Minimum and total reflux

Minimum reflux corresponds to the overlap of an operating line and a tie-line (infinite stages at a pinch point). This concept is similar to minimum solvent flowrate for an extraction process without reflux. Total reflux corresponds to the minimum number of stages. Remember that total reflux means that no streams are going into or out of the column, so that F, B, and D are zero, and A = A.  

Xad = 0.82, same concentration as the Vi stream (solvent-free basis) since Vo is pure solvent. 

Determine (a) the number of equilibrium stages and (b) location of the feed stage. Solution  

Since Vo is pure B and On+i and D have no solvent present, the line connecting pure B and On+i and D must contain Vn, which must also be on the solubility envelope 

Ab is on line through F and A o and also on line through Vo and Oi. Hence, (a) two equilibrium stages are necessary for separation. 

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The minimum reflux ratio is commonly used in specifying operating conditions. For example, we may specify the reflux ratio as L7D = 1.2(L7D)n. Minimum reflux would use the minimum amount of reflux liquid and hence the minimum amount of heat in the reboiler, but the maximum (infinite) number of stages and a maximum (infinite) diameter for a given separation. Obviously, the best operating conditions lies somewhere between minimum and total reflux. As a rule of thumb, the optimum external reflux ratio is between 1.05 and 1.25 times (170). (See Chapter 11 for more details.)... 

The two limiting reflux conditions in a distillation column are minimum and total reflux. Suppose we have an infinite staged column with a constant binary flow of constant composition. 

Figure 13.7. Features of McCabe-Thiele diagrams for constant molal overflow, (a) Operating line equations and construction and minimum reflux construction, (b) Orientations of -lines, with slope = ql q — 1), for various thermal conditions of the feed, (c) Minimum trays, total reflux, (d) Operating trays and reflux, (e) Minimum reflux determined by point of contact nearest xD.

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. 

The number of stages required to separate feed into product and tails of specified composition is a minimum at total reflux, when . Under this condition we have seen that... 

The actual operating reflux ratio to use is in between these two limits. To select the proper value of R requires a complete economic balance on the fixed costs of the tower and operating costs. The optimum reflux ratio to use for lowest total cost per year is between the minimum R and total reflux. This has been shown for many cases to be at an operating reflux ratio between 1.2/ to 1.5i . 

EXAMPLE 11.4-2. Minimum Reflux Ratio and Total Reflux in Rectification... 

Figure 11.4-13. Graphical solution for minimum reflux ratio and total reflux for Example 1.4-2.

In industry many of the distillation processes involve the separation of more than two components. The general principles of design of multicomponent distillation towers are the same in many respects as those described for binary systems. There is one mass balance for each component in the multicomponent mixture. Enthalpy or heat balances are made which are similar to those for the binary case. Equilibrium data are used to calculate boiling points and dew points. The concepts of minimum reflux and total reflux as limiting cases are also used. 

At total reflux the ordinate is 0.0 and the abscissa is 1.0, while at the minimum reflux ratio the ordinate is 1.0 and the abscissa is 0.0. As the reflux ratio is increased from the minimum to total reflux, a given design problem will give a curve that goes from 1,0 to 0,1. It was expected that a series of curves between these two points would be obtained, depending on (1) the degree of separation, (2) the relative... 

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

Minimum total reflux (lbs or mols/hr) corresponding to given total feed will be greater than if only the actual total mols of heavy and light key components were present. Reflux need will be less than if the actual total mols of feed were present, but composed only of light and heavy keys. The more closely non-keyed components are clustered to volatilities of the keys, the nearer are reflux needs to that calculated for the binary and total feed volume. 

From Fenske s equation, the minimum number of equilibrium stages at total reflux is related to their bottoms (B) and distillate or overhead (D) compositions using the average relative volatility, see Equation 8-29. 

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