Countercurrent multistage equilibrium

Figure 5.188. Countercurrent multistage equilibrium extraction unit.

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

To illustrate the principle of an equilibrium-stage cascade, two typical countercurrent multistage devices, one for distillation and one for leaching, are described here. Other types of mass-transfer equipment are discussed in later chapters. 

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. 

Stripping Nicotine from Kerosene. A kerosene flow of 100 kg/h contains 1.4 wt % nicotine and is to be stripped with pure water in a countercurrent multistage tower. It is desired to remove 90% of the nicotine. Using a water rate of 1.50 times the minimum, determine the number of theoretical stages required. (Use the equilibrium data from Example 12.7-3.)... 

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. 

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. 

Figure 8.1.44. (a) Continuous countercurrent gas solid adsorber for species i. (b) Operating line and equilibrium curve for a continuous adsorber, (c) Countercurrent multistage gas-solid adsorber for species i. (d) Operating line for a countercurrent multistage adsorber. 

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... 

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. 

The need for a continuous countercurrent process arises because the selectivity of available adsorbents hi a number of commercially important separations is not high, In die p-xylene system, for instance, if the liquid around the adsorbent particles contains 1% p-xyleiie, llie liquid in the pores contains about 2% p-xylene at equilibrium. Therefore, one stage of contacting cannot provide a good separation, and multistage contacting must be provided in tile same way that multiple trays are required in fractionating materials with relatively low volatilities. 

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