Page 197 - Separation process principles 2

162 Chapter 5 Cascades and Hybrid Systems

Feed Product 1 easier to apply in a batchwise manner. It differs from the
I countercurrent cascade in that the solvent is divided into
portions fed individually to each stage.
Stage
1 A complex diamond variation of the crosscurrent cascade
4 t is shown in Figure 5.2~. Unlike the two former cascades,
which are linear or one-dimensional, the diamond configura-
Stage tion is two-dimensional. One application is to batch crystal-
2 lization. Feed F is separated in stage 1 into crystals, which
t pass to stage 2, and mother liquor, which passes to stage 4.
In each of the other stages, partial crystallization or recrys-
tallization occurs by processing crystals, mother liquor, or
combinations of the two. Final products are p~~rified crystals
E and impurity-bearing mother liquors.
The first three cascades in Figure 5.2 consist of single
Stage
product 2 1 Mass-separating sections with streams entering and leaving only from the
ends. Such cascades are used to recover components from a
feed stream and are not generally useful for making a sharp
agent
separation between two selected feed components, called
Figure 5.1 Cascade of contacting stages.
key components. To do this, it is best to provide a cascade
consisting of two sections. The countercurrent cascade of
In the countercurrent cascade, shown in Figures 5.1 and Figure 5.2d is often used. It consists of one section above
5.2a, the two phases flow countercurrently to each other the feed and one below. If two solvents are used, where S1
between stages. As will be shown in examples, this configu- selectively dissolves certain components of the feed, while
ration is very efficient and is widely used for absorption, S2 is more selective for the other components, the process,
stripping, liquid-liquid extraction, leaching, and washing. referred to as fractional liquid-liquid extraction, achieves a
The crosscurrent cascade, shown in Figure 5.2b, is, in most sharp separation. If S is a liquid absorbent and Sz is a vapor
cases, not as efficient as the countercurrent cascade, but it is stripping agent, added to the cascade, as shown, or produced
internally by condensation heat transfer at the top to give
liquid reflux, and boiling heat transfer at the bottom to give
vapor boilup, the process is simple distillation, for which a
sharp split between two key components can be achieved if
a reasonably high relative volatility exists between the two
key components and if reflux, boilup, and the number of
stages are sufficient.
Figure 5.2e shows an interlinked system of two distilla-
tion columns containing six countercurrent cascade sections.
Reflux and boilup for the first column are provided by the
second column. This system is capable of taking a ternary
(three-component) feed, F, and producing three relatively
pure products, PI, P2, and P3.
In this chapter, algebraic equations are developed for
modeling idealized cascades to illustrate, quantitatively,
their capabilities and advantages. First, a simple countercur-
rent, single-section cascade for a solid-liquid leaching and/
or washing process is considered. Then, cocurrent, crosscur-
rent, and countercurrent single-section cascades, based on
simplified component distribution coefficients, are com-
pared for a liquid-liquid extraction process. A two-section,
countercurrent cascade is subsequently developed for a
vapor-liquid distillation operation. Finally, membrane cas-
cades are described. In the first three cases, a set of linear
algebraic equations is reduced to a single relation for esti-
(e)
Figure 5.2 Examples of cascade configurations: (a) counter- mating the extent of separation as a function of the number
current cascade; (b) crosscurrent cascade; (c) two-dimensional, of stages in the cascade, the separation factor, and the flow
diamond cascade; (d) two-section, countercurrent cascade; ratio of the mass- or energy-separating agent to the feed.
(e) interlinked system of countercurrent cascades. More rigorous models for design and analysis purposes are