Multistage Equilibrium Countercurrent Extraction

Figure 5.188. Countercurrent multistage equilibrium extraction unit.

Figure 8.1.37. (a) Continuous countercurrent multistage solvent extraction cascade of N stages (b) graphical determination of stage numbers in such a cascade of equilibrium extraction stages. 

The modelling approach to multistage countercurrent equilibrium extraction cascades, based on a mass transfer rate term as shown in Sec. 1.4, can therefore usefully be applied to such types of extractor column. The magnitude of the... 

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

The modelling approach to multistage countercurrent equilibrium extraction cascades, based on a mass transfer rate term as shown in Section 1.4, can therefore usefully be applied to such types of extractor column. The magnitude of the mass transfer capacity coefficient term, now used in the model equations, must however be a realistic value corresponding to the hydrodynamic conditions, actually existing within the column and, of course, will be substantially less than that leading to an equilibrium condition. 

In a countercurrent multistage section, the phases to be contacted enter a series of ideal or equilibrium stages from opposite ends. A contactor of this type is diagramatically represented by Fig. 8.1, which could be a series of stages in an absorption, a distillation, or an extraction column. Here L and V are the molal (or mass) flow rates of the heavier and lighter phases, and x,- and y,- the corresponding mole (or mass) fractions of component /, respectively. This chapter focuses on binary or pseudobinary systems so the subscript / is seldom required. Unless specifically stated, y and x will refer to mole (or mass) fractions of the lighter component in a binary mixture, or the species that is transferred between phases in three-component systems. 

If the size of the solid and Af do not change during an extraction, a, the stripping factor, will also remain constant. Then, for multistage equilibrium countercurrent extractions in which solute-free solvent and saturated solids, respectively, are used as the liquid and solid feeds ... 

EXAMPLE 12.7-1. Material Balance for Countercurrent Stage Process Pure solvent isopropyl ether at the rate of, = 600 kg/h is being used to extract an aqueous solution of Lq = 200 kg/h containing 30 wt % acetic acid (/4) by countercurrent multistage extraction. The desired exit acetic acid concentration in the aqueous phase is 4%. Calculate the compositions and amounts of the ether extract and the aqueous raffinate L. Use equilibrium data from Appendix A.3. 

Example 8.1.18 Equilibrium data of the ternary system water (A)-isopropyl ether (B)-acetic acid (C) have been provided in Table 8.1.7. The source of this data acquired at 20 °C is Treybal (1980). Using these data, solve the following problem. Pure isopropyl ether is being used in a countercurrent multistage cascade to extract acetic acid from a feed aqueous solution of 37 wt% acetic acid. The final raflinate product on a solvent-free basis should be 2wt% acetic acid. The feed solution flow rate is 2000 kg/hr. 

We wish to remove acetic acid from water using pure isopropyl ether as solvent. The operation is at 293 K and 1 atm (see Table 7.2). The feed is 45 wt% acetic acid and 55 wt% water. The feed flow rate is 2000 kg/h. A multistage countercurrent extraction cascade is used to produce a final extract that is 20 wt% acetic acid and a final raffinate that is also 20 wt% acetic acid. Calculate how much solvent and how many equilibrium stages are required. 

From the equilibrium data, it is clear that single-stage extraction requires low water concentrations in the solvent phase and high solvent flow rates. Thus, to reduce energy consumption, the process has to be realized in a multistage, countercurrent configuration where residual moisture is extracted with almost pure solvent. 

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