Vapor-liquid equilibrium theory

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

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. 

Kao M, Uhlenbeck G E and Hemmer P 1963 Gn van der Waals theory of vapor-liquid equilibrium. I. Discussion of a one-dimensional model J. Math. Phys. 4 216... 

Several authors, notably Leland and co-workers (L2), have discussed vapor-liquid equilibrium calculations based on corresponding-states correlations. As mentioned in Section II, such calculations rest not only on the general assumptions of corresponding-states theory, but also on the additional assumption that the characterizing parameters for a mixture do not depend on temperature or density but are functions of composition only. Further, it is necessary clearly to specify these functions (commonly known as mixing rules), and experience has shown that if good results are to be obtained, these... 

Over the years, various other theories and models have been proposed for predicting salt effect in vapor-liquid equilibrium, including ones based on hydration, internal pressure, electrostatic interaction, and van der Waals forces. These have been reviewed in detail by Long and McDevit (25), Prausnitz and Targovnik (31), Furter (7), Johnson and Furter (8), and Furter and Cook (I). Although the electrostatic theory as modified for mixed solvents has had limited success, no single theory has yet been able to account for or to predict salt effect on equilibrium vapor composition from pure-component properties alone. 

Isothermal vapor-liquid equilibrium data at 75°, 50° and 25° C for the system of 2-propanol-water-lithium perchlorate were obtained by using a modified Othmer still. In the 2-propanol-rich region 2-propanol was salted out from the aqueous solution by addition of lithium perchlorate, but in the water-rich region 2-propanol was salted in. It is suggested from the experimental data that the simple electrostatic theory cannot account for the salt effect parameter of this system. 

The theory of nucleation begins with the consideration of vapor-liquid equilibrium. The vapor pressure po over a flat liquid surface at equilibrium is given by the Clapeyon equation,... 

Literature pertaining to salt effect in vapor-liquid equilibrium and to extractive distillation using salt effect was recently reviewed by Furter and Cook (10), and the theory and technical aspects were reviewed by Furter (II). Vapor-liquid equilibrium data for 188 systems containing salt were previously compiled by Ciparis (12), who has also published a recent book with Dobroserdov and Kogan on the theory and practice of extractive distillation by salt effect (13). 

The preceding sectionhas described what is observed through experimental observation. When thermodynamics is applied to vapor/liqirid equilibrium, the goal is to find by calculation the ternperatnres, pressures, and compositions of pliases in equilibrium. Indeed, thermodynamics provides the mathematicalframeworkfor the systematic correlation, extension, generalization, evaluation, and interpretation of data. Moreover, it is the means by which the predictions of various theories of molecular physics and statistical mechanics may be applied to practical purposes. None of tliis can be accomphshed without models for the behavior of systems in vapor/liquid equilibrium. The two simplest are Raoult s law and Henry s law. 

As we described in Section III.G, perturbation theories can be extended in a systematic way using cluster expansion techniques. These techniques have recently been applied to the calculation of the thermodynamic properties and vapor-liquid equilibrium of 12-6 diatomics and seem to offer a clear improvement over the first-order perturbation theories. To illustrate this point. Table I shows values of the critical density and critical temperature predicted by the ISF-ORPA theory and the first-order perturbation theory together with results recently obtained from molecular dynamics... 

For vapor-liquid equilibrium calculations up to moderate pressures, the B equation is suitable and convenient for the vapor phase for its applicability and simple form. Formulas have been derived from statistical theory for the calculation of virial coefficients, including B, from intermo-lecular potential energy functions, but intermolecular energy functions are hardly known quantitatively for real molecules. B is found for practical calculations by correlating experimental B values. Pitzer [1] correlated B of normal flnids in a generalized form with acentric factor to as the third parameter. 

Experimental studies were carried out to derive correlations for mass-transfer coefficients, reaction kinetics, liquid holdup and pressure drop for the new catalytic packing MULTIPAK (see [9,10]). Suitable correlations for ROMBOPAK 6M were taken from [70] and [92], The vapor-liquid equilibrium is calculated using the modification of the Wilson method [9]. For the vapor phase, the dimerization of acetic acid is taken into account using the chemical theory to correct vapor-phase fugacity coefficients [93]. Binary diffusion coefficients for the vapor phase and for the liquid phase are estimated via the method purposed by Fuller et al. and Tyn and Calus, respectively (see [94]). Physical properties like densities, viscosities and thermal conductivities are calculated from the methods given in [94]. 

Table 2.4-4 Adsorbed solution theories for the description or prediction of multicomponent adsorption equilibria. In the light gray area new theoretical models are listed. The theories in the double-framed area require experimental data of binary adsorptives. VLE denotes vapor liquid equilibrium. The meaning of VAE is vapor adsorbate equilibrium...

First, we will introduce theory for the drying and method of modeling of the drying proeess. A drying process of liquid coated film can be simulated by setting up heat and mass transfer equations and vapor liquid equilibrium equations with appropriate heat... 

Gross, J., Sadowski, G., Perturbed-chain SAFT An equation of state based on a perturbation theory for chain molecules, oA. Eng. Chm. Res. 40 (2001) 1244-1260. Chapman, W.G., Gubbins, K.E., Jackson, G., Radosz, M., New reference equation of state for associating liquids, Ind. Eng. Chem. Res. 29 (1990) 1709-1721. Diamantonis, N.I., Boulougouris, G.C., Mansoor, E., Tsangaris, D.M., Economou, LG. Evaluation of cubic, SAFT, cmd PC-SAFT equations of state for the vapor-liquid equilibrium modeling of CO2 mixtures with other gases, Ind. Eng. Chem. Res. 52 (2013) 3933-3942. 

Vapor-liquid equilibrium data form the basic information for chemical engineering calculations, in particular the design and operation of distillation plants in the chemical, pharmaceutical, polymer, petrochemical and related industries. The data are also important for understanding molecular interactions and developing theories of pure liquids and liquid mixtures because they are related to the structure and the energy of interaction of the molecules. 

Film Theory and Gas-Liquid and Liquid-Liquid Mass Transfer. The history and literature surrounding interfacial mass transfer is enormous. In the present context, it suffices to say that the film model, which postulates the existence of a thin fluid layer in each fluid phase at the interface, is generally accepted (60). In the context of coupled mass transfer and reaction, two common treatments involve 1) the Hatta number and (2) enhancement factors. Both descriptions normally require a detailed model of the kinetics as well as the mass transfer. The Hatta number is perhaps more intuitive, since the numbers span the limiting cases of infinitely slow reaction with respect to mass transfer to infinitely fast reaction with respect to mass transfer. In the former case all reaction occurs in the bulk phase, and in the latter reaction occurs exclusively at the interface with no bulk reaction occurring. Enhancement factors are usually categorized in terms of reaction order (61). In the context of nonreactive systems, a characteristic time scale (eg, half-life) for attaining vapor-liquid equilibrium and liquid-liquid equilibrium, 6>eq, in typical laboratory settings is of the order of minutes. 

An improved theory for vapor-liquid equilibrium of mixtures based on free-volume considerations was proposed by Prigogine [24, 25]. This theory has been further developed by various workers, e.g., Flory [26]. Bonner and Prausnitz [27] discuss the new theory in detail and describe its application with a number of examples. 

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