Phase Equilibria Of Binary Mixtures Research Articles

Measurements and calculations of phase equilibria in binary mixtures of propane + tetratriacontane

Abstract Peters C.J., de Roo J.L. and de Swaan Arons J., 1992. Measurements and calculations of phase equilibria in binary mixtures of propane + tetratriacontane. Fluid Phase Equilibria , 72: 251-266. This paper reports on the phase behaviour of binary mixtures of propane and tetratriacontane ( n -C 34 H 70 ) in the near-critical region of propane. The measurements cover a temperature region from about 350 K up to 420 K. Pressures up to 10 MPa were applied. It has been found that in the binary mixture propane + tetratriacontane partial miscibility occurs in the liquid phase, i.e. in this binary a three-phase equilibrium liquid + liquid + vapour (1 1 1 2 g) with a lower and upper critical endpoint exists. As well as the measurement of this three-phase equilibrium, various types of two-phase boundaries and the three-phase equilibrium solid tetratriacontane + liquid + vapour (s B 1g) have been determined experimentally. In addition simplified-perturbed-hard-chain theory (SPHCT) was applied to model the vapour + liquid equilibrium data. The results obtained are compared with similar calculations, using the Peng-Robinson (PR) equation of state. The calculations established that when modelling vapour + liquid equilibria of binaries with molecules differing largely in chain-length, the SPHCT equation of state should be preferred over the PR equation.

Measurements and calculations of phase equilibria in binary mixtures of ethane + eicosane

Peters C.J., de Roo J.L. and Lichtenthaler R.N., 1991. Measurements and calculations of phase equilibria in binary mixtures of ethane + eicosane. Part 3. Three-phase equilibria. Fluid Phase Equilibria, 69: 51-66. Experimental data of various three-phase equilibria in binary mixtures of ethane+ eicosane are presented in this contribution. The three-phase equilibrium solid eicosane + liquid + vapour was measured from about 260 K up to the triple point of eicosane (309.65 K) and the three-phase equilibrium liquid + liquid + vapour was determined between its critical endpoints, i.e. from 306.69 to 309.62 K. In order to model the three-phase equilibrium solid eicosane + liquid + vapour, the Soave-Redlich-Kwong equation of state was applied for both fluid phases, and for the representation of the p. V, T behaviour of the solid phase of eicosane an alternative expression was used.

Fluid phase equilibria in water: natural gas component mixtures and their description by the hole group-contribution equation of state

Victorov A.I., Fredenslund Aa. and Smirnova N.A., 1991. Fluid phase equilibria in water:natural gas component mixtures and their description by the hole group-contribution equation of state. Fluid Phase Equilibria, 66: 187-210. Experimental data on fluid phase equilibria in binary mixtures of water with typical natural gas and oil components (light and heavy alkanes, nitrogen, hydrogen sulfide, carbon dioxide) have been examined and the phase behavior of these mixtures over wide ranges of temperature and pressure is reviewed. A quasi-chemical group-contribution hole model is used for calculating the phase equilibria in these systems. With few exceptions the model predicts correctly the basic types of phase behavior and, except for gas-gas equilibria, the accuracy for all the binaries and two multicomponent aqueous mixtures tested is satisfactory.

Computer simulation of fluid–fluid phase coexistence in mixtures of nonadditive soft disks

Fluid–fluid phase equilibrium in binary mixtures of positively nonadditive soft disks is studied using both molecular dynamics and Gibbs ensemble Monte Carlo simulations. The molecular dynamics simulations are unable to provide quantitative results for the phase transition, but they do indicate that some sort of ordering takes place as the temperature is lowered. In contrast, the Gibbs ensemble simulations demonstrate unambiguously the presence of a first-order transition and give quantitative results for the coexistence curve; however, convergence is very slow for mixtures that are not symmetric. Comparison with the Gibbs ensemble results indicates that a simple first-order perturbation theory provides good results far from the consolute point. Closer to the consolute point, the theory does not reproduce the flatness of the coexistence curve; this limitation is intrinsic in any mean-field theory. Comments are made regarding the relative merits of molecular dynamics and Gibbs ensemble simulations for studying fluid–fluid phase coexistence.

