Phase Equilibria for Mixtures

The region of coexistence between liquid and gas phases is delimited by three curves  

Chapter 4. METHODS FOR THE CaLCULA VON OF HYDROCAFBON PHYSICAL PROPERTIES 151 

Gg = partial free energy of component i in the gas phase at temperature T and pressure P [kJ/kmol] 

Utilizing the concept of partial fugacity which is defined by the relation J 

So far, we have described the effect of pressure and temperature on the phase equilibria of a pure substance. We now want to describe phase equilibrium for mixtures. Composition, usually expressed as mole fraction x or j, now becomes a variable, and the effect of composition on phase equilibrium in mixtures becomes of interest and importance. 

In Chapter 5, we showed that the condition of phase equilibrium for multicomponent phases is that the chemical potential of each component must be the same in all the phases. That is 

We will be looking at first-order phase transitions in a mixture so that the Clapeyron equation, as well as the Gibbs phase rule, apply. We will describe mostly binary systems so that C = 2 and the phase rule becomes 

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Cotterman,R.L. R. Bender J. M. Prausnitz Phase Equilibria for Mixtures Containing Very Many Components.Development and Application of Continuous Thermodynamics for Chenmical Process Design Ind. Eng. Chem. Process Des. Dev. 24,194-203(1985). 

Cotterman, R. L., Bender, R., and Prausnitz, J. M., Phase equilibria for mixtures containing very many components Development and application of continuous thermodynamics for chemical process design. Ind. Eng. Chem. Proc. Des. Dev. 24,194 (1985). 

An adequate prediction of multicomponent vapor-liquid equilibria requires an accurate description of the phase equilibria for the binary systems. We have reduced a large body of binary data including a variety of systems containing, for example, alcohols, ethers, ketones, organic acids, water, and hydrocarbons with the UNIQUAC equation. Experience has shown it to do as well as any of the other common models. V7hen all types of mixtures are considered, including partially miscible systems, the... 

Effect of Pressure on Solid + Liquid Equilibrium Equation (6.84) is the starting point for deriving an equation that gives the effect of pressure on (solid + liquid) phase equilibria for an ideal mixture in equilibrium with a pure... 

Geiger, A. B., Newman, J. and Prausnitz, J. M. 2001. Phase equilibria for water-methanol mixtures in perfluorosulfonic-acid membranes. AlChE Journal 47 445-452. 

Meindersma, G.W., Podt, A.J.G., and deHaan, A., Ternary liquid-liquid equilibria for mixtures of toluene + n-heptane + an ionic liquid. Fluid Phase Equilib., 247, 158,2006. 

Ying, Xugeng Ye Ruqiang Hu ying Phase Equilibria for Complex Mixtures. Continuous-thermodynamics Method Based on Spline Fit. Fluid Phase Equilibria, 53, 407-414(1989). 

The equations of state, commonly used for the calculation of phase equilibrium in natural gas systems, are applicable to acid gas mixtures as well. In a study of equilibrium in a single system, Clark et al. claimed that equations of state were not applicable to acid gas systems. Subsequently, Carroll (1999) demonstrated that Clark et al. (1998) were probably incorrect. Carroll (1999) performed a thorough review of the phase equilibria for these systems, which cover many systems, including acid gas and hydrocarbon systems. 

Briones, J.A., J.C. Mullins, M.C. Thies, B.-U. 1987. Ternary phase equilibria for acetic acid-water mixtures with supercritical carbon dioxide. Fluid Phase Equiil. 36 235-246. 

First consider the non-aqueous phase equilibria for the four mixtures. The phase envelopes for the Very Sour Gas and the Acid Gas are shown in figure 13.3. 

The Boltzmann factor in the denominator of this equation corresponds to coupling a distinguished molecule of component a to the solution. This result is reminiscent of local composition free energy models that are widely used to calculate fluid-phase equilibria for multicomponent mixtures of nonelectrolytes. We note that > 1 corresponds to less favorable interactions in the mixtures, and 1 as 1. 

Ying, X., Ye, R., and Hu, Y., Phase equilibria for complex mixtures. Continuous thermodynamics method based on spline fit. Fluid Phase Eq. 53,407 (1989). 

The available experimental data consists essentially of heats of adsorption, AH, and separation factors, S, for an adsorbed phase—gas phase equilibria. For a gaseous mixture of two isotopic species, i and /, in equilibrium with an adsorbed phase, the separation factor, Sij, is defined as follows... 

Equation (5) is an equation-of-state for the adsorption of a pure gas as a function of temperature and pressure. The constants of this equation are the Henry constant, the saturation capacity, and the virial coefficients at a reference temperature. The temperature variable is incorporated in Equation (5) by the virial coefficients for the differential enthalpy. This equation-of-state for adsorption of single gases provides an accurate basis for predicting the thermodynamic properties and phase equilibria for adsorption from gaseous mixtures. 

The Gibbs technique has been used to predict vapor>liquid, liquid-liquid and osmotic equilibria for binary Lennard-Jones mixtures (2) phase transitions for fluids in pores (U), and phase equilibria for quadrupolar systems (Stapleton et al., Mol, Simulation, in press). 

Equation 7-14 is used to calculate the reference state fugacity of liquids. Any equation of state can be used to evaluate ([) . For low to moderate pressures, the virial equation is the simplest to use. The fugacities of pure gases and gas mixtures are needed for estimating many thermodynamic properties, such as entropy, enthalpy, and fluid phase equilibria. For pure gases, the fugacity is... 

A few years ago, we presented a review of the thermodynamic models for the treatment of hydrogen bonding in fluids and their mixtures. In that work, we gave an account of the association models and reviewed the work that was done to that time with models adopting the combinatorial approach. The two approaches were compared and applied to the description of phase equilibria and mixture properties of systems of fluids. The key conclusion was that, in the systems where both approaches apply, they prove to be essentially equivalent. However, the combinatorial approach has a much broader field of applications as it can be applied even to systems forming three-dimensional hydrogen bonding networks. 

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