McCabe-Thiele diagrams bottom operating lines

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. 

Consider a propane concentration of 88 percent in the feed. The McCabe-Thiele diagram, based on the Fig. 7.12a interpretation of the test data, predicts a pinch just below the feed (Fig. 7.12e). Due to the pinch, the concentration of propane in the tower bottom will be 17 percent, i.e,. much higher than the 2 percent propane in the test data. In practice, this pinch will probably be eliminated by increasing the boilup ratio (i.e., reducing the slope of the operating line). However, increasing the boilup ratio means more liquid and vapor traffic, a greater heat load on the reboiler, and possibly, a premature capacity bottleneck. 

Plot the equilibrium data, the top and bottom operating lines, and the y = x line on the same graph. This plot is called a McCabe-Thiele diagram (Figure 30). 

Fig. 5.9 shows the geometric representation of these balances in the McCabe-Thiele diagram. The distillate composition xP is located at the intersection of the condenser operating line and the operating line of the RD section. By specifying xP, the number of reactive trays can be estimated from the classical staircase construction. From the intersection of the operating line of the column section with that of the reboiler line, the bottom composition is determined. 

A mass balance around the whole process reveals that there is no exit for the water fed into the top of the absorber. Hence, some of the bottoms 51 has to be withdrawn as side product S. This fraction meets the specification of commercial hydrochloric acid and can be utilized elsewhere. From the McCabe-Thiele diagram in Fig. 11.1-6 follows the slope of the operating line at the top of the colunm ... 

This is somewhat unusual, because it includes a bottoms concentration leaving the stripping column (column 2). The reflux for this top operating line is liquid of composition p. The McCabe-Thiele diagram for this system is shown in Figure 8-4B and is almost identical to Figure 8-3B. 

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