Page 196 - Separation process principles 2

Chapter 5

Cascades and Hybrid Systems

In the previous chapter, a single equilibrium stage was phase equilibrium is not a consideration and mass-transfer
utilized to separate a mixture. In practice, a single stage rates through the membrane determine the separation,
is rarely sufficient to perform the desired separation. This cascades of membranes can enable separations that cannot
chapter introduces separation cascades, which are collec- be achieved by contact of the feed mixture with a single-
tions of contacting stages. Cascades are used in industrial membrane separator.
processes to ( 1) accomplish separations that cannot be Cascades are prevalent in unit operations, such as
achieved in a single stage, and/or (2) reduce the required distillation, absorption, stripping, and liquid-liquid extrac-
amount of the mass- or energy-separating agent. tion. In cases where the extent of separation by a single-unit
A typical cascade is shown in Figure 5.1, where, in each operation is limited or the energy required is excessive, it is
stage, an attempt is made to bring two or more process worthwhile to consider a hybrid system of two different unit
streams of different phase state and composition into intimate operations, such as the combination of distillation and
contact to promote rapid mass and heat transfer, so as to pervaporation, which is used to separate azeotropic mixtures.
approach physical equilibrium. The resulting phases, whose In the last decade, with increased awareness of the need for
compositions and temperatures are now closer to, or at, equi- conserving energy, much attention is being given to hybrid
librium, are then separated and each is sent to another stage in systems. This chapter introduces both cascades and hybrid
the cascade, or withdrawn as a product. Although equilibrium systems. To illustrate the benefits of cascades, the calcula-
conditions may not be achieved in each stage, it is common to tions are based on simple models. Rigorous models, best
design and analyze cascades using equilibrium-stage models. implemented by computer calculations, are deferred to
Alternatively, in the case of membrane separations, where Chapters 10-12.

5.0 INSTRUCTIONAL OBJECTIVES

After completing this chapter, you should be able to:
• Explain how multi-equilibrium-stage cascades with countercurrent flow can achieve a significantly better
separation than a single equilibrium stage.
• Explain the difference between a single-section cascade and a two-section cascade and the limits of what each
type can achieve.
• Estimate the recovery of a key component in countercurrent leaching and washing cascades.
• Estimate recovery of a key component in each of three types of liquid-liquid extraction cascades.
• Define and explain the significance of absorption and stripping factors.
• Estimate the recoveries of all components in a single-section, countercurrent cascade using the Kremser method.
• Estimate recoveries of all components in a two-section, countercurrent cascade using the Edmister extension of
the Kremser method.
• Configure a membrane cascade to improve a membrane separation.
• Explain the merits and give examples of hybrid separation systems.
• Determine degrees of freedom and a set of specifications for a separation process or any element included in
the process.

5.1 CASCADE CONFIGURATIONS
Depending on the mechanical design of the stages, cascades
Cascades can be configured in many ways, as shown by the may be arranged vertically or horizontally. The feed to be sep-
examples in Figure 5.2, where stages are represented by either arated is designated by F; the mass-separating agent, if used,
boxes, as in Figure 5.1, or as horizontal lines in Figure 5.2d,e. is designated by S; and products are designated by P;.

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