Countercurrent-cascade separation

Such a countercurrent cascade separates feed containing zp fraction of desired component flowing at rate F into product containing yp fraction of desired component flowing at rate P and waste, or tails, containing xw fraction of desired component flowing at rate W. These six compositions and flow rates are called the external variables of the cascade. 

Fig. 5-19. Cascaded system for countercurrent 99 %+ separation of racemic mixtures [75].

Fig. 8.3 Isotope separation stages arranged in a countercurrent cascade. The cascade in this diagram is squared off...

It should be noted that this was a fairly severe test. Having a feed containing equimolar quantities of components whose extractability differs by a factor of only 10 is rare. Usually the differences in extractability are greater, or the less extractable component is present in low concentrations relative to the more extractable. In both these cases, good separations can be achieved in a countercurrent cascade. 

Another important concept is the calculation of the minimum number of equilibrium stages to perform a given separation. This is a theoretical concept since it occurs when one or both flowrates in a countercurrent cascade are infinite. It is useful to calculate since the actual number of stages will be larger (i.e., this is a limit). An analytical equation can be... 

Some extraction systems are such that the solvent and diluent phases are almost completely immiscible in each other. Hence, separation yields an extract phase essentially free of diluent and a raffinate phase that is almost pure diluent. This greatly simplifies the characterization of the system. When partial miscibility for an extraction process is very low, the system may be considered immiscible and application of McCabe-Thiele analysis is appropriate. It is important to note that McCabe-Thiele analysis for immiscible extraction applies to a countercurrent cascade. The McCabe-Thiele analysis for immiscible extraction is analogous to the analysis for absorption and stripping processes. Consider the flow scheme shown in Figure 5.23,... 

Thermodynamic equilibrium between the two liquids determines the direction of mass transfer and the theoretical amount of compound(s) transferred in a given step. The rate of transfer depends on the level of agitation provided to the dispersion and the interfacial areas between the phases. After the extraction step is completed, separation of phases is (hopefully) rapid. As already indicated, the separated phases are often then sent countercurrent to another extraction unit [2]. Countercurrent cascades of mixers and settlers generally provide the most efficient use of solvent. 

The calculation of the concentration of extractable components in a countercurrent cascade of equilibrium solvent extraction stages is first developed for the simple countercurrent extraction section of Fig. 4.3. The theory is then extended to the extracting-scrubbing system of Fig. 4.4 for fractional extraction and is illustrated by a numerical calculation for the separation of zirconium from hafnium, using TBP in kerosene as solvent. 

Because this value is so close to unity, to obtain a useful degree of separation the process must be repeated many times in a countercurrent cascade of gaseous diffusion stages, such as was shown in Fig. 12.2. 

A countercurrent cascade allows for more complete removal of the solute, and the solvent is reused so less is needed. A schematic diagram of a countercurrent cascade is shown in Figure 13-20. All calculations will assume that the column is isothermal and isobaric and is operating at steady state, hi the usual design problem, the column tenperature and pressure, the flow rates and conpositions of streams F and S, and the desired composition (or percent removal) of solute in the raffinate product are specified. The designer is required to determine the number of equilibrium stages needed for the specified separation and the flow rates and conpositions of the oudet raffinate and extract streams. Thus, the known... 

Gas extraction extends the possibilities of separation processes like distillation, absorption and liquid-liquid extraction to the isolation and purification of components of low volatility. Furthermore, it enables separation of components with very similar properties if used in the countercurrent mode. Process temperatures in gas extraction are determined by the critical temperature of the solvent and not, as is the case of distillation of any kind, by the liquid-vapor transition of the feed mixture. As compared to liquid-liquid extraction, gas extraction makes easily possible to operate a two cascade separation column, applying a stripping and an enriching section. Combined, these possibilites allow gas extraction to be operated at very moderate temperatures and as a separation process for difficult separations. 

Here y-p is the isotopic composition at the top stage, P is the product withdrawal rate, and, as before, X,+i is the tails withdrawal rate at the (i + l)th stage. The ratio Xi+JP) is the reflux, which for a simple countercurrent cascade is independent of stage number (i.e., such a cascade is squared off). Note that /, and X4+1 approach each other as Xi+JP approaches infinity, which happens at total reflux. In that case, the number of stages required to carry out a given overall separation is a minimum and is given by the Fenske equation (Fenske 1932) ... 

We understand by distillation complex a countercurrent cascade with branching of flows, with recycles or bypasses of flows. Columns with side stripping or side rectifier and columns with completely connected thermal flows (the so-called Petlyuk columns ) are examples of distillation complexes with branching of flows. A column of extractive distillation, together with a column of entrainer regeneration, make an example of a complex with recycle of flows. Columns of this complex work independently of each other therefore, we do not examine it in this chapter, and the questions of its usage in separation of azeotropic mixtures and questions of determination of entrainer optimal flow rate are discussed in the following chapters. 

Liquid extraction, the only operation in this category, is basically very similar to the operations of gas-liquid contact described in the previous part. The creation of a new insoluble liquid phase by addition of a solvent to a mixture accomplishes in many respects the same result as the creation of a new phase by the addition of heat in distillation operations, for example, or by addition of gas in desorption operations. The separations produced by single stages, the use of countercurrent cascades and reflux to enhance the extent of separation—all have their liquid-extraction counterparts. The similarity between them will be exploited in explaining what liquid extraction can accomplish. 

Separation to any extent, however, can be achieved, so long as their distribution coefficients are different, by the techniques of fractional extraction. The simplest flowsheet for this is shown in Fig. 10.33. Here solutes B and C, which constitute the feed, are introduced into a countercurrent cascade where partly miscible solvents A and D flow countercurrently. At the feed stage, both solutes distribute between the solvents, with solute B favoring solvent A, solute C favoring solvent D. In the section to the left of the feed stage, solvent A preferentially extracts the B from D, and D leaves this section with a solute content rich in C. In the section to the right of the feed stage, solvent D preferentially extracts the C from A, and A leaves with a solute content rich in B. 

This is a respectably high separation factor, but, as shown in Practice Problem 1.6, it leads to a single centrifuge enrichment of only 10%. Because nuclear power plants require to be enriched from its natural abundance level of 0.7% to about 3.5%, considerable staging would still be required. Such staging is achieved in so-called countercurrent "cascades," an example of which is shown in Figure 1.5b. Much more about cascades and their crucial role in separation processes will appear in Chapter 7. 

Figure 9.1.1. (a) Countercurrent cascade of double-entry separating elements as in distillation (e.g). (b) Countercurrent cascade of singleentry separating elements, (c) Compositions of various streams for stages (n - Ij, n and (n -y 1) and separation factors. 

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