Measurements and calculations of phase equilibria in binary mixtures of ethane+eicosane Part II: solid+liquid equilibria

This paper is a continuation of an earlier one on the phase behaviour of binary mixtures of ethane+eicosane. In this contribution experimental results of two-phase equilibrium solid eicosane+liquid are presented. The experimental work covers temperatures from about 260 K to the triple point of eicosane, i.e. 309.65 K. Pressures up to 10 MPa have been applied. Supposing ideal melting behaviour, some experimental data for the two-phase boundary solid eicosane+liquid are compared with the calculated two-phase boundary.

Phase equilibria in binary mixtures of near-critical propane and poly-aromatic hydrocarbons

Experimental results of the phase behavior of binaries of near-critical propane and the poly-aromatic hydrocarbons naphthalene, biphenyl, acenaphtene, fluorene, phenanthrene and triphenylmethane are reported. In comparison with binaries of propane and n-alkanes the phase behavior of the binaries, investigated in this study, is different. The major features will be discussed.

Ising-Potts models and solid-liquid phase equilibria in binary mixtures

An Ising-Potts model is introduced and the Bragg-Williams mean-field method and Monte Carlo simulation are used to study its properties on the FCC lattice. It is shown that for certain values of the parameters in the Hamiltonian the model exhibits phase behaviour that can be interpreted as representing solid-liquid phase equilibria in binary alloy mixtures. The first-order transition properties of the pure six-state Potts model on the FCC lattice are also reported.

Phase equilibria in binary mixtures of ethane and hexadecane

This paper reports experimental results of a study of the phase behaviour of binary mixtures of ethane + hexadecane. In the near-critical region of ethane liquid + vapour and solid hexadecane + liquid two-phase boundaries have been measured. Also the three-phase equilibrium solid hexadecane + liquid + vapour has been determined experimentally. The experimental data cover the complete mole fraction range. Pressures up to 18 MPa were applied and the investigation was performed in a temperature region from about 260 K up to 450 K.

Phase equilibria in binary mixtures of propane + acenaphthene

In the near-critical region of propane, phase equilibria of binary mixtures of propane + acenaphthene have been investigated experimentally. Apart from the three-phase equilibrium solid acenaphthene + liquid + vapour, two-phase boundaries liquid + vapour and solid acenaphthene + liquid have been investigated over the entire mole fraction range. The measurements were performed in the temperature region 350–420 K with pressures up to 10 MPa.

Phase equilibria in binary mixtures of propane and tripalmitin

The possibility of using near-critical propane as an extraction solvent for triglycerides is the subject of investigation. This contribution reports on the phase behaviour of the binary mixture of propane and tripalmitin. The analysis of the experimental data with respect to the phase behaviour indicates various extraction routes. There is evidence that liquid propane just below its critical point will be far more effective in terms of solvent capacity than its supercritical equivalent.

Modelling the phase equilibria in two-component membranes of phospholipids with different acyl-chain lengths

A phenomenological model is proposed to describe the membrane phase equilibria in binary mixtures of saturated phospholipids with different acyl-chain lenghts. The model is formulated in terms of thermodynamic and thermomechanic properties of the pure lipid bilayers, specifically the chain-melting transition temperature and enthalpy, the hydrophobic bilayer thickness, and the lateral area compressibility modulus. The model is studied using a regular solution theory made up of a set of interaction parameters which directly identify that part of the lipid-lipid interaction which is due to hydrophobic mismatch of saturated chains of different lengths. It is then found that there is effectively a single universal interaction parameter which, in the full composition range, describes the phase equilibria in mixtures of DMPC/DPPC, DPPC/DSPC, DMPC/DSPC, and DLPC/DSPC, in excellent agreement with experimental measurements. The model is used to predict the variation with temperature and composition of the specific heat, as well as of the average membrane thickness and area in each of the phases. Given the value of the universal interaction parameter, the model is then used to predict the phase diagrams of binary mixtures of phospholipids with different polar head groups, e.g., DPPC/DPPE, DMPC/DPPE and DMPE/DSPC. By comparison with experimental results for these mixtures, it is shown that difference in acyl-chain lengths gives the major contribution to deviation from ideal mixing. Application of the model to mixtures with non-saturated lipids is also discussed.

