At actual reflux

Figure 8-28 presents the usual determination of optimum or near optimum theoretical trays at actual reflux based on performance. It is not necessarily the point of least cost for all operating costs, febrication costs or types of trays. A cost study should be made to determine the merits of moving to one side or other of the so-called optimum point From the Figure 8-28 ...

St = Theoretical trays/stages at actual reflux, L/D, including reboiler and total condenser Sopt = Optimum stripping factor (SR)i = Separation factor... 

Solution. Assume that the product distribution computed in Example 12.2 based on the Winn equation for total reflux conditions is a good approximation to the distillate and bottom compositions at actual reflux conditions. Therefore... 

An extension of the Underwood method for distillation columns with multiple feeds is given by Barnes, Hanson, and King. Exact computer methods for determining minimum reflux are available. For making rigorous distillation calculations at actual reflux conditions by the computer methods of Chapter 15, knowledge of the minimum reflux is not essential but the minimum number of equilibrium stages is very useful. 

The recommended method to use to determine the actual theoretical stages at an actual reflux ratio is the Erbar/Maddox relationship. In the graph, N is the theoretical stages and R is the actual reflux ratio L/D, where L/D is the molar ratio of reflux to distillate. N, is the minimum theoretical stages and R, is the minimum reflux ratio. 

Because a column cannot operate at total reflux and produce net product from the column, a reflux ratio of about 1.1 to 1.5 times the mmmMm reflux will usually give practical results. Be aware that as the reflux ratio comes down approaching the minimum, the number of theoretical and then corresponding actual trays must increase. 

The combined Fenske-Underwood-Gillilland method developed by Frank [100] is shown in Figure 8-47. This relates product purity, actual reflux ratio, and relative volatility (average) for the column to the number of equilibrium stages required. Note that this does not consider tray efficiency, as discussed elsewhere. It is perhaps more convenient for designing new columns than reworking existing columns, and should be used only on at acent-key systems. 

From the theoretical trays at operating reflux the actual trays for installation are determined ... 

Referring to the data given, at total reflux, the conditions on actual plates in the column are shown as points A, B, C, and D. Considering point A, if equilibrium were achieved on that plate, point E would represent the vapour composition and point F the liquid composition on the next plate. The liquid on the next plate is determined by B however so that the line AGE may be located and the efficiency is given by AG/AE = 0.59 or 59 per cent... 

The distribution of nonkeys actually depends somewhat on the reflux ratio. For instance, in the case of Example 13.10, the distributions at minimum trays (total reflux) and minimum reflux are substantially different. Often it turns out, however, that the distributions predicted by Eq. (13.119) are close to those at finite reflux whenever R is near 1.2Rm, which is often near the economic value for the reflux ratio. Further discussion of this topic is by Hengstebeck (Distillation, 1961) and Stupin and Lockhart (1968) whose work is summarized by King (1980, p. 434). Knowledge of the complete distribution is needed for estimation of top and bottom temperatures and for determination of the minimum reflux by the method to be cited. 

This measure was based upon the ratio of the minimum necessary number of plates, A min (averaged over the reboiler composition) in a column to the actual number of plates in the given column, Nj. Christensen and Jorgensen assumed that the mixture has a constant relative volatility a and the column operates at total reflux using constant distillate composition (x o) strategy (section 3.3.2) and evaluated Nmin using the Fenske equation ... 

Table 13-6 shows subsequent calculations using the Underwood minimum reflux equations. The a and Xo values in Table 13-6 are those from the Fenske total reflux calculation. As noted earlier, the % values should be those at minimum reflux. This inconsistency may reduce the accuracy of the Underwood method but to be useful, a shortcut method must be fast, and it has not been shown that a more rigorous estimation of x values results in an overall improvement in accuracy. The calculated firnin is 0.9426. The actual reflux assumed is obtained from the specified maximum top vapor rate of 0.022 kg- mol/s [ 175 lb-(mol/h)] and the calculated D of 49.2 (from the Fenske equation). 

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