For mass transfer

Other Models for Mass Transfer. In contrast to the film theory, other approaches assume that transfer of material does not occur by steady-state diffusion. Rather there are large fluid motions which constantiy bring fresh masses of bulk material into direct contact with the interface. According to the penetration theory (33), diffusion proceeds from the interface into the particular element of fluid in contact with the interface. This is an unsteady state, transient process where the rate decreases with time. After a while, the element is replaced by a fresh one brought to the interface by the relative movements of gas and Uquid, and the process is repeated. In order to evaluate a constant average contact time T for the individual fluid elements is assumed (33). This leads to relations such as... 

The situation is very much poorer for stmctured rather than random packings, in that hardly any data on Hq and have been pubHshed. Based on a mechanistic model for mass transfer, a way to estimate HETP values for stmctured packings in distillation columns has been proposed (91), yet there is a clear need for more experimental data in this area. 

The Driving Force for Mass Transfer. The rate of mass transfer increases as the driving force, (7 — (7, is increased. can be enhanced as follows. From Dalton s law of partial pressures... 

To obtain an indication of the rate of solute transfer from the particle surface to the bulk of the Hquid, the concept of a thin film providing the resistance to transfer can be used (2) and the equation for mass transfer written as ... 

Static mixing of gas—Hquid systems can provide good interphase contacting for mass transfer and heat transfer. Specific interfacial area for the SMV (Koch/Sulzer) mixer is related to gas velocity and gas holdup ( ) by the following ... 

Using this simplified model, CP simulations can be performed easily as a function of solution and such operating variables as pressure, temperature, and flow rate, usiag software packages such as Mathcad. Solution of the CP equation (eq. 8) along with the solution—diffusion transport equations (eqs. 5 and 6) allow the prediction of CP, rejection, and permeate flux as a function of the Reynolds number, Ke. To faciUtate these calculations, the foUowiag data and correlations can be used (/) for mass-transfer correlation, the Sherwood number, Sb, is defined as Sh = 0.04 S c , where Sc is the Schmidt... 

Likewise, the microscopic heat-transfer term takes accepted empirical correlations for pure-component pool boiling and adds corrections for mass-transfer and convection effects on the driving forces present in pool boiling. In addition to dependence on the usual physical properties, the extent of superheat, the saturation pressure change related to the superheat, and a suppression factor relating mixture behavior to equivalent pure-component heat-transfer coefficients are correlating functions. 

M. Luoma, P. Lappi, and R. Lylykangas, Evaluation of High Cell Density E-Flow Catalyst, SAE 930940, Society of Automotive Engineers, Warrendale, Pa., 1993. Good reference for mass-transfer limited model reactions. 

Specialized heat transfer nomenclature used for radiative heat transfer is defined in the subsection Heat Transmission hy Radiation. Nomenclature for mass transfer is defined in the subsection Mass Transfer. ... 

Units employed in diffusivity correlations commonly followed the cgs system. Similarly, correlations for mass transfer correlations used the cgs or Enghsh system. In both cases, only the most recent correlations employ SI units. Since most correlations involve other properties and physical parameters, often with mixed units, they are repeated here as originally stated. Common conversion factors are listed in Table 1-4. 

Chilton-Colbum factor for mass transfer, Eq. (5-291) Dimensionless Dimensionless... 

As shown in Fig. 13-92, methods of providing column reflux include (a) conventional top-tray reflux, (b) pump-back reflux from side-cut strippers, and (c) pump-around reflux. The latter two methods essentially function as intercondenser schemes that reduce the top-tray-refliix requirement. As shown in Fig. 13-93 for the example being considered, the internal-reflux flow rate decreases rapidly from the top tray to the feed-flash zone for case a. The other two cases, particularly case c, result in better balancing of the column-refliix traffic. Because of this and the opportunity provided to recover energy at a moderate- to high-temperature level, pump-around reflirx is the most commonly used technique. However, not indicated in Fig. 13-93 is the fact that in cases h and c the smaller quantity of reflux present in the upper portion of the column increases the tray requirements. Furthermore, the pump-around circuits, which extend over three trays each, are believed to be equivalent for mass-transfer purposes to only one tray each. Bepresentative tray requirements for the three cases are included in Fig. 13-92. In case c heat-transfer rates associated with the two pump-around circuits account for approximately 40 percent of the total heat removed in the overhead condenser and from the two pump-around circuits combined. 

Plate Efficiency The efficiency of a plate for mass transfer depends upon three sets of design parameters ... 

On tbe basis of tbe two-film model for mass transfer, and relating all efficiencies to gas-pbase concentrations (for convenience only a similar development can be made on tbe basis of bquid concentrations), point efficiency can be expressed in terms of transfer units ... 

Note that the product of the mass-transfer coefficient and the interfacial area is a volumetric coefficient and obviates the need for a value of the interfacial area. While areas for mass transfer on plates have been measured, the experimental contacting equipment cuffered significantly from that used for commercial distillation or gas absorption, and the reported areas are considered unreliable for design purposes. 

To design deep-bed contactors for mass-transfer operations, one must have, in general, predictive methods for the following design parameters ... 

Besides looking at just the mixing, it is important at this time to also consider the settling time of the phases after mixing since this will impact on the settler design. Higher intensity of mixing may decrease the residence time for mass transfer, but at the same time create fine dispersions which are difficult to settle. 

Experimental gas-solid mass-transfer data have been obtained for naphthalene in CO9 to develop correlations for mass-transfer coefficients [Lim et al., Am. Chem. Soc. Symp. Ser, 406, 379 (1989)]. The data were correlated over a wide range of conditions with the following equation for combined natural and forced convection ... 

Thus the driving force for fuming is approximately equal to that for free evaporation. Using dre experimental data, and the normal expression for mass transfer across a boundary layer, it is concluded that the boundary layer thickness which would account for this rate should be about 2 x 10 cm (Turkdogan et al., 1963). 

Cures. Eliminate the source of fogging by using a smaller AT and thus more surface for mass transfer. Try to minimize AT/AY. 

The mass transfer number B represents the ratio of the energy available for vaporization to the energy required for vaporization, and may be thought of as a driving force for mass transfer. It can be expressed as... 

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