Extraction mass transfer coefficients

Ke Over-all extract mass transfer coefficient, lb. moles/(hr.) (sq. ft.) (mole fraction)... 

Interfacial Mass-Transfer Coefficients. Whereas equiHbrium relationships are important in determining the ultimate degree of extraction attainable, in practice the rate of extraction is of equal importance. EquiHbrium is approached asymptotically with increasing contact time in a batch extraction. In continuous extractors the approach to equiHbrium is determined primarily by the residence time, defined as the volume of the phase contact region divided by the volume flow rate of the phases. 

The enhanced rate expressions for regimes 3 and 4 have been presented (48) and can be appHed (49,50) when one phase consists of a pure reactant, for example in the saponification of an ester. However, it should be noted that in the more general case where component C in equation 19 is transferred from one inert solvent (A) to another (B), an enhancement of the mass-transfer coefficient in the B-rich phase has the effect of moving the controlling mass-transfer resistance to the A-rich phase, in accordance with equation 17. Resistance in both Hquid phases is taken into account in a detailed model (51) which is apphcable to the reversible reactions involved in metal extraction. This model, which can accommodate the case of interfacial reaction, has been successfully compared with rate data from the Hterature (51). 

Interfacial Contact Area and Approach to Equilibrium. Experimental extraction cells such as the original Lewis stirred cell (52) are often operated with a flat Hquid—Hquid interface the area of which can easily be measured. In the single-drop apparatus, a regular sequence of drops of known diameter is released through the continuous phase (42). These units are useful for the direct calculation of the mass flux N and hence the mass-transfer coefficient for a given system. 

Sedimentation is also used for other purposes. For example, relative motion of particles and Hquid iacreases the mass-transfer coefficient. This motion is particularly useful ia solvent extraction ia immiscible Hquid—Hquid systems (see Extraction, liquid-liquid). An important commercial use of sedimentation is ia continuous countercurrent washing, where a series of continuous thickeners is used ia a countercurrent mode ia conjunction with reslurrying to remove mother liquor or to wash soluble substances from the soHds. Most appHcations of sedimentation are, however, ia straight sohd—Hquid separation. 

It would be desirable to reinterpret existing data for commercial tower packings to extract the individual values of the interfacial area a and the mass-transfer coefficients fcc and /c in order to facilitate a more general usage of methods for scaling up from laboratory experiments. Some progress in this direction has afready been made, as discussed later in this section. In the absence of such data, it is necessary to operate a pilot plant or a commercial absorber to obtain kc, /c , and a as described by Ouwerkerk (op. cit.). 

Prediction methods attempt to quantify the resistances to mass transfer in terms of the raffinate rate R and the extract rate E, per tower cross-sectional area Af, and the mass-transfer coefficient in the raffinate phase and the extract phase times the interfacial (droplet) mass-transfer area per volume of tower a [Eqs. (15-32) and (15-33)]. 

The mass-transfer coefficients depend on complex functions of diffii-sivity, viscosity, density, interfacial tension, and turbulence. Similarly, the mass-transfer area of the droplets depends on complex functions of viscosity, interfacial tension, density difference, extractor geometry, agitation intensity, agitator design, flow rates, and interfacial rag deposits. Only limited success has been achieved in correlating extractor performance with these basic principles. The lumped parameter deals directly with the ultimate design criterion, which is the height of an extraction tower. 

The case with k = 0.4 s (open squares) is close to the situation where mass transfer resistance is negligible. These differences are due to mass transfer resistances as we can easily conclude by comparing the separation regions obtained for the cases with k = 0.4 and k = 1 s k If mass transfer resistance is important, the region of complete separation can be significantly reduced from the one obtained by the Equilibrium Theory. For example, for a mass transfer coefficient of k = 0.1 s there is no separation region where extract and raffinate are 99.5 % pure. 

In this process, the two streams flow countercurrently through the column and undergo a continuous change in composition. At any location are in dynamic rather than thermodynamic equilibium. Such processes are frequently carried out in packed columns, in which the liquid (or one of the two liquids in the case of a liquid-liquid extraction process) wets die surface of the packing, thus increasing the interfacial area available for mass transfer and, in addition, promoting high film mass transfer coefficients within each phase. 

Experimental gas-solid mass-transfer data have been obtained for naphthalene in CO2 to develop correlations for mass-transfer coefficients [Lim, Holder, and Shah, Am. Chem. Soc. Symp. Ser, 406, 379 (1989)]. The mass-transfer coefficient increases dramatically near the critical point, goes through a maximum, and then decreases gradually. The strong natural convection at SCF conditions leads to higher mass-transfer rates than in liquid solvents. A comprehensive mass-transfer model has been developed for SCF extraction from an aqueous phase to CO2 in countercurrent columns [Seibert and Moosberg, Sep. Sci. Techrwl, 23, 2049 (1988) Brunner, op. cit.]. 

