Mass transfer coefficient enhancement factor

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... 

Note that the tower height is inversely proportional to the enhanced mass-transfer coefficient, or to the enhancement factor itself. 

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, although some theoretical relations for idealized situations have been found. Tables 8.1 and 8.2 show a few spot data. A particular... 

From the above it can be concluded that only the reaction with component B may enhance mass transfer of ozone substantially. And only if the Hatta number HaB is much higher than 1. Therefore it can be expected that whenever we have to deal with an enhancement of mass transfer due to chemical reactions, this influences the selectivity of the oxidation process in a negative way. The factor which has to be considered in this respect is the Hatta number for the reaction of ozone with component B (equation 29). HaB increases with increasing value of kB and CBb and with decreasing value of the mass transfer coefficient for ozone, kHq,... 

The expression for the enhancement factor E, eq. (35), has first been derived by van Krevelen and Hof-tijzer in 1948. These authors used Pick s law for the description of the mass transfer process and approximated the concentration profile of component B by a constant Xb, over the entire reaction zone. It seems worthwhile to investigate whether the same equation can be applied in case the Maxwell-Stefan theory is used to describe the mass transfer process. To evaluate the Hatta number, again an effective mass transfer coefficient given by eq. (34), is required. The... 

Figures 7(a)-(c) show a comparison between the numerically computed absorption flux and the absorption flux obtained from expression (31), using eqs (24), (30) and (34)-(37). From these figures it can be concluded that for both equal and different binary mass transfer coefficients absorption without reaction can be described well with eq. (24), whereas absorption with instantaneous reaction can be described well with eq. (30). If the Maxwell-Stefan theory is used to describe the mass transfer process, the enhancement factor obeys the same expression as the one obtained on the basis of Fick s law [eq. (35)]. Finally, from Figs 7(b) and 7(c) it appears that the use of an effective mass transfer coefficient m the Hatta number again produces satisfactory results.

The chemical method used to estimate the interfacial area is based on the theory of the enhancement factor for gas absorption accompanied with a chemical reaction. It is clear from Equations 6.22-6.24 that, in the range where y > 5, the gas absorption rate per unit area of gas-liquid interface becomes independent of the liquid phase mass transfer coefficient /cp, and is given by Equation 6.24. Such criteria can be met in the case of absorption with... 

A convention used in most literature on ozone mass transfer and in the rest of this book is to define the mass transfer coefficient as the one that describes the mass transfer rate without reaction, and to use the enhancement factor E to describe the increase due to the chemical reaction. Furthermore, the simplification that the major resistance lies in the liquid phase is used throughout the rest of the book. This is also based on the assumption that the mass transfer rate describes physical absorption of ozone or oxygen, since the presence of a chemical reaction can change this. This means that KLa - kLa and the concentration gradient can be described by the difference between the concentration in equilibrium with the bulk gas phase cL and the bulk liquid concentration cL. So the mass transfer rate is defined as ... 

These parameters, such as the coefficient of diffusion, D, mass-transfer coefficient in the gas and liquid phase or film, kg and k], Thiele modulus, Hatta number, Ha, and enhancement factor, E, are all dependent on the pressure. 

It is obvious that re-atomization yields decrease the mean diameter of the liquid droplets and thus an increased interface area at the same time, it results in reduced average transfer coefficients, because heat and mass transfer coefficients between gas flow and particle or droplet are in positive correlation with the diameter of the particle or droplet, while coalescence of droplets yields influences opposite to those described above. In their investigation on the absorption of C02 into NaOH solution, Herskowits et al. [59, 60] determined theoretically the total interface areas and the mass transfer coefficients by comparing the absorption rates with and without reaction in liquid, employing the expression for the enhancement factor due to chemical reaction of second-order kinetics presented by Danckwerts [70],... 

The mass-transfer coefficient with a reactive solvent can be represented by multiplying the purely physical mass-transfer coefficient by an enhancement factor E that depends on a parameter called the Hatta number (analogous to the Thiele modulus in porous catalyst particles). 

If the mass transfer of a gaseous reaction partner into the liquid is accompanied by a chemical reaction, the following case can occur depending on the reaction rate and the mobility of the reaction partners The concentration of A is not only reduced to zero in the solution in addition, the reaction front shifts from the liquid bulk to the liquid-side boundary layer. As a result, the liquid-side boundary is apparently reduced and finally eliminated in a chemical way ( chemisorption ), see Fig. 86. This process increases the mass transfer coefficient by the enhancement factor E as compared to its numerical value for purely physical absorption. 

For a semi-batch operation, the liquid-solid mass-transfer coefficient can also be obtained by monitoring a reaction between the dissolving solid B and a liquid reactant C. If this reaction is instantaneous, the enhancement factor for the reaction is... 

Actually Sato et al. expressed their particle mass-transfer coefficients in terms of an enhancement factor representing the ratio of with two-phase flow to ks at the same liquid flow rate in single-phase flow. For pulsing and dispersed bubble flow this enhancement factor was found to be inversely proportional to liquid holdup j3, which in turn is a function of the two-phase parameter A or A (see Section IV,A,3,a). For comparison, the data for single-phase liquid flow are best represented by an equation of the same form as Eq. (115) but with a constant of 0.8. 

Ho = Henry s law constant (atm/ft /mol) koi = liquid film mass transfer coefficient E = liquid film enhancement factor,... 

Figure 3 illustrates the effect of adipic acid on the overall enhancement of SO2 absorption. It gives the ratio of the overall mass transfer coefficient, Kg, to the gas-film coefficient, kg, as a function of a dimensionless parameters including adipic acid concentration. The overall coefficient includes an effect of k and the liquid-film enhancement factor which increases with adipic acid concentration. The ratio, Kg/kg, represents the fraction resistance of the gas film and cannot exceed 1.0. 

---