Mass transfer generally

Mass transfer Generalized model of Bravo, et al. [113], with discount factors for wetted surfaces. 

This division does not necessarily correspond to any physically measurable boundary. The edge of the boundary layer does not correspond to any sudden change in the flow but rather corresponds to an arbitrary mathematical definition. Even with this simplification, the calculations are very difficult, and in general only approximate mathematical solutions are possible. Nonetheless, this idea clarified numerous unexplained phenomena and provided a much better intellectual basis for discussing complicated flows than had existed previously. As a result, the boundary layer has become a standard idea in the minds of fluid mechanicians. Once it became accepted in fluid mechanics, an analogous idea was tried in heat transfer and in mass transfer, generally with useful results. 

However, a note of caution should be added. In many multiphase reaction systems, rates of mass transfer between different phases can be just as important or more important than reaction kinetics in determining the reactor volume. Mass transfer rates are generally higher in gas-phase than liquid-phase systems. In such situations, it is not so easy to judge whether gas or liquid phase is preferred. 

Equation 28 and its liquid-phase equivalent are very general and valid in all situations. Similarly, the overall mass transfer coefficients may be made independent of the effect of bulk fiux through the films and thus nearly concentration independent for straight equilibrium lines ... 

Experimental Mass Transfer Coefficients. Hundreds of papers have been pubHshed reporting mass transfer coefficients in packed columns. For some simple systems which have been studied quite extensively, mass transfer data may be obtained directiy from the Hterature (6). The situation with respect to the prediction of mass transfer coefficients for new systems is stiU poor. Despite the wealth of experimental and theoretical studies, no comprehensive theory has been developed, and most generalizations are based on empirical or semiempitical equations. 

The term dqljdt represents the overall rate of mass transfer for component / (at time t and distance averaged over a particle. This is governed by a mass transfer rate expression which may be thought of as a general functional relationship of the form... 

The main conclusion to be drawn from these studies is that for most practical purposes the linear rate model provides an adequate approximation and the use of the more cumbersome and computationally time consuming diffusing models is generally not necessary. The Glueckauf approximation provides the required estimate of the effective mass transfer coefficient for a diffusion controlled system. More detailed analysis shows that when more than one mass transfer resistance is significant the overall rate coefficient may be estimated simply from the sum of the resistances (7) ... 

The search for a suitable adsorbent is generally the first step in the development of an adsorption process. A practical adsorbent has four primary requirements selectivity, capacity, mass transfer rate, and long-term stabiUty. The requirement for adequate adsorptive capacity restricts the choice of adsorbents to microporous soUds with pore diameters ranging from a few tenths to a few tens of nanometers. 

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). 

The pulsed-plate column is typically fitted with hori2ontal perforated plates or sieve plates which occupy the entire cross section of the column. The total free area of the plate is about 20—25%. The columns ate generally operated at frequencies of 1.5 to 4 H2 with ampHtudes 0.63 to 2.5 cm. The energy dissipated by the pulsations increases both the turbulence and the interfacial areas and greatly improves the mass-transfer efficiency compared to that of an unpulsed column. Pulsed-plate columns in diameters of up to 1.0 m or mote ate widely used in the nuclear industry (139,140). 

In general, the desorptive behavior of contaminated soils and soHds is so variable that the requited thermal treatment conditions are difficult to specify without experimental measurements. Experiments are most easily performed in bench- and pilot-scale faciUties. Full-scale behavior can then be predicted using mathematical models of heat transfer, mass transfer, and chemical kinetics. 

Manufacture and Processing. Mononitrotoluenes are produced by the nitration of toluene in a manner similar to that described for nitrobenzene. The presence of the methyl group on the aromatic ring faciUtates the nitration of toluene, as compared to that of benzene, and increases the ease of oxidation which results in undesirable by-products. Thus the nitration of toluene generally is carried out at lower temperatures than the nitration of benzene to minimize oxidative side reactions. Because toluene nitrates at a faster rate than benzene, the milder conditions also reduce the formation of dinitrotoluenes. Toluene is less soluble than benzene in the acid phase, thus vigorous agitation of the reaction mixture is necessary to maximize the interfacial area of the two phases and the mass transfer of the reactants. The rate of a typical industrial nitration can be modeled in terms of a fast reaction taking place in a zone in the aqueous phase adjacent to the interface where the reaction is diffusion controlled. 

In considering the effect of mass transfer on the boiling of a multicomponent mixture, both the boiling mechanism and the driving force for transport must be examined (17—20). Moreover, the process is strongly influenced by the effects of convective flow on the boundary layer. In Reference 20 both effects have been taken into consideration to obtain a general correlation based on mechanistic reasoning that fits all available data within 15%. 

The thermal design of cooling towers follows the same general procedures already presented. Integration of equation 35 is usually done numerically using the appropriate software, mass-transfer coefficients, saturation enthalpies, etc. In mechanical-draft towers the air and water dows are both suppHed by machines, and hence dow rates are fixed. Under these conditions the design procedure is straightforward. 

Direct Chlorination of Ethylene. Direct chlorination of ethylene is generally conducted in Hquid EDC in a bubble column reactor. Ethylene and chlorine dissolve in the Hquid phase and combine in a homogeneous catalytic reaction to form EDC. Under typical process conditions, the reaction rate is controlled by mass transfer, with absorption of ethylene as the limiting factor (77). Ferric chloride is a highly selective and efficient catalyst for this reaction, and is widely used commercially (78). Ferric chloride and sodium chloride [7647-14-5] mixtures have also been utilized for the catalyst (79), as have tetrachloroferrate compounds, eg, ammonium tetrachloroferrate [24411-12-9] NH FeCl (80). The reaction most likely proceeds through an electrophilic addition mechanism, in which the catalyst first polarizes chlorine, as shown in equation 5. The polarized chlorine molecule then acts as an electrophilic reagent to attack the double bond of ethylene, thereby faciHtating chlorine addition (eq. 6) ... 

One goal of catalyst designers is to constmct bench-scale reactors that allow determination of performance data truly indicative of performance in a full-scale commercial reactor. This has been accompHshed in a number of areas, but in general, larger pilot-scale reactors are preferred because they can be more fully instmmented and can provide better engineering data for ultimate scale-up. In reactor selection thought must be given to parameters such as space velocity, linear velocity, and the number of catalyst bodies per reactor diameter in order to properly model heat- and mass-transfer effects. 

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