For a linear equilibrium curve with constant film coefficients, Icl and Icq, the overall coefficient, Kl, will also be constant, but for the case of a non-linear equilibrium relationship, the value of m, which is the local slope of the equilibrium curve, will vary with solute concentration. The result is that the overall coefficient, Kl, will also vary with concentration, and therefore in modelling the case of a non-linear equilibrium extraction, further functional relationships relating the mass transfer coefficient to concentration will be required, such that... 

Table 9.3 gives data of common types of L-L contactors. Since the given range of kLa is more than 100/1, this information is not of direct value for sizing equipment. The efficiencies of various kinds of small liquid-liquid contactors for physical extraction are summarized on Figure 8.1. Larger units may have efficiencies less than half of these values. In some cases, however, enhancement of the L-L mass transfer coefficient by reaction may be as appreciable as in some gas-liquid cases. 

Study the effect of the extraction stage on reactor performance by varying the magnitudes of the the mass transfer coefficient Ka, the equilibrium distribution ratio m, the recycle ratio R, the relative reactor and extraction volumes and solvent flowrate. 

Coughlin and Canevari (1%9) have published experimental data on two systems at a variety of operating conditions the extraction of xylene from polypropylene and the extraction of methanol from polypropylene. These studies were conducted in a single screw extruder at low pressures and w was assumed to be small in comparison with w. Coughlin and Canevari developed a model which they used in conjunction with their experimental data to obtain a value for the diffusion coefficient. The values that they computed were of the order of 10 mVsec, which obviously means that the model is incorrect. Coughlin and Canevari also computed values for the mass transfer coefficient and found it to be independent of screw speed. This observation is particularly noteworthy since they saw no evidence of bubble formation. 

On the other hand, if bubble growth is diffusion controlled, then the mass transfer coefficient may be meaningful. However, in this case, the surface area for mass transfer is the surface area of the bubbles entrained in the solution and this depends on the volume of liquid in the extraction zone and not on the surface area of the extraction zone. Clearly, attempts to correlate experimental data for the extraction of a volatile component from a polymeric solution containing entrained bubbles using mass transfer coefficients can be misleading or totally erroneous. 

According to this criterion, when, in the same apparatns, the same dependence of the heat transfer coefficient and the mass transfer coefficient on the stirring rate of the phases is observed, the conclusion can be reached that the extraction occurs in a diffnsional regime. 

It is generally agreed that mass transfer coefficients are only correlated for negligibly small convectional motion of the transitional component, which is vertical to the interface. However, when the mass transfer is mutual and equimolar, no such convections normal to the interface result otherwise the transfer coefficient and the driving force must be corrected with the aid of theories of mass transfer [18]. The transitional rates and, accordingly, convectional flow rates normal to the interface are only low for the extraction process, so that the uncorrected Eq. (9.31) may be used. 

For the reverse process of the extraction of the metal salts from n-butanol to water, there is spontaneous interfacial turbulence which raises the mass-transfer coefficient to about twice the value expected from the correlation 54). 

Dekker et al. [170] studied the extraction process of a-amylase in a TOMAC/isooctane reverse micellar system in terms of the distribution coefficients, mass transfer coefficient, inactivation rate constants, phase ratio, and residence time during the forward and backward extractions. They derived different equations for the concentration of active enzyme in all phases as a function of time. It was also shown that the inactivation took place predominantly in the first aqueous phase due to complex formation between enzyme and surfactant. In order to minimize the extent of enzyme inactivation, the steady state enzyme concentration should be kept as low as possible in the first aqueous phase. This can be achieved by a high mass transfer rate and a high distribution coefficient of the enzyme between reverse micellar and aqueous phases. The effect of mass transfer coefficient during forward extraction on the recovery of a-amylase was simulated for two values of the distribution coefficient. These model predictions were verified experimentally by changing the distribution coefficient (by adding... 

Dekker et al. [170] have also shown that the steady state experimental data of the extraction and the observed dynamic behavior of the extraction are in good agreement with the model predictions. This model offers the opportunity to predict the effect of changes, both in the process conditions (effect of residence time and mass transfer coefficient) and in the composition of the aqueous and reverse micellar phase (effect of inactivation rate constant and distribution coefficient) on the extraction efficiency. A shorter residence time in the extractors, in combination with an increase in mass transfer rate, will give improvement in the yield of active enzyme in the second aqueous phase and will further reduce the surfactant loss. They have suggested that the use of centrifugal separators or extractors might be valuable in this respect. 

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]

Mass-transfer coefficients are also affected by the buoyancy forces in the high Ra = Gr Sc region, as shown in practice by the effect of gravity on the extraction-time for larger Raleigh numbers (Ra = Gr Sc = 108), as shown by Stiiber et al. [25]. 

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