Feed lines optimum location

To determine the optimum feed plate location, draw a line from the feed composition on the y = x line, through the intersection of the top/bottom operating lines, to the equilibrium curve. The step straddling the feed line is the correct feed-plate location. 

Since the column shown in Figure 4-23A has four sections, there will be four operating lines. This is illustrated in the McCabe-Thiele diagram of Figure 4-23B. One would specify that the liquid be withdrawn at flow rate S at either a specified concentration Xg or a given stage locatiom The saturated vapor is at concentration yg = Xg. Thus there is a horizontal feed line at yg. If the optimum location for... 

In Sec. 2.2.4, it was assumed that the feed enters the column at the optimum feed stage, which is located at the intersection of the component balance lines. At that point, the construction was switched from the rectifying section component balance line to the stripping section component balance line,... 

Once the operating lines are plotted, the equilibrium stages are stepped off between the operating line and equilibrium curve as described in Section 5.1.3. The optimum feed tray location is at the step that crosses from one operating line to the other over their intersection point. If the number of stages is fixed, the operating lines are determined by trial and error to match the specified number of stages. 

Stepping off stages starting from xd, step off stages until you reach a i -line, then shift to new operating line for optimum feed location. For Example 4.5 (Figure 4.20), F would be introduced above F2 in the column. 

The transfer from one operating line to the other, and hence the feed-plate location, can be made at any location between points a and b in Fig. 18.15, but if the feed plate is placed anywhere but at the optimum point, an unnecessarily large number of plates is called for. For example, if the feed plate in Fig. 18.15 is number 7, the smaller steps shown by the dashed lines make the number of ideal plates needed about eight plus a reboiler, instead of seven plus a reboiler when the feed is on plate number 5. Note that the liquid on the feed plate does not have the same composition as the feed except by coincidence, even when the feed plate location is optimum. 

When all operating lines have been plotted, step off stages, determine optimum feed plate locations and the total number of stages. If desired, calculate a fractional number of stages. 

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