Phase equilibria by simulation in the Gibbs ensemble

The Gibbs-ensemble Monte Carlo simulation methodology for phase equilibrium calculations proposed by Panagiotopoulos [1] is generalized and applied to mixture and membrane equilibria. An alternative derivation of the Gibbs simulation criteria based on the limiting distributions for the appropriate statistical mechanical ensembles is presented. The method is then generalized for the calculation of phase equilibria of mixtures by simulation in a constantpressure Gibbs ensemble and the calculation of equilibria across semipermeable membranes with an imposed osmotic pressure difference. The method is used to calculate phase equilibria for binary mixtures of Lennard-Jones molecules. Good agreement is found with published results obtained using other simulation techniques. The computer time required for the Gibbs method is only a small fraction of the corresponding requirement for previously available simulation techniques. Calculations for simple osmotic systems are performed for the first time by simulation, ...

Phase equilibria in binary mixtures of ethane + docosane and molar volumes of liquid docosane

Experimental results for various types of phase behaviour which can occur in the binary ethane + docosane system are presented. The experimental data cover various two-phase boundaries and the three-phase equilibria solid docosane + liquid + vapour and liquid + liquid + vapour. In addition, p, V, T measurements of liquid docosane are carried out. The experimental work is performed within a temperature range of ∼ 290–370 K and at pressures of up to 16 MPa.

Measurements and calculations of phase equilibria of binary mixtures of ethane + eicosane. Part I: vapour + liquid equilibria

In a series of papers the several types of phase behaviour which are possible in binary mixtures of ethane + eicosane will be discussed. This study presents experimental results of liquid + vapour equilibria. The measurements have been performed in a temperature range from about 270 up to 450 K and pressures up to 18 MPa. To describe the experimental data, we have used the Soave-Redlich-Kwong equation of state.

Three phase equilibria in binary mixtures of ethane and higher n-alkanes

In binary mixtures of ethane + higher n-alkanes a systematic change in phase behaviour with increasing carbonnumber near the critical point of ethane can be observed. Binaries up to C 17 are completely miscible in the liquid phase and binaries up to C 23 show partial miscibility in the liquid phase with an upper and lower critical endpoint. In the binaries of ethane with C 24 and C 25 the three phase equilibrium solid n-alkane + liquid + vapour intersects the three phase equilibrium liquid + liquid + vapour and a quadruple point solid n-alkane + liquid + liquid + vapour can be observed. As the carbonnumber further increases stable liquid + liquid phasesplit will be obscured by solidification. In this contribution experimental results for the binaries C 2 + C 16, C 2 + C 20, C 2 + C 22, C 2 + C 23, C 2 + C 24, C 2 + C 25 and C 2 + C 26 will be reported and shown to present a logical evolution in phase behaviour.

Liquid-liquid phase equilibria of binary mixtures of methanol with hexane, nonane and decane at pressures up to 150 MPA

Binary mixtures of {xCH 3OH + (1−x) C 2H 2n + 2, n = 6, 9, 10} were investigated over the pressure range from 1 to 150 MPa in an optical high-pressure cell by using the synthetic method. The p(T) isopleths fit to the Simon equation with the same accuracy as the {xCH 3OH + (1−x) C nH 2n + 2, n = 7, 8} systems reported before. The equation used for the fitting of the T(x) isobars was T = T c + k|y−y c| n where y = αx/{1 + x(α − 1)} and y c = αx c/{1 + x c(α−1)}; T c and x c are the critical temperature and mole fraction respectively. The coefficients k and n are fitted by the method of least squares. The equation very successfully describes the T(x) isobars of the above systems. The critical temperatures at p = 25 MPa and 75 MPa are compared with the {xCH 3OH + (1−x) C nH 2n + 2, n = 1, 2, 7, 8} high-pressure results reported in literature. For a comparison with literature data obtained at atmospheric pressure the experimental results were extrapolated to p = 0.1 MPa.

