Methods for Binary Systems

A good understanding of the basic equations developed for binary systems is essential to the understanding of distillation processes. 

The distillation of binary mixtures is covered thoroughly in Richardson et al. (2002) and the discussion in this section is limited to a brief review of the most useful design methods. Though binary systems are usually considered separately, the design methods developed for multicomponent systems (Section 11.6) can obviously also be used for binary systems. With binary mixtures, fixing the composition of one component fixes the composition of the other, and iterative procedures are not usually needed to determine the stage and reflux requirements simple graphical methods are normally used. 

At constant pressure, the stage temperatures will be functions of the vapor and liquid compositions only (dew and bubble points), and the specific enthalpies will therefore also be functions of composition 

Even when the latent heats are substantially different, the error introduced by assuming equimolar overflow to calculate the number of stages is usually small and acceptable. 

CHAPTER 11 SEPARATION COLUMNS (DISTILLATION, ABSORPTION, AND EXTRACTION) 

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The classic papers by Lewis and Matheson [Ind. Eng. Chem., 24, 496 (1932)] and Thiele and Geddes [Ind. Eng. Chem., 25, 290 (1933)] represent the first attempts at solving the MESH equations for multicomponent systems numerically (the graphical methods for binary systems discussed earlier had already been developed by Pon-chon, by Savarit, and by McCabe and Thiele). At that time the computer had yet to be invented, and since modeling a column could require hundreds, possibly thousands, of equations, it was necessary to divide the MESH equations into smaller subsets if hand calculations were to be feasible. Despite their essential simplicity and appeal, stage-to-stage calculation procedures are not used now as often as they used to be. 

Another graphical design method for binary systems is that of Ponchon" and Savarit. This method includes an energy balance on each stage and is totally rigorous for binary systems. However, it requires mixture enthalpy data, often unavailable, and is cumbersome in application. 

Glassification of Phase Boundaries for Binary Systems. Six classes of binary diagrams have been identified. These are shown schematically in Figure 6. Classifications are typically based on pressure—temperature (P T) projections of mixture critical curves and three-phase equiHbria lines (1,5,22,23). Experimental data are usually obtained by a simple synthetic method in which the pressure and temperature of a homogeneous solution of known concentration are manipulated to precipitate a visually observed phase. 

In order to determine the packed height it is necessary to obtain a value of the overall number of transfer units methods for doing this are available for binary systems in any standard text covering distillation (73) and, in a more complex way, for multicomponent systems (81). However, it is simpler to calculate the number of required theoretical stages and make the conversion ... 

An alternate method for binary concentrated liquid systems where activity coefficients are not available or estimable is the method of Leffler and Cullinan previously given in Eq. (2-156). Absolute errors average 25 percent. 

Figure 8-42A-E. Performance analysis of unequal molal overflow for binary systems using Ponchon-Savarit Method.

If the presence of the other components does not significantly affect the volatility of the key components, the keys can be treated as a pseudo-binary pair. The number of stages can then be calculated using a McCabe-Thiele diagram, or the other methods developed for binary systems. This simplification can often be made when the amount of the non-key components is small, or where the components form near-ideal mixtures. 

For binary systems or systems that approach binary, the Fenske-Underwood-Erbar/Maddox Method is recommended. For minimum stages, use the Fenske equation.12... 

The calculations are given elsewhere13 and are not repeated here since the method does not differ in principle from that for binary systems. 

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. 

For these conditions there are two basic methods for determining the number of plates required. The first is due to Sorel(25) and later modified by Lewis126 , and the second is due to McCabe and Thiele(27). The Lewis method is used here for binary systems, and also in Section 11.7.4 for calculations involving multicomponent mixtures. This method is also the basis of modem computerised methods. The McCabe-Thiele method is particularly... 

The Ponchon-Savarit method, using an enthalpy-composition diagram, may also be used to handle sidestreams and multiple feeds, though only for binary systems. This is dealt with in Section 11.5. 

An analytic method has been used to produce pVTxy measurements for binary systems containing methyl oleate and supercritical solvents. A micro dual-sampling system has been added to our apparatus for taking vapor and liquid samples. The systems ethane-methyl oleate and carbon dioxide-methyl oleate were studied along isotherms at 313.15 K and 343.15 K up to pressures substantially greater than the critical pressures of the pure solvents. Comparisons are made between the experimental data and predictions using the Peng-Robinson equation of state. 

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