Ideal Ternary Mixtures

For the purpose of illustration of the relations developed above, RD of an ideal mixture of three components being subject to the reversible liquid-phase reaction A + B o C is considered. The rate of reaction is given by the power law expression 

The chemical equilibrium constant is assumed to be constant, K = 5, and k is taken as independent of temperature. The vapor-liquid equilibrium is described by means of constant relative volatilities with a c 1 bc 1 and a c + asc- 

In this case the reaction product C is the intermediate boiler. All potential singular points are located on an ellipse, which is the dashed curve given in Fig. 5.14. There, for better illustration, the behavior outside the physically relevant composition space is also depicted for the four Damkohler numbers considered. The solid curves represent the location of points fulfilling the kinetic relation of bottom products (5.29). The attainable bottom products at a given Damkohler number are obtained as intersection points of the potential singular point curve and the kinetic curve. 

At Da = 0, there are three intersections, which are the three pure component vertices with different stabilities. At Da = 0.5, there are also three intersections, two of which are the pure A vertex (stable node) and the pure B vertex (unstable node). The third one with x = ( 0.1560, 0.0785) is a saddle point. At Da = 0.7, five intersections exist. The point with x = (—0.4322, 0.4723) is a stable spiral while the points with x= (—0.2736, 0.1674) and x = (—0.0575, 0.9750) are saddle points. The pure A and B vertices remain their stabilities. At Da = 2.33, there are three intersections. The pure A vertex remains stable node but the pure B vertex is now a saddle point. The point with x = (0.6959, 1.0785) is an unstable node. In conclusion for this reaction system, only pure A will be a stable bottom product of a real counter-current RD column. 

In this case the reaction product C is the highest boiler and all potential singular points are located on the two dashed hyperbola branches shown in Fig. 5.15. At Da = 0, only the three pure reaction components are attainable singular points (Fig. 5.15a). At Da = 0.3, besides the pure A vertex (unstable node) and the 

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The solvents chosen, A and B, should be from two of the eight solvent groups and be as different as possible. Since it has been shown that three solvents are better than two, the ideal ternary mixture for normal phase LC should have three solvents chosen from the three apices of the triangle. 

It is worth noting that is a measure of nonideality [15] of the binary mixture a-, because for an ideal mixture A b = 0. For a ternary mixture 1-2-3, 2 i23 also constitutes a measure of nonideality. Indeed, inserting Gjf for an ideal mixture [14] into the expression of Z i23, one obtains that for an ideal ternary mixture 2 123 = 0. One should also mention that the nonideality parameter 2 12 in a binary mixture is connected to the parameter 22 (see Eq. (4)). Indeed, at infinite dilution one can write the following expression ... 

The above ideal ternary mixture with mole fractions x, Xg, and x and molar volume V can also be obtained as an ideal pseudobinary one by mixing the pure solvent 1 and the binary mixture with molar fractions Xg and... 

Ideal ternary mixture [superscript (id) ]- In this case... 

However, Eqs. 3 and 5 are different equations even though they are based on the same definition of the preferential binding parameter and have the same theoretical basis the Kirkwood-Buff theory of solutions. To make a selection between Eqs. 3 and 5 a simple limiting case, the ideal ternary mixture, will be examined using the traditional thermodynamics, and the results will be compared to those provided by Eqs. 3 and 5. 

By inserting Eqs. 12 and 13 into Eq. 9 at infinite dilution of component 2, one obtains the following expression for F23 of an ideal ternary mixture ... 

Let us consider an ideal ternary mixture. According to the definition of an ideal mixture (18), the activities of the components ( i) are equal to their mol fractions (xi) and their partial molar volumes are equal to those of the pure components (V = Tf). 

On the other hand, expressions for F23 for an ideal ternary solution can be also derived by combining Eq. 3 or Eq. 5 with the following Kirkwood-Buff integrals for ideal ternary mixtures (16) ... 

Show that in an ideal ternary mixture, the minimum Gibbs energy is obtained if = X2 =... 

In the second part, the possible products of kinetically controlled catalytic distillation processes are analyzed using residue curve maps. Ideal, as well as non-ideal, ternary mixtures are considered. Current research activities are presented that are focussed on reaction systems exhibiting liquid-phase splitting phenomena such as the hydration of cyclohexene to cyclohexanol at strongly acidic catalyst partides. 

As shown above, reaction kinetics have a significant influence on RD process performance in binary mixtures and the same is true for multicomponent mixtures. In the following, the attainable products of kinetically controlled RD processes are analyzed, first for ideal ternary mixtures, then for non-ideal ternary mixtures occurring in industrially important fuel ether synthesis, and finally for an extremely non-ideal system with potential liquid-phase splitting. In all cases, reversible reactions of type A + B o C are considered. 

After the above discussion on RD of ideal ternary mixtures, in this section two nonideal ternary systems are considered. These are the heterogeneously catalyzed syntheses of the fuel ethers MTBE (methyl tert-butyl ether) and TAME (fert-amyl methyl ether) by etherification of methanol with isobutene or isoamlyenes respectively. Both reaction systems have enormous industrial importance because of the outstanding antiknock properties of MTBE and TAME as gasoline components. 

Fig. 5.2-30 Graphical determination of the minimum reflux ratio of the low-boiler separation from an ideal ternary mixture...

Figure 4.18. (a) Column of autoextractive reversible distillation ofideal ternary mixture (Ki > K2 > K ). (b) Column of opposite autoextractive reversible distillation of ideal ternary mixture (Ki > K2 > K ). 

Figure 6.3. Reversible distillation trajectories of ideal ternary mixtures K > K2 > K3) for intermediate section of two-feed column (a) <0 ...

Figure 6.14. Knch zones in column with side product and intermediate and stripping section trajectories for the ideal ternary mixture (a) side product composition equal to tear-off point composition and (b) side product composition unequal to tear-off point composition. Attraction region of point (Reg ft) is shaded.

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