Equilibrium stages McCabe-Thiele analysis

Figure 31. McCabe-Thiele analysis of equilibrium stages for the ethanol-water system.

The McCabe-Thiele analysis can be used to model physical absorption and stripping processes that use equilibrium stages. 

However, while ideal equilibrium stages may be a poor approximation, they are usually the language in which distillation problems are discussed. Thus anyone who studies distillation should analyze any target separation in terms of a McCabe-Thiele analysis even though he knows that this analysis may not be that close to what actually happens. The graphical picture of what is happening is just too good to abandon. 

The test separation data are analyzed using a McCabe-Thiele diagram (Fig, 7.12a), with an equilibrium curve based on experimental data (average relative volatility of about 1,7), The analysis shows that the stripping section requires 12 theoretical stages. 

Consider an analysis of the same test data, but with an equilibrium curve based on a VLE prediction which gives higher relative volatilities (average of about 2,5) than the experimental data. With the calculated VLE, the McCabe-Thiele diagram (Fig, 7,125) requires only eight theoretical stages. 

D19. Many extraction systems are partially miscible at high concentrations of solute, but close to immiscible at low solute concentrations. At relatively low solute concentrations both the McCabe-Thiele and trianglar diagram analyses are applicable. This problem explores this. We wish to use chloroform to extract acetone from water. Equilibrium data are given in Table 13-4. Find the number of equilibrium stages required for a countercurrent cascade if we have a feed of 1000.0 kg/h of a 10.0 wt % acetone, 90.0 wt % water mixture. The solvent used is chloroform saturated with water (no acetone). Flow rate of stream Eq = 1371 k. We desire an outlet raffinate concentration of 0.50 wt % acetone. Assume immiscibility and use a weight ratio units graphical analysis. Conpare results with Problem 13.D43. 

The concept will be introduced in the context of the McCabe-Thiele construction for the graphical analysis of binary distillation problems. This method uses y-x diagrams of the form shown in figure 6.2. Such diagrams are a graphical representation of equilibrium data, and so if the composition of the resultant vapour from an equilibrium stage is known, then the composition of the resultant liquid (in equilibrium with that vapour) can be obtained from the curve on the appropriate y-x diagram. 

---