factors such as high pressure vapour-liquid equilibrium, high-pressure physical property corrections, gas phase dissolution, and shift of interface. The finite volume method was used for discretization to study the migration and evaporation characteristics of the surrogate fuel for kerosene, which was constituting of (mass fraction)80% n-decane and 20%1,2,4-trimethylbenzene, under supercritical conditions. The results show that, under supercritical conditions, the higher the temperature and the pressure, the easier and the sooner the supercritical migration occurs. Before the supercritical migration occurring, there was obvious boundary between the gas and liquid phases. The mass fraction of component was discontinuous, and the gradient of temperature near the interface was large. After the supercritical migration occurring, the surface of the droplet disappeared, there was no obvious boundary between the gas and liquid phases, and the distribution of the components mass fraction and temperature were continuously. With the increase of the initial temperature of the droplet, the time of the supercritical migration was greatly advanced, the rise rate of the droplet surface temperature increased, and the phenomenon of endothermic expansion no longer appeared.

Optimizing Thermodynamic Models: The Relevance of Molar Fraction Uncertainties

Parameters contained in thermodynamic models are usually optimized over vapor–liquid equilibrium data of binary systems, applying methods that enable consideration of the uncertainty of experimental data, such as the Maximum Likelihood Method (MLM). However, authors of these data generally indicate only the maximum or average uncertainty associated with an overall set of data. Specific uncertainties, associated with each measurement, are rarely mentioned. As a consequence, the optimization of models by, for example, MLM is usually performed by associating constant overall uncertainty values to data points, instead of their specific values. This paper aims to show that results obtained from the application of MLM are strongly affected by the use of constant rather than specific uncertainties. In particular, the optimization of models over highly nonideal high-pressure vapor–liquid equilibrium data is strongly affected by the uncertainty of molar fractions, rather than by the uncertainty of pressure and tem...

Viscosity and self-diffusivity of ionic liquids with compressed hydrofluorocarbons: 1-Hexyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)amide and 1,1,1,2-tetrafluoroethane

The viscosity and self-diffusivity of mixtures of the ionic liquid, 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide ([HMIm][Tf2N]), and the compressed gas, 1,1,1,2-tetrafluoroethane (R-134a), were measured at three different temperatures (298.15 K, 323.15 K, 343.15 K) and pressures to 21 bar. The high-pressure vapor-liquid equilibrium (VLE) of the ionic liquids with R-134a was measured to calculate the composition of the liquid phase at the various pressures encountered in the viscosity and diffusivity measurements. The viscosity of the ionic liquid decreases significantly with increased composition of R-134a at VLE. The “excess” viscosity demonstrates positive values that are believed to represent relatively strong intermolecular forces of the polar R-134a and [HMIm][Tf2N]. The self-diffusivity of mixtures of [HMIm][Tf2N] and liquefied R-134a (298.15 K and 6.7 bar) was measured and increases significantly with increases in the composition of R-134a. The self-diffusivity of [HMIm][Tf2N] in vapor-liquid equilibrium with compressed R-134a gas was measured and indicates similar increases in diffusivity with composition of R-134a. The diffusivity demonstrates close Stokes-Einstein behavior using the measured mixture viscosity data and ambient pressure self-diffusivity.

Performance evaluation of carbon dioxide-alkanolamine- water system by equation of state/excess Gibbs energy models

Numerous thermodynamic techniques have been applied to correlate carbon dioxide- alkanolamine-water systems, with varying accuracy and complexity. With advent of high pressure carbon dioxide absorption in industry, the development of high pressure thermodynamic models have became an exigency. Equation of state/excess Gibbs energy models promises a substantial improvement in this field. Many researchers have shown application of these models to high pressure vapour liquid equilibria of said system with good correlation. However, no study shows the range of application of these models in presence of other competitive techniques. Therefore, this study quantitatively describes the range of application of equation of state/excess Gibbs energy models to carbon dioxide-alkanolamine systems. The model uses Linear Combination of Vidal and Michelsen mixing rule for correlation of carbon dioxide absorption in single aqueous monoethanolamine, diethanolamine and methyldiethanolamine mixtures. The results show that correlation of equation of state/excess Gibbs energy models show a transient change at carbon dioxide loadings of 0.8. Therefore, these models are applicable to the above mentioned system for carbon dioxide loadings beyond 0.8 mol/mol and higher. The observations are similar in behaviour for all tested alkanolamines and are therefore generalized for the system.