Fluid Phase Equilibria of Binary Mixtures of SF6 with Octane, Nonane, Hendecane, and Decahydronaphthalene,cis at Temperatures between 280 K and 440 K and at Pressures up to 140 MPa in Comparison to Mixtures of Hydrocarbons with CO2, CF4, and CHF3

AbstractBinary mixtures of SF6 + octane, + nonane, + hendecane, and + decahydronaphthalene,cis were investigated up to 140 MPa. Measurements were performed according to the synthetic method using an optical high pressure cell. ‐ Going from SF6 + octane to SF6 + nonane the critical p(T)‐curves show a continuous transition between the type of liquid‐liquid (ll) phase equilibrium with upper critical solution temperatures (UCST) and the gas‐gas (gg) equilibrium of the 2nd kind. For the SF6 + n‐alkane systems there is a systematical shift of the high‐pressure branches of the critical curves of about 20 K to higher temperatures per CH2‐unit. The experimental results are discussed in comparison to computer calculations with two semiempirical equations of state. Solvent properties of SF6 are compared to those of CO2, CF4, and CHF3.

Calculation of equilibria between fluid and solid phases in binary mixtures at high pressures from equations of state

The Redlich-Kwong equation and a three-parameter equation of state of our own (Deiters, 1981, 1982), in connection with appropriate mixing rules, have been used to derive expressions for the Gibbs energy and to evaluate the thermodynamic conditions of fluid-fluid phase equilibrium in binary mixtures. With little additional information it is furthermore possible to extend our theory to equilibria between a fluid mixture and a pure solid phase, so that melting diagrams, solid-vapour equilibria, and solid-liquid-gas three-phase lines can be computed. We have calculated isothermal fluid-fluid (vapour-liquid and gas-gas) and solid-fluid phase diagrams for several binary mixtures of nonpolar substances for pressures up to 200 MPa. The Redlich-Kwong equation is found to represent the experimental data well at low pressures only whereas the results of the other equation of state agree well with the experimental data even at very high pressures. Furthermore it is possible to predict solid-fluid equilibria from fluid-fluid equilibrium data successfully.

Calculation of Fluid‐Fluid and Solid‐Fluid Phase Equilibria in Binary Mixtures at High Pressures

AbstractBy integrating an equation of state, an expression for the Gibbs energy of binary fluid mixtures is derived and used to define the thermodynamic conditions of phase equilibrium. These conditions are solved numerically for the equilibrium concentrations. The same equation of state is used for liquid and vapour phases. From additional solid density data and the sublimation/melting pressure, solid‐liquid and solid‐gas equilibria can be calculated, provided that no miscibility occurs in the solid state. ‐ Calculations of phase equilibria have been carried out for several binary mixtures of nonpolar substances (noble gases, CO2 hydrocarbons) for pressures up to 200 MPa, using the Redlich‐Kwong equation and our own equation of state, which has been published earlier [1]. ‐ The Redlich‐Kwong equation represents the experimental phase equilibrium data at low pressures only, whereas the other equation achieves good agreement over the whole pressure range. I f the molecules differ very much in size, deviations from one‐fluid theory can be accounted for by using the Leland‐Mansoori‐Carnahan‐Starling function for rigid sphere mixtures in the repulsion term of our equation of state.

(Solid + liquid) phase equilibria in binary mixtures containing benzene, a cycloalkane, an n-alkane, or tetrachloromethane An equation for representing (solid + liquid) phase equilibria

Complete (solid + liquid) phase diagrams are reported for the 10 mixtures: {(1− x) c-C m H 2 m + xC 6H 6}, m = 6, 7, 8; {(1− x)C m H 2 m+2 + xC 6H 6}, m = 8, 11, 12; {(1− x)C m H 2 m+2 + xc-C 6H 12}, m = 8, 12; and {(1− x)C m H 2 m+2 + xCCl 4}, m = 8, 12. All are simple eutectic systems except for {(1− x)C 8H 18 + xCCl 4}, which has a solid-phase transition present on the CCl 4 side of the diagram. The semi-empirical equation: X E =x(1−x) ∑ J=0 n a j(1−2x) J is proposed for summarizing the curves of melting temperature T against mole fraction x, where T ∗ is the melting temperature of the pure substance and x ∗ is the value of x at T ∗ . The coefficients a J are fitted by the method of least squares. The equation very successfully describes the above systems. It also works very well for more complicated systems including those containing congruently melting or incongruently melting solid addition compounds.