Equilibrium stage extraction

Here the extraction is carried out continuously in a single, perfectly mixed, extraction stage as shown in Fig. 3.30. It is assumed that the outlet flow concen- 

Following an initial transient, the extractor will achieve a steady state operating condition, in which the outlet concentrations remain constant with respect to time. 

At steady state, the quantity of solute entering the extractor is equal to the quantity of solute leaving. A steady-state balance for the combined two-phase system gives 

L and G are the volumetric flow rates of the heavy and the light phases, respectively, X0 and Y0 are the respective inlet solute concentrations of the two phases, Xx and Yj are the respective outlet solute concentrations. 

A simple substitution of the value Yj in the balance equation enables the steady-state concentration Xj to be determined, where 

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Figure 3.52. Model representation of a non-equilibrium staged extraction column.

In designing an equilibrium-staged extraction unit, the partition coefficient, K = y x, is estimated by Eq. (27). We assume that there are two sets of parameters and variables in Eq. (28), including a, b, V, and y., one set for each phase. Dickson et al. (28) have presented a detailed calculation of tins type. 

Figure 1. Continuous equilibrium stage extraction. Solute balances for each phase give ...

The leached solids must be separated from the extract by settling and decantation or by external filters, centrifuges, or thickeners, all of which are treated elsewhere in Sec. 18. The difficulty of solids-extract separation and the fact that a batch stirred tank provides only a single equilibrium stage are its major disadvantages. 

Steady State Equilibrium Stage. Liquid-liquid extractions are used in many different... 

Equilibrium data must be obtained for material balance showing raffinate and extracted phases. A simple separation funnel for single-stage extraction using amyl acetate as organic solvent is shown in Figure 7.13. 

The equilibrium constant is defined by K, K = y/x, and the portion coefficient is also defined by K as a ratio of CAu/CA1 which is constant. Based on the value of K, single or multi-stage extractions are performed to do a perfect job in bioseparation. 

While offering a more inherently realistic method of solution, however, the technique may cause some additional problems in the numerical solution, since high values of Kl can lead to increased stiffness in the differential equations. Thus in using this technique, a compromise between the approach to equilibrium and the speed of numerical solution may have to be adopted. Continuous single-stage extraction is treated in the simulation example EQEX. Reaction with integrated extraction is demonstrated in simulation example REXT. 

The extraction is represented by a single perfectly mixed constant volume, continuous flow equilibrium stage. This may actually consist of separate mixer-settler units. 

A countercurrent multistage extraction system is shown below, which is to be modelled as a cascade of equilibrium stages. 

FIVE STAGE COUNTERCURRENT EXTRACTION CASCADE EQUILIBRIUM STAGE MODEL... 

Figure 5.191. Increasing both flow rates by a factor of 10 results in much lower fractional extraction values for these equilibrium stages.

Five stage countercurrent extraction cascade with backmixing Equilibrium stage model... 

The problems relating to mass transfer may be elucidated out by two clear-cut yet different methods one using the concept of equilibrium stages, and the other built on diffusional rate processes. The selection of a method depends on the type of device in which the operation is performed. Distillation (and sometimes also liquid extraction) are carried out in equipment such as mixer settler trains, diffusion batteries, or plate towers which contain a series of discrete processing units, and problems in these spheres are usually solved by equilibrium-stage calculation. Gas absorption and other operations which are performed in packed towers and similar devices are usually dealt with utilizing the concept of a diffusional process. All mass transfer calculations, however, involve a knowledge of the equilibrium relationships between phases. 

At the prevailing high levels of dispersion normally encountered in such types of extraction columns, the behaviour of these essentially differential type contactors, however, can be represented by the use of a non-equilibrium stage-wise model. 

Sherwood, T. K. and Pigford, R. L. Absorption and Extraction (McGraw-Hill Book Co., New York, 1952). Sherwood, T. K., Pigford, R. L. and Wilke, C. R. Mass Transfer (McGraw-Hill Book Co., New York, 1975). Smith, B. D. Design of Equilibrium Stage Processes (McGraw-Hill Book Co., New York, 1963). 

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