Number of stages. Once the equilibrium curve, ç-line, end points, and slopes of the component balance lines are established, stages can be stepped off. Figure 2.186 (for Example 2.4) gives a total of 15 theoretical stages (not including the reboiler and condenser) with the feed entering at stage 9 (reboiler being stage 0).

Complex columns. The Hengstebeck diagram can be extended to complex columns using the concepts described in Sec. 2.2.10. The derivation, equations, and a worked example are elsewhere (23).

2.3.5 Minimum reflux by Hengstebeck diagram

Hengstebeck (15) recommends the following procedure for minimum reflux:

1. Calculate the limiting flow rate of the light nonkeys in the rectifying section and the limiting flow rate of the heavy nonkeys in the stripping section. These limiting flow rates for each nonkey can be calculated from Eqs. (2.50) and (2.51) as follows:

2. Construct the equilibrium curve for the key components and the q-line (Sec. 2.3.4).

3. Draw a line from the product composition point to the intersection of the g-line with the equilibrium curve. This line has a slope of

[LJ(Le + De)]min. With De (flow rate of keys in the top product) known, Le can be calculated.

4. The minimum reflux can be calculated as the sum of Le and the limiting flows of the light nonkeys, ¿LNK,iim-

Example Calculate the minimum reflux ratio for Example 2.4.

solution The 9-line is not affected by the reflux ratio [see Eq. (2.58)], and therefore there is no need to calculate the limiting flow of the heavy nonkey. The limiting flow of the light nonkeys is given by Eq. (2.60)

, 0.435 x 59.9 n , lci'lim = (15/0.8 - 1> " 1"5

The slope of the component balance line is determined graphically from Fig. 2.18c to be equal to 0.70

De = 24.9 and therefore Le>mIn = 58.1. Adding the limiting flows of the nonkeys

Therefore, minimum reflux ratio is

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