High-pressure Phase Equilibria Research Articles

Determination of Vapor–Liquid Equilibria of the Binary System of Sub- and Supercritical CO2 and Diethyl Fumarate

High-pressure liquid–vapor phase equilibrium data (P–T–x–y) for the binary mixture of the ester diethyl fumarate with CO2 have been measured at temperatures of (373.2, 398.2, 423.2, and 453.2) K over the pressure range from (2.5 to 23) MPa using a static-analytic method. The results show that the molar fraction of CO2 in the liquid phase increases with increasing pressure at the studied temperatures and decreases with increasing temperature at constant pressure, while the composition of the light phase remains more or less unchanged. The experimental results were correlated using the Peng–Robinson equation of state in combination with one fluid mixing rule with two adjustable parameters, and the binary interaction parameters were calculated as functions of temperature. Overall, the absolute average relative deviations of the model from the data obtained for the light and heavy phases ranged from (8 to 10) % and (4 to 12) %, respectively.

High-pressure phase equilibrium calculations for carbon dioxide + cyclopentane binary system

AbstractThe phase behavior of the carbon dioxide + cycloalkane mixtures usually receives low attention, though these systems are important for many industries, e.g. the carbon capture and storage. In this paper calculations results for the carbon dioxide + cyclopentane binary system are presented, based on SRK and PR cubic equations of state with classical van der Waals mixing rules. A single set of binary parameters for each model was proposed to predict the global phase behavior of the system in a wide range of pressure and temperature. Albeit the thermodynamic models used are simple, they are able to represent fairly well the phase behavior of the system analyzed in this paper.

High pressure phase equilibrium of wax: A new thermodynamic model

A problem in the thermodynamic modeling of wax precipitation at high pressure is the extension of liquid to solid fugacity ratio of pure component to high pressure, related to the molar volume integral of pure component in the liquid and solid phases. In this work, overcoming to this is achieved by using the Clapeyron equation to make a relationship between the thermophysical properties and changing of the pure component molar volume during the phase change. These thermophysical properties are enthalpies and pressure–temperature (PT) saturation slope in the solid–liquid (SL) and order–disorder (OD) solid regions. In this work, by the available experimental data, dependency of saturation pressure on temperature is obtained for some pure normal alkanes (n-alkanes). Based on these functions, the average values of 4.5 and 3.5 are calculated for the PT slope in two regions of the SL and OD solid, respectively. By these findings, a new approach is constructed for the liquid to solid fugacity ratio of pure component at high pressure. To demonstrate the priority of the new method, 458 data points of the SL phase change temperature of different n-alkanes mixtures at a wide range of carbon number, composition and pressure are employed. Then, three UNIQUAC models are investigated to combine with the new approach to describe the non-ideal behavior of the solid wax phase. The results justify the reliability of the new model using a recent modified version of UNIQUAC with an average absolute deviation percent (AAD%) of 0.8%.

A novel continuous flow apparatus with a video camera system for high pressure phase equilibrium measurements

A novel continuous flow apparatus with a camera system was developed and constructed for high pressure phase equilibrium measurements. Vapor pressures of ethanol, diphenylmethane, n-heptane, toluene and water and bubble point pressures of three binary systems, ethanol+water, diphenylmethane+n-heptane and diphenylmethane+toluene, were measured at high temperatures and pressures (T=473–597K, P=0.2–12MPa). The results of vapor pressure and the ethanol+water system measurements were compared with literature values. Absolute average vapor pressure deviation was found to be lower than 0.03MPa for all measured vapor pressures. The ethanol+water system were modeled with the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state. Absolute average pressure deviation was 0.09MPa for data points measured in this work whereas the deviation was 0.11MPa for literature data points. To conclude, the measured values in this work agreed well with the data found from literature and the constructed apparatus with the developed measurement method can produce data with good quality. The behavior of diphenylmethane+n-heptane and diphenylmethane+toluene systems was at first predicted with the PC-SAFT and the Peng–Robinson equations of state without binary interaction parameters. Additionally, parameters were regressed to optimize the performance of the used models. Both equations of state modeled the behavior of systems well.

