Binary mixtures phase equilibria

Consequently, at fixed temperature the two phase compositions and the pressure are fixed. Varying the average mole fraction would change the mass distribution between the two phases, but would not change the composition of either phase or the total pressure. That is, when two liquid phases and a vapor phase exist in a binary mixture, the equilibrium pressure depends only on temperature and not on average composition. 

The prerequisite of all types of extraction processes is the existence of a large miscibility gap between raffinate and extract. The thermodynamic principles of phase equilibrium are dealt with in Chap. 2. An extensive collection of liquid-liquid equilibria is given in the Dechema Data Collection (Sorensen and Arlt 1980ff). Volume 1 contains data of miscibility gaps of binary systems. Phase equilibrium data (miscibility gaps and distribution equilibrium) of ternary and quaternary mixtures are listed in volumes 2-7. 

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS 12.3 Binary Mixture in equilibrium with a Pure Phase... 

BINARY MIXTURE IN EQUILIBRIUM WITH A PURE PHASE... 

VPLQFT is a computer program for correlating binary vapor-liquid equilibrium (VLE) data at low to moderate pressures. For such binary mixtures, the truncated virial equation of state is used to correct for vapor-phase nonidealities, except for mixtures containing organic acids where the "chemical" theory is used. The Hayden-0 Connell (1975) correlation gives either the second virial coefficients or the dimerization equilibrium constants, as required. 

The difficulties encountered in the Chao-Seader correlation can, at least in part, be overcome by the somewhat different formulation recently developed by Chueh (C2, C3). In Chueh s equations, the partial molar volumes in the liquid phase are functions of composition and temperature, as indicated in Section IV further, the unsymmetric convention is used for the normalization of activity coefficients, thereby avoiding all arbitrary extrapolations to find the properties of hypothetical states finally, a flexible two-parameter model is used for describing the effect of composition and temperature on liquid-phase activity coefficients. The flexibility of the model necessarily requires some binary data over a range of composition and temperature to obtain the desired accuracy, especially in the critical region, more binary data are required for Chueh s method than for that of Chao and Seader (Cl). Fortunately, reliable data for high-pressure equilibria are now available for a variety of binary mixtures of nonpolar fluids, mostly hydrocarbons. Chueh s method, therefore, is primarily applicable to equilibrium problems encountered in the petroleum, natural-gas, and related industries. 

Thermodynamic models are widely used for the calculation of equilibrium and thermophysical properties of fluid mixtures. Two types of such models will be examined cubic equations of state and activity coefficient models. In this chapter cubic equations of state models are used. Volumetric equations of state (EoS) are employed for the calculation of fluid phase equilibrium and thermophysical properties required in the design of processes involving non-ideal fluid mixtures in the oil and gas and chemical industries. It is well known that the introduction of empirical parameters in equation of state mixing rules enhances the ability of a given EoS as a tool for process design although the number of interaction parameters should be as small as possible. In general, the phase equilibrium calculations with an EoS are very sensitive to the values of the binary interaction parameters. 

In contrast to the Gibbs ensemble discussed later in this chapter, a number of simulations are required per coexistence point, but the number can be quite small, especially for vapor-liquid equilibrium calculations away from the critical point. For example, for a one-component system near the triple point, the density of the dense liquid can be obtained from a single NPT simulation at zero pressure. The chemical potential of the liquid, in turn, determines the density of the (near-ideal) vapor phase so that only one simulation is required. The method has been extended to mixtures [12, 13]. Significantly lower statistical uncertainties were obtained in [13] compared to earlier Gibbs ensemble calculations of the same Lennard-Jones binary mixtures, but the NPT + test particle method calculations were based on longer simulations. 

However, in some special cases, the lost of information due to the thresholding procedure may cause a noticeable systematic error, because each lattice point such that < )(r) > < )0 contributes the same volume fraction 1/L3 regardless of the field magnitude. Consider an asymmetric binary mixture undergoing the phase separation. The local volume fraction distribution P(< >) has maxima at the equilibrium volume fractions, 1, and is asymmetric relatively to... 

Mixture property Define the model to be used for liquid activity coefficient calculation, specify the binary mixture (composition, temperature, pressure), select the solute to be extracted, the type of phase equilibrium calculation (VLE or LLE) and finally, specify desired solvent performance related properties (solvent power, selectivity, etc.)... 

