Dilute solutions mass-transfer coefficients

Gas-phase mass-transfer coefficient for dilute systems kmoP[(s-m )(kPa solute partial pressure)] lbmol/[(h-fF)lbf/in solute partial pressure)]... 

With a reactive solvent, the mass-transfer coefficient may be enhanced by a factor E so that, for instance. Kg is replaced by EKg. Like specific rates of ordinary chemical reactions, such enhancements must be found experimentally. There are no generalized correlations. Some calculations have been made for idealized situations, such as complete reaction in the liquid film. Tables 23-6 and 23-7 show a few spot data. On that basis, a tower for absorption of SO9 with NaOH is smaller than that with pure water by a factor of roughly 0.317/7.0 = 0.045. Table 23-8 lists the main factors that are needed for mathematical representation of KgO in a typical case of the absorption of CO9 by aqueous mouethauolamiue. Figure 23-27 shows some of the complex behaviors of equilibria and mass-transfer coefficients for the absorption of CO9 in solutions of potassium carbonate. Other than Henry s law, p = HC, which holds for some fairly dilute solutions, there is no general form of equilibrium relation. A typically complex equation is that for CO9 in contact with sodium carbonate solutions (Harte, Baker, and Purcell, Ind. Eng. Chem., 25, 528 [1933]), which is... 

The Sherwood number is a nondimensional mass-transfer coefficient that is analogous to the Nusselt number for heat transfer. For the situation of A being dilute in B, the mass transfer at the stagnation surface is derived from the solution to the species equation by... 

In order to permit sizing a tower, data must be available of the height of a transfer unit (HTU). This term often is used interchangeably with the height equivalent to a theoretical stage (HETS), but strictly they are equal only for dilute solutions when the ratio of the extract and raffinate flow rates, E/R, equals the distribution coefficient, K = xE/xR (Treybal, 1963, p. 350). Extractor performance also is expressible in terms of mass transfer coefficients, for instance, KEa, which is related to the number and height of transfer units by... 

According to the data for volumetric mass transfer coefficient measured in the device on a small pilot plant scale, for a certain load of flue gas to be processed, the required total volume of the reactor under consideration would be very small, only about 1/3 that of existing wet FGD equipment. In addition, the arrangement of the internal wet cyclone shown in Fig. 7.23 enables the reactor to have simultaneously high ash-removal efficiency. The reactor is especially suitable for the wet desulfurization of flue gas with hydrated lime or dilute ammonia solution as the absorbent. The design of the large-scale reactor suitable for a power station has now been accomplished and is expected to be applied industrially in the very near future. 

Thus, for dilute solutions, the design equation for an absorber is identical in form to that for heat exchangers with the overall mass transfer coefficient Ky analogous to the overall heat transfer coefficient U and the log-mean of y-y at the two ends of the absorber analogous to the log-mean AT. 

Since concentrations may be defined in a number of equivalent ways, other definitions of mass-transfer coefficients for this case (NB - 0 dilute solutions) are frequently used, such as... 

Notice that in the case of diffusion of A through stagnant B there is a bulk-motion contribution to the total flux that results in a logarithmic form of the concentration driving force. For that reason, the newly defined k-type mass-transfer coefficients are not constant, but usually depend on the concentration driving force. For very dilute solutions, the bulk-motion contibution is negligible and the driving force becomes approximately linear. In mathematical terms, this follows from the fact that for very dilute solutions yB M = xB M = 1.0. 

Therefore, for diffusion of A through stagnant B, equations (2-4), (2-5), (2-7), and (2-8) in terms of the -type mass-transfer coefficients are recommended only for very dilute solutions, otherwise, equations (2-2) and (2-3) should be used. 

The mass-transfer conditions prevailing in the boundary layer described so far correspond to diffusion of A through stagnant B in dilute solutions. Therefore, the flux can be written in terms of a -type mass-transfer coefficient, as described by equation (2-7), using the difference in surface and bulk concentrations as the driving force ... 

For the particular case of the system air-water at near-ambient conditions, we are dealing with very dilute solutions of water vapor in air. For this reason, it is justified to assume that the total gas flow rate will remain relatively constant at its inlet value and that the gas phase will behave as if it were dry air. If we assume that the temperature and pressure will remain constant, it follows that the dimensionless numbers Re and Sc will not change along the column, justifying the assumption of a constant value for the mass-transfer coefficient. Dilute gas solutions, and NB - 0, also justify the use of a k-type coefficient coupled to a linear concentration driving force. These assumptions simplify considerably the analysis of the problem. 

During absorption of low-solubility gases, mass transfer from a highly concentrated gas mixture to a very dilute liquid solution frequently takes place. In that case, although it is appropriate to use a k-type mass-transfer coefficient in the liquid phase, an F-type coefficient must be used in the gas phase. Since dilute liquid solutions usually obey Henry s law, the interfacial concentrations during absorption of low-solubility gases are related through... 

The development of the design equation for a countercurrent packed tower absorber or stripper begins with a differential mass balance of component A in the gas phase, in a manner similar to that of Example 2.12. However, this time we do not restrict the analysis to dilute solutions or to constant molar velocity. If only component A is transferred (4 G = VA[ = 1.0), considering the fact that the gas-phase molar velocity will change along the column, and that F-type mass-transfer coefficients are required for concentrated solutions, the mass balance is... 

For dilute solutions and when Henry s law applies, the equilibrium curve and the operating lines are straight lines. Overall mass-transfer coefficients are convenient in this case. The expression for the height of packing can be written as... 

KG overall convective mass-transfer coefficient for diffusion of A through stagnant B in dilute solutions with driving force in terms of partial pressures mol/m2-s-Pa. 

Table 16.3 Defining equations for mass transfer coefficients based on dilute solutions or equimolar diffusion ...

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