Reflux cascades

The overall separation depends on the single stage separation factor, the number of separating elements, and design and operating characteristics of the cascade. Equations 5-8 are insufficient to determine all the variables. It is instructive to consider three types of cascades the minimum stage cascade, the minimum reflux cascade, and the ideal cascade. The material balance equations from the i + 1 th stage to the product of the cascade lead to... 

The two limiting cascades we have discussed are of little practical value. The minimum stage cascade produces zero amount of the maximum concentration material the minimum reflux cascade produces the maximum amount of material with no enrichment. Both of these cascades... 

The ideal cascade requires twice the number of stages as the minimum stage cascade similarly the reflux ratio in the ideal cacade is twice that in the minimum reflux cascade. 

Figure 6.16 Graphical evaluation of the number of stages for a reflux cascade (enriching section), operated with constant reflux.

The major field of application for pervaporation will be either the separation of organic components with almost identical boiling characteristics or azeotropic mixtures. In most cases, the desired product quality cannot be achieved in a single step-either a combination of different processes or a "multi-stage" process will be necessary. In this case, a reflux-cascade has to be designed. 

Figure 6.44 Optimisation of a reflux cascade for pervaporation influence of selectivity on total permeate flow and number of stages.

Dual solvent fractional extraction (Fig. 7b) makes use of the selectivity of two solvents (A and B) with respect to consolute components C and D, as defined in equation 7. The two solvents enter the extractor at opposite ends of the cascade and the two consolute components enter at some point within the cascade. Solvent recovery is usually an important feature of dual solvent fractional extraction and provision may also be made for reflux of part of the product streams containing C or D. Simplified graphical and analytical procedures for calculation of stages for dual solvent extraction are available (5) for the cases where is constant and the two solvents A and B are not significantly miscible. In general, the accurate calculation of stages is time-consuming (28) but a computer technique has been developed (56). 

Examination of possible systems for boron isotope separation resulted in the selection of the multistage exchange-distillation of boron trifluoride—dimethyl ether complex, BF3 -0(CH3 )2, as a method for B production (21,22). Isotope fractionation in this process is achieved by the distillation of the complex at reduced pressure, ie, 20 kPa (150 torr), in a tapered cascade of multiplate columns. Although the process involves reflux by evaporation and condensation, the isotope separation is a result of exchange between the Hquid and gaseous phases. 

Partially Reversible Processes. In a partially reversible type of process, exemplified by chemical exchange, the reflux system is generally derived from a chemical process and involves the consumption of chemicals needed to transfer the components from the upflow into the downflow at the top of the cascade, and to accomplish the reverse at the bottom. Therefore, although the separation process itself may be reversible, the entire process is not, if the reflux is not accompHshed reversibly. 

Insofar as the consumption of chemicals is concerned, it is obvious that the total consumption of reflux-producing chemicals is proportional to the interstage flows, or width of the cascade, but independent of the number of stages in series, or length of the system. 

Our example system has a flow-controlled feed, and the reboiler heat is controlled by cascade from a stripping section tray temperature. Steam is the heating medium, with the condensate pumped to condensate recovery. Bottom product is pumped to storage on column level control overhead pressure is controlled by varying level in the overhead condenser the balancing line assures sufficient receiver pressure at all times overhead product is pumped to storage on receiver level control and reflux is on flow control. 

Figure 9-34A. Efficiency versus C-factor for various metai packings. Iso-octane/toluene, 740 mm Hg, reflux ratio 14 1,15-in. i.D. column, 10-ft bed height. Not Glitsch test data. Note CMR = Cascade Miniring . Used by permission of Glitsch, Inc., Bull. 345.

A radical carboxyarylation approach was introduced as the key step in the total synthesis of several biologically important natural products (Scheme 27). Treatment of thiocarbonate derivatives 112 (R = Me or TBS) with 1.1 equiv of (TMS)3SiH in refluxing benzene and in the presence of AIBN (0.4 equiv added over 6h) as radical initiator, produced compound 113 in 44% yield. This remarkable transformation resulted from a radical cascade, involving (TMSlsSi radical addition to a thiocarbonyl function (112 114), 5-era cyclization (114->115) and intramolecular 1,5-ipso substitution (115 116) with the final ejection of (TMSlsSiS radical. 

Figure 5.22. (e) Batch distillation, reflux flow cascaded with temperature to maintain constant top composition... 

Figure 9.1 A cascade of equilibrium stages with refluxing and reboiling. (From Smith R and Jobson M, 2000, Distillation, Encyclopedia of Separation Science, Academic Press reproduced by permission).

When a lies close to 1 the minimum reflux ratio is large, but since Xj varies with stage number so does [n(i+1)/P]MiN- At the feed point in a 235U plant enriching to 90% 235U, (nf/P)MiN is 29,100, but at the product end of the cascade it approaches zero. 

A practical isotope separation plant can operate at neither minimum reflux (where the separation is zero, but the rate of production is high), nor at minimum number of stages (where the rate of production is zero, but the separation is high). A compromise is required. Since optimum reflux varies with stage number it is customary to employ tapered cascades for isotope separation. This results in marked savings in material hold-up, and in plant size and investment. 

Because of the very large enrichments required in heavy water production, cascades taper markedly. In the upper stages the relative advantage of chemical exchange over water distillation vanishes. Most heavy water plants carry out the last portion of the enrichment by distillation (from 20% or 30% D to 99.85%). Accordingly both exchange and distillation will be briefly treated below. First, however, to clarify the important distinction between chemical and thermal reflux we treat an example of isotope separation using chemical reflux. 

Additionally, dimedone derivative 241 and propargylamine 234 could be combined to give the alkynyl vinyl amine 242. The rearrangement/cyclization cascade could be induced upon heating until reflux in chlorobenzene. The an-... 

Figure 11.3d shows a process where the manipulated variable affects the two controlled variables and in parallel. An important example is in distilla tion column control where reflux flow aSecte both distillate composition and a tray temperature. The process has a parallel structure and this leads to a parallel cascade control system. 

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