Component equilibria vapor-liquid

Component continuity Vapor-liquid equilibrium Densities of vapor and liquid... 

Assuming constant relative volatilities ay of the components, the vapor-liquid equilibrium is given by ... 

In the example with aniline, the aniline vapor was provided by the equilibrium vapor liquid aniline. Vapor-phase intercalation can be done with compounds that are gases at room temperature and ambient pressure. The most common gas used for intercalation reactions is ammonia. Ammonia intercalation can be accomplished by exposing a host to the vapor generated by a concentrated aqueous ammonia solution. This multi-component vapor containing NH3(g), IfeOQj),... 

When a preferential solvate is formed across salt and a particular component in a solvent mixture, the preferentially solvated component is assumed to be nonvolatile. Hence, the essential concentration of the preferentially solvated component in the solvent mixture is reduced as much as the solvated component. The vapor-liquid equilibrium relation obtained under the addition of a salt may well be considered to be the same as the vapor-liquid equilibrium without the salt for liquid-phase composition from which the solvents forming solvates are excluded. Based on this idea, the essential concentration at the time when salt forms a preferential solvate with the primary component is given by Equation 1. Then we can obtain the preferential solvation number from the observed values of the salt effect. As the concentration of solvent is decreased by the number of solvated molecules, the actual solvent composition participating in the vapor-liquid equilibrium is changed. Assuming that a salt forms the solvate with the first component, the actual composition Xia is given by... 

Component Equilibrium Vapor, Ibmole/hr Equilibrium Liquid, Ibmole/hr /C-value... 

Suppose that an ideal solution of two components (i = 1,2) is in the presence of a noncondensable gas (subscript g). Neglecting the solubility of the gas in the liquid, the liquid contains only the liquid components while the gas contains the noncondensable gas well as vapors of the liquid components. The vapor/liquid equilibrium of the condensable components is described by Raoult s law ... 

Multiequation Approach to Vapor-Liquid Equilibria. The correlations mentioned earlier were developed specifically for hydrocarbon systems and, in general, are not applicable to systems containing polar and associating components. The vapor-liquid equilibrium correlations for systems with such components are best handled with a multi-equation of state procedure using Eq. (5). This method is also used in developing vapor-liquid equilibrium correlations for the design of separation units for close-boiling hydrocarbons. 

Distillation columns can be used to separate chemical components when there are differences in the concentrations of these components in the liquid and vapor phases. These concentration differences are analyzed and quantified using basic thermodynamic principles covering phase equilibrium. Vapor-liquid equilibrium (VLE) data and analysis are vital components of distillation design and operation. 

In this section, we consider the case when three phases are in equilibrium a vapor phase and two liquid phases, a and p. A generic diagram of a system with m components in vapor-liquid-liquid (VLLE) equilibrium is shown in Figure 8.15. How does such behavior come about Let s return to the binary mixture of a and b. Consider the case where we have both an azeotrope in VLE and liquid-liquid equilibrium (ELE). This scenario corresponds to a minimum-boiling azeotrope where the like interactions are stronger than the unlike interactions. Figure 8.16a shows the phase diagram for the case... 

In vapor-liquid equilibria, it is relatively easy to start the iteration because assumption of ideal behavior (Raoult s law) provides a reasonable zeroth approximation. By contrast, there is no obvious corresponding method to start the iteration calculation for liquid-liquid equilibria. Further, when two liquid phases are present, we must calculate for each component activity coefficients in two phases since these are often strongly nonlinear functions of compositions, liquid-liquid equilibrium calculations are highly sensitive to small changes in composition. In vapor-liquid equilibria at modest pressures, this sensitivity is lower because vapor-phase fugacity coefficients are usually close to unity and only weak functions of composition. For liquid-liquid equilibria, it is therefore more difficult to construct a numerical iteration procedure that converges both rapidly and consistently. 

For multicomponent vapor-liquid equilibria, the equation of equilibrium for every condensable component i is... 

To illustrate the criterion for parameter estimation, let 1, 2, and 3 represent the three components in a mixture. Components 1 and 2 are only partially miscible components 1 and 3, as well as components 2 and 3 are totally miscible. The two binary parameters for the 1-2 binary are determined from mutual-solubility data and remain fixed. Initial estimates of the four binary parameters for the two completely miscible binaries, 1-3 and 2-3, are determined from sets of binary vapor-liquid equilibrium (VLE) data. The final values of these parameters are then obtained by fitting both sets of binary vapor-liquid equilibrium data simultaneously with the limited ternary tie-line data. 

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. ... 

UNIQUAC Binary Parameters for Noncondensable Components with Condensable Components. Parameters Obtained from Vapor-Liquid Equilibrium Data in the Dilute Region... 

VALIK calculates vapor-liquid vaporization equilibrium ratios, K(I), for each component in a mixture of N components (N 20) at specified liquid composition, vapor composition, temperature, and pressure. 

FLASH determines the equilibrium vapor and liquid compositions resultinq from either an isothermal or adiabatic equilibrium flash vaporization for a mixture of N components (N 20). The subroutine allows for presence of separate vapor and liquid feed streams for adaption to countercurrent staged processes. 

Illustrates use of subroutine FLASH for vapor-liquid equilibrium separation calculations for up to 10 components and of subroutine PARIN for parameter loading. 

