The McCabe-Thiele Diagram

when R = 3, 3 mol of liquid product are returned to the column for each mole withdrawn. 

Mass Transfer and Separation Processes Principles and Applications 

Details of the rectifying (enriching) section (a) flow diagram and (b) operating diagram. 

Rate of total moles in - Rate of total moles out = 0 

Consequently, using Equation 7.18a and Equation 7.18c yields tiie following  

We first compose the total mole balance, and follow this with an energy balance around the feed tray. We obtain 

These two equations can be combined and rearranged to yield the expression 

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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. 

Figure 14.1 The McCabe-Thiele diagram for the calculation of the number of theoretical stages required to separate two liquids to yield relatively pure products...

Kister shows how the McCabe-Thiele Diagram is an excellent tool for analyzing computer simulation results. It can be used to... 

The familiar steps for the theoretical stages on the McCabe-Thiele diagram are modified on the Ryan plot. The vertical portions remain vertical, but the horizontal portions become slanted with a slope of -1.00 (see Figure 2). 

Ryan, J. M., Ryan Consulting, Inc. (jamesryancon sulting juno.com) Replotting the McCabe-Thiele Diagram , Chemical Engineering, May, 2001, p. 109. 

The situation for any plate n, with liquid composition x corresponding to an equilibrium vapour composition y , but with actual vapour composition y , is represented on a small section of the McCabe-Thiele diagram in Fig. 3.62. 

When concentrations of the more volatile component of either product is very low the steps on the McCabe-Thiele diagram become very small and difficult to plot. This problem can be overcome by replotting the top or bottom sections to a larger scale, or on log-log paper. In a log plot the operating line will not be straight and must be drawn by plotting points calculated using equations 11.21 and 11.22. This technique is described by Alieva (1962) and is illustrated in Example 11.2. 

The McCabe-Thiele diagram is shown in Figure 11.10. Twelve stages required feed on seventh from base. 

From the McCabe-Thiele diagram, at a = 0.05, the slope of the equilibrium line =1.0... 

The number of stages required for a given separation can be determined from the triangular diagram using a method analogous to the McCabe-Thiele diagram used to determine the... 

Figure 9.10 Total and partial condensers in the McCabe-Thiele Diagram.

Thus, from Figure 14.9, the McCabe-Thiele diagram can be used to determine the reflux ratio for a given xa,b-This allows Equation 14.19 to be integrated graphically, as shown in Figure 14.10. 

The catalytic esterification of ethanol and acetic acid to ethyl acetate and water has been taken as a representative example to emphasize the potential advantages of the application of membrane technology compared with conventional distillation [48], see Fig. 13.6. From the McCabe-Thiele diagram for the separation of ethanol-water mixtures it follows that pervaporation can reach high water selectivities at the azeotropic point in contrast to the distillation process. Considering the economic evaluation of membrane-assisted esterifications compared with the conventional distillation technique, a decrease of 75% in energy input and 50% lower investment and operation costs can be calculated. The characteristics of the membrane and the module design mainly determine the investment costs of membrane processes, whereas the operational costs are influenced by the hfetime of the membranes. 

Example 7.1 The next part of the McCabe-Thiele diagram is the operating line. To generate the operating line, the problem for Fig. 7.2 must be stated. The following conditions are given. Find the required solvent rate and number of theoretical equilibrium stages to meet the treated water specification of 1.0% acid remainder. Benzene will be the solvent. Also determine what solvent inlet purity is required to meet this water specification. A step-by-... 

In practice, feeds rarely consist of only two components, and the McCabe-Thiele diagram cannot be used. 

Extension of the x-y diagram to columns containing a second feed or a side product has been discussed by numerous authors (7, 8, 14-17), Yaws et al, (18) extended the McCabe-Thiele diagram to three-feed columns. Kister (19) extended the McCabe-Thiele diagram to columns... 

From the McCabe-Thiele diagram (Fig. 2.15c), 16 theoretical stages are required. The product drawoff is at stage 2. Feeds should enter stageB 5,9, and 13. The intercondenser should be located at stage 7. 

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. 

Consider now a propane concentration of 72 percent in the feed. The McCabe-Thiele diagram, based on the Fig. 7.12a interpretation of the test data, predicts that the propane concentration in the column bottoms will decline to 1 percent (Fig. 7.12c). On the other hand, if the McCabe-Thiele diagram were based on the Fig. 7,125 interpretation of the test data, it would predict 0.5 percent propane in the column bottoms (Fig. 7.12d). This prediction is optimistic. 

Until about 1930, most distillation calculations were based on Raoult s law in extreme cases, where ideal-mixture behavior was clearly incorrect, distillation calculations required experimental data coupled with graphical methods, as in the McCabe-Thiele diagram. 

The McCabe-Thiele diagram for this configuration, shown in Fig. 13-41, shows that the product purities have improved significantly. 

The McCabe-Thiele diagram for this design, showing that the feed is to the optimum stage, is shown in Fig. 13-44. The flow profiles are shown in Fig. 13-45 note the step changes due to both the feed and the sidestream. As was the case in Example 3, the curvature in the flow profiles is due to enthalpy changes. 

A portion of the McCabe-Thiele diagram for the simulation involving plug flow of vapor and dispersion flow of the liquid is shown in Fig. 13-55. For a nonequilibrium column these diagrams can only be constructed from the results of a computer simulation. Note that the triangles that represent the stages extend beyond the curve that represents the equilibrium line this is so because the efficiencies are greater than 100 percent. 

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