Stage calculations design procedure

The other area is the countercurrent liquid-liquid extraction system, shown in Fig. 27, using mixer stages separated by stationary horizontal discs. These have the advantage of only one interface for settling to occur, plus the fact that solids can be handled in one or both phases. Also, all the principals of fluid mixing can be used to design an effective transfer system. The design procedure is also based on the KLa concept, discussed in Section IV, and allows the calculation of reliable full-scale performance, based on pilot plant work, often done in a laboratory column about 6 in. in diameter. 

The literature abounds with information on all phases of distillation calculations and design. There has been such a bewildering flow of Information, dealing especially with the principles of stage calculations, that the engineer who is not a distillation expert finds himself at a loss as to how to select the best procedures for solving his distillation problems. 

Nevertheless, the concept of the equilibrium stage has proved to be extremely useful and is widely applied in design procedures which calculate the number of equilibrium (or so-called theoretical) stages required for a desired separation. When coupled with a stage efficiency based on mass transfer rates, the number of equilibrium stages can be used to determine the number of actual stages required. 

This chapter introduces how continuous distillation columns work and serves as the lead to a series of nine chapters on distillation. The basic calculation procedures for binary distillation are developed in Chapter 4. Multicomponent distillation is introduced in Chapter 5. detailed conputer calculation procedures for these systems are developed in Chapter 6. and sinplified shortcut methods are covered in Chapter 7. More complex distillation operations such as extractive and azeotropic distillation are the subject of Chapter 8. Chapter 9 switches to batch distillation, which is commonly used for smaller systems. Detailed design procedures for both staged and packed columns are discussed in Chapter 10. Finally, Chapter 11 looks at the economics of distillation and methods to save energy (and money) in distillation systems. 

Any design procedure requires a calculation of the number of mass transfer stages required and then a determination of the packed depth required to achieve such a stage. The use of the equilibrium stage concept in liquid-liquid extraction is similar to its use in distillation operations. A theoretical stage of mass transfer is one from which the extract and the raffinate leave in equilibrium. Stated in a different manner, the ratio of the concentration of solute in the extract to the concentration of solute in the raffinate equals the distribution coefficient. 

In concentrated wstems the change in gas aud liquid flow rates within the tower and the heat effects accompanying the absorption of all the components must be considered. A trial-aud-error calculation from one theoretical stage to the next usually is required if accurate results are to be obtained, aud in such cases calculation procedures similar to those described in Sec. 13 normally are employed. A computer procedure for multicomponent adiabatic absorber design has been described by Feiutnch aud Treybal [Jnd. Eng. Chem. Process Des. Dev., 17, 505 (1978)]. Also see Holland, Fundamentals and Modeling of Separation Processes, Prentice Hall, Englewood Cliffs, N.J., 1975. 

When chemical equilibrium is achieved qiiickly throughout the liquid phase (or can be assumed to exist), the problem becomes one of properly defining the physical and chemical equilibria for the system. It sometimes is possible to design a plate-type absorber by assuming chemical-equilibrium relationships in conjunction with a stage efficiency factor as is done in distillation calculations. Rivas and Prausnitz [Am. Tn.st. Chem. Eng. J., 25, 975 (1979)] have presented an excellent discussion and example of the correct procedures to be followed for systems involving chemical equihbria. 

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