Extraction transfer units

The quantity (y — y) is the over-all driving force expressed in terms of extract compositions, as shown in the figure. The over-all number of extract transfer units NtoE for the extraction is then defined by integration of Eq. (9), assuming KEa remains constant ... 

Hioe Height of an over-all extract transfer unit, ft. 

NtoB Number of over-all extract transfer units, dimensionless... 

The height of the extractor will be determined fromh = (NTU)(HTU). Simplified equations for the number of extraction transfer units for the dispersed phase, Ooe-d continuous phase, Ooe-cj defined in the same way as noL in Eq. Q6-26i. are... 

The heights of a transfer unit ia each phase thus contribute to the overall heights of a transfer unit. Data on values of HTU for various types of countercurrent equipment have been reviewed (1,10). In normal operating practice, the extraction factor is chosen to be not greatiy different from unity, within the range of 0.5—2. 

FIG. 14-5 Nnmher of overall gas-phase mass-transfer units in a packed absorption tower for constant mGf /LM solution of Eq. (14-23). (From Sherwood and Pigford, Absorption and Extraction, McGraw-Hill, New York, 1952. )... 

The main objective for calculating the number of theoretical stages (or mass-transfer units) in the design of a hquid-liquid extraction process is to evaluate the compromise between the size of the equipment, or number of contactors required, and the ratio of extraction solvent to feed flow rates required to achieve the desired transfer of mass from one phase to the other. In any mass-transfer process there can be an infinite number of combinations of flow rates, number of stages, and degrees of solute transfer. The optimum is governed by economic considerations. 

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. 

The concept of a mass-transfer unit was developed many years ago to represent more rigorously what happens in a differential contactor rather than a stagewise contactor. For a straight operating line and a straight equilibrium line with an intercept of zero, the equation for calculating the number of mass-transfer units based on the overall raffinate phase N r is identical to the Kremser equation except for the denominator when the extraction factor is not equal to 1.0 [Eq. (15-23)]. 

The contribution to the height of a transfer unit overall based on the raffinate-phase compositions is the sum of the contribution from the resistance to mass transfer in the raffinate phase plus the contribution from the resistance to mass transfer in the extract phase divided bythe extraction factor [Eq. (15-31)]. 

At high extraction factors the height of a transfer unit is mostly dependent on the resistance to the transfer of solute from the raffinate phase. 

Spray Towers These are simple gravity extractors, consisting of empty towers with provisions for introducing and removing liquids at the ends (see Fig. 15-32). The interface can be run above the top distributor, below the bottom distributor, or in the middle, depending on where the best performance is achieved. Because of severe axial back mixing, it is difficult to achieve the equivalent of more than one or two theoretical stages or transfer units on one side of the interface. For this reason they have only rarely been applied in extraction applications. 

Calculate the overall extraction coefficient based on the concentrations in the ketone phase, and the height of the corresponding overall transfer unit. 

The height of an overall transfer unit based on concentrations in the extract phase is given by equation 13.26 ... 

L e height of overall transfer unit based on Kga concentration in extract phase... 

Clearly the concept of a stage has no meaning in such a tower. Instead, we deal with differential transfer units, which are a measure of the change in concentration per unit of difference in concentration (recall that the rate of extraction is determined largely by the difference between the actual and the equilibrium concentration of a solute, or driving force ). 

At each point in the tower, a component A has an actual concentration [A] and an equivalent equilibrium concentration [A]. Then the number of transfer units (NTU) required for the extraction is given a first approximation by ... 

The previous chapters have demonstrated that liquid-liquid extraction is a mass transfer unit operation involving two liquid phases, the raffinate and the extract phase, which have very small mutual solubihty. Let us assume that the raffinate phase is wastewater from a coke plant polluted with phenol. To separate the phenol from the water, there must be close contact with the extract phase, toluene in this case. Water and toluene are not mutually soluble, but toluene is a better solvent for phenol and can extract it from water. Thus, toluene and phenol together are the extract phase. If the solvent reacts with the extracted substance during the extraction, the whole process is called reactive extraction. The reaction is usually used to alter the properties of inorganic cations and anions so they can be extracted from an aqueous solution into the nonpolar organic phase. The mechanisms for these reactions involve ion pah-formation, solvation of an ionic compound, or formation of covalent metal-extractant complexes (see Chapters 3 and 4). Often formation of these new species is a slow process and, in many cases, it is not possible to use columns for this type of extraction mixer-settlers are used instead (Chapter 8). 

The Croy V series belt-driven dual extraction pump can extract from 5 to 30/gal min of liquid, and uses a 75 actual cubic feet per minute groundwater/vapor extraction transfer pump. The unit has a purchase price of 13,000 and can be rented for 1300 per month (D17804V, p. 11). 

The Croy E series direct-drive dual extraction pump can be adjusted to pump from 5 to 60 gal/min during fluid transfer, and 500 actual cubic feet per minute during ground water/vapor extraction. The unit can be purchased for 20,000 and rents for 2000 per month. All units can be trailer mounted for mobility. Trailer costs are dependent on system size, number of axles required for transport, and other factors (D17804V, p. 17). 

As the potentialities of liquid extraction as a separation method were developed, the need for efficient, continuously operated, multistage equipment became apparent. It was natural therefore to turn to devices which had been so successful in other similar fluid-contacting operations, such as the bubble-tray tower and the packed tower of distillation. These devices have proved to be disappointing in liquid-extraction service, however for example, bubble-tray towers provide tray efficiencies in liquid-extraction operations of less than 5% (S7), and conventional packed towers show heights of transfer units of 10 to 20 ft. or more (T3). 

Otos could be computed. All the Hixson and Smith data plot well in this fashion, and the straightness of the lines indicate the utility of the time-of-a-transfer-unit concept. Hixson, Drew, and Knox (H3) showed that a characteristic agitation number may be defined as the product of 0tOE and a velocity term for the agitated system. If then the mass transfer coefficient varies as the first power of the chosen velocity term, the agitation number would be constant for a given ratio of interfacial surface to total number of moles of extract phase. In liquid extraction, speed of agitation influences both terms of the quantity Ke[Pg.307]

In order to permit sizing a tower, data must be available of the height of a transfer unit (HTU). This term often is used interchangeably with the height equivalent to a theoretical stage (HETS), but strictly they are equal only for dilute solutions when the ratio of the extract and raffinate flow rates, E/R, equals the distribution coefficient, K = xE/xR (Treybal, 1963, p. 350). Extractor performance also is expressible in terms of mass transfer coefficients, for instance, KEa, which is related to the number and height of transfer units by... 

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