Efficiencies of Multicomponent Systems

SOLUTION The values of both Qj and Qji were determined in Example 12.1.2. The values were 

Armed with the point efficiency we may calculate the composition of the vapor above the tray as 

A horizontal concentration gradient will develop in the liquid due to mass transfer into and from the liquid as the liquid flows across the tray. Thus, the composition of the vapor above the froth will change as we traverse the tray even if the composition of the vapor just below the tray is uniform. The point efficiency defined in the preceding section models the mass transfer processes at a particular point on the tray but does not take into account the fact that the liquid may have a significant concentration change as it crosses the tray. Thus, the point efficiency must be related to the tray efficiency before it can be used in column design calculations. 

There are many different models for liquid flow across a distillation tray. We consider the two simplest here. 

If the liquid is completely mixed in the horizontal direction (a reasonable approximation for small diameter columns) then the tray efficiency and the point efficiency are one and the same (all points being equal as it were) and = E y 

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Design Methods. Improvements ia the ability to predict multicomponent equilibrium and mass-transfer rate performance will allow significant improvements ia the design of new adsorption systems and ia the energy efficiency of existing systems. 

The prediction of efficiencies for multicomponent systems is also discussed by Chan and Fair (1984b). For mixtures of dissimilar compounds the efficiency can be very different... 

The extension of this approach to artificial leaves based on titanates, niobates, tantalates, metal nitrides and phosphides, metal sulfides, and other transition metal oxides appears possible and useful in order to enhance the photocatalytic efficiency. In addition, the construction of multicomponent systems such as Ti02-CdS or MoS2-CdSe for overall water splitting could also lead to further improvements. This... 

For multicomponent systems (i.e., those with more than two components) there are c - 1 independent component efficiencies, and there are sound theoretical reasons as well as experimental evidence for not assuming the individual component efficiencies to be alike indeed, they may take values between plus and minus infinity. Component efficiencies are more likely to differ for strongly nonideal mixtures. While models exist for estimating efficiencies in multicomponent systems [see chapter 13 in Taylor and Krishna, (op. cit.) for a review of the literature], they are not widely used and nave not (yet) been included in any of the more widely used commercial simulation programs. 

The fact that component efficiencies in multicomponent systems are unbounded means that the arithmetic average of the component Murphree efficiencies is useless as a measure of the performance of a multicomponent distillation process. Taylor, Baur, and Krishna [AIChE J., 50, 3134 (2004)] proposed the following efficiency for multicomponent systems ... 

In fact, through use of matrix models of mass transfer in multicomponent systems (as opposed to effective diffusivity methods) it is possible to develop methods for estimating point and tray efficiencies in multicomponent systems that, when combined with an equilibrium stage model, overcome some of the limitations of conventional design methods. The purpose of this chapter is to develop these methods. We look briefly at ways of solving the set of equations that model an entire distillation column and close with a review of experimental and simulation studies that have been carried out with a view to testing multicomponent efficiency models. 

Vogelpohl, A., Murphree Efficiencies in Multicomponent Systems, The Institution of Chemical Engineers Symposium Series, No. 56, Distillation 1979, 2.1/25 -2.1/31 (1979). 

Most distillation systems ia commercial columns have Murphree plate efficiencies of 70% or higher. Lower efficiencies are found under system conditions of a high slope of the equiHbrium curve (Fig. lb), of high Hquid viscosity, and of large molecules having characteristically low diffusion coefficients. FiaaHy, most experimental efficiencies have been for biaary systems where by definition the efficiency of one component is equal to that of the other component. For multicomponent systems it is possible for each component to have a different efficiency. Practice has been to use a pseudo-biaary approach involving the two key components. However, a theory for multicomponent efficiency prediction has been developed (66,67) and is amenable to computational analysis. 

Chan, H. and Fair, J. R. (1984b) Ind. Eng. Chem. Proc. Des. Dev. 23, 820. Prediction of point efficiencies on sieve trays. 2. multicomponent systems. 

Of course, isotope filtering is not restricted to such binary systems, but can also be applied to multicomponent systems such as multiprotein complexes, or one or more ligands bound to proteins or protein complexes. It is also conceivable to construct single molecules from sections with different isotopic labeling in order to selectively observe one part by isotopic filtering. However, in these cases a specific synthetic approach has to be designed to allow for efficient incorporation of the isotope labels into the appropriate parts only (for example, by fragment condensation or inteins see also Chapt. 1) [5]. 

In multicomponent systems A"0 can be written as a sum of the individual absorption coefficients A ot = 2TA , where each AT,(A ) depends in a different way on the wavelength. If one or more of the components are fluorescent, their excitation spectra are mutually attenuated by absorption filters of the other compounds. This effect is included in Eqs. (8.27) and (8.28) so that examples like that of Figure 8.4 can be quantified. The two fluorescent components are monomeric an aggregated pyrene, Mi and Mn. The fluorescence spectra of these species are clearly different from each other but the absorption spectra overlap strongly. Thus the excitation spectrum of the minority component M is totally distorted by the Mi filter (absorption maxima of Mi appear as a minima in the excitation spectrum ofM see Figure 8.4, top). In transparent samples this effect can be reduced by dilution. However, this method is not very efficient in scattering media as can be seen by solving Eqs. (8.27 and 8.28) for bSd — 0. Only the limit d 0 will produce the desired relation where fluorescence intensity and absorption coefficient of the fluorophore are linearly proportional to each other in a multicomponent system. 

Figure 8.11 shows how the equilibrium curve shrinks in the presence of inefficiencies. In multicomponent systems where there is mutual interference in extraction by several components, the efficency shrinkage comes on top of the other reductions in the equilibrium curve, and for this reason there is stress in such systems on achieving high efficiency. 

Uses of Oldershaw columns to less conventional systems and applications were described by Fair, Reeves, and Seibert [Topical Conference on Distillation, AIChE Spring Meeting, New Orleans, p. 27 (March 10-14, 2002)]. The applications described include scale-up in the absence of good VLE, steam stripping efficiencies, individual component efficiencies in multicomponent distillation, determining component behavior in azeotropic separation, and foam testing. 

Radicals add to unsaturated bonds to form new radicals, which then undergo addition to other unsaturated bonds to generate further radicals. This reaction sequence, when it occurs iteratively, ultimately leads to the production of polymers. Yet the typical radical polymerization sequence also features the essence of radical-induced multicomponent assembling reactions, assuming, of course, that the individual steps occur in a controlled manner with respect to the sequence and the number of components. The key question then becomes how does one control radical addition reactions such that they can be useful multicomponent reactions Among the possibilities are kinetics, radical polar effects, quenching of the radicals by a one-electron transfer and an efficient radical chain system based on the judicious choice of a radical mediator. This chapter presents a variety of different answers to the question. Each example supports the view that a multicomponent coupling reaction is preferable to uncontrolled radical polymerization reactions, which can decrease the overall efficiency of the process. 

Enter an alpha value if you have chosen F or T for the method. Enter a K value for a light key component if you chose A. Input the factor alpha or K. Alpha is defined as simply the light key K divided by the heavy key K component. The K factor is simply the particular component s vapor phase mole fraction divided by its liquid mole fraction. The alpha value is therefore a ratio of the chosen two key components. These key components should be those that readily point to how well the fractionator is doing its job of separation. For example, for a depropanizer tower, choose propane as the light key component and butane as the heavy key, since you wish to separate the propane from the butane to make a propane product specification. For a multicomponent system, you may try several components to determine a controlling alpha and/or to factor an average tray efficiency. 

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