Vapor–liquid phase equilibrium of carbon dioxide with mixed solvents of DMSO + ethanol and chloroform + methanol including near critical regions

A visual and volume-variable high-pressure phase equilibrium analyzer was used for measuring the vapor–liquid phase boundaries of the ternary systems containing carbon dioxide and mixed solvents of dimethyl sulfoxide (DMSO)+ethanol or chloroform+methanol at temperatures from 298.15K to 348.15K over wide composition ranges including near critical points. Four pseudo-binary systems of carbon dioxide plus mixed solvents with constant molar ratios of DMSO/ethanol=3/7, 5/5, 7/3, and chloroform/methanol=1/2, were studied in this work. The critical conditions at each investigated temperature were estimated from the experimental isothermal phase boundaries by interpolation. The Peng–Robinson equation of state with the two-parameter van der Waals mixing rules was applied to calculate the phase boundaries. The experimental values were compared with the predicted results from the Peng–Robinson equation using the binary interaction parameters determined from the vapor–liquid equilibrium data of the constituent binaries. The agreement is reasonably well for carbon dioxide+chloroform+methanol, but obvious overestimations are found near the critical regions of carbon dioxide+DMSO+ethanol, especially at higher temperatures.

Avances sobre Métodos de Consistencia Termodinámica de datos de Equilibrio entre Fases de Mezclas Binarias que Contienen Líquidos Iónicos

In this paper the advances done by the research groups of the University of La Serena and University of Concepcion on thermodynamic consistency tests of low to high pressure phase equilibrium data of binary mixtures are presented. The main advances of the group consist of the extension of a thermodynamic consistency test previously proposed by the Group of La Serena to mixtures containing an ionic liquid. The method has been especially designed to analyze data sets that do not cover the whole concentration range and is based on the Gibbs-Duhem equation and an appropriate application of equations of state, mixing rules and combining rules. The proposed method allows analyzing single data from an experimental data set and determining thermodynamic consistency or inconsistency of the equilibrium data in all cases.

Properties and Performance of Gas-Expanded Lubricants in Tilting Pad Journal Bearings

Lubricants enable proper function and reduce friction in rotating machinery, but they can also contribute to power loss and heat buildup. Gas-expanded lubricants (GELs) have been proposed as tunable mixtures of lubricant and CO2 under pressure with properties such as viscosity that can be controlled directly in response to changing environmental or rotordynamic conditions. In this work, experimental results of GEL viscosity, gas diffusivity, and thermal conductivity were combined with high-pressure phase equilibrium data to understand how these mixtures will behave in tilting pad journal bearings under a range of industry-relevant high-speed conditions. Simulations were carried out using the experimental data as inputs to a thermoelastohydrodynamic model of tilting pad journal bearing performance. Viscosity could be easily tuned by controlling the composition of the GEL and the effect on bearing efficiency was appreciable, with 14–46% improvements in power loss. This trend held for a range of lubricant chemistries with polyalkylene glycols, polyalpha olefins, and a polyol ester tested in this work. Diffusivity, which drives how readily CO2 and lubricants form homogenous mixtures, was found to be a function of the viscosity of the synthetic lubricant, with more viscous lubricants having a lower diffusivity than less viscous formulations. Model results for a bearing in a pressurized housing suggested that cavitation would be minimal for a range of speed conditions. Other bearing parameters, such as eccentricity, temperature, and minimum film thickness were relatively unchanged between conventionally lubricated and GEL-lubricated bearings, suggesting that the efficiency improvements could be achieved with few performance tradeoffs.

Calculation of the high pressure phase equilibrium in hyperbranched polymer systems with the lattice-cluster theory

Currently, the lattice-cluster theory (LCT) is the most convenient thermodynamic tool to describe the branching influence on the phase equilibrium of hyperbranched polymer systems. Unfortunately, until now all applications of the LCT to such systems were restricted to moderate pressure because of the assumption of a rigid lattice. However, there is also a compressible version of the LCT known since a long time. Here, unoccupied lattice sites (voids) are permitted to make the system compressible. Thus, a binary system A+B is treated as ternary system A+B+C where C represents the voids. In this paper, the very complex equations are essentially simplified resulting in an applicable notation. On this base a LCT equation of state is developed and applied to the calculation of the high pressure phase equilibria of carbon dioxide+Boltorn U3000 and of propane+Boltorn H3200. The polymers are fatty acid modified Boltorn H30 molecules (hyperbranched polyester of generation number g=3). The calculated results agree reasonably well with the experimental data from literature.

