Stage efficiencies

In contrast to continuous packed bed columns, each stage, whether cocurrent or countercurrent, can be considered to be at equilibrium for many multi-phase mass-transfer processes such as distillation, absorption, extraction etc. Such stages are usually called ideal stages . 

It is clear from the above that the main concepts used in the mass balance for one-phase systems can be extended to heterogeneous system by simply writing mass-balance equations for each phase and taking the interaction (mass transfer) between the phases into account. The same applies when there are reactions in both phases. Then the rate of reaction terms must be included in the phase mass balances as shown earlier. 

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Scale-up and performance of a 1.47-m Scheibel column have been reported (98,154,155), as have detailed description and design criteria for the Scheibel column (156) and scale-up procedures (157). The same stage efficiency can be maintained on scale-up, and total throughput can be increased by three and one-half times at the expense of higher HETS. As of this writing, Scheibel columns up to 2.75 m in diameter are in service. 

Likewise for polytropic efficiency which is often considered as the small stage efficiency or the hydraulic efficiency ... 

A characteristic of polytropic efficiency is that the polytropic efficiency of a mnltistage unit is equal to the stage efficiency if each stage has the same efficiency. 

Stage Efficiency The use of the Murphree plate ejficiency is par-ticulany convenient on y-x diagrams. The Murphree efficiency is defined for the vapor phase as... 

When chemical equilibrium is achieved qiiickly throughout the liquid phase (or can be assumed to exist), the problem becomes one of properly defining the physical and chemical equilibria for the system. It sometimes is possible to design a plate-type absorber by assuming chemical-equilibrium relationships in conjunction with a stage efficiency factor as is done in distillation calculations. Rivas and Prausnitz [Am. Tn.st. Chem. Eng. J., 25, 975 (1979)] have presented an excellent discussion and example of the correct procedures to be followed for systems involving chemical equihbria. 

Ryan et al. [Chem. Eng. Progr, 90(8X 83 (1994)] showthat separate mass and heat transfer-rate modeling of an HCl absorber predicts 2 percent fog in the vapor. The impact is equivalent to lowering the stage efficiency to 20 percent. 

The separation of components by liquid-liquid extraction depends primarily on the thermodynamic equilibrium partition of those components between the two liquid phases. Knowledge of these partition relationships is essential for selecting the ratio or extraction solvent to feed that enters an extraction process and for evaluating the mass-transfer rates or theoretical stage efficiencies achieved in process equipment. Since two liquid phases that are immiscible are used, the thermodynamic equilibrium involves considerable evaluation of nonideal solutions. In the simplest case a feed solvent F contains a solute that is to be transferred into an extraction solvent S. 

Even staged eqmpment may be modeled best by the number of mass-transfer units when the extrartion fartor is much higher than 1.5, especially if the stage efficiencies are low. 

STAGE EFFICIENCY AND HEIGHT OF A THEORETICAL STAGE OR TRANSFER UNIT... 

The overall stage efficiency of a staged extraction system is simply the number of theoretical stages divided by the number of actual stages times 100 [Eq. (15-28)]. 

Percent stage efficiency = lOON/number of actual stages (15-28)... 

Overall Coefficients and Stage Efficiency If it is assumed that values of a, ., kc, ko (and therefore Kd) can somehow be estimated, the stage efficiency can be calculated through... 

See also Treybal [Am. ln.st. Chem. Eng. J., 4, 202 (1958) 6, 5M (I960)] and Olander [Chem. Eng. Sci, 18, 47 (1963) 19, 275 (1964)]. The remaining discussion is confined to measured values of stage efficiency or volumetric overall coefficients. These are largely of value only for the particiilar systems studied. For this reason, one fairly complete study will be described, and the others will only be mentioned. 

Flynn and Treybal [Am. Inst. Chem. Eng. J., I,. 324 (1955)]. Continuous extraction of benzoic acid from toluene and kerosine into water baffled vessels, turbine agitators. Stage efficiency is correlated with agitator energy per unit of liquid treated. 

Overall Stage Efficiencies The mixer-settler extractors described have generally produced overall stage efficiencies in excess of 80 percent, usually nearly 90 to 95 percent. 

The system of Fig. 15-38 is one of high interfacial tension, so that the heights of transfer units are relatively high and stage efficiency low. For systems of low interfacial tension, on the other hand, stage efficiencies may be very much improved. Table 15-8 lists sources of mass-transfer data. 

Compartment opening, mm Maximum stage efficiency Minimum HETS, mm Flow rate kg s" m" ... 

The above approach will usually result in a conservative design, since the stage efficiency is usually much higher in the production column than in the pilot column. A comparison of the controlling parameters which exist in the pilot and production scales are depicted in Fig. 15-43. 

FIG. 15-47 Correlation of mixing-stage efficiency with power input and liquid flow rates. [Scheihel in Lo, Baird, Hanson, Handbook of Solvent Extraction, p. 428 John Wiley h- Sons, NY, 1983. Used with peimission.]... 

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