For a binary mixture under constant pressure conditions the vapour-liquid equilibrium curve for either component is unique so that, if the concentration of either component is known in the liquid phase, the compositions of the liquid and of the vapour are fixed. It is on the basis of this single equilibrium curve that the McCabe-Thiele method was developed for the rapid determination of the number of theoretical plates required for a given separation. With a ternary system the conditions of equilibrium are more complex, for at constant pressure the mole fraction of two of the components in the liquid phase must be given before the composition of the vapour in equilibrium can be determined, even for an ideal system. Thus, the mole fraction yA in the vapour depends not only on X/ in the liquid, but also on the relative proportions of the other two components. 

Equilibrium Phase Behaviour. Phase studies were performed using approximately 10 g samples of oil-surfactant mixture diluted sequentially by the weighed addition of water. The initial binary mixture contained 5-70 w/w surfactant at 5 intervals. Phase boundaries were determined to + 0.5 water. The ternary mixtures in Pyrex glass tubes fitted with PTFE lined caps were equilibrated to the required temperature (20-65 0.1°C) for 2 hours and then thoroughly mixed for 5 minutes using a Fisons orbitsil whirlimixer. The tubes were then returned to the waterbath and left undisturbed for 48 hours before identification of the phase type using a crossed polarised viewer and an optical microscope. 

Phase Behaviour. The differences in the self-emulsifying behaviour of Tagat TO - Miglyol 812 binary mixtures can, in part, be explained from considerations of their phase behaviour. Figures 4a-4d show the representative equilibrium phase diagrams obtained when binary mixtures containing 10,25,30 and 40J surfactant were sequentially diluted with water. The phase notation used is based on that of Mitchell et ai (li). 

Fig. 2. Phase diagram describing lateral phase separations in the plane of bilayer membranes for binary mixtures of dielaidoylphosphatidylcholine (DEPC) and dipalmitoyl-phosphatidylcholine (DPPC). The two-phase region (F+S) represents an equilibrium between a homogeneous fluid solution F (La phase) and a solid solution phase S presumably having monoclinic symmetry (P(J. phase) in multilayers. This phase diagram is discussed in Refs. 19, 18, 4. The phase diagram was derived from studies of spin-label binding to the membranes.

Two approaches have been used in correlating the phase equilibrium behavior of complex mixtures involving a non-volatile salt dissolved in a binary solvent mixture. Johnson and Furter (i) developed what appears to be the most popular approach by correlating the ratio of relative volatilities of the solvents as a function of salt concentration. Meranda and Furter (2) review this approach and present experimental determinations of the necessary parameters as a function of mole fraction of one of the solvents. 

The thermodynamic excess functions for the 2-propanol-water mixture and the effects of lithium chloride, lithium bromide, and calcium chloride on the phase equilibrium for this binary system have been studied in previous papers (2, 3). In this paper, the effects of lithium perchlorate on the vapor-liquid equilibrium at 75°, 50°, and 25°C for the 2-propanol-water system have been obtained by using a dynamic method with a modified Othmer still. This system was selected because lithium perchlorate may be more soluble in alcohol than in water (4). 

In a binary system more than two fluid phases are possible. For instance a mixture of pentanol and water can split into two liquid phases with a different composition a water-rich liquid phase and a pentanol-rich liquid-phase. If these two liquid phases are in equilibrium with a vapour phase we have a three-phase equilibrium. The existence of two pure solid phases is an often occuring case, but it is also possible that solid solutions or mixed crystals are formed and that solids exists in more than one crystal structure. 

Experimental data on only 26 quaternary systems were found by Sorensen and Arlt (1979), and none of more complex systems, although a few scattered measurements do appear in the literature. Graphical representation of quaternary systems is possible but awkward, so that their behavior usually is analyzed with equations. To a limited degree of accuracy, the phase behavior of complex mixtures can be predicted from measurements on binary mixtures, and considerably better when some ternary measurements also are available. The data are correlated as activity coefficients by means of the UNIQUAC or NRTL equations. The basic principle of application is that at equilibrium the activity of each component is the same in both phases. In terms of activity coefficients this... 

Phase equilibrium resulting in a UCST is the most common type of binary (liquid + liquid) equilibrium, but other types are also observed. For example, Figure 14.5 shows the (liquid + liquid) phase diagram for (xiH20 + jc2(C3H7)2NH. 7 A lower critical solution temperature (LCST) occurs in this system/ That is, at temperatures below the LCST, the liquids are totally miscible, but with heating, the mixture separates into two phases. 

---