McCabe-Thiele diagrams examples

For certain simplified cases it is possible to calculate directly the number of stages required to attain a desired product composition for a given set of feed conditions. For example, if equilibrium is attained in all stages and if the underflow mass rate is constant, both the equilibrium and operating lines on a modified McCabe-Thiele diagram are straight, and it is possible to calculate direc tly the number of ideal stages required to accommodate arw rational set of terminal flows and compositions (McCabe, Smith, and Harriott, op. cit.) ... 

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 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-... 

Figure S.2 Batch distillation of benzene-toluene at constant reflux ratio, Example 5,3, ia-e) McCabe-Thiele diagram for progressively reducing still concentration to 0.13 mole fraction benzene.

Hgwe 5.3 (Continued) Batch distillation of benzene-toluene with Wriable reflux ratio, Example 5.4. (o-e) McCabe-Thiele diagram fcr progressively increasing reflux ratio to 13 1. 

In traditional applications of thermodynamics, the goal is to find the free energy and its derivatives for direct use in chemical engineering design a classic example is the equilibrium curve in a McCabe-Thiele diagram. In emerging applications of thermodynamics, the free energy and its derivatives are not of interest in themselves but serve only as intermediates to find the material structure which provides optimum conditions for some particular process. 

Mole fraction dye intermediate in liquid, x FIGURE 8.21 Second McCabe-Thiele diagram for Example 8.6. 

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. 

McCabe Delta-L law, ciystallization, 533 calculation example, 534 McCabe-Thiele diagram, distillation, 381 Magnesium sulfate/water diagram, 526, 529... 

For all other things to be equal, the amounts of the species must be the same and the relative volatility between all adjacent pairs of species must also be the same. For example, in the case of a four-species feed having equal amounts of each species (e.g., 1 kmol/h each) and relative volatilities of ad 1-2 = 1.728, bd = 1-2 = 1.44, q cd = 1-2 = 1.2, and Odd = 1.2 = 1, all other aspects of the problem [would be] equal. For each binary split (e.g., A/B or B/C), the McCabe-Thiele diagram would be drawn with the equilibrium curve based on a relative volatility of 1.2. 

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