Theoretical extraction stages

In extraction (qv), the distribution coefficient value is the slope of the equiUbrium line. In practice, the slope of the operating line is set at a value somewhat less than the distribution coefficient to provide driving force and fix the required theoretical extraction stages at some reasonable number. 

GC exhibits such large theoretical extraction stages (more than hundred thousands) that analysis with a high resolution power is achieved. 

Therefore, the state points of the extract and raffinate phases E and in a common column cross section lie on the binodal curve and connecting line E, R,U (lines through the pol U) (Fig. 6-25). The state points of the phases leaving a theoretical extraction stage ( jy, E, R2 , etc.) lie on... 

To design such a process, the McCabe-Thiele method may be used to determine the number of theoretical separation stages, as examined in Sections 3.3.2-3.3.4 for distillation, absorption (gas scrubbing), and liquid-liquid-extraction. Thus, we obtain the number of theoretical extraction stages of a countercurrent extraction column based on the equilibrium curve (solubility of extract in the solvent for a given content in the solid) and the operating line. The latter depends on the extract content of the solid feed and residue, and on the in- and outlet extract concentration in the solvent The extract content of the feed is fixed, and the value of the residue is specified by the required degree of extraction. The inlet content of the extract in the solvent is also fixed, as either pure solvent is used or the value is specified by separation of the extract from the used solvent after the extraction. Therefore, the only parameter that is left is the outlet concentration of the extract in the solvent, which depends on the ratio of the solvent flow to the feed rate of the solid feedstock (mass balance). 

V = volume ratio, gasoline to caustic, a = number of theoretical extraction stages plus one, h number of theoretical regeneration stages plus one... 

A theoretical or equihbrium stage is a device or combination of devices that accomplishes the effect of intimately mixing two immiscible liquids until equilibrium concentrations are reached, then physically separating the two phases into clear layers. Crosscurrent extraction (Fig. 15-4) is a cascade, or series of stages, in which the raffinate R from one extraction stage is contacted with additional fresh solvent S in a subsequent stage. 

The other common objective for calculating the number of countercurrent theoretical stages (or mass-transfer units) is to evaluate the performance of hquid-liquid extraction test equipment in a pilot plant or to evaluate production equipment in an industrial plant. Most liq-uid-hquid extraction equipment in common use can oe designed to achieve the equivalent of 1 to 8 theoretical countercurrent stages, with some designed to achieve 10 to 12 stages. 

Thermodynamic design the ratio of extract to raffinate flow rate, the phase ratio, and the number of theoretical separation stages necessary for the separation task can be worked out from mass balances in connection with the solution equilibria (see Chapters 2-8). 

Although the most useful extraction process is with countercurrent flow in a multistage battery, other modes have some application. Calculations may be performed analytically or graphically. On flowsketches like those of Example 14.1 and elsewhere, a single box represents an extraction stage that may be made up of an individual mixer and separator. The performance of differential contactors such as packed or spray towers is commonly described as the height equivalent to a theoretical stage (HETS) in ft or m. 

The chlorobenzene from the extraction stage is used for the next nitration batch. Chloronitrobenzene is sent to a tile-lined, 10 m3 washing tank. Here it is agitated three times with 3000 1. of water at 60-70°C by an air stream until neutral to Congo red. Then it is washed with 20 kg of sodium carbonate in 3000 1. of water, and finally with hot water to neutrality. The product is dried at 90-100°C under reduced pressure in a 7 m3 drying vessel heated by a heating coil. The yield is 98% of the theoretical. 

We use rigorous simulation to determine feasible separations using water as a solvent. For a theoretical ten-stage liquid/liquid extraction process, we find that rather little water is needed to recover virtually all methanol from the pentane. At higher solvent flowrates the water-rich extract contains more and more acetone, but it cannot produce a complete separation of acetone and pentane. Thus, we select the solvent flow at which the methanol-pentane separation is sufficiently sharp. Figure 35 gives the separation selected. 

According to a graphical method by Hunter and Nash [6.17], the required number of theoretical separation stages N, for the distribution of the key component between the extract phase and the raffinate phase may then be determined using the Gibbs triangle. One has only to consider that the state points... 

Introducing the concept of height of a theoretical separation stage, NETS to evaluate the actual height of an extraction column giving the same effect, the total height of the column Z for mass transfer is... 

Table 6-3. Specific extraction variables influencing the separation effect (exchange ratio, height of a theoretical separation stage HETS, height of a transfer unit HTU).

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