Triangle Diagrams

The simplest form of ternary RCM, as exemplified for the ideal normal-paraffin system of pentane-hexane-heptane, is illustrated in Fig. 13-58 7, using a right-triangle diagram. Maps for all other non-azeotropic ternary mixtures are qiiahtatively similar. Each of the infinite number of possible residue curves originates at the pentane vertex, travels toward and then away from the hexane vertex, and terminates at the heptane vertex. 

These results can, in general, be applied to any two points on the triangle diagram. If a mixture R is continuously diluted with mixture S, the mixture composition follows the straight line between points R and S. As the dilution continues, the mixture composition moves closer and closer to point S. Eventually, at infinite dilution the mixture composition is at point S. 

Fig. 9. Logarithm of the cation activity coefficient versus the square root of the concentration for the system of manganese ions and cation vacancies in sodium chloride at 500°C. Filled-in circles represent the association theory with Rq = 2a, and open circles the association theory with R = 6/2. Crosses represent the present theory with cycle diagrams plus diagrams of two vertices, and triangles represent the same but with triangle diagram contributions added.

The widest investigation on nitration of D-mannitol in nitric acid-sulphuric acid nitration mixture at 0°C was recently reported by Kunz and Giber [16b]. The authors built a triangle diagram (Fig. 68) known as Sapozhnikov diagram described in detail in the chapter dedicated to nitrocellulose (p. 333). The curves of equal... 

Unlike the flash equilibrium of Chap. 2, the extract and raffinate phases (compared to vapor-liquid) are miscible to some degree, as seen in the triangle diagram. Point D, for example, shows how much of the solvent (benzene) can dissolve into the feed (water) at equilibrium of the two liquid phases. Similarly, point M shows how much feed water will dissolve into benzene at equilibrium. 

For a better understanding of liquid-liquid equilibrium, a brief study of a three-component triangle diagram is recommended. Using Fig. 7.1 as a reference, the following observations should be realized for any such diagram ... 

Fig. 1. The QED contributions of order a/it) to the bound-electron gj factor depicted as Feynman diagrams. Double lines indicate bound fermions, wavy bnes indicate photons. The interaction with the magnetic field is denoted by a triangle. Diagram (a) is also termed SE, ve (self-energy vertex correction), diagrams (c) and (e) SE, wf (self-energy wave-function correction), diagram (b) VP, pot (vacuum-polarization potential correction), and diagrams (d) and (f) VP, wf (vacuum-polarization wave-function correction)...

Fig. 2.6 Triangle diagram for a system with two partly immiscible components...

Fig. 2. 7 Construction of the distribution diagram from the triangle diagram...

Fig, 2,8 Depiction of a single-stage extraction in a triangle diagram 2.1.1.3.2 Multi-Stage Liquid-Liquid Extraction... 

Fig. 2.12 Determination of the number of theoretical plates in a triangle diagram...

To visualize all possible operating points for sections II and III, the dimensionless flow rate ratio mm is plotted versus mn in the so-called triangle diagram. For linear isotherms all possible operating points that fulfill the constraints are within the triangle shown in Fig. 7.18. 

Figure 7.18 Operating or triangle diagram for linear isotherms.

Figure 7.19 Operating or triangle diagram for nonlinear isotherms. Here EMD53986 (cveea = 2.5 gl ) ...

Many extraction systems involve three components which form two immiscible phases. For example, acetone and water are miscible in all proportions. When an organic solvent, methyl isobutyl ketone (MIK) is added to a water-rich acetone solution, two phases are formed a water rich phase and an MIK-rich phase, both phases containing all three components. The composition of the two phases can be graphically represented by means of tie lines on a triangle diagram. ... 

In this system, acetone is completely miscible in both water and MIK, but MIK is only slightly soluble in water and water is only slightly soluble in MIK. This is an example of a Type I triangle diagram. 

A very different looking triangle diagram results when one of the liquids is not completely miscible with either of other two. The diagram at right is for the system aniline-heptane-methylcyclohexane. This is an example of a Type II triangle diagram. 

Notice in the Type I triangle diagram that as the fraction of acetone gets higher, the tie lines get shorter. Eventually, the tie line becomes infinitesimally short, such that the composition of the two immiscible phases become equal at the... 

Regardless of the type of triangle diagram that is being used, remember that the weight fractions of each phase must add up to one ... 

This is a useful check to confirm that a triangle diagram is read correctly. 

Figure 3.21 Graphical representation of mass balances for a two-liquid feed stream on a right triangle diagram.

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