Measurement and Modeling of High Pressure Vapor–Liquid Equilibrium for Methyl Acetate or Ethyl Acetate with 2-Butanol. Isobaric Data at 1.5 MPa

Vapor–liquid equilibrium data for the binary systems methyl acetate + 2-butanol and ethyl acetate+2-butanol, have been determined at 1.5 MPa employing a metal ebulliometer with recirculation of both phases. The thermodynamic consistency of experimental data has been verified with the Van Ness point-to-point test, using the routine in Fortran proposed by Fredenslund et al. in which the second and third virial coefficients were calculated using the Tsonopoulos method and the Orbey and Vera procedure, respectively. Different group contribution models were employed for prediction of high pressure data. The UNIFAC–Lyngby model returned good overall predictions. The ϕ–ϕ approach was applied using the perturbed-chain statistical associating fluid theory model. This equation of state produces an acceptable agreement between experimental and calculated data in both systems.

Carbon Dioxide Solubility in Aqueous Potassium Lysinate Solutions: High Pressure Data and Thermodynamic Modeling

In present study, the solubility of carbon dioxide has been determined in aqueous potassium lysinate solutions for a wide range of pressure (150 – 4040 KPa), temperature (313.15 – 353.15K) and concentration (1 – 2.5M). It was found that lysine has good absorptive capacity for carbon dioxide and is comparable to conventional alkanolamines. An enhanced Kent Eisenberg model developed for high pressure vapor-liquid equilibrium data has been used to correlate carbon dioxide solubility in aqueous potassium lysinate solutions. The model results are coherent with experimental findings.

MHV1-SRK-ASOGモデルによる二酸化炭素，メタンを含む系の高圧気液平衡の推算

高圧気液平衡を3次型状態式と過剰自由エネルギー型混合則で算出する方法が数多く提案され，現在PSRKやLCVMが実用的に広く使われている．本研究はSoave-Redlich-Kwong (SRK)3次型状態式とMHV1混合則にグループ寄与法ASOGを組み合わせたモデルMHV1-SAを提案し，先ず，5種の2成分系について常圧用ASOGグループ対パラメータを用いて高圧気液平衡の推算を行った．次にグループCO2，CH4を含む30対のグループ対パラメータを新たに決定し，二酸化炭素，メタンを含む2成分系高圧気液平衡を推算した．さらに，PSRK，LCVM，PRASOGによる推算値との比較を行ったものである．

Determination of vapor-liquid equilibrium data in microfluidic segmented flows at elevated pressures using Raman spectroscopy.

A fast, noninvasive, and efficient analytical measurement strategy for the characterization of vapor-liquid equilibria (VLE) is presented, which is based on phase (state of matter) selective Raman spectroscopy in multiphase flows inside microcapillay systems (MCS). Isothermal VLE data were measured in binary and ternary mixtures composed of acetone, water, carbon dioxide or nitrogen at elevated pressures up to 10 MPa and temperatures up to 333 K. For validation, the obtained data were compared with literature data and reference measurements in a high-pressure variable volume cell. Additionally, the mixtures were investigated at temperatures and pressures where no data is available in literature to extend the high-pressure VLE database.

High pressure vapor–liquid equilibria of methyl acetate or ethyl acetate with 2-propanol at 1.5 MPa. Experimental data and predictions

Isobaric vapor–liquid equilibrium data for the binary systems methyl acetate+2-propanol and ethyl acetate+2-propanol at 1.5MPa were obtained. The data quality was verified by using the point-to-point test of Van Ness and the Fortran routine of Fredenslund et al., which was implemented to third virial coefficient using the method of Orbey and Vera. Experimental data satisfied the validation criterion of Fredenslund et al. The azeotropic point of ethyl acetate+2-propanol was not found at 1.5MPa. The ASOG low pressure group contribution models and different versions of UNIFAC were employed for the verification of high pressure vapor–liquid equilibrium data predictions. The ϕ–ϕ approach was applied by using the Peng–Robinson equation of state and employing quadratic mixing rules. The UNIFAC-Lyngby model returned good overall predictions; however the modeling for both systems was best when the Peng–Robinson equation of state was applied.

