Vapor/liquid equilibrium thermodynamics

W. Reid Thompson, J.A. Zollweg, D.H. Gabis, Vapor-liquid equilibrium thermodynamics of N2+ CH4 model and Titan apphcations. ICARUS 97(2), 187-199 (1992)... 

American Petroleum Institute, Bibliographies on Hydrocarbons, Vols. 1-4, "Vapor-Liquid Equilibrium Data for Hydrocarbon Systems" (1963), "Vapor Pressure Data for Hydrocarbons" (1964), "Volumetric and Thermodynamic Data for Pure Hydrocarbons and Their Mixtures" (1964), "Vapor-Liquid Equilibrium Data for Hydrocarbon-Nonhydrocarbon Gas Systems" (1964), API, Division of Refining, Washington. 

Maczynski, A. "Thermodynamic Data for Technology—Verified Vapor-Liquid Equilibrium Data," Panstwowe Wydawnictwo Naukawa, Warsaw, Volume 1, 1976 Volume 2, 1978. 

The computer subroutines for calculation of vapor-liquid equilibrium separations, including determination of bubble-point and dew-point temperatures and pressures, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements for these subroutines are given in Appendix J their execution times are strongly dependent on the separations being calculated but can be estimated (CDC 6400) from the times given for the thermodynamic subroutines they call (essentially all computation effort is in these thermodynamic subroutines). 

Propylene oxide is a colorless, low hoiling (34.2°C) liquid. Table 1 lists general physical properties Table 2 provides equations for temperature variation on some thermodynamic functions. Vapor—liquid equilibrium data for binary mixtures of propylene oxide and other chemicals of commercial importance ate available. References for binary mixtures include 1,2-propanediol (14), water (7,8,15), 1,2-dichloropropane [78-87-5] (16), 2-propanol [67-63-0] (17), 2-methyl-2-pentene [625-27-4] (18), methyl formate [107-31-3] (19), acetaldehyde [75-07-0] (17), methanol [67-56-1] (20), ptopanal [123-38-6] (16), 1-phenylethanol [60-12-8] (21), and / /f-butanol [75-65-0] (22,23). 

A tabulation of the partial pressures of sulfuric acid, water, and sulfur trioxide for sulfuric acid solutions can be found in Reference 80 from data reported in Reference 81. Figure 13 is a plot of total vapor pressure for 0—100% H2SO4 vs temperature. References 81 and 82 present thermodynamic modeling studies for vapor-phase chemical equilibrium and liquid-phase enthalpy concentration behavior for the sulfuric acid—water system. Vapor pressure, enthalpy, and dew poiat data are iacluded. An excellent study of vapor—liquid equilibrium data are available (79). 

Additional compilations of vapor-pressure data include Boubhk, Fried, and Hala, The Vapor Pre.s.sure.s of Pure Substances, Elsevier, Amsterdam, 1984. See also Hirata, Ohe, and Nagahama, Computer Aided Data Book of Vapor-Liquid Equilibria, Kodansha/Elsevier, Tokyo, 1975 Weishaupt, Landolt-Bornstein New Series Group TV, vol. 3 Thermodynamic Equilibria of Boiling Mixtures, Springer-Verlag, Berhn, 1975 Wichterle, Linek, and Hala, Vapor-Liquid Equilibrium Data Bibliography, Elsevier, Amsterdam, 1973 suppl. 1, 1976 suppl. 2,1982. 

Vapor/liquid equilibrium (XT E) relationships (as well as other interphase equihbrium relationships) are needed in the solution of many engineering problems. The required data can be found by experiment, but such measurements are seldom easy, even for binaiy systems, and they become rapidly more difficult as the number of constituent species increases. This is the incentive for application of thermodynamics to the calculation of phase-equilibrium relationships. 

Data on the gas-liquid or vapor-liquid equilibrium for the system at hand. If absorption, stripping, and distillation operations are considered equilibrium-limited processes, which is the usual approach, these data are critical for determining the maximum possible separation. In some cases, the operations are are considerea rate-based (see Sec. 13) but require knowledge of eqmlibrium at the phase interface. Other data required include physical properties such as viscosity and density and thermodynamic properties such as enthalpy. Section 2 deals with sources of such data. 

Vapor-liquid equilibrium data are said to be thermodynamically consistent when they satisfy the Gibbs-Duhem equation. When the data satisfy this equation, it is likely, but by no means guaranteed, that they are correct however, if they do not satisfy this equation, it is certain that they are incorrect. 

Thermodynamic energy terms (and equilibrium constants) may differ for compounds containing different isotopic species of an element. This effect is described in theoretical detail by Urey (1947), and applications to geochemistry are discussed by Broecker and Oversby (1971) and Faure (1977). A good example is the case of the vapor/liquid equilibrium for water. The vapor pressure of a lighter isotopic species, H2 0, is higher relative to that of heavier species, (or HD O), and others. 

Several activity coefficient models are available for industrial use. They are presented extensively in the thermodynamics literature (Prausnitz et al., 1986). Here we will give the equations for the activity coefficients of each component in a binary mixture. These equations can be used to regress binary parameters from binary experimental vapor-liquid equilibrium data. 

Equation 4.26 defines the relationship between the vapor and liquid mole fractions and provides the basis for vapor-liquid equilibrium calculations on the basis of equations of state. Thermodynamic models are required for (/) and [ from an equation of state. Alternatively, Equations 4.21, 4.22 and 4.25 can be combined to give... 

