Extraction McCabe-Thiele diagrams

Alternative approaches are to be found in the hterature. Derivations of the above equations are given in numerous texts (2,10—12), which also describe graphical or analytical solutions to the problem. Many of these have direct analogues in other separation processes such as distillation (qv) and hquid—hquid extraction, and use plots such as the McCabe-Thiele diagram or Ponchon-Savarit diagram. 

The extraction isotherms constructed from these data can be used in the construction of a McCabe-Thiele diagram (see Chapter 8). 

The graphical construction of an extraction isotherm, an operating line, and the stepwise evaluation of the number of stages in this manner is known as a McCabe-Thiele diagram. Flistorically, it found great application in a variety of mass transfer operations, from gas adsorption through distillation to solvent extraction. Flowever, the advent of modern computational techniques has made it largely redundant, as it is often easier and certainly more accurate to calculate the cascade directly. 

Fig. 8.11 McCabe-Thiele diagram showing the effect of reduced efficiency of extraction.

Figure 32 A McCabe-Thiele diagram for a five-stage counter-current solvent extraction process...

Figure 33 McCabe-Thiele diagrams for (a) a five-stage counter-current back-extraction process and (b) a process involving three stages of extraction and two scrub stages...

This result is very close to that obtained by using a McCabe-Thiele diagram (Fig. 15-23). From solubility data at Y = 0.1039 kg acetic acid/kg MIBK (given in Table 15-8), the extract layer contains 5.4/85.7 = 0.0630 kg water/kg MIBK, and Ye = (0.097)/( 1 -t- 0.097 -t- 0.063) = 0.084 mass fraction acetic acid in the extract. 

Given this number of stages, construction of a similar McCabe-Thiele diagram for other components in the feed, such as impurities, allows the calculation of the extent to which these impurities extract into the organic phase. If two or more extractable components are each in sufficient concentration to affect the distribution coefficient of the other species, e.g., TBP extraction of U02(N03)j and HNOa, the equilibrium lines for the two components cannot be specified in advance but must be calculated by an iterative procedure, similar to that to be illustrated in Sec. 6.6 for the zirconium-hafnium separation. 

FIGURE 20.13 McCabe-Thiele diagram extraction (Example 20.3). 

It was seen how readily the McCabe-Thiele diagram can be applied to extraction, provided the coordinates are adjusted to allow for the inert carriers. The same is true of the Ponchon diagram. 

McCabe-Thiele diagrams for adsorption, 320 for binary distillation, 326, 329, 330, 332, 334 for countercurrent multistage separator, 309 for extraction, 317 for ion exchange, 322 for rectifying column, 314 McCabe-Thiele method for distillation, 310-315, 322-340... 

Dilute multicomponent extraction can be analyzed on a McCabe-Thiele diagram if we add one more assumption. 

Figure 13-7. McCabe-Thiele diagram for fractional extraction (A) solute A, (B) solute B...

The McCabe-Thiele diagrams are useful for more complicated extraction columns such as those with two feeds or extract reflux fWankat. 1982. 1988). 

C4. Develop the solution method for a dilute multicomponent extraction in a cross-flow cascade. Sketch the McCabe-Thiele diagrams. 

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