McCabe-Thiele Liquid Feed

McCabe-Thiele Method - This MathCAD document creates a McCabe-Thiele Diagram for a binary distillation. Data are from Example 6-5. 

MathCAD File Name McCabe2001-liquid-feed.MCD 

It uses activity coefficient methods to calculate vapor-liquid equilibrium. It will estimate a minimum reflux ratio (Rmin) assuming no pinch point in the rectifying section. The actual reflux ratio (RR) is set as a multiple of Rmin (R = C Rmin). 

Copyright John Hwalek, 2001 All rights reserved. This document is for your private use. 

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Figure 7.38 shows a complete McCabe-Thiele diagram. Feed is introduced as liquid at its boiling point (q = 1). The column requires 6 theoretical plates. 

Operating Lines The McCabe-Thiele method is based upon representation of the material-balance equations as operating lines on the y-x diagram. The lines are made straight (and the need for the energy balance obviated) by the assumption of constant molar overflow. The liqmd-phase flow rate is assumed to be constant from tray to tray in each sec tiou of the column between addition (feed) and withdrawal (produc t) points. If the liquid rate is constant, the vapor rate must also be constant. 

The reason for this simple relationship is that the concept of minimum reflux implies an infinite number of stages and thus no change in composition from stage to stage for an infinite number of stages each way from the pinch point (the point where the McCabe-Thiele operating lines intersect at the vapor curve for a well-behaved system, this is the feed zone). The liquid refluxed to the feed tray from the tray above is thus the same composition as the flash liquid. 

The McCabe-Thiele method can be used for the design of columns with side streams and multiple feeds. The liquid and vapour flows in the sections between the feed and take-off points are calculated and operating lines drawn for each section. 

A feed mixture of methanol and water containing a mole fraction of methanol of 0.4 is to be separated by distillation at a pressure of 1 atm. The overhead product should achieve a purity of 95 mole % methanol and the bottoms product a purity of 95 mole% water. Assume the feed to be saturated liquid. Using the x—y diagram constructed in Exercise 1 and the McCabe-Thiele construction ... 

A fractionating column is required to distill a liquid containing 25 per cent benzene and 75 per cent toluene by mass, to give a product of 90 per cent benzene. A reflux ratio of 3.5 is to be used, and the feed will enter at its boiling point. If the plates used are 100 per cent efficient, calculate by the Lewis-Sorel method the composition of liquid on the third plate, and estimate the number of plates required using the McCabe-Thiele method. 

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. 

The liquid-phase composition profiles are shown in Figure 14.8, the temperature profiles in Figure 14.9. In this example, the liquid and vapor temperatures are almost equal. The pressure profile is not shown since it was more or less a straight line between the specified top tray pressure and the computed bottom pressure reported in Table 14.3. The pseudo McCabe-Thiele diagram and efficiency profiles are shown in Figures 14.10 and 14.11. In this case we see that the efficiencies of acetone and methanol are essentially equal over most of the column with the efficiency of water somewhat higher. Interestingly, the efficiencies decrease in the lower portion of the column below the acetone-methanol feed. 

The McCabe-Thiele method will be used. The side draw is more concentrated in acetone than either feed and should therefore be located above the feeds. Calculate the internal liquid and vapor flow rates and the slope of the operating line between the condenser and the side draw ... 

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