Chapter 17 - Vapor-liquid equilibrium (VLE) data are important for designing and modeling of process equipments. Since it is not always possible to carry out experiments at all possible temperatures and pressures, generally thermodynamic models based on equations on state are used for estimation of VLE. In this paper, an alternate tool, i.e. the artificial neural network technique has been applied for estimation of VLE for the binary systems viz. tert-butanol+2-ethyl-l-hexanol and n-butanol+2-ethyl-l-hexanol. The temperature range in which these models are valid is 353.2-458.2K at atmospheric pressure. The average absolute deviation for the temperature output was in range 2-3.3% and for the activity coefficient was less than 0.009%. The results were then compared with experimental data. 

In general, the formulation of the problem of vapor-liquid equilibria in these systems is not difficult. One has the mass balances, dissociation equilibria in the solution, the equation of electroneutrality and the expressions for the vapor-liquid equilibrium of each molecular species (equality of activities). The result is a system of non-linear equations which must be solved. The main thermodynamic problem is the relation of the activities of the species to be measurable properties, such as pressure and composition. In order to do this a model is needed and the parameters in the model are usually obtained from experimental data on the mixtures involved. Calculations of this type are well-known in geological systems O) where the vapor-liquid equilibria are usually neglected. 

Another type of ternary electrolyte system consists of two solvents and one salt, such as methanol-water-NaBr. Vapor-liquid equilibrium of such mixed solvent electrolyte systems has never been studied with a thermodynamic model that takes into account the presence of salts explicitly. However, it should be recognized that the interaction parameters of solvent-salt binary systems are functions of the mixed solvent dielectric constant since the ion-molecular electrostatic interaction energies, gma and gmc, depend on the reciprocal of the dielectric constant of the solvent (Robinson and Stokes, (13)). Pure component parameters, such as gmm and gca, are not functions of dielectric constant. Results of data correlation on vapor-liquid equilibrium of methanol-water-NaBr and methanol-water-LiCl at 298.15°K are shown in Tables 9 and 10. 

The semi-empirical Pitzer equation for modeling equilibrium in aqueous electrolyte systems has been extended in a thermodynamically consistent manner to allow for molecular as well as ionic solutes. Under limiting conditions, the extended model reduces to the well-known Setschenow equation for the salting out effect of molecular solutes. To test the validity of the model, correlations of vapor-liquid equilibrium data were carried out for three systems the hydrochloric acid aqueous solution at 298.15°K and concentrations up to 18 molal the NH3-CO2 aqueous solution studied by van Krevelen, et al. 

Equation 27 is similar to the solid-liquid equilibrium relation used for non-electrolytes. As in the case of the vapor-liquid equilibrium relation for HC1, the solid-liquid equilibrium expression for NaCl is simple since the electrolyte is treated thermodynamically the same in both phases. 

Since the vast majority of chemical engineering systems involve liquid and vapor phases, many vapor-liquid equilibrium relationships are used. They range from the very simple to the very complex. Some of the most commonly used relationships are listed below. More detailed treatments are presented in many thermodynamics texts. Some of the basic concepts are introduced by Luyben aM... 

For continuous systems, molar flow rates Q can be used instead of n. The thermodynamic activity (ax) can be calculated according to Equation 2, but requires knowledge of the saturation pressure of the pure compound (Ppsatx). This data can be obtained from the saturation curves (vapor-liquid equilibrium curves) and is taken at the working temperature of the gas stream. The thermodynamic activity is then calculated using the following equation ... 

A review is presented of techniques for the correlation and prediction of vapor-liquid equilibrium data in systems consisting of two volatile components and a salt dissolved in the liquid phase, and for the testing of such data for thermodynamic consistency. The complex interactions comprising salt effect in systems which in effect consist of a concentrated electrolyte in a mixed solvent composed of two liquid components, one or both of which may be polar, are discussed. The difficulties inherent in their characterization and quantitative treatment are described. Attempts to correlate, predict, and test data for thermodynamic consistency in such systems are reviewed under the following headings correlation at fixed liquid composition, extension to entire liquid composition range, prediction from pure-component properties, use of correlations based on the Gibbs-Duhem equation, and the recent special binary approach. 

The use of a dissolved salt in place of a liquid component as the separating agent in extractive distillation has strong advantages in certain systems with respect to both increased separation efficiency and reduced energy requirements. A principal reason why such a technique has not undergone more intensive development or seen more than specialized industrial use is that the solution thermodynamics of salt effect in vapor-liquid equilibrium are complex, and are still not well understood. However, even small amounts of certain salts present in the liquid phase of certain systems can exert profound effects on equilibrium vapor composition, hence on relative volatility, and on azeotropic behavior. Also extractive and azeotropic distillation is not the only important application for the effects of salts on vapor-liquid equilibrium while used as examples, other potential applications of equal importance exist as well. 

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). 

If a fluid composed of more than one component (e.g., a solution of ethanol and water, or a crude oil) partially or totally changes phase, the required heat is a combination of sensible and latent heat and must be calculated using more complex thermodynamic relationships, including vapor-liquid equilibrium calculations that reflect the changing compositions as well as mass fractions of the two phases. 

Until recently the ability to predict the vapor-liquid equilibrium of electrolyte systems was limited and only empirical or approximate methods using experimental data, such as that by Van Krevelen (7) for the ammonia-hydrogen sulfide-water system, were used to design sour water strippers. Recently several advances in the prediction and correlation of thermodynamic properties of electrolyte systems have been published by Pitzer (5), Meissner (4), and Bromley ). Edwards, Newman, and Prausnitz (2) established a similar framework for weak electrolyte systems. 

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