Simulating the capture of CO2 from natural gas: New data and improved models for methane + carbon dioxide + methanol

The simulation of carbon capture unit operations often involves predicting the vapor liquid equilibrium (VLE) for mixtures containing polar, non-polar and quadrupolar compounds. In this work, we investigate how well a simple cubic equation of state (EOS) can predict the results of new low temperature, high-pressure VLE measurements of the ternary methane+carbon dioxide+methanol system, which is important to the Rectisol process used for capturing CO2 from natural gas. The ternary p, T, x measurements presented here are the first such data for this system reported in the open literature. First, predictions made with the Peng Robinson (PR) EOS as implemented in a commercial process simulator were compared to binary p, T, x data measured in this work and also taken from the literature. Significant deviations were found between the measured liquid mole fractions and those predicted with the EOS using the default binary interaction parameters (BIP): the relative standard errors were 39%, 77% and 17% for the methane+methanol, methane+carbon dioxide and methanol+carbon dioxide binaries, respectively. Regression of the PR EOS to the binary VLE data by adjusting the BIPs improved the liquid phase mole fraction predictions for the ternary mixture data by a factor of about 2.5 for methane and methanol. However, improvement by a factor of 4.4 in the carbon dioxide liquid mole fraction was achieved by describing the carbon dioxide+methanol binary with an asymmetric composition and temperature dependent mixing rule and tuning the BIPs therein to VLE data for this binary over a wide temperature range. This reduced the standard error in the liquid phase CO2 mole fractions predicted for the ternary mixture using the optimized model by 79% relative to the default model.

Modeling high pressure vapor–liquid equilibrium of ternary systems containing supercritical CO2 and mixed organic solvents using Peng–Robinson equation of state

High pressure vapor–liquid equilibrium (VLE) of CO2-expanded organic solvents was investigated using Peng–Robinson-LCVM-UNIFAC equation of state. Bubble pressure of several ternary mixtures was predicted using this model and correlations were developed based only on binary experimental data. A sensitivity study of the LCVM parameter numerical value was done by considering the coherence between the mathematical features of the mixing rule and the quality of the simulation. The results provided by PR-LCVM-UNIFAC were compared with those ones given by Peng–Robinson equation of state using the classical quadratic mixing rules (PR-CMR). Despite the use of two adjustable parameters for each binary system, PR-CMR is not able to provide good results when applied to ternary systems. The capability of PR-LCVM-UNIFAC model to predict liquid mixture density for ternary systems using parameters regressed only from bubble pressure experimental data was also investigated. Due to the lack of liquid density experimental data, it was possible to perform only a qualitative assessment of the density curves calculated by this equation of state.

초임계 이산화탄소에서 소르비탄 모노팔미테이트 계면활성제의 상거동에 관한 연구

Phase behavior of carbon dioxide + surfactant binary system and carbon dioxide + surfactant + water ternary system was investigated at the temperatures from 318 K to 348 K by using high pressure vapor liquid equilibrium apparatus containing variable-volume view cell. Sorbitan monopalmitate was used as the surfactant. The cloud point pressures for the binary mixture of carbon dioxide + sorbitan monopalmitate increased with an increasing of system temperatures and the maximum cloud point pressure was observed at the composition of 0.226 wt% of sorbitan monopalmitate. On the other hand, as the temperatures and compositions of water increased, the cloud point pressures for ternary system containing 0.1 wt% of sorbitan monopalmitate in- creased significantly. For the ternary system of constant 0.2 wt% of water, the cloud point pressure curves show relatively flat according to the change of compositions of surfactant. The cloud point pressures increased when the temperatures and composi- tions of water increased.