For mixtures containing more than two species, an additional degree of freedom is available for each additional component. Thus, for a four-component system, the equihbrium vapor and liquid compositions are only fixed if the pressure, temperature, and mole fractious of two components are set. Representation of multicomponent vapor-hquid equihbrium data in tabular or graphical form of the type shown earlier for biuaiy systems is either difficult or impossible. Instead, such data, as well as biuaiy-system data, are commonly represented in terms of ivapor-liquid equilibrium ratios), which are defined by... 

As discussed in Sec. 4, the icomplex function of temperature, pressure, and equilibrium vapor- and hquid-phase compositions. However, for mixtures of compounds of similar molecular structure and size, the K value depends mainly on temperature and pressure. For example, several major graphical ilight-hydrocarbon systems. The easiest to use are the DePriester charts [Chem. Eng. Prog. Symp. Ser 7, 49, 1 (1953)], which cover 12 hydrocarbons (methane, ethylene, ethane, propylene, propane, isobutane, isobutylene, /i-butane, isopentane, /1-pentane, /i-hexane, and /i-heptane). These charts are a simplification of the Kellogg charts [Liquid-Vapor Equilibiia in Mixtures of Light Hydrocarbons, MWK Equilibnum Con.stants, Polyco Data, (1950)] and include additional experimental data. The Kellogg charts, and hence the DePriester charts, are based primarily on the Benedict-Webb-Rubin equation of state [Chem. Eng. Prog., 47,419 (1951) 47, 449 (1951)], which can represent both the liquid and the vapor phases and can predict K values quite accurately when the equation constants are available for the components in question. 

The phase-distribution restrictions reflect the requirement that ff =ff at equilibrium where/is the fugacity. This may be expressed by Eq. (13-1). In vapor-hquid systems, it should always be recognized that all components appear in both phases to some extent and there will be such a restriction for each component in the system. In vapor-liquid-hquid systems, each component will have three such restrictions, but only two are independent. In general, when all components exist in all phases, the uumDer of restricting relationships due to the distribution phenomenon will be C(Np — 1), where Np is the number of phases present. 

Interface Equilibrium (C Equations) Component vapor-liquid equilibrium ... 

In distillation towers, entrainment lowers the tray efficiency, and 1 pound of entrainment per 10 pounds of liquid is sometimes taken as the hmit for acceptable performance. However, the impact of entrainment on distiUation efficiency depends on the relative volatility of the component being considered. Entrainment has a minor impact on close separations when the difference between vapor and liquid concentration is smaU, but this factor can be dominant for systems where the liquid concentration is much higher than the vapor in equilibrium with it (i.e., when a component of the liquid has a very lowvolatiUty, as in an absorber). 

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

Note that this equation holds for any component in a multi-component mixture. The integral on the right-hand side can only be evaluated if the vapor mole fraction y is known as a function of the mole fraction Xr in the still. Assuming phase equilibrium between liquid and vapor in the still, the vapor mole fraction y x ) is defined by the equilibrium curve. Agitation of the liquid in tire still and low boilup rates tend to improve the validity of this assumption. 

By using vapor-liquid equilibrium data the above integral can be evaluated numerically. A graphical method is also possible, where a plot of l/(y - xj versus Xr is prepared and the area under the curve over the limits between the initial and fmal mole fraction is determined. However, for special cases the integration can be done analytically. If pressure is constant, the temperature change in the still is small, and the vapor-liquid equilibrium values (K-values, defined as K=y/x for each component) are independent from composition, integration of the Rayleigh equation yields ... 

The most important equilibrium pliase relationship is diat between liquid and vapor. Raoult s mid Henry s laws theoretically describe liquid-vapor behavior mid, mider certain conditions, are applicable in practice. Raoult s law, sometimes useful for mi.vtures of components of similar structure, states diat die partial pressure of any component in die vapor is equal to die product of the vapor pressure of the pure component and die mole fracdon of tliat component in die liquid. It may be written in die following maimer... 

Figure 8-2 illustrates a typical normal volatility vapor-liquid equilibrium curve for a particular component of interest in a distillation separation, usually for the more volatile of the binary mixture, or the one where separation is important in a multicomponent mixture. 

K-factors for vapor-liquid equilibrium ratios are usually associated with various hydrocarbons and some common impurities as nitrogen, carbon dioxide, and hydrogen sulfide [48]. The K-factor is the equilibrium ratio of the mole fraction of a component in the vapor phase divided by the mole fraction of the same component in the liquid phase. K is generally considered a function of the mixture composition in which a specific component occurs, plus the temperature and pressure of the system at equilibrium. 

The minimum number of trays necessary to debutanize the effluent from an alkylation reactor will be calculated. The feed, products, and vapor-liquid equilibrium costants of the key components at conditions of temperature and pressure corresponding to the top tray and reboiler are shown in Table 8-1. 

Multicomponent distillations are more complicated than binary systems due primarily to the actual or potential involvement or interaction of one or more components of the multicomponent system on other components of the mixture. These interactions may be in the form of vapor-liquid equilibriums such as azeotrope formation, or chemical reaction, etc., any of which may affect the activity relations, and hence deviations from ideal relationships. For example, some systems are known to have two azeotrope combinations in the distillation column. Sometimes these, one or all, can be broken or changed in the vapor pressure relationships by addition of a third chemical or hydrocarbon. 

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