Dispersed systems mass transfer

For hquid systems v is approximately independent of velocity, so that a plot of JT versus v provides a convenient method of determining both the axial dispersion and mass transfer resistance. For vapor-phase systems at low Reynolds numbers is approximately constant since dispersion is determined mainly by molecular diffusion. It is therefore more convenient to plot H./v versus 1/, which yields as the slope and the mass transfer resistance as the intercept. Examples of such plots are shown in Figure 16. 

Specific interface in gas/liquid systems Mass-transfer coefficient Time-dependent dispersion coefficient Knudscn number Reaction rate constant... 

System efficiency good packing quality and low band-broadening due to axial dispersion and mass transfer resistance are necessary... 

The term. .overload" has, notably, been introduced by analytical chemists. Here a column should not be. .overloaded" in order to achieve a constant retention time for a reproducible analytical detection of each component peak. Preparative chromatography has a different aim, which is called. .productivity". To achieve this goal the columns are operated under so-called. .overloaded" conditions. From the engineering view point overloaded systems are nonlinear because of nonlinear isotherms as well as dispersion and mass transfer effects. 

Skelland, A.H.P. Xien, H. Dispersed-phase mass transfer in agitated liquid-liquid systems. Ind. Eng. Chem. Res. 1990, 29, 415-420. 

Measurements [380] in the water/oil/aerial oxygen system (gas oil, i.e. kerosene and n-paraffins, were utilized as the oil phase) have shown, that despite Jcla being higher in the water/air system than in oil/air system, mass transfer in oil is nevertheless faster due to factor of 10 higher Ac G/V = k aAa The main resistance in supplying oxygen to an oil/water dispersion consists in the gas/water transfer step. The following mechanism applies ... 

Figure 9.7 Combined effects of axial dispersion and mass-transfer resistance for a Langmuir system with (5 — 0.33. The curves are normalized to the point T(mid), (C/C ) = 0.5 6 is the parameter. [After D.M. Ruthven, Principles of Adsorption and Adsorption Processes, reprinted with permission of John Wiley and Sons, New York, (NY), (1984).]...

The major difficulty in the analysis of chromatographic data is separating the axial dispersion and mass-transfer contributions since, except for gaseous systems at very low flow rates, the axial dispersion coefficient (Dl) is velocity dependent. For liquid systems Dl varies essentially linearly with velocity so a plot of HETP vs. superficial velocity (ev) should be linear with the mass-transfer resistance directly related to the slope (Fig. 6). For gaseous systems at a high Reynolds number this same plot can be used, but in the low Reynolds number region a plot oiH/v vs. 1 /v may be more convenient since in this region Dl is essentially constant and the intercept thus yields the mass-transfer resistance [43-45]. 

The addition of various surfactants and micelle-forming agents in the biphasic hydroformylation of olefins was also considered as a tool for enhancement of the reaction rates (see Section 2.3.4). Whereas the presence of a surfactant leads to a lower droplet size in the dispersed phase, thus increasing the liquid-liquid interfadal area and hence the mass-transfer rate, the formation of emulsions is considered as a maj or drawback of this system. Mass-transfer effects in biphasic hydroformylation of 1-octene in the presence of cetyltrimethylammonium bromide (CTAB) was studied by Lekhal et al. [37]. A mass-transfer model based on Higbie s penetration theory was proposed to predict the rate of hydroformylation in a gas-liquid-liquid system. 

Skelland, A. H. P., and H. Xien, Dispersed-Phase Mass Transfer in Agitated Liquid-Liquid Systems, Ind Eng. Chem. Research, 29, 415 (1990). 

