Extraction continuous-phase mass transfer coefficients

There are few studies of dispersed-phase mass-transfer coefficients in mixers. Frank et al. (2008) recommend the correlation of Skelland and Xien for transfer from the dispersed phase to the continuous phase. Skelland and Xien (19901 studied batch extraction in a baffled mixer with six-flat-blade turbines. Their correlation is... 

JVimp is the impeller speed in revolutions/time, and the Schmidt number of the continuous phase, Sc, is li /p Dic. The correlations (3.1.167) and (3.1.168) for the dispersed-phase Sherwood number may be utilized to determine the value of the dispersed-phase mass-transfer coefBcient fc. For an aqueous-organic system, if the organic phase is assumed to be the extract phase as well as the dispersed phase, we can follow relations (3.4.18) and (3.4.19), and obtain, in terms of molar concentration differences, the following relations between the overall mass-transfer coefficient based on a particular phase and the individual phase mass-transfer coefficients ... 

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. 

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. 

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. 

In extraction columns, it is possible to find droplet swarms where the local velocities near the droplet surface are higher, this being due to the lower free area available for the countercurrent flowing continuous phase. Wake and Marangoni influences make the prediction of a physical mass transfer coefficients difficult. With reactive extraction the influence of interfacial kinetics on overall mass transfer is generally not negligible. In any case, a combination of reactive kinetics with any eddy mass transfer model is recommended, whereas the latter could rely on correlations derived for specific column geometries. 

A droplet containing a mixture of acetone(l)-benzene(2)-methanol(3) has a diameter of 8 mm and attains a velocity of 0.1 m/s in a sieve tray extraction column when it is dispersed in a continuous hydrocarbon phase. Use the penetration model to estimate the matrix of low flux mass transfer coefficients [A ] inside the droplet. 

Acetone is being removed from water by contacting with toluene in a packed extraction column. Water is the continuous [heavy] phase, and toluene is the dispersed [light] phase. Calculate the overall mass transfer coefficient for this process. 

In Eqs. (15-65) and (15-66), rrifo = dCd/dCc is the local slope of the equilibrium line, with the equilibrium concentration of solute in the dispersed phase plotted on the ordinate (y axis), and the equilibrium concentration of solute in the continuous phase plotted on the abscissa (x axis). Note that rrC is expressed on a volumetric basis (denoted by superscript vol), i.e., in terms of mass or mole per unit volume, because of the way the mass-transfer coefficients are defined. The mass-transfer coefficients will not necessarily be the same for each solute being extracted, so depending upon the application, mass-transfer coefficients may need to be determined for a range of different solutes. As noted earlier, other systems of units also may be used as long as they are consistently applied. 

Packed columns are often used for distillation, liquid-liquid extraction, and humidification as well as for gas absorption. The design can be based on overall transfer coefficients or on the number of transfer units and the height of a transfer unit. For distillation or humidification, where the gas phase is continuous and the liquid flows in rivulets over the packing, the mass-transfer coefficients and flooding characteristics are similar to those for gas absorption, and the same generalized correlations would apply. 

At the liquid-SC CO2 inter ce, a constant, and sufficient high concentration of extractant Cyanex 302 is assumed. Concentration effects of generated metal-complexes are assumed to be negligible, due to diffusion coefficient of solutes in supercritical fluids of about 10" m /s (17), which is approximately 2 orders of magnitude fester than in the aqueous phase. A continuous flow of solvent during extraction even reduces surfece effects, due to both continuous supply of exbactant and continuous removal of metal-extractant complex. Thus, mass transfer is a limiting factor at the liquid-SC CO2 interface, as studied previously by Tai et al. (18). Furdier research is required to study a possible impact on the overall extraction of SFE from humid MSWI fly ash. 

To evaluate the performance of a two-phase separator (gas-liquid or liquid-liquid) the mass transfer coeflicient or the extraction efficiency need to be known. A number of models have been developed for gas-Uquid systems, which estimate the mass transfer coefficient in the continuous liquid phase. In these models the individual contributions of the caps of the plugs and of the fully developed film separating the plugs from the channel wall are estimated. A study... 

Inthis eqquation, pni is defined in Eq. Q3-53I is defined in Eq. (13-55). N is the inpeller speed in rps, to is the initial time (s) that the dispersed phase is injected, and tp gs is the time (s) at which 95% of mass transfer has occurred. In a continuous mixer (tp 95 - to) can be considered the residence time of the dispersed phase in the mixer, which will result in 95% extraction of the solute. Additional correlations for mass-transfer coefficients are available (Treybal. 1980 Wankat and Knaebel. 20081. 

Kumemura and Korenaga demonstrated the extraction of aluminum in a continuous phase extracted with 2,2-dihydroxyazobenzene (DHAB) as a metal chelate (AP -D H AB) from buffer solution to tributyl phosphate (TBP, dispersed phase) [39]. As shown in Figure 12.12, a T-shaped channel 600 [tm wide and 200 j,m deep in the continuous phase and 70 pm wide and 20 xm deep in the dispersed phase is used for the extraction. The device is made of Pyrex glass. Using this device, the droplet volume can be controlled in the range 0.6-32 nL. The extraction time is 1 s, which is 90 times shorter than that of a conventional extraction method using a separating funnel. The overall mass transfer coefficient is estimated to be 57 x 10 mm s with 0.6 nL droplets. 

Several differential mass balance models have been proposed to characterize mass transfer kinetics. Among them, the model proposed by Sovova (1994), based on extraction from broken and intact cells (BICs), has been widely used. In this model, the solutes are stored in particle cells and protected by the cell wall. During the pretreatment step, to reduce the particle size and increase the surface area between the solute and fluid, some of the cells are broken and solutes become accessible to the fluid. These easily accessible solutes are denoted as x. The remaining solutes retained in unbroken cells are referred to as intact cells and defined as x. Thus, internal and external resistance control the extraction. Sovova (2005) also proposed a more complete model with additional parameters to consider equilibrium relationships. However, this modified model has not been widely used, due to its complexity, and most published work continues to use the older BIC model with mass transfer coefficients in the fluid (k ) and solid (k) phases, and x as the main parameter. The following assumptions are usually considered ... 

Such reactions can take place predominantly in either the continuous or disperse phase or in both phases or mainly at the interface. Mutual solubilities, distribution coefficients, and the amount of interfadal surface are factors that determine the overall rate of conversion. Stirred tanks with power inputs of 5-10 HP/1000 gal or extraction-type equipment of various kinds are used to enhance mass transfer. Horizontal TFRs usually are impractical unless sufficiently stable emulsions can be formed, but mixing baffles at intervals are helpful if there are strong reasons for using such equipment. Multistage stirred chambers in a single shell are used for example in butene-isobutane alkylation with sulfuric acid catalyst. Other liquid-liquid processes listed in Table 17.1 are numbers 8, 27, 45, 78, and 90. 

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