Development and testing of a new apparatus for the measurement of high-pressure low-temperature phase equilibria

A new apparatus for the study of high-pressure phase equilibria at low temperatures using an analytical method was designed, assembled and tested. The apparatus was specially developed for the study of multi-phase equilibria in systems containing hydrocarbons, water and hydrate inhibitors, at temperatures ranging from 213K to 353K and pressures up to 40MPa. The core of the apparatus is a variable-volume equilibrium cell, equipped with a 360° sapphire window and connected to an analytical system by three capillary samplers.The quality of the apparatus was confirmed through several tests, including the study of the system methane+water. An equilibrium point for the quaternary system methane+n-hexane+methanol+water is also presented.

High pressure phase equilibrium of carbon dioxide and benzaldehyde binary system

The high-pressure phase equilibria of carbon dioxide+benzaldehyde binary system were measured at temperatures from 298.55 to 345.15K and pressures from 2.20 to 14.96MPa. The experimental method used in this work was a static-analytical method with liquid and vapor phase sampling. The experimental results are discussed and compared with available literature data. The experimental data were correlated with the Peng–Robinson equation of state (PR EoS) using classical van der Waals (two-parameter conventional mixing rule) mixing rules, which could correlate well the binary phase behavior with an average absolute relative deviation of 3.4%.

Equilibrium Conditions of Methane in Semiclathrate Hydrates of Tetra-n-butylammonium Chloride

The phase equilibrium data for semiclathrate hydrates of tetra-n-butylammonium chloride (TBAC) + methane with TBAC mass fractions (w) of 0.0500, 0.0997, 0.2000, and 0.3001 are measured in the temperature range of (281.65 to 292.85) K using a visual high-pressure phase equilibrium apparatus.The experimental data are generated using an isochoric step-heating method (T-cycle method). Methane partially occupied the small cages of TBAC semiclathrate hydrates, which increases the stability of the hydrates. The phase equilibrium pressure of TBAC + methane hydrates increases with the increase of temperature at a specified TBAC concentration. The experimental results present that the presence of TBAC decreases the formation pressure of methane hydrate greatly. Moreover, pressure reduction is dependent on the TBAC concentration. The experimental data also show that TBAC is a kind of promoter for methane hydrate formation.

Supercritical Phase Equilibria Modeling of Glyceride Mixtures and Carbon Dioxide Using the Group Contribution EoS

The Group Contribution Equation of State (GC-EoS) was extended to represent high-pressure phase equilibria behavior of mixtures containing mono-, di-, triglycerides, and carbon dioxide (CO2). For this purpose, the alcohol-ester and the alcohol-triglyceride binary group interaction parameters were regressed in this work, using experimental phase equilibria data from the literature. The capability of the parameters obtained was assessed by applying the GC-EoS model to simulate the supercritical CO2 fractionation of a complex glyceride mixture, which was produced by the ethanolysis of sunflower oil. Experimental data was obtained in a countercurrent packed extraction column at pressures ranging from 16 to 25 MPa and temperatures from 313 to 368 K. The GC-EoS model was applied in a completely predictive manner to simulate the phase equilibria behavior of the multistage separation process. The chemical analysis of the glyceride mixture allowed a significant simplification of its complex composition and thus, a simple and satisfactory simulation of the supercritical extraction process was achieved.

High pressure phase equilibria in methane + waxy systems. 3. Methane + a synthetic distribution of paraffin ranging from n-C 13 to n-C 22

Liquid–vapor and fluid–waxy solid phase transitions were measured under pressure on a pseudo binary system made up of methane + a waxy distribution of normal paraffins ranging from C 13 to C 22. The composition of the paraffins in the waxy fraction was defined in order to obtain an average molecular weight equal to that of pure heptadecane. Measurements were carried out up to 90 MPa by using a synthetic method on various mixtures ranging from 0 to 99% of methane. Results were compared to the phase equilibrium data of the binary system methane + heptadecane in the same conditions.

High-Pressure Phase Equilibrium and Raman Spectroscopic Studies on the 1,1-Difluoroethane (HFC-152a) Hydrate System

High-pressure phase equilibrium relations of the 1,1-difluoroethane (HFC-152a) + water binary system were investigated in a temperature range of (275.03 to 319.30) K and a pressure range up to 370 MPa. Four three-phase coexisting curves of hydrate + aqueous + gas phases, hydrate + HFC-152a-rich liquid + gas phases, hydrate + aqueous + HFC-152a-rich liquid phases, and aqueous + HFC-152a-rich liquid + gas phases originate from the quadruple point of hydrate + aqueous + HFC-152a-rich liquid HFC-152a + gas phases located at (288.05 ± 0.15) K and (0.44 ± 0.01) MPa. The structure of HFC-152a hydrate remains structure I (s-I) in the pressure range up to 370 MPa. Raman spectra of the HFC-152a molecule in the HFC-152a hydrate indicate that the HFC-152a molecules occupy only large cages of s-I HFC-152a hydrate in the presence of completely vacant small cages at a pressure up to 370 MPa.