This section illustrates PSA calculations for the sinplest possible case— the local equilibrium theory for trace conponents for an isothermal system. If the mole fraction of the strongly adsorbed conponent is higher in Ae feed, the isotherm is likely to be nonlinear and the velocity will vary along the length of the column. In addition, operation is much more likely to be adiabatic instead of isothermal. It is also common to have both coirponents adsorb or to have more than two conponents. If dispersion and mass transfer resistances are iirportant, detailed simulations will be required. In addition, PSA has spawned a large number of inventive cycles to acconplish different purposes. If you need to understand any of these situations, Ruthven et al. (1294) provide an advanced treatment. White and BarWey 119891 and White... 

The above influences of the mass transfer direction are particularly pronounced for systems having a high surface tension. In these systems, mass transfer from disperse continuous allows a considerably larger loading limit than reverse direction. The separation efficiency increases with increasing pulse frequency and smaller filling material dimensions. Mass transfer from continuous - disperse is more favorable here. 

As an alternative to conventional sorption rate measurements it is also possible to derive diffusional time constants from the dynamic response of a packed column to a change in sorbate concentration. In a chromatographic system the broadening of the response peak results from the combined effects of axial dispersion and mass transfer resistance. By making measurements over a range of gas velocities it is possible to separate the dispersion and mass transfer effects and so to determine the effective overall mass transfer coefficient or the diffusional time constant. Further details are given in Section 8.5. 

FIGURE 8.10. Comparison of linear driving force approximation (model lo) with modified mass transfer coefficient defined by Eq. (8.42) and exact solution for breakthrough curve with axial dispersion, external mass transfer and diffusiqnal resistances (model 3/>). (Linear system)... 

FIGURE 8,22. Combined effects of axial dispersion and mass transfer resistance for a favorable Langmuir equilibrium system ( ==0.33). a) Constant pattern breakthrough curves for various values of (fluid film resistances + axial dispersion), (h) The same curves plotted on a modified time scale with 7 = t/(1 + B). [Reprinted with permission from Chem. Eng. Sci 30. Garg and Ruthvcn (ref. 54). Copyright 1975, Pcrgamon Press, Ltd.)... 

An equivalent analysis of the combined effects of axial dispersion and mass transfer resistance has been presented by Rhee and Amundson, based on shock layer theory. From the mass balance over the shock layer it may be shown that the propagation velocity [Eq. (8.13)] is not affected by mass transfer resistance or axial dispersion. For an equilibrium system with axial dispersion the differential mass balance [Eq. (8.1)] becomes, under constant pattern conditions. 

The equilibrium theory of binary and multicomponent isothermal adsorption systems appears to have been first developed by Glueckauf. More general and comprehensive treatments have been developed by Rhee, Aris, and Amundson and by Helfferich and Klein. The former treatment exploits the analogy between chromatographic theory and the theory of kinematic waves. The detailed quantitive theory has been developed only for ideal Langmuir systeiris without axial dispersion or mass transfer resistance and in which the initial and boundary conditions represent constant steady states. Subject to these constraints the treatment is sufficiently general to allow the dynamic behavior to be predicted for systems with any number of components, provided only that the separation factors are known. In the... 

These multistage, countercurrent towers are very effective, both with respect to liquid-handling capacity and extraction efficiency, particularly for systems of low interfacial tension which do not require m hanical agitation for good dispersion. Their mass-transfer effectiveness results because (I) axial mixing of... 

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 ... 

Eor a linear system f (c) = if, so the wave velocity becomes independent of concentration and, in the absence of dispersive effects such as mass transfer resistance or axial mixing, a concentration perturbation propagates without changing its shape. The propagation velocity is inversely dependent on the adsorption equiUbrium constant. 

Fluid mixing is a unit operation carried out to homogenize fluids in terms of concentration of components, physical properties, and temperature, and create dispersions of mutually insoluble phases. It is frequently encountered in the process industry using various physical operations and mass-transfer/reaction systems (Table 1). These industries include petroleum (qv), chemical, food, pharmaceutical, paper (qv), and mining. The fundamental mechanism of this most common industrial operation involves physical movement of material between various parts of the whole mass (see Supplement). This is achieved by transmitting mechanical energy to force the fluid motion. 

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