Differential contactors

To determine the required size of an absorption or stripping nrtl, it is necessary to know not only the equilibrium soluhility of the solute in the solvent and the material balance atound the column bas also the rate at which solute is transferred from one phase to the other within the tower. This rale directly affects the volume of packing needed in a packed tower, the degree of dispersion requited in a spray contactor, and (somewhat less directly) the number of trays required in a nay tower. The last effect occurs as a result of the influence of mass transfer rms on tray efficiency which is discussed in a later section. Because of its direct effect ou packed tower design and the importance of this type of contactor in absoiption. this discussion of mass transfer is aimed primarily at the packed tower case. A more detailed review of mass transfer theoty is given in Chapter 2. 

FIGURE 6.3 1 Diagram of two-film concept. Cj and p, represent equitibriion conditions at the interface. 

Hie application of this equation to design requires information ou concentrations at the interface which is seldom known. As a result, absorption data frequently are correlated in terms of overall coefficients. These are based on the total driving force from the main body of the gas to the main body of the liquid. The overall cnefficients Kg and K,. are defined try the ftoBowing reJatioaship  

C = concentration in a solution in equilibrium with the main body of gas 

If a suitable equilibrium relationship exists for relating gas-phase partial pressures and liquid-phase concentrations, the overall coefficients can be expressed in terms of the individual film coefficients. For die case where Henry s Law applies, die following rontiouships hold  

FIGURE 6.3-1 Diagnun of two-film concqx. C/ and p,- represent equilibriom conditions at the interfiKe. 

When the solute is veiy soluble, the Hemy s Law constant H is low which makes the term HIki, much smaller than Ukg so that lIKg — l/kg. In such a case, the gas film represents the controlling resistance, and mass transfer data can be correlated best in terms of Kg. The reverse is true with low-solubility gases the liquid film is controlling and Kt is the preferred overall coefficient. 

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Fig. 8. Mass transfer in a differential contactor. Terms are defined in the text.

Although the stagewise model is not physically reaUstic for differential contactors, it is sometimes used. The number of equivalent theoretical stages N can be determined graphically usiag the stepwise constmction illustrated ia Figure 7. For the case where both the equihbrium and operating lines are linear, it can be shown that ... 

Equations 27—32 are appHcable only to dilute, immiscible systems. If the amount of mass transfer is significant ia comparison to the total dow rates, more compHcated treatments of differential contactors are required (5,28). 

Two alternative approaches are used ia axial mixing calculations. For differential contactors, the axial dispersion model is used, based on an equation analogous to equation 13 ... 

Rota.ryAgita.ted Columns. Because of the mechanical advantages of rotary agitation, most modem differential contactors employ this method. The best known of the commercial rotary agitated contactors are shown in Eigure 15. Eeatures and appHcations of these columns ate given in Table 3. 

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)]. 

Heat may be transferred between two insoluble liquids in countercurrent flowthrough an extractor, and the performance can be evaluated in the same general manner as in mass transfer (Fig. 15-20). For a differential contactor the number of overall heat-transfer units based on the hot phase can be derived from the same equations used for the number of mass-transfer units based on the feed (raffinate) phase [Eq. (15-36)]. 

The second type of mass-exchange units is the differential (or continuous) contactor. In this category, the two phases flow through the exchanger in continuous contact throughout without intermediate phase separation and recontacting. Examples of differential contactors include packed columns (Fig. 2.6), spray towers (Fig. 2.7), and mechanically agitated units (Fig. 2.8). 

Figure 1.27. Concentration profiles for countercurrent, differential contactor.

Countercurrent flow produced by Phase interdispersion by Differential contactors Stagewise contactors... 

The more important types of stage-wise and differential contactors are discussed in Sections 13.6 and 13.7 respectively. 

If separation is difficult in a mixer-settler unit, a centrifugal extractor may be used in which the mixing and the separation stages are contained in the same unit which operates as a differential contactor. 

In stagewise equipment, the design and scale-up is simple and is often determined from bench data. The stage efficiency is usually high, and the capacity is determined by the settler design necessary to achieve coalescence of the dispersed phases. For differential contactors, such as columns, the flow capacity is determined by the droplet size and the type of internals (see... 

Some advantages and disadvantages of stagewise and differential contactors are shown in Table 7.1 [1]. 

There followed a brief discussion of equipment for carrying out solvent extraction in industrial practice, both by stagewise and differential contact. Some of the first principles for the design of differential contactors were outlined and the part played by the efficiency of extraction in continuous equipment was discussed. Finally there was an outline of methods for the control of solvent loss which forms probably the most important environmental aspect of the application of solvent extraction. 

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. 

Centrifugal Contactors. These devices have large capacities per unit, short residence times, and small holdup. They can handle systems that emulsify easily or have small density differences or large interfacial tensions or need large ratios of solvent to feed. Some types are employed as separators of mixtures made in other equipment, others as both mixers and settlers, and some as differential contactors. 

In this section, the equations are presented for the common types of contactors differential contactors and stage-wise contactors. The equations are developed for the case of steady-state, countercurrent contacting of liquid and gas with negligible heat effects, with a single-component absorption. Some discussion of extensions to other situations follows. 

Differential contactors include packed towers, spray towers, and falling-film absorbers, and are often called counterflow contactors. In such devices gas and liquid flow more or less continuously as they move through the equipment. 

Many types of countercurrent equipment (e.g., packed columns) do not contain discrete compartments and therefore cannot be treated as combinations of discrete stages (Fig. 5b). The term differential contactor is used to describe this category, and a somewhat different design... 

Specifically this paper describes an expression for the entropy production due to the mass fluxes in binary mass transfer systems with application to continuous differential contactors. 

Countercurrent extraction (Fig. 15-5) is an extraction scheme in which the extraction solvent enters the stage or end of the extraction farthest from where the feed F enters and the two phases pass coun-tercurrently to each other. The objective is to transfer one or more components from the feed solution F into the extract E. When a staged contactor is used, the two phases are mixed with droplets of one phase suspended in the other, but the phases are separated before leaving each stage. When a differential contactor is used, one of the phases can remain dispersed as droplets throughout the contactor as the phases pass countercurrently to each other. The dispersed phase is then allowed to coalesce at the end of the device before being discharged. 

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