Calculation of vapour-liquid equilibria

It is a simple matter to obtain the equilibrium curve of an ideal or an almost completely insoluble mixture by calculation, and for partially soluble mixtures the calculation is fairly straightforward. For non-ideal but completely miscible systems calculation is less accurate and takes rather longer, and where some degree of precision is required equilibrium data should be obtained experimentally. However, considerable experience is needed if reliable equilibria are to be measured, and the procedures are time-consuming, particularly if materials have to be purified. 

In the last few years many contributions dealing with the calculation of phase equilibria have been published. It would lead us too far to mention all of these, particularly since this subject is exhaustively treated by Schuberth [17] and Hala et al. [78]. Their books include extensive bibliographies. Of particular interest in this context is a remark made by Spath (cf. chap. 3, ref. [17]) about a simplification in representing and evaluating vapour-liquid equihbria. 

A purely phenomenological description of the effects occurring in high-pressure vapour-liquid equilibria was given by Wichterle [83b] in the first part of a series of papers. 

The work was continued by Wichterle et al. [83d] and resulted in a generalized method of calculating and predicting vapour-liquid equilibria at high pressures. 

The practical application of molecular thermodynamics to the calculation of pihase equilibria is illustrated by Prausnitz [83c]. 

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Sub-programs for thermodynamic routines such as the calculation of vapour-liquid equilibria and stream enthalpies. 

Jaques and Furter [95] derived an equation for the salt effect on the water-vapour equilibrium in binary mixtures which correlates the temperature and the liquid concentration of the three components ethanol, water and salt. The equation has 6 constants. The theory of the salt effect has been discussed by Furter and Meranda [96]. On the basis of simplifying assumptions Sada et al. [97] have established a relation for the calculation of vapour-liquid equilibria for non-aqueous binary systems in which the salt is dissolved only in one component e.g., benzene-ethanol with lithium or calcium chloride). 

B. Sander, A. Fredenslund and P. Rasmussen, Calculation of Vapour-Liquid Equilibria in Mixed Solvent Salt Systems Using an Extended UNIQUAC Equation, presented at the American Institute of Chemical Engineers Annual Meeting, San Francisco, California, CA, 1984. 

Although in favourable cases S can be determined to 1 to 2 cm mol the uncertainty in B depends on the precision with which the virial coefficients of the pure components are known. On the other hand, for some applications, such as the calculation of enthalpies of mixing or the correction of vapour-liquid equilibria data, is the quantity of interest. Pressure-change measurements are not likely to be of utility for obtaining information about interaction third virial coefficients because the contribution of the second virial coefficients to the... 

Plocker, U., Knapp, H. and Prausnitz, J. (1978) Ind. Eng. Chem. Proc. Des. and Dev. 17, 243. Calculation of high-pressure vapour-liquid equilibria from a corresponding-states correlation with emphasis... 

At present there are two fundamentally different approaches available for calculating phase equilibria, one utilising activity coefficients and the other an equation of state. In the case of vapour-liquid equilibrium (VLE), the first method is an extension of Raoult s Law. For binary systems it requires typically three Antoine parameters for each component and two parameters for the activity coefficients to describe the pure-component vapour pressure and the phase equilibrium. Further parameters are needed to represent the temperature dependence of the activity coefficients, therebly allowing the heat of mixing to be calculated. 

Prausnitz, J. M., Eckert, C. A., Orye, R. V. and O Connell, J. P. (1967) Computer Calculation of Multi-component Vapour-liquid Equilibria (Prentice-Hall). 

The emphasis on vapour-liquid equilibria (including vapour pressure) is inherant in the petroleum industry due to the importance of distillation in separations. If separations by extraction are to be undertaken, then liquid-liquid equilibrium is equally important. Fugacities for thermodynamic equilibrium (flash calculations) are probably one of the most sought-after properties. This is because fugacities and enthalpies often provide sufficient information to calculate a mass and energy balance. 

Peters, C. J., J. L. de Roo, and R. N. Lichtenthaler. 1987. Measurements and calculations of phase equilibria of binary mixtures of ethane + eicosane. Part I Vapour + liquid equilibria. J. Fluid Phase Equil. 34 287-308. 

