Enhancement factor, mass transfer rate

Equation 10.30 is known as Stefan s Law(3). Thus the bulk flow enhances the mass transfer rate by a factor Cj/Cjj, known as the drift factor. The fluxes of the components are given in Table 10.1. 

Recall that the enhancement factor q, as defined in Chapter 6 is a measure of enhancement in mass transfer rate due to reaction ... 

Here again, as in the case of the catalyst particle, the resulting concentration profile does not yield information of immediate interest, and is translated instead into a quantity of greater engineering usefulness. The quantity in question is the so-called enhancement factor Eh. which is defined as the ratio of mass transfer with reaction to the mass transfer rate without reaction. In contrast to the catalyst effectiveness factor, the value of E is above rather than below unity. This is because the reaction continuously removes reactant, thus sharpening its gradient and in consequence enhancing the mass transfer rate. 

For many laboratoiy studies, a suitable reactor is a cell with independent agitation of each phase and an undisturbed interface of known area, like the item shown in Fig. 23-29d, Whether a rate process is controlled by a mass-transfer rate or a chemical reaction rate sometimes can be identified by simple parameters. When agitation is sufficient to produce a homogeneous dispersion and the rate varies with further increases of agitation, mass-transfer rates are likely to be significant. The effect of change in temperature is a major criterion-, a rise of 10°C (18°F) normally raises the rate of a chemical reaction by a factor of 2 to 3, but the mass-transfer rate by much less. There may be instances, however, where the combined effect on chemical equilibrium, diffusivity, viscosity, and surface tension also may give a comparable enhancement. 

For a more general and quantitative description of the mass transfer rate and in the absence of mass transfer limitations on the gas side, the enhancement factor E> 1 is defined as ... 

Regimes 2 and 3 - moderate reactions in the bulk (2) or in thefdm (3) and fast reactions in the bulk (3) For higher reaction rates and/or lower mass transfer rates, the ozone concentration decreases considerably inside the film. Both chemical kinetics and mass transfer are rate controlling. The reaction takes place inside and outside the film at a comparatively low rate. The ozone consumption rate within the film is lower than the ozone transfer rate due to convection and diffusion, resulting in the presence of dissolved ozone in the bulk liquid. The enhancement factor E is approximately one. This situation is so intermediate that it may occur in almost any application, except those where the concentration of M is in the micropollutant range. No methods exist to determine kLa or kD in this regime. 

Regime 5 - instantaneous reactions at an reaction plane developing inside the film For very high reaction rates and/or (very) low mass transfer rates, ozone reacts immediately at the surface of the bubbles. The reaction is no longer dependent on ozone transfer through the liquid film kL or the reaction constant kD, but rather on the specific interfacial surface area a and the gas phase concentration. Here the resistance in the gas phase may be important. For lower c(M) the reaction plane is within the liquid film and both film transfer coefficients as well as a can play a role. The enhancement factor can increase to a high value E > > 3. 

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 ... 

The acceleration of mass transfer due to chemical reactions in the interfacial region is often accounted for via the so-called enhancement factors [19, 26, 27]. These parameters are defined as a relationship between the mass transfer rate with reaction and mass transfer rate without reaction, assuming the same mass transfer driving force. 

The enhancement of the mass transfer rate in the first part of the reactor, resulting from the developing concentration profile, is negligible. It was stated in Section III that for relative pitches larger than 1.1 this assumption is valid, and that even for smaller relative pitches the effect of the enhanced mass transfer rate is small, except when film layer mass transfer is the limiting factor in the reactor performance. 

Certain fast or instantaneous reactions (for example, proton transfer reactions) are always mass-transfer controlled. The enhancement factor, I, acconnts for the effect of chemical reactions on mass transfer and is dehned as the ratio of the process rate over the mass-transfer rate in absence of a chemical reaction. 

Fog formation is favored by conditions which slow the mass transfer rates and enhance the heat transfer rate. Factors which favor fog formation by slowing the mass transfer rates are a high ratio of noncondensables to condensable vapor, and a high molecular weight (low diffusivity). Factors which favor fog formation by speeding the heat transfer are a high temperature difference between the vapor and interface and low initial superheat. 

In the region of extremely rapid reaction the utilization factor approach, which refers the observed rate to the maximum possible chemical rate, has the drawback of requiring accurate values of the rate coefficient, k. An alternate way is to refer to the physical liquid phase mass transfer rate, which is increased by the chemical reaction. This then leads to the definition of an enhancement factor, Fa ... 

Obviously > 1, so that the mass transfer rate is enhanced by the chemical reaction. As is increased, Eq. 6.3.C-10 indicates that the enhancement factor, Fg, increases, but only until the critical value is attained, Eq. 6.3.C-9. 

In contrast to rigid particles, there exists an internal circulation in drops that enhances mass transfer rates. This internal convection is accounted for by an enhancement factor E which is combined with the diffusion coefficient... 

There are important qualitative differences between the behavior in the irreversible limit and in the pinched limit. In the irreversible limit, the enhancement factor is independent of temperature, and the mass transfer rate is almost independent of... 

If a substance is transferred from the gas phase into the liquid phase and bonded chemically, the mass transfer rate increases. The influence of the reaction on the mass transfer is defined by an enhancement factor E given in Eq. (3-33). In the case of a chemical reaction superimposed on the mass transfer is... 

Fig. 3-12. Enhancement factor as a function of Hatta number Ha, as a ratio of the reaction rate and mass transfer rate of an irreversible 2" order reaction (parameter Ri according to Eq. (3-35). Ha Hatta number E Enhancement factor...

If the reaction in the liquid film leads to an increase in the concentration gradient of the reactant at the interface, the mass transfer of the absorbed gas from the interface into the liquid phase is enhanced compared to the absence of reaction. This effect is considered by the enhancement factor , which depends on Ha. For a slow reaction (small Ha), the mass transfer rate is not enhanced. For a fast reaction, the conversion mostly takes place in the liquid film. For an instantaneous reaction, the absorbed reactant A and the liquid reactant B do not coexist, and conversion takes place at a reaction plane. 

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