High-pressure vaporization modeling of multi-component petroleum–biofuel mixtures under engine conditions

Numerical simulation of the vaporization of multi-component liquid fuels under high-pressure conditions is conducted in this study. A high-pressure drop vaporization model is developed by considering the high-pressure phase equilibrium which equates the fugacity of each component in both liquid and vapor phases. Peng–Robinson equation of state is used for the calculation of fugacity. To model the vaporization of diesel fuel under high-pressure conditions, continuous thermodynamics based on a gamma distribution is coupled with phase equilibrium by correlating the parameters of the equation of state with the molecular weights of the continuous components. The high-pressure vaporization model is validated using the experimental data of n-heptane drops under different ambient pressures and temperatures. Good levels of agreement are obtained in drop size history. Predicted results of the vaporization of diesel fuel drops show that increasing ambient pressure leads to a shorter drop lifetime under high temperature conditions (e.g., 900 K). On the other hand, at a slightly lower temperature of 700 K, the drop lifetime increases as the ambient pressure increases. It is found that the net affects of high ambient pressure on drop vaporization are determined by two competing factors, namely, reduced mass transfer number and reduced enthalpy of vaporization. The model was further applied to biodiesel and its blends with diesel fuel. The fuel blend is modeled based on a method that continuous thermodynamics is used to model diesel fuel and biodiesel is modeled as a mixture of its five representative components. Results of single drop vaporization history show that drop lifetime increases as the volume fraction of biodiesel in the fuel blend increases. This phenomenon reveals the low vaporization rate of biodiesel that has a higher critical temperature than diesel fuel. It is also observed that the volume fraction of biodiesel in the fuel blend increases during vaporization and its vapor concentrates near the tip of the liquid spray while diesel fuel vapor is around the entire liquid spray.

High pressure phase equilibrium measurements of long chain alcohols in supercritical ethane

High pressure phase equilibrium measurements of long chain 1-alcohols (1-decanol through 1-docosanol) in supercritical ethane and their prediction are presented. The data were measured in a high pressure view cell above the melting points of these alcohols, i.e. between 308 and 356 K, and with 1-alcohol mass fractions ranging from 0.0173 to 0.648. The results show a linear relationship between the phase transition pressure and the system temperature. The phase transition pressure increases with increasing molecular mass of 1-alcohol at constant temperature and composition. Furthermore, a linear relationship exists between the phase transition pressure and the number of carbon atoms of the 1-alcohol, making it easy to predict phase transition by simple interpolation within the experimental boundaries. Additionally, the state-of-the-art sPC-SAFT EOS model, as now typically included in process simulators, is unable to predict the phase equilibria, although it tends to give better results than the classic Peng Robinson EOS.

High-Pressure Multiphase Behavior of the Ternary Systems (Ethene + Water + Acetone) and (Ethane + Water + Acetone)

The high-pressure phase equilibrium of two ternary systems—(ethene + water + acetone) and (ethane + water + acetone)—was investigated by a static−analytical method. Both systems exhibit the “salting-out” phenomenon upon pressurization by the gaseous compound. The composition of the two coexisting liquid phases L1 and L2 of the high-pressure liquid−liquid−vapor (L1L2V) equilibrium was determined at (293, 313, and 333) K over the entire pressure range that spans from about (2.9 to 8.0) MPa for (ethene + water + acetone) and from about (2.3 to 5.8) MPa for (ethane + water + acetone), respectively. Additionally, the coordinates of both critical end point lines (i.e., the lower ((L1 = L2)V) and the upper (L1(L2 = V)), respectively) bordering the L1L2V equilibrium were recorded between (278 and 353) K. For both systems, it was found that, at constant temperature, increasing the pressure has a stronger impact on the L2 phase (resulting in higher contents of the gas), whereas the composition of the water-rich L1 ...

