Multicomponent mass transfer

Rate equations 28 and 30 combine the advantages of concentration-independent mass transfer coefficients, even in situations of multicomponent diffusion, and a familiar mathematical form involving concentration driving forces. The main inconvenience is the use of an effective diffusivity which may itself depend somewhat on the mixture composition and in certain cases even on the diffusion rates. This advantage can be eliminated by working with a different form of the MaxweU-Stefan equation (30—32). One thus obtains a set of rate equations of an unconventional form having concentration-independent mass transfer coefficients that are defined for each binary pair directiy based on the MaxweU-Stefan diffusivities. 

Discussion of the concepts and procedures involved in designing packed gas absorption systems shall first be confined to simple gas absorption processes without compHcations isothermal absorption of a solute from a mixture containing an inert gas into a nonvolatile solvent without chemical reaction. Gas and Hquid are assumed to move through the packing in a plug-flow fashion. Deviations such as nonisotherma1 operation, multicomponent mass transfer effects, and departure from plug flow are treated in later sections. 

R. Krishna and R. Taylor, Multicomponent Mass Transfer,John Wiley Sons, Inc., New York, 1991. 

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. 

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%. 

Work in the area of simultaneous heat and mass transfer has centered on the solution of equations such as 1—18 for cases where the stmcture and properties of a soHd phase must also be considered, as in drying (qv) or adsorption (qv), or where a chemical reaction takes place. Drying simulation (45—47) and drying of foods (48,49) have been particularly active subjects. In the adsorption area the separation of multicomponent fluid mixtures is influenced by comparative rates of diffusion and by interface temperatures (50,51). In the area of reactor studies there has been much interest in monolithic and honeycomb catalytic reactions (52,53) (see Exhaust control, industrial). Eor these kinds of appHcations psychrometric charts for systems other than air—water would be useful. The constmction of such has been considered (54). 

Taylor and Krishna, Multicomponent Mass Transfer, Wiley, 1993. Toumie, Laguerie, and Couderc, Chem. Engr. Sd., 34, 1247 (1979). Treybal, Mass Transfer Operations, 3d ed., McGraw-Hill, 1980. 

Problem Solving Methods Most, if not aU, problems or applications that involve mass transfer can be approached by a systematic-course of action. In the simplest cases, the unknown quantities are obvious. In more complex (e.g., iTmlticomponent, multiphase, multidimensional, nonisothermal, and/or transient) systems, it is more subtle to resolve the known and unknown quantities. For example, in multicomponent systems, one must know the fluxes of the components before predicting their effective diffusivities and vice versa. More will be said about that dilemma later. Once the known and unknown quantities are resolved, however, a combination of conservation equations, definitions, empirical relations, and properties are apphed to arrive at an answer. Figure 5-24 is a flowchart that illustrates the primary types of information and their relationships, and it apphes to many mass-transfer problems. 

When two or more gases are absorbed in systems involving chemical reac tions, the situation is much more complex. This topic is discussed later in the subsection Absorption with Chemical Reac tion. Graphical Design Method for Dilute Systems The following notation for multicomponent absorption calculations has been adapted from Sherwood, Pigford, and Wilke (Mass Transfer, McGraw-Hill, New York 1975, p. 415) ... 

L. Coupled Heat Transfer and Multicomponent Mass Transfer, with Residence-... 

The general case of coupled heat-transfer and multicomponent mass-transfer in swarms of bubbles with residence-time and size distributions is treated in Section IV, L. In previous sections simplified cases of uncoupled mass transfer are considered starting from the most simplified models available for gas-liquid dispersions. 

In this section, a general formulation will be given for the effect of bubble residence-time and bubble-size distributions on simultaneous and thermodynamically coupled heat- and mass-transfer in a multicomponent gas-liquid dispersion consisting of a large number of spherical bubbles. Here one can... 

The proposed technique will be used here to illustrate the case of interfacial heat and multicomponent mass transfer in a perfectly mixed gas-liquid disperser. Since in this case the holding time is also the average residence time, the gas and liquid phases spend the same time on the average. If xc = zd = f, then for small values of t, the local residence times tc and td of adjacent elements of the continuous and dispersed phases are nearly of the same order of magnitude, and hence these two elements remain in the disperser for nearly equal times. One may conclude from this that the local relative velocity between them is negligibly small, at least for small average residence times. Gal-Or and Walatka (G9) have recently shown that this is justified especially in dispersions of high <6 values and relatively small bubbles in actual practice where surfactants are present. Under this domain, Eqs. (66), (68), (69) show that as the bubble size decreases, the quantity of surfactants necessary to make a bubble behave like a solid particle becomes smaller. Under these circumstances (pd + y) - oo and Eq. (69) reduces to... 

Multicomponent mass transfer is discussed in more detail by Taylor and KRISHNA031, Cusslhr04 and Zielinski and Hanley 151... 

Taylor, R., and Krishna, R. Multicomponent Mass Transfer (Wiley, New York, 1993). 

According to Maxwell s law, the partial pressure gradient in a gas which is diffusing in a two-component mixture is proportional to the product of the molar concentrations of the two components multiplied by its mass transfer velocity relative to that of the second component. Show how this relationship can be adapted to apply to the absorption of a soluble gas from a multicomponent mixture in which the other gases are insoluble and obtain an effective diffusivity for the multicomponent system in terms of the binary diffusion coefficients. 

If the resistance to mass transfer is mainly in the liquid phase, the difference between the binary and multicomponent efficiencies will be small. 

The model described in the previous sections is very complicated and therefore in Part I only isothermal studies will be reported. This limiting situation can be obtained by putting //, = 0 (i = 1,. ..,n) and setting the bulk temperatures equal to To in eq. (16b). In this paper the influence of multicomponent transport phenomena on the mass transfer rate between a gas/vapour and a liquid will be studied in detail for both non-reactive and reactive conditions. It should be stressed that the validity of the model developed in... 

Sivasubramanian, M. S. and Boston, J. F., 1990, The heat and mass transfer rate-based approach for modelling multicomponent separation processes, in Computer Applications in Chemical Engineering, pp. 331-336. Elsevier, Amsterdam. 

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