Distillation minimum stages

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) ... 

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-... 

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. 

Minimum surges are stepped off when the operating lines Coincide with die diagonal line and have a slope of unity from Eq. (5.3-24) it can be seen that al this condition of minimum stages there can be no net product distillate takeoff. This is the condition of total reflux and is an important condition for starting up columns and for conducting efficiency tests on columns. 

Batch distillation columns may be operated uader either of two reflux policies, constant reflux with varying distillate composition, and variable reflux, with constant distillate composition. These policies have the usual limitations of total reflux and minimum stages,... 

Thus, the minimum number of equilibrium stages depends on the degree of separation of the two key components and their relative volatility, but is independent of feed-phase condition. Equation (12-12) in combination with (12-13) is exact for two minimum stages. For one stage, it is equivalent to the equilibrium flash equation. In practice, distillation columns are designed for separations corresponding to as many as 150 minimum equilibrium stages. 

Minimum stages for total reflux. Just as in binary distillation, the minimum number of theoretical stages or steps, can be determined for multicomponent distillation for total reflux. The Fenske equation (11.4-23) also applies to any two components in a multicomponent system. When applied to the heavy key H and the light key L, it... 

Before outlining the method in details, we provide a list of general considerations Specified data Charge composition, distillate composition, stage holdup, vapor rate or boiling duty, and either operation time or minimum recovery. 

The operation of a binary distillation has two important limiting cases minimum and maximum stages for a given separation. Minimum stages occur when the column is operated with total reflux (i.e., no top product is withdrawn). This situation, when applied to the McCabe-Thiele method, uses the y = x line as the mass balance for both rectifying and stripping. The situation is depicted in Figure 12-11. 

As with distillation, the cases of minimum reflux (infinite stages) and minimum stages (infinite reflux ratio) occur in extraction. The minimum reflux takes place in the extract section when an extended tie line meets a 2 as close to Se as possible (in Figure 13-14). Also, for the raffinate section an extended tie line... 

This value is vastly inferior to that obtained by the centrifuge method (1.18, see Illustration 1.3). It implies that extensive staging is required to separate the isotopes by diffusion. The actual number of stages ultimately used in the production unit (Figure 3.6) amounted to more than 4000. Of particular interest to chemical engineers is tiie fact that the minimum stage requirement, which applies under conditions of no product withdrawal, was calculated by an equation derived some 10 years earlier by Fenske for multistage distillation at total reflux Ind. Eng. Chem. 24, 482 [1932] see Illustration 7.10). 

McCabe-Thie/e Example. Assume a binary system E—H that has ideal vapor—Hquid equiHbria and a relative volatiHty of 2.0. The feed is 100 mol of = 0.6 the required distillate is x = 0.95, and the bottoms x = 0.05, with the compositions identified and the lighter component E. The feed is at the boiling point. To calculate the minimum reflux ratio, the minimum number of theoretical stages, the operating reflux ratio, and the number of theoretical stages, assume the operating reflux ratio is 1.5 times the minimum reflux ratio and there is no subcooling of the reflux stream, then ... 

Fig. 11. Limiting conditions in binary distillation, (a) Minimum reflux and infinite number of theoretical stages (b) total reflux and minimum number of...

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