A Fortran programme has been elaborated by Williams and Henley [89] for tlie computation of multicomponent vapour-liquid equilibria. To take into account real behaviours a number of subprogrammes are available which enable fugacities to be calculated by means of the virial equation, the Redlich-Kwong relation or according to Chao-Seader. Activity coefficients may be considered following Wilson, van baar or Hildebrand. The state of the art of precalculating vapour-liquid equilibria in multicomponent mixtures was surveyed by Hala [89a]. Lu and Polak [89b] discussed the special requirements for the calculation of phase equilibria at low temperatures (20 K to room temperature). 

This activity coefficient is so defined that it becomes unity at infinite dilution of the solute in the solvent, in contrast to the one commonly used for liquid mixtures, which becomes unity for the pure liquid solute. The pure liquid-solute-based activity coefficient can be calculated by combining the melting data with vapour-liquid equilibria data at the melting temperature of the solvent. When vapour-liquid equilibria data are known only at higher temperatures, it is necessary to know the molar excess enthalpies of the mixture over the temperature range. 

This formalism is known as the gamma-phi approach for calculating vapour-liquid equilibria. The fugacity coefficient of each component that accounts for the non-ideality of the vapour phase can be evaluated from an equation of state model, while the activity coefficient/)- to describe the non-ideal behaviour of the liquid phase can be obtained from an excess Gibbs function model. 

Figure 73 Experimental and calculated vapour-liquid equilibria for carbon dioxide with oleic acid (see text for note of caution). Line B gives the terminal slope of the bubble-point curve as obtained from gas solubility measurements at normal pressure.

Weber, W., Petkov, S., Brunner, G. (1999). Vapour-liquid-equilibria and calculations using the Redlich-Kwong-Aspen-equation of state for tristeaiin, tripahnitin, and triolein in CO2 and propane. Fluid Phase Equilibria, 158-160, 695-706. 

P. L. Chuch and J. M. Prausnitz Calculation of high-pressure vapour-liquid equilibria. Ind. Eng. 

The (liquid 4- liquid) equilibria diagram for (cyclohexane + methanol) was taken from D. C. Jones and S. Amstell, The Critical Solution Temperature of the System Methyl Alcohol-Cyclohexane as a Means of Detecting and Estimating Water in Methyl Alcohol , J. Chem. Soc., 1930, 1316-1323 (1930). The G results were calculated from the (vapor 4- liquid) results of K. Strubl, V. Svoboda, R. Holub, and J. Pick, Liquid-Vapour Equilibrium. XIV. Isothermal Equilibrium and Calculation of Excess Functions in the Systems Methanol -Cyclohexane and Cyclohexane-Propanol , Collect. Czech. Chem. Commun., 35, 3004-3019 (1970). The results are from M. Dai and J.-P.Chao, Studies on Thermodynamic Properties of Binary Systems Containing Alcohols. II. Excess Enthalpies of C to C5 Normal Alcohols + 1,4-Dioxane , Fluid Phase Equilib., 23, 321-326 (1985). 

We shall show in the next paragraph that the vapour pressure constants play an important part in the calculation of chemical equilibria in gases. The first problem which Nernst had to solve after the discovery of his theorem was therefore the calculation of at least the approximate value of C for as many simple substances as possible. For this purpose he made use of the theorem of corresponding states, and assumed further that the specific heat of solid and liquid bodies diminishes to a small but finite value (viz. nx 1 5, where n is the number of atoms in the molecule) as the temperature is lowered. On the evidence of the measurements published up to that time he also assumed that the molecular specific heat of gases and vapours is a linear function of the temperature which approaches the value 3-5-l-7ixl-5 at very low temperatures. In this way he arrived at the vapour pressure formula... 

Clarke, M.A. Bishnoi, P.R. Development of a new equation of state for mixed salt and mixed solvent systems, and application to vapour liquid equilibrium and solid (hydrate) vapour liquid equilibrium calculations. Fluid Phase Equilibria 2004, 220, 21-35. 

Several assumptions have to be made for the calculation of solution densities, vapour-liquid phase equilibria (VLE), and MIAC of electrolyte solutions ... 

Liquid-vapour equilibria for Cl -COCl have been calculated on the assumption that the system conforms to ideality [541]. In the region of low dichlorine concentration (<2.5%), the system has been shown, by analysis of the gas and liquid phases, to behave consistently with these calculations. The temperature-composition diagrams are illustrated in Fig. 6.13 at 101.3 and 152.0 kPa [541]. 

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