Dispersed-phase mass-transfer coefficient

The dispersed phase mass transfer coefficient of a liquid drop with internal circulation (65) takes higher values than are observed in the case of the stagnant droplet. For example, the long-time solution takes the form... 

The prediction of the dispersed phase mass transfer coefficient is more complex... 

By comparison to solid particles, drops are not only subject to deformation but also to internal circulation and oscillation. This affects not only the values of the continuous but also of the dispersed phase mass transfer coefficients. Relevant theoretical and empirical correlations are collected in literature (24, 25). For oscillating drops the equations of Clift et al. (26) give usually a good prediction (27)... 

Treybal (I960) estimated the overall mass-transfer coefficient and the stage efficiency for a mixer (0.5 m high and 0.5 m diameter, = 0.1963 m, Vrimer 0.09817 m ) extracting benzoic acid from water into solvent pure toluene. The water plus benzoic acid flow rate was Qp = 0.003 m /s, and the toluene flow rate was Qp, = 0.0003 m /s. The tank was well mixed. Toluene was the dispersed phase, ( )e) was estimated as 0.0824. The estimated dispersed-phase surface to dispersed-phase volume ratio ap, = 1940 m dispersed phase/m dispersed phase. The estimated overall dispersed-phase mass-transfer coefficient Kpp, = 2.01 x 10 kmol benzoic/[m s(kmol benzoic/m )]. Additional data. Ptoiuene 865 kg/m, — 92.14 kg/kmol. Equilibrium is — 20.8 ( extract... 

A third conplicating factor is that mass transfer of solute usually lowers the interfacial tension a and reduces d riticai circulation however, the presence of small amounts of surfactants or dirt that collects at the interface will reduce internal circulation markedly and may introduce a resistance to mass transfer at the interface that is not included in Eq. M 6-80bk Because industrial plants are usually not scrupulously clean, dispersed-phase mass-transfer coefficients in plant operations will often be significantly lower than the values obtained in scrupulously clean laboratories. 

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... 

D21. Mass transfer continues in settlers. Estimate the overall dispersed phase mass transfer coefficient for the settler in Example 13-5. Use the drop diameter calculated for the mixer in Example 16-6 as the drop diameter in the settler instead of the 150 pm assumed in Exanple 13-5. Recalculate the Stokes velocity, estimate an average in the settler, estimate the value of a in the settler, estimate kc and Kl, then determine Since the settler is not well mixed, use the... 

Fio. 10.25. Dispersed-phase mass-transfer coefficients spray tower, 2-in. diam. (51). 

Liquid-phase mass transfer coefficient Gas-liquid interfacial area per unit volume of dispersion Gas volume fraction in dispersion Diffusivity of cyanogen in solution Henry law coefficient... 

The individual, or phase, mass transfer coefficients (i.e., for the dispersed phase and for the continuous phase) are defined as ... 

Diffusivity of 02 in liquid xylene Da = 1.4 x 10 9 m2/s Equipment performance characteristics Gas volume fraction in the dispersion (1 - eg) = 0.34 Mean diameter of the bubbles present in the dispersion = 1.0 mm Liquid-phase mass transfer coefficient kL = 4.1 x 10 4 m/s... 

From equations (7-40) and (7-46), it is evident that an estimate of EMD requires generalized correlations of experimental data for the interfacial area for mass transfer and for the dispersed- and continuous-phase mass-transfer coefficients. The population of dispersed-phase droplets in an agitated vessel will cover a range of sizes and shapes. For each droplet, it is useful to define de, the equivalent diameter of a spherical drop, using the method of Lewis et al. (1951) ... 

Koide, K., Kurematsu, K., Iwamoto, S., Iwata, Y., and Horibe, K. (1983a), Gas holdup and volumetric hquid-phase mass transfer coefficient in bubble column with draught tube and with gas dispersion into tube, Journal of Chemical Engineering of Japan, 16(5) 413-418. 

An interesting situation arises in processes where the reaction product P evaporates and is taken out of the reactor with the gas phase (the supply phase). Let us assume that there are no chemical reactions in the gas phase, e.g., l ause the liquid phase reaction is catalysed. We consider the case of rapid reactions, so that all the desired product P is formed in the diffusion layer in the liquid phase, close to the interface. When P can undergo undesired reactions in the liquid phase it is essential to remove P as effectively as we can, e.g., by creating a large surface area and very high gas-phase mass transfer coefficients. At the same time it is essential that the volume of the liquid phase is minimized, since decomposition of P will occur just there. The obvious choice would then be a configuration where the liquid is the dispersed phase, such as in a spray tower or a spray cyclone, provided the heat removal rate is sufficient. Another suitable arrangement could be a gas/liquid packed bed or a wetted wall column. The latter reactor type is very suitable for heat removal (section 4.6.3.1)... 

The liquid phase mass transfer coefficients can be highest in parallel flow, and lowest in the liquid-in-gas dispersion. 

For making a choice it is best to look at the main reaction first. If this is a relatively slow liquid phase reaction, it will require a certain liquid volume, so that a gas-in-liquid dispersion is generally the most suitable configuration. For suppressing competitive or consecutive reactions high liquid phase mass transfer coefficients are favourable (section 5.3.5). 

When a consecutive reaction has to be minimized, the liquid volume should be small (section S.4.2.2), and a liquid-in-gas dispersion or a parallel flow arrangement are the best choices. When a competitive reaction (of the transferred reactant) has to be minimized, the gas-phase mass transfer coefficient should be as high as possible (section S.4.2.2, eq. (5.45)), and again a liquid-in-gas dispersion or parallel flow are to be preferred. 

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 ... 

The values of k and hence Sb depend on whether the phase under consideration is the continuous phase, c, surrounding the drop, or the dispersed phase, d, comprising the drop. The notations and Sh are used for the respective mass-transfer coefficients and Sherwood numbers. 

Axial Dispersion Effects In adsorption bed calculations, axial dispersion effects are typically accounted for by the axial diffusionhke term in the bed conservation equations [Eqs. (16-51) and (16-52)]. For nearly linear isotherms (0.5 < R < 1.5), the combined effects of axial dispersion and mass-transfer resistances on the adsorption behavior of packed beds can be expressed approximately in terms of an apparent rate coefficient for use with a fluid-phase driving force (column 1, Table 16-12) ... 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

Gal-Or and Hoelscher (G5) have recently developed a fast and simple transient-response method for the measurement of concentration and volumetric mass-transfer coefficients in gas-liquid dispersions. The method involves the use of a transient response to a step change in the composition of the feed gas. The resulting change in the composition of the liquid phase of the dispersion is measured by means of a Clark electrode, which permits the rapid and accurate analysis of oxygen or carbon dioxide concentrations in a gas, in blood, or in any liquid mixture. 

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