Vaporization multicomponent

Respectively, a vaporous multicomponent mixture starts condensing if the following relation is tme ... 

The accuracy of our calculations is strongly dependent on the accuracy of the experimental data used to obtain the necessary parameters. While we cannot make any general quantitative statement about the accuracy of our calculations for multicomponent vapor-liquid equilibria, our experience leads us to believe that the calculated results for ternary or quarternary mixtures have an accuracy only slightly less than that of the binary data upon which the calculations are based. For multicomponent liquid-liquid equilibria, the accuracy of prediction is dependent not only upon the accuracy of the binary data, but also on the method used to obtain binary parameters. While there are always exceptions, in typical cases the technique used for binary-data reduction is of some, but not major, importance for vapor-liquid equilibria. However, for liquid-liquid equilibria, the method of data reduction plays a crucial role, as discussed in Chapters 4 and 6. 

The calculation of single-stage equilibrium separations in multicomponent systems is implemented by a series of FORTRAN IV subroutines described in Chapter 7. These treat bubble and dewpoint calculations, isothermal and adiabatic equilibrium flash vaporizations, and liquid-liquid equilibrium "flash" separations. The treatment of multistage separation operations, which involves many additional considerations, is not considered in this monograph. 

O Connell, and R. V. Orye "Computer Calculations for Multicomponent Vapor-Liquid Equilibria," Prentice-Hall, Englewood Cliffs, N.J., 1967. 

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

To predict vapor-liquid or liquid-liquid equilibria in multicomponent systems, we require a method for calculating the fugacity of a component i in a liquid mixture. At system temperature T and system pressure P, this fugacity is written as a product of three terms... 

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... 

The results shown in Table 2 indicate that UNIQUAC can be used with confidence for multicomponent vapor-liquid equilibria including those that exhibit large deviations from ideality. 

Our experience with multicomponent vapor-liquid equilibria suggests that for system temperatures well below the critical of every component, good multicomponent results are usually obtained, especially where binary parameters are chosen with care. However, when the system temperature is near or above the critical of one (or more) of the components, multicomponent predictions may be in error, even though all binary pairs are fit well. 

The multicomponent form of the Underwood equation can be used to calculate the vapor flow at minimum reflux in each column of the sequence. The minimum vapor rate in a single column is obtained by alternate use of two equations ... 

Equation (5.8) tends to predict vapor loads slightly higher than those predicted by the full multicomponent form of the Underwood equation. The important thing, however, is not the absolute value but the relative values of the alternative sequences. Porter and Momoh have demonstrated that the rank order of total vapor load follows the rank order of total cost. 

Distillation Columns. Distillation is by far the most common separation technique in the chemical process industries. Tray and packed columns are employed as strippers, absorbers, and their combinations in a wide range of diverse appHcations. Although the components to be separated and distillation equipment may be different, the mathematical model of the material and energy balances and of the vapor—Hquid equiUbria are similar and equally appHcable to all distillation operations. Computation of multicomponent systems are extremely complex. Computers, right from their eadiest avadabihties, have been used for making plate-to-plate calculations. 

J. M. Prausnit2 and co-workers. Computer Calculations for Multicomponent Vapor—Eiquid and Eiquid—Eiquid Equilibria Prentice-Hall, Inc., Englewood Cliffs, N.J., 1980. 

Residue Curve Maps. Residue curve maps are useful for representing the infinite reflux behavior of continuous distillation columns and for getting quick estimates of the feasibiHty of carrying out a desired separation. In a heterogeneous simple distillation process, a multicomponent partially miscible Hquid mixture is vaporized ia a stiH and the vapor that is boiled off is treated as being ia phase equiHbrium with all the coexistiag Hquid phases. 

The general XT E problem involves a multicomponent system of N constituent species for which the independent variables are T, P, N — 1 liquid-phase mole fractions, and N — 1 vapor-phase mole fractions. (Note that Xi = 1 and y = 1, where x, and y, represent liquid and vapor mole fractions respectively.) Thus there are 2N independent variables, and application of the phase rule shows that exactly N of these variables must be fixed to estabhsh the intensive state of the system. This means that once N variables have been specified, the remaining N variables can be determined by siiTUiltaneous solution of the N equihbrium relations ... 

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... 

For preliminary studies of batch rectification of multicomponent mixtures, shortcut methods that assume constant molal overflow and negligible vapor and liquid holdup are useful. The method of Diwekar and Madhaven [Ind. Eng. Chem. Res., 30, 713 (1991)] can be used for constant reflux or constant overhead rate. The method of Sundaram and Evans [Ind. Eng. Chem. Res., 32, 511 (1993)] applies only to the case of constant remix, but is easy to apply. Both methods employ the Fenske-Uuderwood-GiUilaud (FUG) shortcut procedure at successive time steps. Thus, batch rectification is treated as a sequence of continuous, steady-state rectifications. 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binaiy and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predic tive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilib-... 

Solvent Recovery The largest current industrial use of pei vapo-ration is the treatment of mixed organic process streams that have become contaminated with small (10 percent) quantities of water. Pei vaporation becomes vei y attractive when dehydrating streams down to less than 1 percent water. The advantages result from the small operating costs relative to distillation and adsorption. Also, distillation is often impossible, since azeotropes commonly form in multicomponent organic/water mixtures. 

Distillation, extractive distillation, liquid-liquid extraction and absorption are all techniques used to separate binary and multicomponent mixtures of liquids and vapors. Reference 121 examines approaches to determine optimum process sequences for separating components from a mixture, primarily by distillation. 

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. 

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