Phase Equilibrium and Dissociation Enthalpies for Cyclopentane + Methane Hydrates in NaCl Aqueous Solutions

The phase equilibrium data of cyclopentane (CP) + methane hydrates in brine water with NaCl mass fractions of w = 0.0.035, 0.070, and 0.100 were measured in the temperature range (284.4 in 301.3) K using a visual high-pressure phase equilibrium apparatus. The dissociation enthalpies of CP + methane hydrates in hot brine water were determined via the Clausius-Clapeyron equation based on these phase equilibrium data. The effect of help gas and salinity on the phase equilibrium of CP hydrate and CP + methane hydrates was studied, respectively. Liquid CP forms hydrates with small-molecule help gas at a temperature region much higher than the quadruple point of pure CP hydrate. Methane partially occupied the small cages of structure II hydrate, which accelerates the nucleation and growth of CP + methane hydrates and increases the stability of the hydrates. The phase equilibrium pressure of CP + methane hydrates increases with the increase in temperature, and it increases linearly with the increase in NaCl concentration in solutions. The higher the temperature, the more remarkable effect the temperature and salinity has on the phase equilibrium pressure. The dissociation enthalpy decreases with the increase in temperature and the NaCl concentration.

Cloud-Point and Vapor−Liquid Behavior of Binary and Ternary Systems for the Poly(dodecyl acrylate) + Cosolvent and Dodecyl Acrylate in Supercritical Solvents

High-pressure phase behavior data were reported for poly(dodecyl acrylate) [P(DDA)] in propane, propylene, butane, 1-butene, and dimethyl ether (DME), as well as for the P(DDA) + dodecyl acrylate (DDA) (or DME) in CO2. Cloud-point curves for P(DDA) in C4 hydrocarbons were about 90 K higher than P(DDA) + C3 hydrocarbon curves, at a fixed pressure of about 10.0 MPa. The cloud-point curve for the P(DDA) + DME mixture was located between C3 and C4 hydrocarbons at pressures below about 20.0 MPa. The location of the P(DDA) + CO2 cloud-point curve shifts to lower temperatures and pressures upon the addition of DDA or DME. High-pressure phase equilibrium data were presented for the CO2 + DDA system at temperatures ranging from (313.2 to 393.2) K and pressures up to about 26.14 MPa. The CO2 + DDA system exhibits type I phase behavior with a continuous critical mixture curve and was adequately modeled using the Peng−Robinson equation of state.

MODELLING OF HIGH‐PRESSURE PHASE EQUILIBRIUM IN SYSTEMS OF INTEREST IN THE FOOD ENGINEERING FIELD USING THE PENG‐ROBINSON EQUATION OF STATE WITH TWO DIFFERENT MIXING RULES

ABSTRACT In this work, thermodynamic models for fitting the phase equilibrium of binary systems were applied, aiming to predict the high pressure phase equilibrium of multicomponent systems of interest in the food engineering field, comparing the results generated by the models with new experimental data and with those from the literature. Two mixing rules were used with the Peng‐Robinson equation of state, one with the mixing rule of van der Waals and the other with the composition‐dependent mixing rule of Mathias et al. The systems chosen are of fundamental importance in food industries, such as the binary systems CO2‐limonene, CO2‐citral and CO2‐linalool, and the ternary systems CO2‐Limonene‐Citral and CO2‐Limonene‐Linalool, where high pressure phase equilibrium knowledge is important to extract and fractionate citrus fruit essential oils. For the CO2‐limonene system, some experimental data were also measured in this work. The results showed the high capability of the model using the composition‐dependent mixing rule to model the phase equilibrium behavior of these systems.PRACTICAL APPLICATIONSThe use of the Peng–Robinson equation of state (PR‐EOS) in description of phase equilibrium of systems at high pressure has been largely reported in the scientific literature. On the other hand, the low prediction capability of the PR‐EOS to thermodynamic properties of polar multicomponent systems has been provided with the development and application of new mixing rules. The main purpose of the present work was to study a thermodynamic model to correlate systems of interest in the food engineering field, applying the PR‐EOS to a composition‐dependent mixing rule, by comparing the results with those represented by the classical mixing rule of van Der Waals (PR‐EOS). In spite of the large interest in applying supercritical technology in obtaining highly purified extracts from food, available data from systems at high pressure related to food process, and passable to be modeled, are scarce in the literature. Therefore, the investigation of simple and effective models on the description of these systems is of great importance and is a valuable tool in the study of the high‐pressure systems behavior in the food processing field.