F D
+ + • ■ ■  Dxd Fi + F2 +D
the 45° diagonal and the intersection of the feed gline with the equilibrium curve. The line drawn is the minimum reflux component balance line; the minimum reflux ratio can be determined from the intercept of this line on they axis (Sec. 2.2.6).
The procedure for finding minimum reflux in each section of a complex fractionator is similar. First, the point of intersection of the component balance line with the 45° diagonal is found by using Eq. (2.38). Second, the point of intersection of the <jline for the feed or side product with the equilibrium curve is graphically determined. A straight line is then drawn between the two points. This line is the minimum reflux component balance line. The minimum reflux is found from the intercept of this line on the y axis, using Eq. (2.40).
In case of heat removal or addition, there is no qrline. In such a case, the second point that is used to construct the minimumreflux component balance line is the point on the equilibrium curve representing the compositions of the liquid and vapor stream leaving the heataddition or heatremoval stage.
Design procedure. The minimum refluxes computed for each section are compared with each other. The highest value is the minimum reflux for the column. From Eq. (2.35) the corresponding minimum liquid flow in the section is calculated. This flow can be multiplied by a certain factor, commonly between 1.05 and 1.3 to give the optimum flow. Guidelines for selecting factors are given in Sec. 3.1.6. The liquid flow can now be resubstituted into Eq. (2.35) and the actual reflux ratio calculated.
The intercept of each component balance line on the y axis can now be calculated from Eq. (2.40), using the actual reflux ratio. Each com ponent balance line is drawn by connecting this intercept with the point of intersection of the component balance line with the 45° diagonal line, already determined during the minimum reflux calculation.
This procedure can be simplified if there are no points of heat addition or removal, and qlines exist between all adjacent sections. In this case, the only intercept on they axis that is actually required is that of the first section. Once the component balance line for this section is drawn, its points of intersection with the first gline are used, instead of the intercept on the y axis, to construct the second component balance line, etc.
After the component balance lines have been determined, stages can be stepped off in the usual manner.
Example 2.3 (from H. Z. Kister, Chemical Engineering, January 21, 1985, pp. 97104. Reproduced courtesy of Chemical Engineering) illustrates the extension of the xy diagram to complex columns:
Example 2.3 Benzene is to be separated from toluene in a distillation column.
Three feed streams are available, having the following characteristics:
Stream number 

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