Stage minimum

Simple analytical methods are available for determining minimum stages and minimum reflux ratio. Although developed for binary mixtures, they can often be applied to multicomponent mixtures if the two key components are used. These are the components between which the specification separation must be made frequendy the heavy key is the component with a maximum allowable composition in the distillate and the light key is the component with a maximum allowable specification in the bottoms. On this basis, minimum stages may be calculated by means of the Fenske relationship (34) ... 

FIG. 13-37 McCabe-Thiele diagrams for limiting cases, a) Minimum stages for a column operating at total reflux with no feeds or products, (h) Minimum reflux for a binary system of normal volatility. 

McCormick [97] presents a correlation for Gilliland s chart relating reflux, minimum reflux, number of stages, and minimum stages for multicomponent distillation. Selecting a multiplier for actual reflux over minimum reflux is important for any design. Depending on the com-... 

The Fenske equation (Fenske, 1932) can be used to estimate the minimum stages required at total reflux. The derivation of this equation for a binary system is given in Volume 2, Chapter 11. The equation applies equally to multicomponent systems and can be written as ... 

For binary systems or systems that approach binary, the Fenske-Underwood-Erbar/Maddox Method is recommended. For minimum stages, use the Fenske equation.12... 

A short-cut design method for distillation is another subroutine. This method is based upon the minimum reflux of Underwood (17, 18, 19, 20), the minimum stages of Fenske (21) and Winn (22), and the reflux vs stages correlation of Erbar and Maddox (23) and Gray (24). In SHORT, which uses polynomial K and H values, the required number of equilibrium stages may be found for a specified multiple of minimum reflux, or alternatively, the reflux ratio may be found for a given multiple of minimum stages. 

Figure 3.e Calculating minimum reflux and minimum stages by extrapolating the reflux stages curve obtained by computer simulation. Depropanizer In Example 3.4. D = 59.9 lb-mole/h. 

It is important to use a consistent set of minimum reflux/minimum stages/reflux-stages correlation (27). Both the Gilliland and the Erbar and Maddox methods are consistent with the popular Fenske (Sec. 3,2.1) and Underwood (Sec, 3,2.2) methods. 

Gilliland (45) used the Fenske method (Sec. 3.2.1) to compute minimum stages, and his own method for computing minimum reflux. However, it was shown (11,48) that the Underwood method (Sec. 3.2.2) for minimum reflux can also be used. 

Chempak . 427, 429. 500, 616, 645, 885 Chemstation, 180 Chien s minimum reflux, 103, 104 Chien s minimum stages, 105 CMR (see Cascade Mini-Ring) Colburn ... 

Minimum Stages A column operating at total reflux is represented in Fig. 13-28(1. Enough material has been charged to the column to fill the reboiler, the trays, and the overhead condensate drum to their working levels. The column is then operated with no feed and with all the condensed overhead stream returned as reflux (Lf/+i = Vf/ and D = 0). Also all the liquid reaching the reboiler is... 

Equation-Based Design Methods Exact design equations have been developed for mixtures with constant relative volatility. Minimum stages can be computed with the Fenske equation, minimum reflux from the Underwood equation, and the total number of stages in each section of the column from either the Smoker equation (Trans. Am. Inst. Chem. Eng., 34, 165 (1938) the derivation of the equation is shown, and its use is illustrated by Smith, op. cit.), or Underwoods method. A detailed treatment of these approaches is given in Doherty and Malone (op. cit., chap. 3). Equation-based methods have also been developed for nonconstant relative volatility mixtures (including nonideal and azeotropic mixtures) by Julka and Doherty [Chem. Eng. Set., 45,1801 (1990) Chem. Eng. Sci., 48,1367 (1993)], and Fidkowski et al. [AIChE /., 37, 1761 (1991)]. Also see Doherty and Malone (op. cit., chap. 4). 

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